Courses of Study : Mathematics

Foundations of Counting
Know number names and the count sequence.
Note on number reversals: Learning to write numerals is generally more difficult than learning to read them. It is common for students to reverse numerals at this stage.
Mathematics (2019)
Grade(s): K
All Resources: 8
Learning Activities: 2
Classroom Resources: 6
1. Count forward orally from 0 to 100 by ones and by tens. Count backward orally from 10 to 0 by ones.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Count correctly from 0 to 100 by ones without skipping numbers, repeating numbers, or hesitating.
  • Count correctly from 0 to 100 by tens without skipping numbers, repeating numbers, or hesitating.
  • Count backwards from 10 to 0 by ones without skipping numbers, repeating numbers, or hesitating.
Teacher Vocabulary:
  • Count forward orally
  • Count backwards orally
Knowledge:
Students know:
  • how to count by ones and tens orally. This includes counting forward and counting backward.
Skills:
Students are able to:
  • orally count forward.
  • orally count backward.
Understanding:
Students understand that:
  • Counting from 0 to 100 is a sequence.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.1.1: Count backwards from 5 to 0 by ones.
M.K.1.2: Mimic counting backwards from 5 to 0 by ones.
M.K.1.3: Count to 50 by ones.
M.K.1.4: Count to 50 by tens.
M.K.1.5: Count to 20 by ones.
M.K.1.6: Count to 10 by ones.
M.K.1.7: Mimic counting by tens.
M.K.1.8: Mimic counting by ones.

Prior Knowledge Skills:
  • Count to 20 and above.
  • Mimic counting by ones.
  • Recognize numbers from one to ten.
  • Become interested in how many objects she/he has.
  • Continue to have an interest in counting.
  • Understand the concept of size and amount.
  • Pair the number of objects counted with "how many."
  • Understand that the last number name tells the number of objects counted.
  • Pair a group of objects with a number representing the total number of objects in the group (up to ten objects).
  • Count objects one-by-one using only one number per object (up to ten objects).
  • Recognize that numbers and numerals have meaning.
  • Recognize numerals 0 (zero) through 10.
  • Rote count to ten.
  • Communicate some number words.
  • Communicate the number word one.
  • Recognize after.
  • Recognize before.
  • Enjoy playing with all kinds of objects.
  • Point to matching or similar objects.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.1 Using vocalization, sign language, augmentative communication, or assistive technology, count to 15 by ones starting with one.


Mathematics (2019)
Grade(s): K
All Resources: 8
Learning Activities: 4
Classroom Resources: 4
2. Count to 100 by ones beginning with any given number between 0 and 99.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Count correctly to 100 by ones starting with any given number other than 0 without skipping numbers, repeating numbers, or hesitating.
Teacher Vocabulary:
  • Count
Knowledge:
Students know:
  • how to rote count from 0 to 100 starting with any given number.
Skills:
Students are able to:
  • orally count.
Understanding:
Students understand that:
  • Counting from 0 to 100 is a sequence and you can begin with any number.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.2.1: Count forward to 100 from a number over 50.
M.K.2.2: Count forward to 100 from a number between 2 and 50.
M.K.2.3: Count forward to 50 from a given number.
M.K.2.4: Count to 100 by ones.
M.K.2.5: Mimic counting to 100 by ones.
M.K.2.6: Count to 50 by ones.
M.K.2.7: Mimic counting to 50 by ones.

Prior Knowledge Skills:
  • Count to 20 and above.
  • Mimic counting by ones.
  • Recognize numbers from one to ten.
  • Become interested in how many objects she/he has.
  • Continue to have an interest in counting.
  • Understand the concept of size and amount.
  • Pair the number of objects counted with "how many."
  • Understand that the last number name tells the number of objects counted.
  • Pair a group of objects with a number representing the total number of objects in the group (up to ten objects).
  • Count objects one-by-one using only one number per object (up to ten objects).
  • Recognize that numbers and numerals have meaning.
  • Recognize numerals 0 (zero) through 10.
  • Rote count to ten.
  • Communicate some number words.
  • Recognize after.
  • Recognize before.
  • Enjoy playing with all kinds of objects.
  • Point to matching or similar objects.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.1 Using vocalization, sign language, augmentative communication, or assistive technology, count to 15 by ones starting with one.


Mathematics (2019)
Grade(s): K
All Resources: 7
Learning Activities: 4
Lesson Plans: 1
Classroom Resources: 2
3. Write numerals from 0 to 20.

a. Represent 0 to 20 using concrete objects when given a written numeral from 0 to 20 (with 0 representing a count of no objects). 
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Write numerals correctly from 0 to 20.
  • Represent numbers using concrete objects when given a written numeral from 0 to 20.
Teacher Vocabulary:
  • Numeral
  • Number
Knowledge:
Students know:
  • how to match numeral name with sets of objects.
Skills:
Students are able to:
  • write numerals from 0 to 20.
  • Represent numbers from 0 to 20.
Understanding:
Students understand that:
  • a written numeral represents a number of objects.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.3.1: Write numbers 0 to 10.
M.K.3.2: Match numerals to quantity 11 to 20.
M.K.3.3: Match numerals to quantity 0 to 10.
M.K.3.4: Recognize written numerals 0 to 20.
M.K.3.5: Demonstrate one to one correspondence for a group of objects 6 to 20.
M.K.3.6: Demonstrate one to one correspondence for a group of objects 0 to 5.
M.K.3.7: Trace numerals 0 to 20.
M.K.3.8: Make purposeful marks such as lines and circles.

Prior Knowledge Skills:
  • Count to 20 and above.
  • Mimic counting by ones.
  • Recognize numbers from one to ten.
  • Become interested in how many objects she/he has.
  • Continue to have an interest in counting.
  • Understand the concept of size and amount.
  • Notice same/different and some/all.
  • Understand that words can label sameness and differences.
  • Understand that some have more, and some have less.
  • Become more interested in the concept of some and all.
  • Make purposeful marks.
  • Given a set number of objects one through ten, answer the question "How many?"
  • Pair the number of objects counted with "how many."
  • Understand that the last number name tells the number of objects counted.
  • Establish one-to-one correspondence between numbers and objects when given a picture, a drawing or objects.
  • Pair a group of objects with a number representing the total number of objects in the group (up to ten objects).
  • Count objects one-by-one using only one number per object (up to ten objects).
  • Recognize that numbers and numerals have meaning.
  • Recognize numerals 0 (zero) through 10.
  • Identify the difference between written numbers and other written things.
  • Identify the difference between written numbers and objects.
  • Rote count to ten.
  • Communicate some number words.
  • Recognize after.
  • Recognize before.
  • Enjoy playing with all kinds of objects.
  • Point to matching or similar objects.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.1 Using vocalization, sign language, augmentative communication, or assistive technology, count to 15 by ones starting with one.


Count to tell the number of objects.
Mathematics (2019)
Grade(s): K
All Resources: 9
Learning Activities: 6
Lesson Plans: 1
Classroom Resources: 2
4. Connect counting to cardinality using a variety of concrete objects.

a. Say the number names in consecutive order when counting objects.

b. Indicate that the last number name said tells the number of objects counted in a set.

c. Indicate that the number of objects in a set is the same regardless of their arrangement or the order in which they were counted.

d. Explain that each successive number name refers to a quantity that is one larger.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Count an object saying the number name.
  • Tell the number of objects in a set.
  • Specify the number of objects in a set regardless of arrangement.
  • Explain "one more".
Teacher Vocabulary:
  • Cardinality
  • One to one correspondence
  • Hierarchical inclusion
Knowledge:
Students know:
  • Use one to one correspondence when counting objects.
  • how to rote count in consecutive order.
Skills:
Students are able to:
  • count objects with one to one correspondence.
  • Indicate the number of objects.
  • Explain one more.
Understanding:
Students understand that:
  • a number represents a quantity.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.4.1: Define number and counting.
M.K.4.2: Identify correct number of objects for a given number up to 20.
M.K.4.3: Identify different size groups of objects up to 10.

a.
M.K.4.4: Count to 20 by ones.
M.K.4.5: Mimic counting objects.

b.
M.K.4.6: Know that the last number tells how many when counting 0 to 5 objects.
M.K.4.7: Mimic counting objects up to 20.
M.K.4.8: Count to 20 by ones.
M.K.4.9: Mimic counting to 20 by ones.

c.
M.K.4.10: Define one larger/one more.
M.K.4.11: Count objects in a group and identify total after adding one more.
M.K.4.12: Count in sequential order.
M.K.4.13: Mimic counting in sequential order.

Prior Knowledge Skills:
  • Count to 20 and above.
  • Mimic counting by ones.
  • Recognize numbers from one to ten.
  • Become interested in how many objects she/he has.
  • Continue to have an interest in counting.
  • Understand the concept of size and amount.
  • Notice same/different and some/all.
  • Understand that words can label sameness and differences.
  • Understand that some have more, and some have less.
  • Become more interested in the concept of some and all.
  • Given a set number of objects one through ten, answer the question "how many?"
  • Pair the number of objects counted with "how many."
  • Understand that the last number name tells the number of objects counted.
  • Establish one-to-one correspondence between numbers and objects when given a picture, a drawing or objects.
  • Pair a group of objects with a number representing the total number of objects in the group (up to ten objects).

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.4 Demonstrate one-to-one correspondence, pairing each object with one, and only one, number and each number with one, and only one, object (limit numbers and objects to five).


Mathematics (2019)
Grade(s): K
All Resources: 6
Learning Activities: 3
Classroom Resources: 3
5. Count to answer "how many?" questions.

a. Count using no more than 20 concrete objects arranged in a line, a rectangular array, or a circle.

b. Count using no more than 10 concrete objects in a scattered configuration.

c. Draw the number of objects that matches a given numeral from 0 to 20.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Answer questions regarding how many objects are in a set in various configurations.
Teacher Vocabulary:
  • Rectangular array
  • Subitize
Knowledge:
Students know:
  • how to use one-to-one correspondence when counting objects.
  • how to demonstrate number word sequence.
Skills:
Students are able to:
  • count sequentially.
  • Use one to one correspondence.
  • Subitize.
  • Represent a number of objects within 0 to 20.
Understanding:
Students understand that:
  • numbers name quantities regardless of their arrangement.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.5.1: Define how many, all together, and in all.
M.K.5.2: Demonstrate one to one correspondence.
Example: Point to only one object when counting, and stop counting when all objects have been touched.
M.K.5.3: Count to 20 by ones.


Prior Knowledge Skills:
  • Understand amount words, such as more, less, and another.
  • Begin to understand that parts of an object can make a whole.
  • Be interested in who has more or less.
  • Understand the concept of "less than".
  • Mimic counting by ones.
  • Recognize numbers from one to ten.
  • Become interested in how many objects she/he has.
  • Continue to have an interest in counting.
  • Understand the concept of size and amount.
  • Make purposeful marks.
  • Given a set number of objects one through ten, answer the question "How many?"
  • Pair the number of objects counted with "how many."
  • Understand that the last number name tells the number of objects counted.
  • Establish one-to-one correspondence between numbers and objects when given a picture, a drawing or objects.
  • Pair a group of objects with a number representing the total number of objects in the group.
  • Count objects one-by-one using only one number per object.
  • Recognize that numbers and numerals have meaning.
  • Recognize numerals 0 through 10.
  • Rote count to ten.
  • Communicate number words.
  • Recognize after.
  • Recognize before.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.5 Using vocalization, sign language, augmentative communication, or assistive technology, count out up to five objects from a larger set, pairing each object with one, and only one, number name to tell how many.


Compare numbers.
Mathematics (2019)
Grade(s): K
All Resources: 6
Learning Activities: 4
Lesson Plans: 1
Classroom Resources: 1
6. Orally identify whether the number of objects in one group is greater/more than, less/fewer than, or equal/the same as the number of objects in another group, in groups containing up to 10 objects, by using matching, counting, or other strategies.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Explain and justify answers to questions such as "which group has more?" or "which group has less?".
  • Answer questions such as which group has more or less by matching, recognizing without counting (subitizing), or counting up to 10 objects.
Teacher Vocabulary:
  • Compare
  • Greater than
  • More than
  • Less than
  • Fewer than
  • Equal
Knowledge:
Students know:
  • how to identify which number is larger and which number is smaller.
  • number word sequence.
Skills:
Students are able to:
  • Count sequentially.
Understanding:
Students understand that:
  • a set of objects is either greater than, less than, or equal to another set of objects.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.6.1: Define greater than, less than, and equal to.
M.K.6.2: Count to 20 by ones.
M.K.6.3: Count objects up to ten.

Prior Knowledge Skills:
  • Understand amount words, such as more, less, and another.
  • Begin to understand that parts of an object can make a whole.
  • Become more interested in the concept of some and all.
  • Be interested in who has more or less.
  • Understand the concept of "less than".
  • Mimic counting by ones.
  • Recognize numbers from one to ten.
  • Become interested in how many objects she/he has.
  • Understand the concept of size and amount.
  • Given a set number of objects one through ten, answer the question "how many?"
  • Pair the number of objects counted with "how many."
  • Understand that the last number name tells the number of objects counted.
  • Establish one-to-one correspondence between numbers and objects when given a picture, a drawing or objects.
  • Pair a group of objects with a number representing the total number of objects in the group.
  • Count objects one-by-one using only one number per object.
  • Recognize that numbers and numerals have meaning.
  • Recognize numerals 0 through 10.
  • Rote count to ten.
  • Communicate number words.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.6 Identify whether the number of objects in one group is more or less than (e.g., when the quantities are clearly different) or equal to the number of objects in another group.


Mathematics (2019)
Grade(s): K
All Resources: 2
Learning Activities: 1
Classroom Resources: 1
7. Compare two numbers between 0 and 10 presented as written numerals (without using inequality symbols).
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Justify their identification of the larger or smaller pair of numerals using a variety of strategies such as referring to their order in the counting sequence, modeling the quantities, and using relational thinking.
Teacher Vocabulary:
  • Relational thinking
  • Inequality symbols
Knowledge:
Students know:
  • how to identify which number is larger and which number is smaller with number 0 - 10.
  • number word sequence.
Skills:
Students are able to:
  • count sequentially.
  • Apply strategies for comparing numbers.
Understanding:
Students understand that:
  • successive number names refer to quantities that are larger than the previous numbers in the counting sequence.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.7.1: Compare numbers 1 to 10 using objects.
M.K.7.2: Name numerals 1 to 10.
M.K.7.3: Identify numerals 1 to 10.
M.K.7.4: Count to 10 by ones.

Prior Knowledge Skills:
  • Recognize numbers from one to ten.
  • Understand amount words, such as more, less, and another.
  • Begin to understand that parts of an object can make a whole.
  • Become more interested in the concept of some and all.
  • Be interested in who has more or less.
  • Understand the concept of "less than".
  • Mimic counting by ones.
  • Recognize numbers from one to ten.
  • Become interested in how many objects she/he has.
  • Understand the concept of size and amount.
  • Given a set number of objects one through ten, answer the question "how many?"
  • Pair the number of objects counted with "how many."
  • Understand that the last number name tells the number of objects counted.
  • Establish one-to-one correspondence between numbers and objects when given a picture, a drawing or objects.
  • Pair a group of objects with a number representing the total number of objects in the group.
  • Recognize less/fewer.
  • Recognize greater/more.
  • Recognize same/equal.
  • Count objects one-by-one using only one number per object.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.6 Identify whether the number of objects in one group is more or less than (e.g., when the quantities are clearly different) or equal to the number of objects in another group.


Operations and Algebraic Thinking
Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
*Note: Drawings need not be detailed but should show the mathematics in the problem.
Mathematics (2019)
Grade(s): K
All Resources: 1
Classroom Resources: 1
8. Represent addition and subtraction up to 10 with concrete objects, fingers, pennies, mental images, drawings, claps or other sounds, acting out situations, verbal explanations, expressions, or equations.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Create representations of the quantities and the actions in the situations using physical, pictorial, or symbolic representations.
  • Explain the representations of the quantities and actions in the situations using physical, pictorial, or symbolic representations.
Teacher Vocabulary:
  • Expression
  • Equation
Knowledge:
Students know:
  • how to represent addition and subtraction using models, pictures or symbolic representations.
  • how to explain representations of quantities.
Skills:
Students are able to:
  • Represent quantities and operations physically, pictorially, or symbolically.
  • Use informational and mathematical language to communicate the connections among addition and subtraction.
Understanding:
Students understand that:
  • both putting together and adding to can be viewed as addition.
  • both taking apart and taking from can be viewed as subtraction.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.8.1: Define addition as combining groups of objects.
M.K.8.2: Define subtraction as separating groups of objects.
M.K.8.3: Represent numbers with objects or drawings.
M.K.8.4: Separate sets with nine or fewer objects.
M.K.8.5: Combine objects to form sets up to nine.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Subtract one from a set of objects (up to 10 objects).
  • Add one to a set of objects (up to 10 objects).
  • Given a group of objects (ten or less), divide the group into smaller groups in various ways.
  • Given small groups of objects, create larger groups by combining the small groups.
  • Take away objects from a large group to create two smaller groups.
  • Put together two small groups of objects to create a larger group.
  • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
  • Rote count to ten.
  • Enjoy playing with all kinds of objects.
  • Point to matching or similar objects.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.8 Demonstrate an understanding of addition as "putting together" or subtraction as "taking from" in everyday activities, limited to 5 objects.


Mathematics (2019)
Grade(s): K
All Resources: 2
Learning Activities: 1
Classroom Resources: 1
9. Solve addition and subtraction word problems, and add and subtract within 10, by using concrete objects or drawings to represent the problem.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Explain and justify solutions using connections among a variety of representations given oral addition and subtraction word problems within ten.
Teacher Vocabulary:
  • Concrete objects
  • Drawings
Knowledge:
Students know:
  • Characteristics of addition and subtraction contexts such as putting together, adding to, taking apart, and taking from.
Skills:
Students are able to:
  • represent quantities and operations physically, pictorially, or symbolically.
  • Strategically use a variety of representations to solve addition and subtraction word problems.
  • Use informal and mathematical language to communicate addition and subtraction representations.
  • Accurately compute sums and differences.
Understanding:
Students understand that:
  • both putting together and adding to can be viewed as addition.
  • both taking apart and taking from can be viewed as subtraction.
  • Mathematical problems can be solved using a variety of strategies and representations.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.9.1: Understand key words in addition and subtraction word problems.
Examples: all together, how many more, how many are left, in all.
M.K.9.2: Represent numbers with objects or drawings.
M.K.9.3: Separate sets with nine or fewer objects.
M.K.9.4: Combine objects to form sets up to nine.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Use models, solve word problems with two given sets (e.g., objects, drawings); using "putting together"; add within nine.
  • Use models, solve word problems with two given sets (e.g., objects, drawings); using "putting together"; add within five.
  • Represent addition and subtraction with objects, pictures, fingers, or sounds within nine.
  • Understand addition as putting together and subtraction as taking from.
  • Establish one-to-one correspondence between numbers and objects.
  • Rote count to 10.
  • Enjoy playing with all kinds of objects.
  • Point to matching or similar objects.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.8 Demonstrate an understanding of addition as "putting together" or subtraction as "taking from" in everyday activities, limited to 5 objects.


Mathematics (2019)
Grade(s): K
All Resources: 9
Learning Activities: 6
Classroom Resources: 3
10. Decompose numbers less than or equal to 10 into pairs of smaller numbers in more than one way, by using concrete objects or drawings, and record each decomposition by a drawing or equation.

Example: 5 = 2 + 3 and 5 = 4 + 1
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use objects or drawings to decompose the given number into at least two pairs of smaller numbers.
  • Record their solutions using pictures or equations.
Teacher Vocabulary:
  • Decompose
  • Equation
Knowledge:
Students know:
  • "equal to" and the concept of equality meaning "the same as."
  • Addition is putting together numbers and subtraction is taking apart numbers.
Skills:
Students are able to:
  • Represent quantities physically, pictorially, and symbolically.
Understanding:
Students understand that:
  • quantities may be named in a variety of ways.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.10.1: Identify plus, minus, and equal signs.
M.K.10.2: Match numerals to objects or drawings.
M.K.10.3: Identify numerals 1 to 10.
M.K.10.4: Count 0 to 10.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Recognize numbers from one to ten.
  • Subtract one from a set of objects (up to five objects).
  • Add one to a set of objects (up to five objects).
  • Given a group of objects (ten or less), divide the group into smaller groups in various ways.
  • Given small groups of objects, create larger groups by combining the small groups.
  • Take away objects from a large group to create two smaller groups.
  • Put together two small groups of objects to create a larger group.
  • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
  • Rote count to ten.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.8 Demonstrate an understanding of addition as "putting together" or subtraction as "taking from" in everyday activities, limited to 5 objects.


Mathematics (2019)
Grade(s): K
All Resources: 4
Learning Activities: 4
11. For any number from 0 to 10, find the number that makes 10 when added to the given number, by using concrete objects or drawings, and record the answer with a drawing or equation.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given any number from 0 to 10 use a variety of representations and problem solving strategies to determine the number that when added to the given number equals 10.
Teacher Vocabulary:
  • Compose
Knowledge:
Students know:
  • Characteristics of addition and subtraction contexts such as putting together, adding to, taking apart, and taking from.
Skills:
Students are able to:
  • Represent quantities and operations physically, pictorially, or symbolically.
Understanding:
Students understand that:
  • two smaller quantities join to create a larger target quantity.
  • A quantity may be broken into smaller quantities.
  • Mathematical tools and representations (ten frames and ten fingers) can be used to solve problems efficiently.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.11.1: Write numerals from 0 to 10.
M.K.11.2: Represent a given numeral 1 to 10 with objects or drawings.
M.K.11.3: Count forward from a given number 1 to 10.
M.K.11.4: Model joining sets of objects to total 10.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Recognize numbers from one to ten.
  • Add one to a set of objects (up to five objects).
  • Given small groups of objects, create larger groups by combining the small groups.
  • Put together two small groups of objects to create a larger group.
  • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
  • Rote count to ten.
  • Understand number words.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.8 Demonstrate an understanding of addition as "putting together" or subtraction as "taking from" in everyday activities, limited to 5 objects.


Mathematics (2019)
Grade(s): K
All Resources: 2
Learning Activities: 2
12. Fluently add and subtract within 5.

Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use an efficient strategy to accurately name the sums or differences within 5.
Teacher Vocabulary:
  • Fluently
Knowledge:
Students know:
  • characteristics of addition and subtraction contexts such as putting together, adding to, taking apart, and taking from.
  • Strategies for efficiently determining sums and differences within five.
Skills:
Students are able to:
  • Use addition strategies efficiently.
Understanding:
Students understand that:
  • Fluency involves a mixture of "just knowing" answers, knowing answers from patterns, and knowing answers from the use of strategies. The word fluently is used in the standards to mean accurately, efficiently, and flexibly.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.12.1: Decompose numbers up to 5 using objects or drawings.
M.K.12.2: Compose numbers up to 5 using objects or drawings.
M.K.12.3: Count backward from 5.
M.K.12.4: Count forward to 5.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Subtract one from a set of objects (up to five objects).
  • Given a group of objects (ten or less), divide the group into smaller groups in various ways.
  • Take away objects from a large group to create two smaller groups.
  • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
  • Understand number words.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.8 Demonstrate an understanding of addition as "putting together" or subtraction as "taking from" in everyday activities, limited to 5 objects.


Understand simple patterns.
Mathematics (2019)
Grade(s): K
All Resources: 0
13. Duplicate and extend simple patterns using concrete objects.

Unpacked Content
Evidence Of Student Attainment:
Students:
  • Duplicate and extend the sequence when given a simple pattern.
Teacher Vocabulary:
  • Simple pattern
  • Sequence
Knowledge:
Students know:
  • how to sort and group objects before being able to duplicate and extend simple patterns.
Skills:
Students are able to:
  • Duplicate and extend simple patterns.
Understanding:
Students should understand that:
  • looking for, describing, and extending patterns helps them develop the skills in all mathematical situations.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.13.1: Define ones and tens.
M.K.13.2: Match the number in the ones and tens position to a pictorial representation or manipulative of the value.
M.K.13.3: Add numbers 1-9 to ten to create teen numbers using manipulatives or place value blocks.
M.K.13.4: Count objects up to 10.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
  • Understand first and next.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.13 Using vocalization, sign language, augmentative communication, or assistive technology, duplicate and extend simple patterns using concrete objects.


Operations with Numbers
Work with numbers 11- 19 to gain foundations for place value.
Mathematics (2019)
Grade(s): K
All Resources: 3
Classroom Resources: 3
14. Compose and decompose numbers from 11 to 19 by using concrete objects or drawings to demonstrate understanding that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given any two-digit number from 11 and 19, use drawings or concrete objects to show and explain the decomposition of the number into one group of 10 and the correct number of ones.
Teacher Vocabulary:
  • Compose
  • Decompose
Knowledge:
Students know:
  • the number sequence to 19.
  • Strategies to decompose a number into tens and ones.
Skills:
Students are able to:
  • Use objects to compose and decompose numbers.
Understanding:
Students understand that:
  • ten things can be represented as one ten or as ten ones.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.14.1: Define ones and tens.
M.K.14.2: Match the number in the ones and tens position to a pictorial representation or manipulative of the value.
M.K.14.3: Add numbers 1-9 to ten to create teen numbers using manipulatives or place value blocks.
M.K.14.4: Count objects up to 10.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Recognize numbers from zero to ten.
  • Add one to a set of objects (up to 10 objects).
  • Given small groups of objects, create larger groups by combining the small groups.
  • Subtract one from a set of objects (up to five objects).
  • Put together two small groups of objects to create a larger group.
  • Given a group of objects (ten or less), divide the group into smaller groups in various ways.
  • Take away objects from a large group to create two smaller groups.
  • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
  • Rote count to ten.
  • Understand number words.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.14 Compose numbers from 11-15 by using concrete objects or drawings to demonstrate understanding that these numbers are composed of ten ones and one, two, three, four, or five ones.


Data Analysis
Collect and analyze data and interpret results.
Mathematics (2019)
Grade(s): K
All Resources: 4
Learning Activities: 1
Lesson Plans: 2
Classroom Resources: 1
15. Classify objects into given categories of 10 or fewer; count the number of objects in each category and sort the categories by count.

a. Categorize data on Venn diagrams, pictographs, and "yes-no" charts using real objects, symbolic representations, or pictorial representations.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a group of objects,
  • sort the objects into categories (no more than ten objects in any category).
  • Count the number of objects in each category.
  • Order the categories by count.
  • Justify their reasoning.
  • Discuss information conveyed in analyzing graphs.
Teacher Vocabulary:
  • Classify
  • Venn diagrams
  • Pictographs
  • Yes/no charts
  • Bar graphs
  • Symbolic representations
  • Pictorial representations
Knowledge:
Students know:
  • how to count.
  • Sort objects.
  • Category descriptors (e.g. triangles, rectangles, round, curved sides, color, etc).
Skills:
Students are able to:
  • sort objects.
  • Effectively use strategies to count groups of objects.
  • Read and understand graphs.
Understanding:
Students understand that:
  • objects can be grouped into categories based on like characteristics.
  • They can gain information from graphs.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.15.1: Identify more and less when given two groups of objects.
M.K.15.2: Identify object attributes.
Examples: color, shape, size, texture, use.
M.K.15.3: Count objects up to ten.
M.K.15.4: Count to 10 by ones.

Prior Knowledge Skills:
  • Participate in creating charts or graphs to represent data collection.
  • Notice same/different and some/all.
  • Recognize numbers from one to ten.
  • Given a group of objects (ten or less), divide the group into smaller groups in various ways.
  • Given small groups of objects, create larger groups by combining the small groups.
  • Take away objects from a large group to create two smaller groups.
  • Put together two small groups of objects to create a larger group.
  • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
  • Rote count to ten.
  • Begin to name and match colors, sizes, and shapes.
  • Enjoy playing with all kinds of objects.
  • Point to matching or similar objects.
  • Understand that words can label sameness and differences.
  • Understand that some have more, and some have less.
  • Sort objects based on shape or color.
  • Name and match primary colors.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.15 Explore a simple pictograph (limited to two categories and limit a combined quantity of 5 for both categories).


Measurement
Describe and compare measurable attributes.
Mathematics (2019)
Grade(s): K
All Resources: 6
Learning Activities: 2
Lesson Plans: 2
Classroom Resources: 1
Unit Plans: 1
16. Identify and describe measurable attributes (length, weight, height) of a single object using vocabulary such as long/short, heavy/light, or tall/short.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given a variety of 2D and 3D objects, use informal language (short, tall, heavy, light, fat, skinny, etc.) to describe measurable attributes of objects such as length or weight.
Teacher Vocabulary:
  • Attribute
Knowledge:
Students know:
  • how to describe similarities and differences in objects.
Skills:
Students are able to:
  • Describe measurable attributes of objects using informal language.
Understanding:
Students understand that:
  • objects can be described by using measurable attributes.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.16.1: Define length and weight.
M.K.16.2: Explore objects in relationship to length and weight.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Begin to name and match colors, sizes, and shapes.
  • Enjoy playing with all kinds of objects.
  • Point to matching or similar objects.
  • Understand that words can label sameness and differences.
  • Understand that some have more, and some have less.
  • Sort a variety of objects in a group that have one thing in common.
  • Recognize and sort familiar objects with the same size.
  • Have an interest in the order of things.
  • Understand the concept of smallest and shortest.
  • Understand the concept of same shape and size.
  • Understand the concept of smallest and shortest.
  • Understand the concept of light and heavy.
  • Understand the concept long and short.
  • Classify common objects according to height (tall/short).
  • Classify common objects according to length (long/short).
  • Classify common objects according to weight (heavy/light).

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.16 Classify objects according to attributes (e.g., big/small, heavy/light, tall/short).


Mathematics (2019)
Grade(s): K
All Resources: 4
Lesson Plans: 2
Classroom Resources: 2
17. Directly compare two objects with a measurable attribute in common to see which object has "more of" or "less of" the attribute and describe the difference.

Example: Directly compare the heights of two children and describe one child as "taller" or "shorter."
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use direct comparisons of physical objects to determine and explain which object has more of or less of the attribute.
Teacher Vocabulary:
  • Attribute
Knowledge:
Students know:
  • how to describe similarities and differences in objects.
Skills:
Students are able to:
  • Directly compare two objects and explain which object has more of or less of the attribute.
Understanding:
Students understand that:
  • objects and geometric figures have measurable attributes that allow them to be compared.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.17.1: Use vocabulary related to length and weight.
Example: longer, shorter, heavier, lighter.
M.K.17.2: Identify objects by length and weight.
Example: shortest pencil, heaviest rock.
M.K.17.3: Sort objects according to measurable attributes.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Begin to name and match colors, sizes, and shapes.
  • Enjoy playing with all kinds of objects.
  • Point to matching or similar objects.
  • Understand that words can label sameness and differences.
  • Understand that some have more, and some have less.
  • Sort objects based on shape or color.
  • Name and match primary colors.
  • Sort objects on the basis of both color and shape.
  • Sort a variety of objects in a group that have one thing in common.
  • Recognize and sort familiar objects with the same color, shape, or size.
  • Understand the concept of same shape and size.
  • Understand the concept of smallest and shortest.
  • Understand the concept of light and heavy.
  • Understand the concept long and short.
  • Classify common objects according to height (tall/short).
  • Classify common objects according to length (long/short).
  • Classify common objects according to weight (heavy/light).
  • Classify common objects according to size (big/small).
  • Communicate long, short, heavy, light, big, small.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.16 Classify objects according to attributes (e.g., big/small, heavy/light, tall/short).


Geometry
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
Mathematics (2019)
Grade(s): K
All Resources: 1
Learning Activities: 1
18. Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Describe objects in the environment using name of shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
  • Describe the relative position of these objects using terms such as above, below, beside, in front of, behind, and next to.
Teacher Vocabulary:
  • Two dimensional
  • Three dimensional
Knowledge:
Students know:
  • 2D and 3D shapes.
Skills:
Students are able to:
  • Describe objects in the environment using names of shapes.
  • Describe the relative position of objects.
Understanding:
Students understand that:
  • the world is made up of geometric shapes.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.18.1: Recognize location and position.
Examples: above, below, beside, in front of, behind, next to.
M.K.18.2: Identify cubes, cones, cylinders, and spheres.
M.K.18.3: Imitate actions to place items.
Examples: in, on, under.
M.K.18.4: Match shapes.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Begin to name and match colors, sizes, and shapes.
  • Enjoy playing with all kinds of objects.
  • Point to matching or similar objects.
  • Understand that words can label sameness and differences.
  • Understand that some have more, and some have less.
  • Sort objects based on shape or color.
  • Name and match primary colors.
  • Sort objects on the basis of both color and shape.
  • Sort a variety of objects in a group that have one thing in common.
  • Recognize and sort familiar objects with the same color, shape, or size.
  • Understand and point to a triangle, a circle, and a square, rectangle.
  • Understand the concept of same shape and size.
  • Have an interest in the order of things.
  • Understand the concept of smallest and shortest.
  • Begin to learn positional words.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.18 Recognize and match shapes of the same size and orientation, and describe the relative positions using in front of and behind (limited to circle, square, rectangle, and triangle).


Mathematics (2019)
Grade(s): K
All Resources: 2
Learning Activities: 2
19. Correctly name shapes regardless of their orientations or overall sizes.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use visual characteristics of shapes to orally justify naming 2D and 3D shapes in a variety of sizes and orientations.
Teacher Vocabulary:
  • Two dimensional
  • Three dimensional
Knowledge:
Students know:
  • 2D and 3D shapes.
Skills:
Students are able to:
  • Use geometric reasoning and visual characteristics of shapes to name shapes in a variety of sizes and orientations.
Understanding:
Students understand that:
  • geometric shapes can be sorted based on like characteristics.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.19.1: Recognize shapes.
M.K.19.2: Sort shapes with different attributes.
Examples: sort different size or color squares, circles, triangles, rectangles or hexagons.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Begin to name and match colors, sizes, and shapes.
  • Enjoy playing with all kinds of objects.
  • Point to matching or similar objects.
  • Understand that words can label sameness and differences.
  • Understand that some have more, and some have less.
  • Sort objects based on shape or color.
  • Name and match primary colors.
  • Sort objects on the basis of both color and shape.
  • Sort a variety of objects in a group that have one thing in common.
  • Recognize and sort familiar objects with the same color, shape, or size.
  • Understand and point to a triangle, a circle, a square and rectangle.
  • Understand the concept of same shape and size.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.18 Recognize and match shapes of the same size and orientation, and describe the relative positions using in front of and behind (limited to circle, square, rectangle, and triangle).


Mathematics (2019)
Grade(s): K
All Resources: 2
Learning Activities: 1
Classroom Resources: 1
20. Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid").
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use visual characteristics of shapes (flat, fat, sticking out, solid, etc.) to justify categorizing shapes as 2D or 3D.
Teacher Vocabulary:
  • Two dimensional
  • Three dimensional
Knowledge:
Students know:
  • Characteristics of 2D and 3D shapes.
Skills:
Students are able to:
  • Use geometric reasoning and visual characteristics of shapes to designate shapes as 2D or 3D.
Understanding:
Students understand that:
  • geometrics shapes can be grouped into classes of 2D or 3D shapes based on their physical characteristics.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.20.1: Define two-dimensional and three-dimensional.
Example: two-dimensional shapes are flat, three-dimensional figures are solid.
M.K.20.2: Sort flat and solid objects.
M.K.20.3: Explore two-dimensional shapes and three-dimensional figures.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Begin to name and match sizes and shapes.
  • Enjoy playing with all kinds of objects.
  • Point to matching or similar objects.
  • Understand that words can label sameness and differences.
  • Sort objects on the basis of shape.
  • Recognize and sort familiar objects with the same shape or size.
  • Understand and point to a triangle, a circle, a square and rectangle.
  • Understand the concept of same shape and size.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.18 Recognize and match shapes of the same size and orientation, and describe the relative positions using in front of and behind (limited to circle, square, rectangle, and triangle).


Analyze, compare, create, and compose shapes.
Mathematics (2019)
Grade(s): K
All Resources: 3
Classroom Resources: 3
21. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (number of sides and vertices or "corners"), and other attributes.

Example: Having sides of equal length.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use informal language to describe, compare, and contrast a variety of 2D and 3D shapes.
Teacher Vocabulary:
  • Attributes
Knowledge:
Students know:
  • attributes of shapes (sides, corners, vertices, faces, edges, etc.).
  • Informal language to describe these components.
Skills:
Students are able to:
  • Use geometric reasoning and attributes to compare and contrast a variety of shapes.
Understanding:
Students understand that:
  • geometric shapes can be grouped into classes of shapes that all seem to be alike based on their visual characteristics.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.21.1: Define similar and different.
M.K.21.2: Use vocabulary related to two-dimensional shapes and three-dimensional figures.
Examples: vertices (corners), faces (flat surfaces), edges, sides, angles.
M.K.21.3: Recognize vocabulary related to two-dimensional shapes and three-dimensional figures.
M.K.21.4: Identify two-dimensional shapes and three-dimensional figures.
M.K.21.5: Identify shapes.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Begin to name and match sizes and shapes.
  • Enjoy playing with all kinds of objects.
  • Point to matching or similar objects.
  • Understand that words can label sameness and differences.
  • Sort objects on the basis of shape.
  • Recognize and sort familiar objects with the same shape or size.
  • Understand and point to a triangle, a circle, a square and rectangle.
  • Understand the concept of same shape and size.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.21 Match a shape to common objects in the same or different sizes and orientations (real or picture; limited to circle, square, rectangle, and triangle).


Mathematics (2019)
Grade(s): K
All Resources: 1
Classroom Resources: 1
22. Model shapes in the world by building them from sticks, clay balls, or other components and by drawing them.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.
Knowledge:
Students know:
  • 2D and 3D shapes (triangle, square, rectangle, hexagon, rhombus, circle, cube, cylinder, sphere, cone).
Skills:
Students are able to:
  • Compose shapes with known attributes using a variety of materials (pipe cleaners, marshmallows/toothpicks, etc.).
Understanding:
Students understand that:
  • geometric shapes can be constructed and represented using a variety of physical materials.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.22.1: Recognize attributes of shapes.
M.K.22.2: Identify cubes, cones, cylinders, and spheres.
M.K.22.3: Identify squares, circles, triangles, rectangles, and hexagons.
M.K.22.4: Identify shapes in the environment.
M.K.22.5: Trace shapes.
M.K.22.6: Make purpose marks such as lines and circles.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Begin to name and match sizes and shapes.
  • Enjoy playing with all kinds of objects.
  • Point to matching or similar objects.
  • Understand that words can label sameness and differences.
  • Sort objects on the basis of shape.
  • Recognize and sort familiar objects with the same shape or size.
  • Understand and point to a triangle, a circle, a square and rectangle.
  • Understand the concept of same shape and size.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.21 Match a shape to common objects in the same or different sizes and orientations (real or picture; limited to circle, square, rectangle, and triangle).


Mathematics (2019)
Grade(s): K
All Resources: 1
Classroom Resources: 1
23. Use simple shapes to compose larger shapes.

Example: Join two triangles with full sides touching to make a rectangle.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Combine simple shapes to construct known larger shapes.
Knowledge:
Students know:
  • 2D and 3D shapes (triangle, square, rectangle, hexagon, rhombus, circle, cube, cylinder, sphere, cone).
Skills:
Students are able to:
  • Combine simple shapes to form larger shapes.
Understanding:
Students understand that:
  • geometric shapes can be composed of and decomposed into smaller shapes.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.K.23.1: Combine shapes to fill the area of a given shape.
M.K.23.2: Decompose pictures made of simple shapes.
M.K.23.3: Match shapes.
M.K.23.4: Match pieces by color, image, or shape to complete a puzzle.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Begin to name and match sizes and shapes.
  • Enjoy playing with all kinds of objects.
  • Point to matching or similar objects.
  • Understand that words can label sameness and differences.
  • Sort objects on the basis of shape.
  • Recognize and sort familiar objects with the same shape or size.
  • Understand and point to a triangle, a circle, a square and rectangle.
  • Understand the concept of same shape and size.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.K.23 Using a model of a larger shape outline, use simple shapes to compose larger shapes.
Example: Join two triangles with full sides touching to make a rectangle.


Operations and Algebraic Thinking
Represent and solve problems involving addition and subtraction.
Note: Students use properties of operations and different strategies to find the sum of three whole numbers, such as counting on, making tens, decomposing numbers, doubles, and near doubles.
Mathematics (2019)
Grade(s): 1
All Resources: 7
Learning Activities: 5
Classroom Resources: 2
1. Use addition and subtraction to solve word problems within 20 by using concrete objects, drawings, and equations with a symbol for the unknown number to represent the problem.

a. Add to with change unknown to solve word problems within 20.

b. Take from with change unknown to solve word problems within 20.

c. Put together/take apart with addend unknown to solve word problems within 20.

d. Compare quantities, with difference unknown, bigger unknown, and smaller unknown while solving word problems within 20.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use a variety of representations to solve word problems.
  • Justify and explain answers using concrete objects and drawings.
Teacher Vocabulary:
  • Change unknown
  • Put together
  • Take apart
  • Compare
Knowledge:
Students know:
  • addition and subtraction strategies and models.
  • how to form an equation.
Skills:
Students are able to:
  • represent quantities and operations (addition & subtraction) with concrete objects, pictorially, or symbolically.
  • Use informal and mathematical language to communicate the representations.
  • Accurately compute sums and differences.
Understanding:
Students understand that:
  • addition is both putting together and adding to. subtraction is taking apart, taking from, and comparisons.
  • Mathematical problems can be solved using a variety of strategies. models, and representations.
  • variables in the form of blanks, boxes, or letters, represent unknown quantities when representing mathematical situations algebraically.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.1.1.1: Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
M.1.1.2: Understand key words in addition and subtraction word problems.
Examples: sum, difference, all together, how many more, how many are left, in all.
M.1.1.3: Define subtraction as separating groups of objects, taking from, or taking apart.
M.1.1.4: Define addition as combining groups of objects, adding to, or putting together.
M.1.1.5: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
M.1.1.6: Represent numbers with objects or drawings.
M.1.1.7: Use objects to combine and separate groups.

Prior Knowledge Skills:
  • Define how many, all together, and in all.
  • Count to 20 by ones.
  • Demonstrate 1:1 correspondence.
  • Mimic counting objects in sequential order arranged in a line, circle, or array.
  • Count no more than 5 objects in a scattered configuration.
  • Mimic counting no more than 5 objects in a scattered configuration.
  • Count to 10 by ones.
  • Count in sequential order.
  • Mimic counting in sequential order.
  • Demonstrate one to one correspondence.
  • Make purposeful marks such as lines and circles.
  • Understand amount words, such as more, less, and another.
  • Begin to understand that parts of an object can make a whole.
  • Be interested in who has more or less.
  • Understand the concept of "less than".
  • Mimic counting by ones.
  • Recognize numbers from one to ten.

Alabama Alternate Achievement Standards
AAS Standard:
M. AAS.1.1 Represent addition as "add to/put together" and subtraction as "take from/take apart" with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, or verbal explanations (limited to 10).


Mathematics (2019)
Grade(s): 1
All Resources: 4
Learning Activities: 4
2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 by using concrete objects, drawings, or equations with a symbol for the unknown number to represent the problem.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Compute the sum of three whole numbers using a variety of representations such as concrete objects, drawings, or equations.
  • Explain and justify the answer using the representations.
Teacher Vocabulary:
  • Concrete objects
Knowledge:
Students know:
  • how to solve for addition by using strategies and understanding the relationship between addition and subtraction.
Skills:
Students are able to:
  • efficiently apply strategies for solving multiple addend problems.
  • Use symbols to represent unknown quantities in equations.
  • Accurately compute sums.
Understanding:
Students understand that:
  • more than two quantities can be combined in a problem.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.1.2.1: Solve addition word problems with sums less than or equal to 10, e.g., by using objects or drawings to represent the problem.
M.1.2.2: Understand key words in addition word problems.
Examples: sum, all together, how many more, in all
M.1.2.3: Define addition as combining groups of objects, adding to, or putting together.
M.1.2.4: Represent addition with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
M.1.2.5: Represent numbers with objects or drawings.
M.1.2.6: Use objects to combine groups.

Prior Knowledge Skills:
  • Understand key words in addition and subtraction word problems.
    Examples: all together, how many more, how many are left, in all.
  • Represent numbers with objects or drawings.
  • Separate sets with nine or fewer objects.
  • Combine objects to form sets up to nine.
  • Represent addition and subtraction with objects, pictures, fingers, or sounds within twenty.
  • Understand addition as putting together and subtraction as taking from.
  • Establish one-to-one correspondence between numbers and objects.
  • Rote count to 20.
  • Notice same/different and some/all.
  • Establish one-to-one correspondence between numbers and objects.
  • Point to matching or similar objects.

Alabama Alternate Achievement Standards
AAS Standard:
M. AAS.1.1 Represent addition as "add to/put together" and subtraction as "take from/take apart" with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, or verbal explanations (limited to 10).


Understand and apply properties of operations and the relationship between addition and subtraction.
Note: Students need not use formal terms for these properties.
Mathematics (2019)
Grade(s): 1
All Resources: 3
Lesson Plans: 2
Classroom Resources: 1
3. Apply properties of operations as strategies to add and subtract.

Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known (commutative property of addition).
To add 2 + 6 + 4, the second and third numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12 (associative property of addition).
When adding 0 to a number, the result is the same number (identity property of zero for addition).
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use informal language of properties to justify their sums and differences ("I already figured out that 8 + 3 = 11, and 3 + 8 is just the turn around of that so it must be 11, too.").
Teacher Vocabulary:
  • Commutative property of addition
  • Associative property of addition
  • Identity property of zero for addition
Knowledge:
Students know:
  • addition and subtraction strategies.
  • how to form an equation.
  • li>how the commutative property works.
Skills:
Students are able to:
  • Strategically apply properties of addition in order to find sums.
Understanding:
Students understand that:
  • the order in which addends are joined doesn't change the sum.
  • numbers may be composed or decomposed in a variety of ways.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.1.3.1: Define addition and subtraction.
M.1.3.2: Recognize properties of operations.
M.1.3.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
M.1.3.4: Apply signs +, -, = to actions of joining and separating sets. M 1.3.5: Identify fact families to ten.
M.1.3.6: Recognize the value of zero.

Prior Knowledge Skills:
  • Decompose numbers up to 5 using objects or drawings.
  • Compose numbers up to 5 using objects or drawings.
  • Count backward from 5.
  • Count forward to 5.
  • Write numerals from 0 to 10.
  • Represent a given numeral 1 to 10 with objects or drawings.
  • Count forward from a given number 1 to 10.
  • Model joining sets of objects to total 10.
  • Identify plus, minus, and equal signs.
  • Match numerals to objects or drawings.
  • Identify numerals 1 to 10.
  • Count 0 to 10.
  • Add and subtract numbers within 20 using objects, pictures and fingers.
  • Understand key words in addition and subtraction word problems.
    Examples: all together, how many more, how many are left, in all.
  • Represent numbers with objects or drawings.
  • Separate sets with nine or fewer objects.
  • Combine objects to form sets up to nine.
  • Count items in a set up to twenty.
  • Establish one-to-one correspondence between numbers and objects.
  • Using counting, find one less than a number 2 through 20.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.1.3 Demonstrate "putting together" two sets of objects to solve the problem.


Mathematics (2019)
Grade(s): 1
All Resources: 4
Learning Activities: 1
Lesson Plans: 1
Classroom Resources: 2
4. Explain subtraction as an unknown-addend problem.

Example: subtracting 10 - 8 by finding the number that makes 10 when added to 8
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use a pictorial or physical model to explain the connection between subtraction and addition.
Teacher Vocabulary:
  • Addend
Knowledge:
Students know:
  • The relationship between addition and subtraction.
  • how to explain subtraction as an unknown addend.
Skills:
Students are able to:
  • use symbols such as blanks, boxes, or letters to represent unknown quantities in equations.
  • Communicate the connections between subtraction and addition.
  • Use the inverse relationship between addition and subtraction to find differences.
  • Choose and apply addition and subtraction strategies to accurately determine sums and differences within 20.
Understanding:
Students understand that:
  • addition and subtraction have an inverse relationship that can be used to solve problems.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.1.4.1: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
M.1.4.2: Identify fact families to ten.
M.1.4.3: Recall basic addition facts to ten.
M.1.4.4: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Prior Knowledge Skills:
  • Decompose numbers up to 5 using objects or drawings.
  • Compose numbers up to 5 using objects or drawings.
  • Count backward from 5.
  • Count forward to 5.
  • Add and subtract numbers within 20 using objects, pictures and fingers.
  • Pair "taking away" with subtraction.
  • Take a smaller set out of a larger set.
  • Pair putting together with adding.
  • Combine two sets to make a larger set up to twenty.
  • Separate from a larger group to make 2 smaller groups.
  • Count items in a set up to twenty.
  • Establish one-to-one correspondence between numbers and objects.
  • Understand one less than a number 2 through 20.
  • Understand one more than a number 1 through 20.
  • Rote count to 20.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.1.3 Demonstrate "putting together" two sets of objects to solve the problem.


Add and subtract within 20.
Note: Fluency involves a mixture of "just knowing" answers, knowing answers from patterns, and knowing answers from the use of strategies. The word fluently is used in the standards to mean accurately, efficiently, and flexibly.
Mathematics (2019)
Grade(s): 1
All Resources: 6
Learning Activities: 4
Lesson Plans: 1
Classroom Resources: 1
5. Relate counting to addition and subtraction.

Example: counting on 2 to add 2
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use modeling strategies (number paths, counting objects) to justify solutions (both counting on and counting back) and to show the relationship between counting, addition, and subtraction.
Teacher Vocabulary:
  • Number paths
Knowledge:
Students know:
  • how to count on or count back from a given number within 20.
Skills:
Students are able to:
  • Explain counting strategies for addition and subtraction.
Understanding:
Students understand that:
  • counting patterns can be used to find solutions in addition and subtraction situations.
  • A variety of models and tools can be used to communicate justifications for mathematical ideas and solutions.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.1.5.1: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
M.1.5.2: Count forward and backward from a given number.
M.1.5.3: Count to 20 by ones.

Prior Knowledge Skills:
  • Mimic counting backwards from 5 to 0 by ones.
  • Count to 50 by ones.
  • Count to 50 by tens.
  • Count to 20 by ones.
  • Count to 10 by ones.
  • Mimic counting by tens.
  • Mimic counting by ones.
  • Add and subtract numbers within 20 using objects, pictures and fingers.
  • Pair "taking away" with subtraction.
  • Take a smaller set out of a larger set.
  • Pair putting together with adding.
  • Combine two sets to make a larger set up to twenty.
  • Separate from a larger group to make 2 smaller groups.
  • Count items in a set up to twenty.
  • Establish one-to-one correspondence between numbers and objects.
  • Understand one less than a number 2 through 20.
  • Understand one more than a number 1 through 20.
  • Rote count to 20.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.1.5 Use manipulatives or visual representations to indicate the number that results when adding one more. Apply knowledge of "one less" to subtract one from a number.


Mathematics (2019)
Grade(s): 1
All Resources: 8
Learning Activities: 4
Lesson Plans: 2
Classroom Resources: 2
6. Add and subtract within 20.

a. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by counting on.

b. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by making ten.

c. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by decomposing a number leading to a ten.

Example: 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9

d. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by using the relationship between addition and subtraction.

Example: Knowing that 8 + 4 = 12, one knows 12 - 8 = 4.

e. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by creating equivalent but easier or known sums.

Example: adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use an efficient strategy (e.g., recall, doubles, counting on 1 or 2, close to doubles) to add numbers within 20.
  • Fluently add and subtract within 10.
Teacher Vocabulary:
  • Fluency
Knowledge:
Students know:
  • Strategies for finding sums and differences within 20.
Skills:
Students are able to:
  • Use addition and subtraction strategies.
Understanding:
Students understand that:
  • Addition and subtraction strategies can be used to compute sums and differences, and how.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.1.6.1: Decompose numbers less than or equal to 10.
M.1.6.2: Add and subtract within 5.
M.1.6.3: Count forward and backward from a given number.
M.1.6.4: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Prior Knowledge Skills:
  • Identify plus, minus, and equal signs.
  • Match numerals to objects or drawings.
  • Identify numerals 0 to 10.
  • Count 0 to 10.
  • Understand key words in addition and subtraction word problems.
    Examples: all together, how many more, how many are left, in all.
  • Represent numbers with objects or drawings.
  • Separate sets with nine or fewer objects.
  • Combine objects to form sets up to nine.
  • Define addition as combining groups of objects.
  • Define subtraction as separating groups of objects.
  • Represent numbers with objects or drawings.
  • Separate sets with nine or fewer objects.
  • Combine objects to form sets up to nine.
  • Add and subtract numbers within 10 using objects, pictures and fingers.
  • Pair "taking away" with subtraction.
  • Take a smaller set out of a larger set.
  • Pair putting together with adding.
  • Combine two sets to make a larger set up to twenty.
  • Separate from a larger group to make 2 smaller groups.
  • Count items in a set up to twenty.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.1.6 Add and subtract numbers 1 to 15 using objects, pictures, and fingers.


Work with addition and subtraction equations.
Mathematics (2019)
Grade(s): 1
All Resources: 1
Classroom Resources: 1
7. Explain that the equal sign means "the same as." Determine whether equations involving addition and subtraction are true or false.

Example: determining which of the following equations are true and which are false: 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Justify the truth of the statement on each side of the equal sign.
Teacher Vocabulary:
  • Equation
  • Meaning of the equal sign
Knowledge:
Students know:
  • strategies for finding the value of simple addition and subtraction equations.
  • Strategies for comparing quantities between 0 and 20.
  • Strategies to show equality or inequality.
Skills:
Students are able to:
  • efficiently apply strategies for determining the value of simple addition and subtraction equations.
  • Justify and explain their thinking.
Understanding:
Students understand that:
  • the equal sign represents a relationship of balance between numerical expressions rather than performing an operation.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.1.7.1: Define true, false, and equal.
M.1.7.2: Demonstrate equal using manipulatives or object drawings.
M.1.7.3: Recall basic addition facts to ten.
M.1.7.4: Recognize equation symbols in vertical and horizontal addition and subtraction problems.
M.1.7.5: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Prior Knowledge Skills:
  • Identify plus, minus, and equal signs.
  • Match numerals to objects or drawings.
  • Identify numerals 1 to 10.
  • Count 0 to 10.
  • Add and subtract numbers within 20 using objects, pictures and fingers.
  • Understand true, false, same (equal).
  • Take a smaller set out of a larger set.
  • Combine two sets to make a larger set up to twenty.
  • Count items in a set up to twenty.
  • Establish one-to-one correspondence between numbers and objects.
  • Using counting, find one less than a number 2 through 20.
  • Using counting, find one more than a number 1 through 20.
  • Rote count to 20.
  • Understand adding numbers up and down is the same as side by side.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.1.7 Given three related whole numbers, construct a number sentence that is true, in relation to addition and subtraction.


Mathematics (2019)
Grade(s): 1
All Resources: 6
Learning Activities: 4
Lesson Plans: 2
8. Solve for the unknown whole number in various positions in an addition or subtraction equation, relating three whole numbers that would make it true.

Example: determining the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? - 3, and 6 + 6 = ?
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Solve single operation addition/subtraction equations containing a single unknown.
Teacher Vocabulary:
  • Equation
  • Knowledge:
    Students know:
    • Strategies for solving simple addition or subtraction equations with one unknown.
    Skills:
    Students are able to:
    • solve simple addition and subtraction equations.
    • Justify and explain their thinking.
    Understanding:
    Students understand that:
    • equalities contain expressions that name the same amount on each side of the equal sign, even with quantities unknown.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.8.1: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
    M.1.8.2: Identify fact families as a relationship between addition and subtraction.
    M.1.8.3: Recall basic addition and subtraction facts to ten.
    M.1.8.4: Identify plus, minus, and equal signs.
    M.1.8.5: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

    Prior Knowledge Skills:
    • Add numbers 1-9 to ten to create teen numbers using manipulatives or place value blocks.
    • Count objects up to 10.
    • Write numerals from 0 to 10.
    • Represent a given numeral 1 to 10 with objects or drawings.
    • Count forward from a given number 1 to 10.
    • Model joining sets of objects to total 10.
    • Match numerals to objects or drawings.
    • Identify numerals 1 to 10.
    • Count from 0 to 10.
    • Add and subtract numbers within 20 using objects, pictures and fingers.
    • Understand true, false, same (equal).
    • Take a smaller set out of a larger set.
    • Combine two sets to make a larger set up to twenty.
    • Count items in a set up to twenty.
    • Establish one-to-one correspondence between numbers and objects.
    • Understand one less than a number 2 through 20.
    • Understand one more than a number 1 through 20.
    • Understand positional terms with equal signs.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.7 Given three related whole numbers, construct a number sentence that is true, in relation to addition and subtraction.


    Mathematics (2019)
    Grade(s): 1
    All Resources: 0
    9. Reproduce, extend, and create patterns and sequences of numbers using a variety of materials.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Reproduce a pattern.
    • Extend a pattern.
    • Create patterns.
    • Create sequences of numbers.
    Teacher Vocabulary:
    • Number patterns
    Knowledge:
    Students know:
    • how to duplicate simple patterns.
    • how to extend simple patterns.
    Skills:
    Students are able to:
    • reproduce given patterns.
    • Extend given patterns.
    • Create patterns.
    • Create sequences of numbers.
    Understanding:
    Students should understand that:
    • looking for, describing, and extending patterns can be used to help them develop skills in all mathematical situations.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.9.1: Duplicate and extend simple patterns by using concrete objects.
    M.1.9.2: Identify simple patterns.
    M.1.9.3: Mimic simple patterns.
    M.1.9.4: Match a simple object.

    Prior Knowledge Skills:
    • Define ones and tens.
    • Match the number in the ones and tens position to a pictorial representation or manipulative of the value.
    • Add numbers 1-9 to ten to create teen numbers using manipulatives or place value blocks.
    • Count objects up to 10.
    • Notice same/different and some/all.
    • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
    • Understand first and next.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.9 Using vocalization, sign language, augmentative communication, or assistive technology, duplicate, extend, and create simple patterns using concrete objects.


    Operations with Numbers: Base Ten
    Extend the counting sequence.
    Mathematics (2019)
    Grade(s): 1
    All Resources: 4
    Learning Activities: 3
    Classroom Resources: 1
    10. Extend the number sequence from 0 to 120.

    a. Count forward and backward by ones, starting at any number less than 120.

    b. Read numerals from 0 to 120.

    c. Write numerals from 0 to 120.

    d. Represent a number of objects from 0 to 120 with a written numeral.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use the pattern and regularity in the counting sequence to recognize the position of any number between 0 and 120 and then continue counting in sequence from the given number.
    • Count backwards by ones from any given number 0 to 120.
    • Write the corresponding numeral when given a number orally or given a quantity of objects from 0 to 120.
    Teacher Vocabulary:
    • Number
    • Numeral
    Knowledge:
    Students know:
    • number/numeral correspondence (from 0-120).
    • Strategies for counting sets of objects.
    • how to read numbrs from 0 - 120.
    • how to write numbers from 0 - 120.
    Skills:
    Students are able to:
    • strategically apply counting strategies.
    • Write numerals 0-20.
    Understanding:
    Students understand that:
    • there are patterns in our base ten number system.
    • quantities can be represented both physically and symbolically (numerals).
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.10.1: Write numerals from 0 to 20.
    M.1.10.2: Recognize numerals to 100.
    M.1.10.3: Match the numeral to the number objects or picture of objects.
    M.1.10.4: Count to 100 by ones.
    M.1.10.5: Count to 20 by ones.
    M.1.10.6: Identify and name numerals 0-9.
    M.1.10.7: Trace numerals 0-9.

    Prior Knowledge Skills:
    • Count forward to 100 from a number over 50.
    • Count forward to 100 from a number between 2 and 50.
    • Count forward to 50 from a given number.
    • Count to 100 by ones.
    • Mimic counting to 100 by ones.
    • Count to 50 by ones.
    • Mimic counting to 50 by ones.
    • Mimic counting backwards from 5 to 0 by ones.
    • Count to 50 by tens.
    • Count to 20 by ones.
    • Count to 10 by ones.
    • Mimic counting by tens.
    • Mimic counting by ones.
    • Count to 50 and above.
    • Mimic counting forward and backward by ones.
    • Recognize numbers from 1-50.
    • Become interested in how many objects she/he has.
    • Continue to have an interest in counting.
    • Understand the concept of size and amount.
    • Pair the number of objects counted with "how many".
    • Understand that the last number name tells the number of objects counted.
    • Pair a group of objects with a number representing the total number of objects in the group (up to ten objects).
    • Count objects one-by-one using only one number per object (up to ten objects).
    • Recognize that numbers have meaning.
    • Rote count to 50.
    • Communicate number words.
    • Recognize before and after.
    • Trace numerals 1- 20.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.10 Count forward to 30 by ones, starting with any number less than 30. Recognize numerals 0 through 15 as written. When given a numeral 0 to 15, represent the numeral with objects.


    Understand place value.
    Mathematics (2019)
    Grade(s): 1
    All Resources: 4
    Learning Activities: 3
    Classroom Resources: 1
    11. Explain that the two digits of a two-digit number represent amounts of tens and ones.
    a. Identify a bundle of ten ones as a "ten."

    b. Identify the numbers from 11 to 19 as composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

    c. Identify the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 as one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use a variety of representations (symbolic: 10+8. pictorial: one line and 8 dots. physical: place value blocks, bundles of sticks, or groups of fingers, etc.) to show and explain the decomposition of the number into groups of 10 and ones.
    Teacher Vocabulary:
    • Base ten
    • Decompose
    Knowledge:
    Students know:
    • how to decompose numbers 11-19.
    Skills:
    Students are able to:
    • Use place value models or mental strategies to decompose numbers.
    Understanding:
    Students understand that:
    • a two-digit number represents amounts of tens and ones.
    • Ten things can be represented as one ten or as ten ones.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.11.1: Match the number in the ones and tens position to a pictorial representation or manipulative of the value.
    M.1.11.2: Represent numbers with multiple models.
    Examples: models—base ten blocks, number lines, linking cubes, straw bundles.
    M.1.11.3: Count to 100 by tens.
    M.1.11.4: Count 10 objects.
    M.1.11.5: Count to 10 by ones.
    M.1.11.6: Name numerals 0 to 19.

    Prior Knowledge Skills:
    • Define ones and tens.
    • Match the number in the ones and tens position to a pictorial representation or manipulative of the value.
    • Add numbers 1-9 to ten to create teen numbers using manipulatives or place value blocks.
    • Count objects up to 10.
    • Notice same/different and some/all.
    • Recognize numbers from 1-50.
    • Add one to a set of objects (up to 10 objects).
    • Given small groups of objects, create larger groups by combining the small groups.
    • Understand ten and 1 (ten 1's =10).
    • Put together two small groups of objects to create a larger group.
    • Understand number words.
    • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
    • Rote count to 10.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.11 Recognize and create sets of ten (limit to three sets).


    Mathematics (2019)
    Grade(s): 1
    All Resources: 4
    Learning Activities: 3
    Classroom Resources: 1
    12. Compare pairs of two-digit numbers based on the values of the tens and ones digits, recording the results of comparisons with the symbols >, =, and < and orally with the words "is greater than," "is equal to," and "is less than."
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use place value terminology and concepts to explain and justify the use of <, =, > to compare the numbers and create true equalities and inequalities.
    Teacher Vocabulary:
    • Equalities
    • Inequalities
    Knowledge:
    Students know:
    • how to compare quantities using the terminology "greater than", "equal to", and "less than".
    Skills:
    Students are able to:
    • compare 2-digit numbers.
    Understanding:
    Students understand that:
    • numbers can be decomposed to determine if the amount is greater than, equal to, or less than, how that can be done.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.12.1: Define greater than, less than and equal to.
    M.1.12.2: Demonstrate greater than, less than, and equal to using manipulatives, object drawings or numbers 0 to 10.
    M.1.12.3: Use comparison vocabulary.
    Examples: greater than, equal to, and less than.
    M.1.12.4: Recognize symbols for greater than, less than and equal to.
    M.1.12.5: Determine the value of the digits in the ones and tens place.
    M.1.12.6: Identify sets with more, less or equal objects.
    M.1.12.7: Imitate creating sets of a given size.

    Prior Knowledge Skills:
    • Define ones and tens.
    • Match the number in the ones and tens position to a pictorial representation or manipulative of the value.
    • Add numbers 1-9 to ten to create teen numbers using manipulatives or place value blocks.
    • Count objects up to 10.
    • Define greater than, less than, and equal to.
    • Count to 20 by ones.
    • Count objects up to ten.
    • Understand amount words, such as more, less, and another.
    • Begin to understand that parts of an object can make a whole.
    • Become more interested in the concept of some and all.
    • Be interested in who has more or less.
    • Understand the concept of "less than"
    • Mimic counting by ones.
    • Recognize numbers from one to ten.
    • Become interested in how many objects she/he has.
    • Understand the concept of size and amount.
    • Given a set number of objects one through ten, answer the question "how many?"
    • Pair the number of objects counted with "how many?"
    • Understand that the last number name tells the number of objects counted.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.12 Using vocalization, sign language, augmentative communication, or assistive technology, compare two groups of 10 or fewer items using appropriate vocabulary (e.g., more, less, equal) when the number of items in each group is similar.


    Use place value understanding and properties of operations to add and subtract.
    Mathematics (2019)
    Grade(s): 1
    All Resources: 2
    Learning Activities: 1
    Lesson Plans: 1
    13. Add within 100, using concrete models or drawings and strategies based on place value.

    a. Add a two-digit number and a one-digit number.

    b. Add a two-digit number and a multiple of 10.

    c. Demonstrate that in adding two-digit numbers, tens are added to tens, ones are added to ones, and sometimes it is necessary to compose a ten.

    d. Relate the strategy for adding a two-digit number and a one-digit number to a written method and explain the reasoning used.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Add within 100.
    • Explain their reasoning using concrete models or drawings, or using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
    • Relate the strategy used to a written method (symbolic and numeric recording of the steps used).
    Teacher Vocabulary:
    • Compose
    • Multiple of 10
    Knowledge:
    Students know:
    • how to add within 100 using place vaue strategies.
    • how to identify tens and ones.
    • how to compose two digit numbers.
    • how to decompose two digit numbers.
    Skills:
    Students are able to:
    • add within 100.
    • Model addition problems using visual models.
    • Record strategies for solving addition problems.
    • Communicate the relationship between models and symbolic (numeric) representations.
    Understanding:
    Students understand that:
    • relationships between models of addition problems and written strategies of those models can be used to justify solutions.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.13.1: Demonstrate regrouping, total sum, and solve using drawings and concrete models.
    M.1.13.2: Model written method for recording horizontal addition problems.
    M.1.13.3: Determine the value of the number in the ones and tens place.
    M.1.13.4: Match the number in the ones, tens, and hundreds position to a pictorial representation or manipulative of the value.
    M.1.13.5: Represent numbers with multiple models.
    Examples: models—base ten blocks, number lines, linking cubes, straw bundles.
    M.1.13.6: Recall single-digit addition facts.

    Prior Knowledge Skills:
    • Define ones and tens.
    • Match the number in the ones and tens position to a pictorial representation or manipulative of the value.
    • Add numbers 0-9 to ten to create teen numbers using manipulatives or place value blocks.
    • Count objects up to 10.
    • Recognize numbers from 0-10.
    • Become interested in how many objects she/he has.
    • Understand the concept of size and amount.
    • Given a set number of objects one through ten, answer the question "how many?"
    • Pair the number of objects counted with "how many?"
    • Understand that the last number name tells the number of objects counted.
    • Understand that 10 1's = 10.
    • Establish one-to-one correspondence between numbers and objects when given a picture, a drawing or objects.
    • Pair a group of objects with a number representing the total number of objects in the group.
    • Count objects one-by-one using only one number per object.
    • Recognize that numbers and numerals have meaning.
    • Rote count to 10.
    • Communicate number words.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.13 Compose and decompose numbers from 1 to 15 into one ten and ones using objects, drawings, or pictures.


    Mathematics (2019)
    Grade(s): 1
    All Resources: 3
    Learning Activities: 2
    Classroom Resources: 1
    14. Given a two-digit number, mentally find 10 more or 10 less than the number without having to count, and explain the reasoning used.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Can efficiently find 10 more or 10 less than the given number.
    • Explain their mental strategies.
    Teacher Vocabulary:
    • Ten more
    • Ten less
    Knowledge:
    Students know:
    • how to mentally find 10 more or 10 less of a two digit number and explain reasoning.
    • place value vocabulary: tens, ones.
    Skills:
    Students are able to:
    • mentally add or subtract 10 from a number in the range from 1-100.
    • Explain their reasoning using place value understanding and patterns.
    Understanding:
    Students understand that:
    • patterns in the place value system can be used to mentally compute sums and differences.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.14.1: Define more and less.
    M.1.14.2: Demonstrate conceptual understanding of adding or subtracting 10 using concrete models.
    M.1.14.3: Count backward from 100 by tens.
    M.1.14.4: Count forward to 100 by tens.
    M.1.14.5: Count to 100 by ones.

    Prior Knowledge Skills:
    • Define ones and tens.
    • Match the number in the ones and tens position to a pictorial representation or manipulative of the value.
    • Add numbers 1-9 to ten to create teen numbers using manipulatives or place value blocks.
    • Count objects up to 10.
    • Count to 50 and above.
    • Mimic counting by ones.
    • Recognize numbers from 1-50.
    • Understand the concept of amount.
    • Pair the number of objects counted with "how many?"
    • Understand that the last number name tells the number of objects counted.
    • Pair a group of objects with a number representing the total number of objects in the group (up to ten objects).
    • Count objects one-by-one using only one number per object (up to ten objects).
    • Recognize that numbers have meaning.
    • Recognize numbers 1-10.
    • Rote count to 50.
    • Communicate number words.
    • Add one to a set of objects (up to 10 objects).

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.13 Compose and decompose numbers from 1 to 15 into one ten and ones using objects, drawings, or pictures.


    Mathematics (2019)
    Grade(s): 1
    All Resources: 1
    Classroom Resources: 1
    15. Subtract multiples of 10 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • subtract multiples of 10 from more tens using concrete models, drawings, and written equations.
    • look for and describe patterns they find.
    • explain their reasoning using place value and patterns.
    Teacher Vocabulary:
    • Multiple of 10
    Knowledge:
    Students know:
    • place value models for adding and subtracting numbers less than 100.
    • strategies for adding and subtracting multiples of 10.
    Skills:
    Students are able to:
    • use models and strategies to find and record solutions to problems where a multiple of 10 is subtracted.
    • explain their strategies.
    Understanding:
    Students understand that:
    • patterns in the place value system can be used to mentally compute sums and differences.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.15.1: Demonstrate conceptual understanding of subtraction using concrete models.
    M.1.15.2: Model written method for recording problems involving subtraction of 10 from multiples of 10.
    M.1.15.3: Count backward from 100 by tens.
    M.1.15.4: Count forward to 100 by tens. M 1.15.5: Mimic counting to 100 by tens.

    Prior Knowledge Skills:
    • Define subtraction as separating groups of objects.
    • Represent numbers with objects or drawings.
    • Separate sets with nine or fewer objects.
    • Combine objects to form sets up to nine.
    • Notice same/different and some/all.
    • Subtract one from a set of objects (up to five objects).
    • Given a group of objects (ten or less), divide the group into smaller groups in various ways.
    • Take away objects from a large group to create two smaller groups.
    • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
    • Understand number words.
    • Understand that 10 1's = 10.
    • Count forward to 50 by tens.
    • Count backwards from 50 by tens.
    • Mimic counting to 50 by tens.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.13 Compose and decompose numbers from 1 to 15 into one ten and ones using objects, drawings, or pictures.


    Data Analysis
    Collect and analyze data and interpret results.
    Mathematics (2019)
    Grade(s): 1
    All Resources: 5
    Learning Activities: 1
    Lesson Plans: 4
    16. Organize, represent, and interpret data with up to three categories.

    a. Ask and answer questions about the total number of data points in organized data.

    b. Summarize data on Venn diagrams, pictographs, and "yes-no" charts using real objects, symbolic representations, or pictorial representations.

    c. Determine "how many" in each category using up to three categories of data.

    d. Determine "how many more" or "how many less" are in one category than in another using data organized into two or three categories.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • will create a table or chart to organize and represent data with up to three categories using physical objects, tally mark graphs, pictographs, Venn diagrams, yes/no charts, or bar graphs.
    • analyze and interpret the data verbally and in writing by asking and answering questions about the total number of data points, how many in each category, or how many more or less are in one category than in another.
    • use measurement vocabulary such as most, least, more than, less than, and similar comparison words.
    Teacher Vocabulary:
    • Tally mark graphs
    • Pictographs
    • Venn diagrams
    • Yes/no charts
    • Bar graphs
    Knowledge:
    Students know:
    • objects can be grouped into categories based on like characteristics.
    • they can gain information from graphs.
    Skills:
    Students are able to:
    • create, analyze, and interpret data.
    Understanding:
    Students understand that:
    • questions concerning mathematical contexts can be answered by collecting and organizing data.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.16.1: Define more and less.
    M.1.16.2: Describe methods for representing data.
    Examples: pictographs, tally charts, bar graphs, and Venn Diagrams.
    M.1.16.3: Locate information on data displays.
    M.1.16.4: Classify objects into given categories; count the number of objects in each category, and sort the categories by count.
    M.1.16.5: Recognize different types of data displays.

    Prior Knowledge Skills:
    • Identify more and less when given two groups of objects.
    • Identify object attributes.
      Examples: color, shape, size, texture, use.
    • Count objects up to ten.
    • Count to 10 by ones.
    • Understand a different types of graphs (ex. Venn diagram, bar graphs and pictograph).
    • Identify more and less when given two groups of objects of 10 or fewer.
    • Count objects up to 10.
    • Count to 10 by ones.
    • Understand categories.
    • Identify object attributes.
      Examples: color, shape, size, texture, purpose.
    • Count to 1-20.
    • Mimic counting by ones.
    • Recognize numerals from 0-20.
    • Understand the concept of amount.
    • Pair the number of objects counted with "how many?"
    • Understand that the last number name tells the number of objects counted.
    • Pair a group of objects with a number representing the total number of objects in the group (up to ten objects).

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.16 Sort objects or pictures into common categories (e.g., shapes, pets, fruits; limited to two categories and a combined total of 15 objects/pictures for the categories).


    Measurement
    Describe and compare measurable attributes.
    Mathematics (2019)
    Grade(s): 1
    All Resources: 2
    Classroom Resources: 2
    17. Order three objects by length; compare the lengths of two objects indirectly by using a third object.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • use measurement vocabulary to first estimate, describe, and then compare the measurable attributes.
    Teacher Vocabulary:
    • Measurable attributes
    Knowledge:
    Students know:
    • how to correctly align the objects.
    Skills:
    Students are able to:
    • use direct and indirect comparison to order objects by length.
    Understanding:
    Students understand that:
    • measurable attributes of objects can be used to describe and compare the objects.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.17.1: Define length.
    M.1.17.2: Use vocabulary related to length.
    Examples: longer, shorter, longest, shortest, taller.
    M.1.17.3: Identify objects by length.
    Examples: shortest pencil, tallest boy.
    M.1.17.4: Sort objects according to length.
    Example: sort short pencils from long pencils.
    M.1.17.5: Explore objects in relationship to length.

    Prior Knowledge Skills:
    • Use vocabulary related to length and weight.
      Example: longer, shorter, heavier, lighter.
    • Identify objects by length and weight.
      Example: shortest pencil, heaviest rock.
    • Sort objects according to measurable attributes.
    • Define length and weight.
    • Explore objects in relationship to length and weight.
    • Define more, less, length.
    • Use vocabulary related to length.
      Examples: longer, shorter.
    • Identify objects by length.
      Examples: shortest pencil, heaviest rock.
    • Sort objects according to measurable attributes.
    • Use comparative language (longer/shorter, taller/shorter) for the attributes of objects related to length.
    • Communicate long, tall, short.
    • Recognize the length attributes of objects (long/short, tall/short).
    • Recognize length as the measurement of something from end to end.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.17 Compare and determine lengths of objects using non-standard units of measurements (real or pictures) in terms of longer/shorter and taller/shorter.


    Mathematics (2019)
    Grade(s): 1
    All Resources: 2
    Lesson Plans: 1
    Classroom Resources: 1
    18. Determine the length of an object using non-standard units with no gaps or overlaps, expressing the length of the object with a whole number.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • accurately measure length using non-standard units (e.g., paper clips, Cuisenaire rods).
    • understand that units must be laid end to end with no gaps or overlaps when measuring.
    Teacher Vocabulary:
    • Non-standard units
    • Iteration
    Knowledge:
    Students know:
    • measurable attributes of objects, specifically length.
    Skills:
    Students are able to:
    • accurately measure length using non-standard units (to the nearest whole unit).
    Understanding:
    Students understand that:
    • the smaller the unit, the more units will be needed to measure the object.
    • the larger the unit, the fewer units needed to measure an object.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.18.1: Describe gap and overlap.
    M.1.18.2: Describe what it means to measure using non-standard units.
    M.1.18.3: Model measuring using non-standard units.

    Prior Knowledge Skills:
    • Use vocabulary related to length and weight.
      Example: longer, shorter, heavier, lighter.
    • Identify objects by length and weight.
      Example: shortest pencil, heaviest rock.
    • Sort objects according to measurable attributes.
    • Define length and weight.
    • Explore objects in relationship to length and weight.
    • Define more, less, length, width, weight and height.
    • Use vocabulary related to length, width, weight and height.
      Examples: longer, shorter, heavier, lighter, small, big.
    • Identify objects by length, weight and height.
      Examples: shortest pencil, heaviest rock.
    • Sort objects according to non-measurable attributes.
    • Understanding concepts of small, big, heavy, light, tall, short.
    • Understand concept of too much or too little.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.17 Compare and determine lengths of objects using non-standard units of measurements (real or pictures) in terms of longer/shorter and taller/shorter.


    Work with time and money.
    Mathematics (2019)
    Grade(s): 1
    All Resources: 4
    Learning Activities: 1
    Lesson Plans: 1
    Classroom Resources: 2
    19. Tell and write time to the hours and half hours using analog and digital clocks.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • tell and write time in hours and half-hours using analog and digital clocks.
    Teacher Vocabulary:
    • Analog
    • Digital
    Knowledge:
    Students know:
    • how to tell time to the hour and half hour using analog and digital clocks.
    • how to tell time to the hour and half hour using analog and digitial clocks.
    Skills:
    Students are able to:
    • accurately read and write time to the hour and half hour from analog and digital clocks.
    Understanding:
    Students understand that:
    • analog and digital clocks represent the time at any particular moment and show the passage of time with the movement of the hands or the changing of the digits.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.19.1: Describe the short hand as the hour hand and the long hand as the minute hand on an analog clock.
    M.1.19.2: Describe the first number as the hour, and the numbers after the colon as the minutes on a digital clock.
    M.1.19.3: Count to 30 by fives.
    M.1.19.4: Recognize numbers 1 to 12, and 30.
    M.1.19.5: Trace numerals 1 to 12, and 30.
    M.1.19.6: Associate digital and analog clocks with the measurement of time.

    Prior Knowledge Skills:
    • Identify numbers 1 to 12.
    • Count by 5s.
    • Identify activities on a daily schedule that come before, next, after other activities.
    • Know before, next and after.
    • Use a daily schedule containing times (in hours) and activities (in pictures).
    • Tell time in hours on an analog clock.
    • Demonstrate an understanding of yesterday, today, tomorrow, morning, afternoon, day, and night.
    • Recognize yesterday, today, tomorrow.
    • Recognize morning, afternoon, evening/night.
    • Recognize day and night.
    • Understand the concept of time.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.19 Demonstrate an understanding of the concept of time using words such as yesterday, today, tomorrow, morning, afternoon, day, and night; identify activities that come before, next, and after on a daily schedule using a clock limited to time in hours.


    Mathematics (2019)
    Grade(s): 1
    All Resources: 0
    20. Identify pennies and dimes by name and value.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • identify pennies by name and value.
    • identify dimes by name and value.
    Knowledge:
    Students know:
    • how to count by ones and identify a penny.
    • how to count by tens and identify a dime.
    Skills:
    Students are able to:
    • identify a penny by name and its value as 1 cent.
    • identify a dime by name and its value as 10 cents.
    Understanding:
    Students understand that:
    • pennies represents counting by ones.
    • a dime represents counting by tens.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.20.1: Identify that a penny has a value of one cent and demonstrate that 10 pennies has the same value as 1 dime.
    M.1.20.2: Recognize the value of 1 and 10.
    M.1.20.3: Sort pennies and dimes.
    M.1.20.4: Count 10 objects.

    Prior Knowledge Skills:
    • Count to 1-10.
    • Understand the concept of amount.
    • Pair the number of objects counted with "how many?"
    • Understand that the last number name tells the number of objects counted.
    • Pair a group of objects with a number representing the total number of objects in the group.
    • Count objects one-by-one using only one number per object.
    • Recognize that numbers have meaning.
    • Recognize numerals 1-10.
    • Communicate number words.
    • Point to matching or similar objects.
    • Identify a penny, dime by attributes (color, size).
    • Recognize a penny as 1 cent.
    • Differentiate coins from other objects.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.20 Using vocalization, sign language, augmentative communication, or assistive technology, identify U.S. coins by name (e.g., penny & dime).


    Geometry
    Reason with shapes and their attributes.
    Note: Students do not need to learn formal names such as "right rectangular prism."
    Mathematics (2019)
    Grade(s): 1
    All Resources: 1
    Classroom Resources: 1
    21. Build and draw shapes which have defining attributes.

    a. Distinguish between defining attributes and non-defining attributes.

    Examples: Triangles are closed and three- sided, which are defining attributes; color, orientation, and overall size are non-defining attributes.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • build and draw two dimensional shapes.
    • define attributes such as number of sides and the name of the shape.
    Teacher Vocabulary:
    • Defining attribute
    • Non defining attribute
    • Closed
    Knowledge:
    Students know:
    • defining characteristics of basic shapes (triangles, rectangles, squares, circles).
    Skills:
    Students are able to:
    • use defining characteristics to build/draw and identify basic shapes.
    Understanding:
    Students understand that:
    • shapes may be sorted by many sets of attributes, but their geometric classification is based on certain defining attributes.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.21.1: Define side, angle, closed and open.
    M.1.21.2: Describe attributes of shapes.
    Examples: number of sides, number of angles.
    M.1.21.3: Identify two-dimensional shapes.
    M.1.21.4: Sort two-dimensional shapes.
    M.1.21.5: Identify basic attributes.
    Examples: color, shape, size.

    Prior Knowledge Skills:
    • Recognize attributes of shapes.
    • Identify cubes, cones, cylinders, and spheres.
    • Identify squares, circles, triangles, rectangles, and hexagons.
    • Identify shapes in the environment.
    • Trace shapes.
    • Make purpose marks such as lines and circles.
    • Notice same/different and some/all.
    • Begin to name and match sizes and shapes.
    • Enjoy playing with all kinds of objects.
    • Point to matching or similar objects.
    • Understand that words can label sameness and differences.
    • Sort objects on the basis of shape or color.
    • Understand and point to a triangle, a circle, a square and rectangle.
    • Understand the concept of same shape and size.
    • Understand that some have more, and some have less.
    • Name and match primary colors.
    • Sort objects on the basis of both color and shape.
    • Sort a variety of objects in a group that have one thing in common.
    • Recognize and sort familiar objects with the same color, shape, or size.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.21 Determine similarities and differences among shapes of the same size or different sizes and orientations (limited to circle, square, rectangle, and triangle).


    Mathematics (2019)
    Grade(s): 1
    All Resources: 1
    Classroom Resources: 1
    22. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • compose 2D shapes from smaller 2D shapes (e.g., use two right triangles to make a square or two squares to make a rectangle).
    • compose 3D shapes from smaller 3D shapes (e.g., use two cubes to make a rectangular prism or two triangular prisms to make a rectangular prism).
    Teacher Vocabulary:
    • Trapezoid
    • Right rectangular prism
    • Right circular cone
    • Right circular cylinder
    • Composite shape
    • Two dimensional
    Knowledge:
    Students know:
    • attributes of basic shapes (rectangles, squares, trapezoids, triangles, half-circles, quarter-circles, cubes, right rectangular prisms, right circular cones, and right circular cylinders).
    Skills:
    Students are able to:
    • use shape manipulatives to create composite shapes.
    Understanding:
    Students understand that:
    • composite shapes and figures are created by joining two or more geometric shapes together to create a different shape.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.22.1: Combine shapes to fill in the area of a given shape.
    M.1.22.2: Replicate composite shapes.
    M.1.22.3: Decompose pictures made of simple shapes.
    M.1.22.4: Name shapes.
    Examples: square, circle, triangle, rectangle, and hexagon.
    M.1.22.5: Recognize shapes.

    Prior Knowledge Skills:
    • Combine shapes to fill the area of a given shape.
    • Decompose pictures made of simple shapes.
    • Match shapes.
    • Match pieces by color, image, or shape to complete a puzzle.
    • Define similar and different.
    • Use vocabulary related to two-dimensional shapes and three-dimensional figures.
      Examples: vertices (corners), faces (flat surfaces), edges, sides, angles.
    • Recognize vocabulary related to two-dimensional shapes and three-dimensional figures.
    • Identify two-dimensional shapes and three-dimensional figures.
    • Identify shapes.
    • Notice same/different and some/all.
    • Begin to name and match sizes and shapes.
    • Enjoy playing with all kinds of objects.
    • Point to matching or similar objects.
    • Understand that words can label sameness and differences.
    • Sort objects on the basis of shape.
    • Recognize and sort familiar objects with the same shape or size.
    • Understand and point to a triangle, a circle, a square and rectangle.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.22 Sort shapes of the same size and orientation (limited to circle, square, rectangle, and triangle).


    Mathematics (2019)
    Grade(s): 1
    All Resources: 2
    Classroom Resources: 2
    23. Partition circles and rectangles into two and four equal shares and describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.

    a. Describe "the whole" as two of or four of the shares of circles and rectangles partitioned into two or four equal shares.

    b. Explain that decomposing into more equal shares creates smaller shares of circles and rectangles.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • divide shapes into two and four equal shares.
    • describe the whole as cut into halves, fourths, and quarters.
    • describe a set of like pieces as halves, fourths, quarters.
    • describes a single piece as half of, fourth of, or quarter of when compared to the whole.
    • describe the whole as two of, or four of the shares.
    • explain that cutting the shape into more shares creates smaller pieces.
    Teacher Vocabulary:
    • Partition
    Knowledge:
    Students know:
    • how to patition shapes into halves or fourths describe the shares using academic vocabulary.
    Skills:
    Students are able to:
    • decompose circles and rectangles into halves and fourths.
    • explain the size of pieces using the appropriate fraction terminology.
    • explain the relative size of halves and fourths by reasoning about the number of shares created.
    Understanding:
    Students understand that:
    • fractional parts of a whole are equal-sized portions of that whole.
    • decomposing into more equal shares creates smaller shares.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.1.23.1: Define halves, fourths, quarters, whole, parts (shares) and equal.
    M.1.23.2: Demonstrate sharing situations to show equal smaller shares.
    M.1.23.3: Distinguish between equal and non-equal parts.
    M.1.23.4: Decompose pictures made of simple shapes.
    M.1.23.5: Identify squares, circles, triangles and rectangles.

    Prior Knowledge Skills:
    • Combine shapes to fill the area of a given shape.
    • Decompose pictures made of simple shapes.
    • Match shapes.
    • Match pieces by color, image, or shape to complete a puzzle.
    • Define similar and different.
    • Use vocabulary related to two-dimensional shapes and three-dimensional figures.
      Examples: vertices (corners), faces (flat surfaces), edges, sides, angles.
    • Recognize vocabulary related to two-dimensional shapes and three-dimensional figures.
    • Identify two-dimensional shapes and three-dimensional figures.
    • Identify shapes.
    • Notice same/different and some/all.
    • Begin to name and match sizes and shapes.
    • Enjoy playing with all kinds of objects.
    • Point to matching or similar objects.
    • Understand that words can label sameness and differences.
    • Sort objects on the basis of shape.
    • Recognize and sort familiar objects with the same shape or size.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.1.23 Put together two equal size pieces to make a shape that relates to a whole (e.g., two semicircles to make a circle, two squares to make a rectangle).


    Operations and Algebraic Thinking
    Represent and solve problems involving addition and subtraction.
    Note: Second grade problem types include adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions.
    Mathematics (2019)
    Grade(s): 2
    All Resources: 7
    Lesson Plans: 1
    Classroom Resources: 6
    1. Use addition and subtraction within 100 to solve one- and two-step word problems by using drawings and equations with a symbol for the unknown number to represent the problem.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • solve a variety of addition and subtraction problems, using concrete and pictorial representations.
    • explain and justify solutions using connections among a variety of representations (e.g., manipulatives, drawings, and equations with a symbol for the unknown number).
    • write equations that represent the work they have shown.
    Teacher Vocabulary:
    • One-step word problems
    • Two-step word problems
    Knowledge:
    Students know:
    • addition and subtraction strategies to solve one- and two-step word problems within a 100.
    Skills:
    Students are able to:
    • represent quantities and operations (addition & subtraction) physically, pictorially, or symbolically.
    • strategically use a variety of representations to solve addition and subtraction word problem.
    • use informal and mathematical language to communicate the connections among addition and subtraction.
    • accurately compute sums and differences.
    • use symbols to represent unknown quantities in equations.
    Understanding:
    Students understand that:
    • addition is both putting together and adding to.
    • subtraction is taking apart, taking from, and comparisons.
    • mathematical problems can be solved using a variety of strategies, models, representations.
    • variables represent unknown quantities when representing mathematical situations algebraically.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.1.1: Solve one-step addition and subtraction word problems with an unknown by using drawings and equations with a symbol for the unknown number to represent the problem.
    M.2.1.2: Understand key words in addition and subtraction word problems.
    Examples: adding to, taking from, putting together, taking apart, sum, difference, all together, how many more, how many are left, in all.
    M.2.1.3: Locate the unknown regardless of position.
    Examples: start unknown, change unknown, and result unknown.
    M.2.1.4: Apply signs +, -, = to actions of joining and separating sets.
    M.2.1.5: Add and subtract within 50, e.g., by using objects or drawings to represent the problem.
    M.2.1.6: Solve addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects or drawings to represent the problem.
    M.2.1.7: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
    M.2.1.8: Represent numbers with objects or drawings.

    Prior Knowledge Skills:
    • Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
    • Understand key words in addition and subtraction word problems.
      Examples: sum, difference, all together, how many more, how many are left, in all.
    • Define subtraction as separating groups of objects, taking from, or taking apart.
    • Define addition as combining groups of objects, adding to, or putting together.
    • Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
    • Represent numbers with objects or drawings.
    • Use objects to combine and separate groups.
    • Define how many, all together, and in all.
    • Count to 20 by ones.
    • Demonstrate 1:1 correspondence.
    • Mimic counting objects in sequential order arranged in a line, circle, or array.
    • Count no more than 5 objects in a scattered configuration.
    • Mimic counting no more than 5 objects in a scattered configuration.
    • Count to 10 by ones.
    • Count in sequential order.
    • Mimic counting in sequential order.
    • Demonstrate one to one correspondence.
    • Make purposeful marks such as lines and circles.
    Add and subtract within 20.
    See note regarding fluency vs. automaticity in the Overview.
    Mathematics (2019)
    Grade(s): 2
    All Resources: 3
    Learning Activities: 2
    Classroom Resources: 1
    2. Fluently add and subtract within 20 using mental strategies such as counting on, making ten, decomposing a number leading to ten, using the relationship between addition and subtraction, and creating equivalent but easier or known sums.

    a. State automatically all sums of two one-digit numbers.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • find sums and differences of basic facts through sums of 20.
    • use an efficient mental strategy (recall, inverse to addition, derived facts) to find the difference (large minus small) of two numbers less than twenty.
    • show fluency (efficiency and accuracy based on understanding) with sums of 20.
    • when given two one-digit numbers can state their sum with minimal hesitation (by the end of 2nd grade).
    Teacher Vocabulary:
    • Fluently
    Knowledge:
    Students know:
    • how to use mental strategies to add and subtract within 20.
    Skills:
    Students are able to:
    • use addition and subtraction strategies efficiently.
    Understanding:
    Students understand that:
    • fluency involves a mixture of "just knowing" answers, knowing answers from patterns, and knowing answers from the use of strategies. The word fluently is used in the standards to mean accurately, efficiently, and flexibly.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.2.1: Recall single-digit subtraction facts with minuends of 10 or less.
    M.2.2.2: Recall single-digit addition facts with sums up to 10.
    M.2.2.3: Apply addition and subtraction strategies.
    Examples: doubles, doubles plus one, doubles minus one.
    M.2.2.4: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

    Prior Knowledge Skills:
    • Define addition and subtraction.
    • Recognize properties of operations.
    • Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
    • Apply signs +, -, = to actions of joining and separating sets.
    • Identify fact families to ten.
    • Recognize the value of zero.
    • Decompose numbers up to 5 using objects or drawings.
    • Compose numbers up to 5 using objects or drawings.
    • Count backward from 5.
    • Count forward to 5.
    • Write numerals from 0 to 10.
    • Represent a given numeral 1 to 10 with objects or drawings.
    • Count forward from a given number 1 to 10.
    • Model joining sets of objects to total 10.
    • Identify plus, minus, and equal signs.
    • Match numerals to objects or drawings.
    • Identify numerals 1 to 10.
    • Count 0 to 10.
    • Add and subtract numbers within 20 using objects, pictures and fingers.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.2 Represent addition as "add to/put together" and subtraction as "take from/take apart" with objects, drawings, fingers, or sounds (within 30).


    Work with equal groups of objects to gain foundations for multiplication.
    Mathematics (2019)
    Grade(s): 2
    All Resources: 1
    Classroom Resources: 1
    3. Use concrete objects to determine whether a group of up to 20 objects is even or odd.

    a. Write an equation to express an even number as a sum of two equal addends.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • determine whether the set has an odd or even number of objects.
    • explain odd + odd = odd, even + even = even, odd + even = odd.
    Teacher Vocabulary:
    • Concrete objects
    • Equation
    • Equal addends
    Knowledge:
    Students know:
    • how to make equal groups and determine if that group has an odd or even amount of objects.
    Skills:
    Students are able to:
    • use strategies to determine whether numbers are odd or even.
    • communicate reasoning for a label of odd or even.
    Understanding:
    Students understand that:
    • numbers are classified as odd or even based on their characteristics.
    • the term even describes numbers that can be divided into groups of 2 with no leftovers.
    • the term odd describes numbers that when divided into groups of 2 will have one item leftover.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.3.1: Define pair, odd and even.
    M.2.3.2: Recall doubles addition facts with sums to 20.
    M.2.3.3: Apply signs + and = to actions of joining sets.
    M.2.3.4: Model written method for composing equations.
    M.2.3.5: Skip count by 2s.

    Prior Knowledge Skills:
    • Mimic skip counting by 2s.
    • Recognize numbers from 1-10.
    • Become interested in how many objects she/he has.
    • Understand the concept of size and amount.
    • Given a set number of objects one through ten, answer the question "how many?"
    • Pair the number of objects counted with "how many".
    • Understand that the last number name tells the number of objects counted.
    • Understand that 10 1's = 10.
    • Establish one-to-one correspondence between numbers and objects when given a picture, a drawing or objects.
    • Pair a group of objects with a number representing the total number of objects in the group.
    • Count objects one-by-one using only one number per object.
    • Recognize that numbers and numerals have meaning.
    • Rote count to 10.
    • Identify plus, minus, and equal signs.
    • Match numerals to objects or drawings.
    • Communicate number words.
    • Recognize after.
    • Recognize before.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.3 Equally distribute even numbers of up to 20 objects between two groups.


    Mathematics (2019)
    Grade(s): 2
    All Resources: 6
    Learning Activities: 4
    Lesson Plans: 1
    Classroom Resources: 1
    4. Using concrete and pictorial representations and repeated addition, determine the total number of objects in a rectangular array with up to 5 rows and up to 5 columns.

    a. Write an equation to express the total number of objects in a rectangular array with up to 5 rows and up to 5 columns as a sum of equal addends.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • use rectangular arrays to determine the total number of objects.
    • use repeated addition to determine the total number of objects.
    • write equations expressing the total number of objects with repeated addition.
    Teacher Vocabulary:
    • Rectangular array
    • Rows
    • Columns
    Knowledge:
    Students know:
    • how to use arrays and repeated addition as multiplication strategies.
    Skills:
    Students are able to:
    • represent the total number of objects in a rectangular array as the sum of repeated addition.
    • choose and apply addition strategies to accurately compute sums for multiple addend problems.
    Understanding:
    Students understand that:
    • repeated addition determines the total number of items in a rectangular array.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.4.1: Distinguish between rows and columns.
    M.2.4.2: Use repeated addition to solve problems with multiple addends.
    M.2.4.3: Count forward in multiples from a given number.
    Examples: 3, 6, 9, 12; 4, 8, 12, 16.
    M.2.4.4: Recall doubles addition facts.
    M.2.4.5: Model written method for composing equations.

    Prior Knowledge Skills:
    • Give two sets of objects repeatedly from a larger group to represent multiples.
    • Establish one-to-one correspondence between numbers and objects.
    • Identify the = sign as equal.
    • Pair same and equal.
    • Know same when comparing numbers of objects.
    • Recognize cue words for plus (add, plus, combine).
    • Identify the + sign as plus.
    • Use manipulatives and counting, recognize and represent the number 20 as two sets of ten.
    • Use manipulatives and counting, recognize and represent the numbers 1 through 40.
    • Establish one-to-one correspondence between numbers and objects.
    • Rote count to forty.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.4 Use repeated addition to find the sum of objects arranged in equal groups up to 10.


    Understand simple patterns.
    Mathematics (2019)
    Grade(s): 2
    All Resources: 0
    5. Reproduce, extend, create, and describe patterns and sequences using a variety of materials.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • reproduce a pattern.
    • extend a pattern.
    • create patterns.
    • describe number patterns and sequences.
    Teacher Vocabulary:
    • Number patterns
    Knowledge:
    Students know:
    • how to duplicate simple patterns.
    • how to extend simple patterns.
    • how to create simple patterns.
    Skills:
    Students are able to:
    • reproduce given patterns.
    • extend given patterns.
    • create patterns.
    • describe patterns.
    • describe numbers patterns.
    Understanding:
    Students should be engaged in looking for, describing, and extending patterns to help them develop the skills in all mathematical situations.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.5.1: Describe a pattern of colors, shapes, and/or numbers using a variety of materials.
    M.2.5.2: Create a pattern of colors, shapes, and/or numbers using a variety of materials.
    M.2.5.3: Extend a pattern of colors, shapes, and/or numbers.
    M.2.5.4: Mimic a simple pattern of colors, shapes, and/or numbers.
    M.2.5.5: Match a simple pattern of colors, shapes, and/or numbers.

    Prior Knowledge Skills:
    • Notice same/different and some/all.
    • Establish one-to-one correspondence between numbers and objects when given a picture, a drawing, or objects.
    • Understand first and next.
    • Sort objects on the basis of shape.
    • Recognize and sort familiar objects with the same shape or size.
    • Understand and point to a triangle, a circle, a square and rectangle.
    • Understand the concept of same shape and size.
    • Mimic a pattern presented.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.5 Using vocalization, sign language, augmentative communication, or assistive technology, duplicate, extend, create, and describe simple patterns using concrete objects.


    Operations with Numbers: Base Ten
    Understand place value.
    Mathematics (2019)
    Grade(s): 2
    All Resources: 5
    Learning Activities: 1
    Lesson Plans: 1
    Classroom Resources: 3
    6. Explain that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.

    a. Explain the following three-digit numbers as special cases: 100 can be thought of as a bundle of ten tens, called a "hundred," and the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • use concrete materials to bundle groups of 10 to represent numbers (including 100, 200, 300) as bundles of one hundred with no tens and no ones.
    • describe multiples of 100 using words that include the number of groups of a hundred as a unit.
    • recognize and explain a variety of names for a single quantity up to 1,000 (706 as 706 ones, 70 tens and 6 ones, and 7 hundreds and 6 ones).
    Teacher Vocabulary:
    • Digit
    Knowledge:
    Students know:
    • vocabulary of the structure of numbers (place value: ones, tens, hundreds, etc.).
    • patterns and regularities that exist in the place value system (ten ones make a ten, ten tens make a hundred, etc.).
    Skills:
    Students are able to:
    • represent numbers using a variety of models (physical, visual, and symbolic).
    • explain the relationships among various representations and models of three-digit numbers.
    Understanding:
    Students understand that:
    • three digit numbers are made up of a variety of base ten representations.
    • one hundred can be thought of as one group of 100, ten groups of 10, or 100 ones.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.6.1: Match the number in the ones, tens, and hundreds position to a pictorial representation or manipulative of the value.
    M.2.6.2: Represent numbers with multiple concrete models.
    Examples: concrete models—base ten blocks, number lines, linking cubes, straw bundles.
    M.2.6.3: Count to 1000 by hundreds.
    M.2.6.4: Count to 100 by tens.
    M.2.6.5: Create groups of 10.
    M.2.6.6: Match the numeral in the ones and tens position to a pictorial representation or manipulative of the value.
    M.2.6.7: Match the numeral to the number of objects or picture of objects.

    Prior Knowledge Skills:
    • Notice same/different and some/all.
    • Recognize numbers from 1-50.
    • Add one to a set of objects (up to 10 objects).
    • Given small groups of objects, create larger groups by combining the small groups.
    • Understand ten and 1 (ten 1's =10).
    • Put together two small groups of objects to create a larger group.
    • Understand number words.
    • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
    • Rote count to 50 by tens.
    • Rote count to 500 by hundreds.
    • Mimic counting to 100 by tens.
    • Mimic counting to 900 by hundreds.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.6 Recognize and represent numbers up to 30 with sets of tens and ones (objects, columns, arrays).


    Mathematics (2019)
    Grade(s): 2
    All Resources: 6
    Classroom Resources: 6
    7. Count within 1000 by ones, fives, tens, and hundreds.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • use the pattern and regularity in the counting sequence to recognize the position of any number between 1 and 1000 and then continue counting in sequence from the given number.
    • given any multiple of 5, 10, or 100, continue counting by the corresponding base (count by 5s from any multiple of 5, count by 10s from any multiple of 10, etc.).
    Knowledge:
    Students know:
    • how to count from 0 to 1,000 by ones, fives, tens, and hundreds.
    Skills:
    Students are able to:
    • use patterns and regularity in counting sequences to count by 1s, 5s, 10s, & 100s to 1000.
    Understanding:
    Students understand that:
    • patterns and regularities in the counting sequence are useful in reasoning about numbers and solving problems.
    • there are patterns in our base ten number system.
    • quantities can be represented both physically and symbolically (numerals).
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.7.1: Create a number pattern.
    M.2.7.2: Count backward from 100 by fives and tens.
    M.2.7.3: Count forward to 100 by fives and tens.
    M.2.7.4: Count to 100 by ones.

    Prior Knowledge Skills:
    • Add and subtract numbers 0-30 using numbers.
    • Recognize numbers 0-30 as representing quantities.
    • Add and subtract numbers 0-30 using pictures.
    • Add and subtract numbers 0-30 using objects.
    • Know mathematical symbols for add and subtract.
    • Given a set of objects, find the total number of objects when a given set is removed.
    • Given a set of objects, find the total number of objects when another set is combined with the original set.
    • Given two sets of objects (less than ten objects each), count the total number of objects.
    • Count objects to thirty.
    • Establish one-to-one correspondence between numbers and objects.
    • Identify the = sign as equal.
    • Pair same and equal.
    • Know same when comparing numbers of objects.
    • Recognize cue words for minus (subtract, take away, separate).
    • Identify the "-" sign as minus.
    • Recognize cue words for plus (add, plus, combine).
    • Identify the + sign as plus.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.7 Using vocalization, sign language, augmentative communication, or assistive technology, count and recognize numerals 0 to 50 by ones. When given a numeral 0 to 25, name the next two numbers in a three-item sequence.


    Mathematics (2019)
    Grade(s): 2
    All Resources: 3
    Classroom Resources: 3
    8. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • read and write numbers represented in expanded form.
    • read the number name the physical model represents.
    • read number names without physical models.
    Teacher Vocabulary:
    • Expanded form
    Knowledge:
    Students know:
    • how to read and write numbers up to 1,000.
    • how to read and write numbers in expanded form up to 1,000.
    Skills:
    Students are able to:
    • represent quantities in a variety of forms including words, base-ten numerals, and expanded form.
    Understanding:
    Students understand that:
    • there are patterns and regularities in the counting sequence.
    • the same quantity can be represented with words, base-ten numerals, or expanded form, and all forms are useful in different situations.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.8.1: Identify zero as a place holder in two-digit and threedigit numbers.
    M.2.8.2: Match the number in the ones, tens, and hundreds position to a pictorial representation or manipulative of the value.
    M.2.8.3: Identify the value of number in the ones, tens and hundreds place.
    M.2.8.4: Identify place value for ones, tens and hundreds.
    M.2.8.5: Read number names one through one hundred.
    M.2.8.6: Write numerals 1 to 100.
    M.2.8.7: Recognize number names one through twenty.
    M.2.8.8: Trace numerals 0 to 100.

    Prior Knowledge Skills:
    • Notice same/different and some/all.
    • Recognize numbers from 1-100.
    • Add one to a set of objects (up to 10 objects).
    • Given small groups of objects, create larger groups by combining the small groups.
    • Understand ten and 1 (ten 1's =10).
    • Understand that 10 (tens) = 100.
    • Put together two small groups of objects to create a larger group.
    • Understand number words.
    • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
    • Rote count to 10.
    • Understand the value of 0 (zero).
    • Write numbers 1-100.
    • Understand number words 1-100.
    • Trace numbers 1-100.
    Mathematics (2019)
    Grade(s): 2
    All Resources: 4
    Lesson Plans: 1
    Classroom Resources: 3
    9. Compare two three-digit numbers based on the value of the hundreds, tens, and ones digits, recording the results of comparisons with the symbols >, =, and < and orally with the words "is greater than," "is equal to," and "is less than."
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • use place value terminology and concepts to explain and justify the placement of <, =, > to compare two 3-digit numbers and create true equalities and inequalities.
    Teacher Vocabulary:
    • Equalities
    • Inequalities
    Knowledge:
    Students know:
    • how to compare 3-digit numbers using the terminology "greater than," "equal to," and "less than".
    Skills:
    Students are able to:
    • compare 3-digit numbers using place value concepts.
    • justify their reasoning as they compare numbers.
    Understanding:
    Students understand that:
    • the three digits of a 3-digit number represent groups of hundreds, tens, and ones.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.9.1: Define greater than, less than and equal to.
    M.2.9.2: Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
    M.2.9.3: Arrange two-digit numbers in order from greatest to least or least to greatest.
    M.2.9.4: Identify zero as a place holder in two-digit and three-digit numbers.
    M.2.9.5: Model using >, =, and < symbols to record the results of comparisons of two two-digit numbers.
    M.2.9.6: Select numbers on a number line that are more than, less than or equal to a specified number.
    M.2.9.7: Match the words greater than, equal to and less than to the symbols >, =, and <.
    M.2.9.8: Determine the value of the digits in the ones and tens place.
    M.2.9.9: Identify sets with more, less or equal objects.

    Prior Knowledge Skills:
    • Understand amount words, such as more, less, and another.
    • Become more interested in the concept of some and all.
    • Be interested in who has more or less.
    • Understand the concept of "less than" "more than".
    • Mimic counting by ones.
    • Recognize numbers from one to 100.
    • Become interested in how many objects she/he has.
    • Understand the concept of size and amount.
    • Given a set number of objects one through ten, answer the question "how many?"
    • Pair the number of objects counted with "how many".
    • Understand that the last number name tells the number of objects counted.
    • Establish one-to-one correspondence between numbers and objects when given a picture, a drawing or objects.
    • Pair a group of objects with a number representing the total number of objects in the group.
    • Count objects one-by-one using only one number per object.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.9 Using vocalization, sign language, augmentative communication, or assistive technology, compare sets of objects and numbers using appropriate vocabulary (greater than, less than, equal to; limited to thirty objects in a group).


    Use place value understanding and properties of operations to add and subtract.
    Mathematics (2019)
    Grade(s): 2
    All Resources: 5
    Learning Activities: 3
    Classroom Resources: 2
    10. Fluently add and subtract within 100, using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • solve addition examples with sums to 100 using a variety of strategies.
    • solve subtraction examples with differences within 100 using a variety of strategies.
    • justify solutions and explain the reasoning for the strategy chosen.
    Teacher Vocabulary:
    • Properties of operations
    Knowledge:
    Students know:
    • strategies and methods for symbolically (numerically) recording strategies for fluently solving addition and subtraction problems.
    Skills:
    Students are able to:
    • record strategies for solving addition and subtraction problems.
    • communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems.
    Understanding:
    Students understand that:
    • models/strategies can be used to justify their answers.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.10.1: Add within 100, including adding a two-digit number and a one-digit number and adding two two-digit numbers, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used.
    M.2.10.2: Add within 20, demonstrating fluency for addition within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; and creating equivalent but easier or known sums.
    M.2.10.3: Determine the value of the number in the ones, tens and hundreds place.
    M.2.10.4: Model written method for recording horizontal and vertical addition problems.
    M.2.10.5: Understand that the two digits of a two-digit number represent amounts of tens and ones.
    M.2.10.6: Match the number in the ones and tens position to a pictorial representation or manipulative of the value.

    Prior Knowledge Skills:
    • Notice same/different and some/all.
    • Subtract one from a set of objects (up to 10 objects).
    • Given a group of objects (20 or less), divide the group into smaller groups in various ways.
    • Take away objects from a large group to create two smaller groups.
    • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
    • Understand number words.
    • Understand that 10 1's = 10.
    • Count forward to 100 by tens.
    • Count backwards from 100 by tens.
    • Mimic counting to 100 by tens.
    • Recognize numbers from 1-100.
    • Become interested in how many objects she/he has.
    • Understand the concept of size and amount.
    • Given a set number of objects one through ten, answer the question "How many?"
    • Pair the number of objects counted with "how many".

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.10 Using vocalization, sign language, augmentative communication, or assistive technology, identify the meaning of the + sign (add, plus, put together) and the sign (subtract, take away, take from) and the = sign (equal, the same as); compose and decompose numbers up to 20 using objects, pictures, drawings, or numbers.


    Mathematics (2019)
    Grade(s): 2
    All Resources: 1
    Classroom Resources: 1
    11. Use a variety of strategies to add up to four two-digit numbers.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • add up to four 2-digit numbers using strategies based on place value and/or properties of operations.
    • justify solutions and explain the reasoning for the strategy chosen.
    Teacher Vocabulary:
    • Properties of operations
    Knowledge:
    Students know:
    • to use place value strategies to add up tp four 2-digit numbers and justify their thinking.
    Skills:
    Students are able to:
    • strategically choose and then record methods for efficiently and accurately solving addition problems with multiple addends.
    Understanding:
    Students understand that:
    • choosing efficient strategies for finding sums of multiple addends depends on the numbers in the problem.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.11.1: Add within 100, including adding a two-digit number and a one-digit number and adding two two-digit numbers, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used.
    M.2.11.2: Add within 20, demonstrating fluency for addition within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; and creating equivalent but easier or known sums.
    M.2.11.3: Determine the value of the number in the ones, tens and hundreds place.
    M.2.11.4: Model written method for recording horizontal and vertical addition problems.
    M.2.11.5: Understand that the two digits of a two-digit number represent amounts of tens and ones.
    M.2.11.6: Match the number in the ones and tens position to a pictorial representation or manipulative of the value.

    Prior Knowledge Skills:
    • Subtract one from a set of objects (up to 10 objects).
    • Given a group of objects (20 or less), divide the group into smaller groups in various ways.
    • Take away objects from a large group to create two smaller groups.
    • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
    • Understand number words.
    • Understand that 10 1's = 10.
    • Count backwards from 100 by tens.
    • Mimic counting to 100 by tens.
    • Recognize numbers from 1-100.
    • Understand the concept of size and amount.
    • Understand that the last number name tells the number of objects counted.
    • Understand that 10 1's = 10.
    • Understand that 10 (tens) = 100.
    • Pair a group of objects with a number representing the total number of objects in the group.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.10 Using vocalization, sign language, augmentative communication, or assistive technology, identify the meaning of the + sign (add, plus, put together) and the sign (subtract, take away, take from) and the = sign (equal, the same as); compose and decompose numbers up to 20 using objects, pictures, drawings, or numbers.


    Mathematics (2019)
    Grade(s): 2
    All Resources: 9
    Learning Activities: 4
    Classroom Resources: 5
    12. Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method.

    a. Explain that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • add and subtract within 1000.
    • explain their reasoning using concrete models or drawings, or using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
    • relate the strategy used to a written method (symbolic and numeric recording of the steps used).
    Teacher Vocabulary:
    • Compose
    • Decompose
    Knowledge:
    Students know:
    • how to count to 1,000.
    • how to identify hundreds, tens, and ones.
    • how to compose numbers.
    • how to decompose two digit numbers.
    • how to record strategies for solving addition and subtraction problems.
    Skills:
    Students are able to:
    • add and subtract within 1000.
    • model addition problems using visual models.
    • record strategies for solving addition problems.
    • communicate the relationship between models and symbolic (numeric) representations.
    Understanding:
    Students understand that:
    • relationships between models of addition/subtraction problems and written strategies of those models can be used to justify solutions.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.12.1: Define regrouping, total, sum, difference and solve.
    M.2.12.2: Add and subtract two two-digit numbers with and without regrouping.
    M.2.12.3: Determine the value of the number in the ones, tens, hundreds and thousands place using concrete models or drawings and strategies based on place value.
    M.2.12.4: Match the number in the ones, tens, hundreds and thousands position to a pictorial representation or manipulative of the value.
    M.2.12.5: Model written method for recording horizontal and vertical addition and subtraction problems.
    M.2.12.6: Represent two- and three-digit numbers with multiple models.
    Examples: models—base ten blocks, number lines, linking cubes, straw bundles.
    M.2.12.7: Recall single-digit addition and subtraction facts.
    M.2.12.8: Add and subtract within 20, e.g., by using objects or drawings to represent the problem.

    Prior Knowledge Skills:
    • Notice same/different and some/all.
    • Recognize numerals from 1-50.
    • Add one to a set of objects (up to 10 objects).
    • Given small groups of objects, create larger groups by combining the small groups.
    • Understand ten and 1 (ten 1's =10).
    • Put together two small groups of objects to create a larger group.
    • Subtract one from a set of objects (up to 10 objects).
    • Given a group of objects (20 or less), divide the group into smaller groups in various ways.
    • Take away objects from a large group to create two smaller groups.
    • Understand number words.
    • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
    • Rote count to 10.
    • Understand amount words, such as more, less, and another.
    • Begin to understand that parts of an object can make a whole.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.10 Using vocalization, sign language, augmentative communication, or assistive technology, identify the meaning of the + sign (add, plus, put together) and the sign (subtract, take away, take from) and the = sign (equal, the same as); compose and decompose numbers up to 20 using objects, pictures, drawings, or numbers.


    Mathematics (2019)
    Grade(s): 2
    All Resources: 3
    Classroom Resources: 3
    13. Mentally add and subtract 10 or 100 to a given number between 100 and 900.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use a variety of materials and strategies to add or subtract 10 or 100 from a three-digit number in the range of 100 to 900.
    Knowledge:
    Students know:
    • use place value models for adding and subtracting numbers from 1 to 1000.
    • use strategies for mentally adding and subtracting multiples of 10 and 100.
    Skills:
    Students are able to:
    • use patterns and regularity in counting sequences and understandings of place value to add or subtract a "ten" or a "hundred".
    • communicate reasoning and solution strategies.
    Understanding:
    Students understand that:
    • the digits of a 3-digit number represent amounts of hundreds, tens and ones.
    • patterns in the place value system can be used to mentally compute sums and differences.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M. 2.13.1: Demonstrate conceptual understanding of adding or subtracting 10 using concrete models.
    M.2.13.2: Recognize the place value of ones, tens and hundreds.
    M.2.13.3: Count forward and backward by 100.
    M.2.13.4: Count forward and backward by 10.
    M.2.13.5: Recall single-digit subtraction facts.
    M.2.13.6: Recall single-digit addition facts.

    Prior Knowledge Skills:
    • Recognize numerals from 1-50.
    • Become interested in how many objects she/he has.
    • Understand the concept of size and amount.
    • Given a set number of objects one through ten, answer the question "how many?"
    • Pair the number of objects counted with "how many?"
    • Understand that the last number name tells the number of objects counted.
    • Understand that 10 1's = 10.
    • Establish one-to-one correspondence between numbers and objects when given a picture, a drawing or objects.
    • Pair a group of objects with a number representing the total number of objects in the group.
    • Count objects one-by-one using only one number per object.
    • Recognize that numbers and numerals have meaning.
    • Mimic counting forward and backward by 100.
    • Mimic counting forward and backward by 10.
    • Communicate number words.
    • Recognize after.
    • Recognize before.
    • Understand one less than a number 2 through 20.
    • Understand one more than a number 1 through 20.
    Mathematics (2019)
    Grade(s): 2
    All Resources: 4
    Classroom Resources: 4
    14. Explain why addition and subtraction strategies work, using place value and the properties of operations.

    Note: Explanations may be supported by drawings or objects.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • solve addition and subtraction problems using objects, pictures, words and numbers. Explain and justify strategies for adding and subtracting.
    Teacher Vocabulary:
    • Properties of operations
    Knowledge:
    Students know:
    • strategies for finding sums and differences.
    • physical (manipulative) models and pictorial models (place value blocks, lines and dots, bundles and sticks, etc.) for representing numbers using place value concepts.
    Skills:
    Students are able to:
    • use logical reasoning, place value concepts and vocabulary, and properties of numbers and operations to justify strategies for finding sums and differences.
    Understanding:
    Students understand that:
    • relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and strategies.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.14.1: Explain addition and subtraction problems using concrete objects, pictures.
    M.2.14.2: Use multiple strategies to add and subtract including counting on, counting back and using doubles.
    M.2.14.3: Recall single-digit subtraction facts.
    M.2.14.4: Recall single-digit addition facts.
    M.2.14.5: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

    Prior Knowledge Skills:
    • Match numerals to objects or drawings.
    • Identify numerals 1 to 10.
    • Count from 0 to 10.
    • Add and subtract numbers within 20 using objects, pictures and fingers.
    • Take a smaller set out of a larger set.
    • Combine two sets to make a larger set up to twenty.
    • Count items in a set up to twenty.
    • Establish one-to-one correspondence between numbers and objects.
    • Understand one less than a number 2 through 20.
    • Understand one more than a number 1 through 20.
    • Understand positional terms with equal signs.
    Data Analysis
    Collect and analyze data and interpret results.
    Mathematics (2019)
    Grade(s): 2
    All Resources: 2
    Lesson Plans: 1
    Unit Plans: 1
    15. Measure lengths of several objects to the nearest whole unit.

    a. Create a line plot where the horizontal scale is marked off in whole-number units to show the lengths of several measured objects.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • use line plots (whole number scale) to display the data generated by measuring lengths of several objects.
    • communicate questions and descriptions related to the data display.
    Teacher Vocabulary:
    • Line plots
    • Repeated measurement
    • Whole unit
    Knowledge:
    Students know:
    • to use graphs to make observations about the data.
    Skills:
    Students are able to:
    • use standard units and the related tools to measure length to the nearest whole unit.
    • organize and represent length measurement data on a line plot.
    • analyze data.
    Understanding:
    Students understand that:
    • questions concerning mathematical contexts can be answered by collecting and organizing data and displaying the data in line plots.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.15.1: Define length and line plot.
    M.2.15.2: Use vocabulary related to comparison of length.
    Examples: longer, shorter, longest, shortest, taller.
    M.2.15.3: Demonstrate rounding up to the nearest whole unit on measurement tools.
    M.2.15.4: Demonstrate measuring length using standard units.
    M.2.15.5: Describe a line plot.
    M.2.15.6: Model measuring length using standard units.
    M.2.15.7: Identify objects by length.
    M.2.15.8: Sort objects according to length.
    M.2.15.9: Explore objects in relationship to length.

    Prior Knowledge Skills:
    • Define more, less, length, width, weight and height.
    • Identify objects by length and height.
      Examples: shortest pencil, heaviest rock.
    • Identify objects by length.
      Examples: shortest pencil, heaviest rock.
    • Sort objects according to measurable attributes.
    • Sort objects according to non-measurable attributes.
    • Use comparative language (longer/shorter, taller/shorter) for the attributes of objects related to length.
    • Communicate long, tall, short.
    • Recognize the length attributes of objects (long/short, tall/short).
    • Recognize length as the measurement of something from end to end.
    • Understanding concepts of small, big, tall, short.
    • Use manipulatives and counting.
    • Establish one-to-one correspondence between numbers and objects.
    • Write numerals 0-20.
    • Mimic marking Xs on number line.
    Mathematics (2019)
    Grade(s): 2
    All Resources: 6
    Learning Activities: 1
    Lesson Plans: 2
    Classroom Resources: 3
    16. Create a picture graph and bar graph to represent data with up to four categories.

    a. Using information presented in a bar graph, solve simple "put-together," "take-apart," and "compare" problems.

    b. Using Venn diagrams, pictographs, and "yes-no" charts, analyze data to predict an outcome.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • collect data.
    • represent data in picture graph or bar graph format.
    • share a summary of that data.
    • share conclusions.
    Teacher Vocabulary:
    • Pictographs
    • Venn diagrams
    • Yes/no charts
    • Bar graphs
    Knowledge:
    Students know:
    • strategies for collecting, organizing, and recording data.
    • strategies for counting and comparing quantities.
    • strategies for solving addition and subtraction problems.
    Skills:
    Students are able to:
    • choose and apply appropriate strategies for organizing and recording data.
    • read and interpret graphical representations (pictographs and bar graphs) of data.
    • communicate and defend solutions and solution paths.
    Understanding:
    Students understand that:
    • questions concerning mathematical contexts can be answered by collecting and organizing data on pictographs and bar graphs.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.16.1: Use addition and subtraction within 20 to solve addition and subtraction word problems with an unknown number.
    M.2.16.2: Describe picture graph and bar graph.
    M.2.16.3: Demonstrate conceptual understanding of adding or subtracting using a variety of materials.
    M.2.16.4: Use vocabulary related to comparing data.
    Examples: more than, less than, most, least, equal.
    M.2.16.5: Recognize attributes of data displays.
    M.2.16.6: Locate information on data displays.
    M.2.16.7: Classify objects into given categories.
    M.2.16.8: Sort the categories by count.
    M.2.16.9: Recognize different types of data displays.
    M.2.16.10: Count objects up to 50.

    Prior Knowledge Skills:
    • Understand different types of graphs (ex. Venn diagram, bar graphs and pictograph).
    • Identify more and less when given two groups of objects of 10 or fewer.
    • Understand that words can label sameness and differences.
    • Understand categories.
    • Identify object attributes.
      Examples: color, shape, size, texture, purpose.
    • Sort objects on the basis of both color and shape.
    • Sort a variety of objects in a group that have one thing in common.
    • Recognize numerals from 0-20.
    • Understand the concept of amount.
    • Understand that the last number name tells the number of objects counted.
    • Pair a group of objects with a number representing the total number of objects in the group (up to ten objects).
    • Recognize numerals 0-10.
    • Add one to a set of objects (up to 10 objects).
    • Put together two small groups of objects to create a larger group to represent adding.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.16 Using vocalization, sign language, augmentative communication, or assistive technology, use a graph, limited to 2 categories, to answer more/less, most/least, or equal to questions (a combined total of no more than 30 objects/pictures shown for the 2 categories).


    Measurement
    Measure and estimate lengths in standard units.
    Mathematics (2019)
    Grade(s): 2
    All Resources: 8
    Lesson Plans: 4
    Classroom Resources: 3
    Unit Plans: 1
    17. Measure the length of an object by selecting and using standard units of measurement shown on rulers, yardsticks, meter sticks, or measuring tapes.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • choose appropriate tools and units of measurement based on size of object.
    • measure objects correctly.
    Teacher Vocabulary:
    • Standard units of measurement
    Knowledge:
    Students know:
    • standard units of length measure (inches, feet, yards, centimeters and meters) and the related tools.
    Skills:
    Students are able to:
    • measure length in standard units (inches, feet, yards, centimeters and meters).
    • choose and accurately use appropriate measurement tools and units of measure.
    Understanding:
    Students understand that:
    • without overlaps or gaps.
    • the length of the object is expressed as the number of unit lengths needed to cover the same distance.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.17.1: Identify units of measurement for length.
    Examples: inches, feet, yard; centimeter, meters.
    M.2.17.2: Demonstrate how to use measurement tools.
    Example: avoiding gaps and overlaps.
    M.2.17.3: Identify measurement tools.
    M.2.17.4: Model measuring using non-standard units.
    M.2.17.5: Order three objects by length.
    M.2.17.6: Compare the lengths of two objects indirectly by using a third object.
    M.2.17.7: Describe measurable attributes of objects such as length or weight.

    Prior Knowledge Skills:
    • Define more, less, length, width, weight and height.
    • Identify objects by length and height.
      Examples: shortest pencil, heaviest rock.
    • Identify objects by length.
      Examples: shortest pencil, heaviest rock.
    • Sort objects according to measurable attributes.
    • Sort objects according to non-measurable attributes.
    • Use comparative language (longer/shorter, taller/shorter) for the attributes of objects related to length.
    • Communicate long, tall, short.
    • Recognize the length attributes of objects (long/short, tall/short).
    • Recognize length as the measurement of something from end to end.
    • Understanding concepts of small, big, tall, short.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.17 Using vocalization, sign language, augmentative communication, or assistive technology, identify standard tools associated with measurement (clock, ruler, scale, measuring cup); measure the lengths of objects using nonstandard units (e.g., hands, paper clips).


    Mathematics (2019)
    Grade(s): 2
    All Resources: 1
    Classroom Resources: 1
    18. Measure objects with two different units, and describe how the two measurements relate to each other and the size of the unit chosen.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • accurately measure the length of objects using two different standard units.
    • describe how the two measurements relate to each other.
    Teacher Vocabulary:
    • Units
    Knowledge:
    Students know:
    • standard units of length measure (inches, feet, yards, centimeters and meters) and the related tools.
    Skills:
    Students are able to:
    • measure length in standard units.
    • choose and accurately use appropriate measurement tools and units of measure.
    Understanding:
    Students understand that:
    • the smaller the unit of measure the more of that unit it takes to measure a length.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.18.1: Identify units of measurement for length.
    Examples: inches, feet, yard; centimeter, meters.
    M.2.18.2: Demonstrate how to use measurement tools.
    Example: avoiding gaps and overlaps.
    M.2.18.3: Identify units of measure on measurement tools.
    M.2.18.4: Use vocabulary related to comparison of length.
    Examples: longer, shorter, longest, shortest, taller.
    M.2.18.5: Identify numerals one to 50.

    Prior Knowledge Skills:
    • Define more, less, length, width, weight and height.
    • Use vocabulary related to length, width, weight and height.
      Examples: longer, shorter, small, big.
    • Identify objects by length and height.
      Examples: shortest pencil, heaviest rock.
    • Identify objects by length.
      Examples: shortest pencil, heaviest rock.
    • Sort objects according to measurable attributes.
    • Sort objects according to non-measurable attributes.
    • Use comparative language (longer/shorter, taller/shorter) for the attributes of objects related to length.
    • Communicate long, tall, short.
    • Recognize the length attributes of objects (long/short, tall/short).
    • Recognize length as the measurement of something from end to end.
    • Understanding concepts of small, big, tall, short.
    • Identify numerals 0-25.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.17 Using vocalization, sign language, augmentative communication, or assistive technology, identify standard tools associated with measurement (clock, ruler, scale, measuring cup); measure the lengths of objects using nonstandard units (e.g., hands, paper clips).


    Mathematics (2019)
    Grade(s): 2
    All Resources: 1
    Classroom Resources: 1
    19. Estimate lengths using the following standard units of measurement: inches, feet, centimeters, and meters.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • estimate lengths using the standard units of inches, feet, centimeters, and meters.
    Teacher Vocabulary:
    • Estimate
    • Standards units of measurement
    Knowledge:
    Students know:
    • personal benchmarks (e.g. fingernail for centimeter, door knob to floor for meter) for the length of standard units.
    Skills:
    Students are able to:
    • use strategies for using personal benchmarks for estimating lengths in standard units.
    • explain and justify length estimates.
    Understanding:
    Students understand that:
    • estimating before measuring helps them develop a benchmark for the length of an object.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.19.1: Define estimate.
    M.2.19.2: Measure objects using standard and non-standard units.
    M.2.19.3: Identify units of measure on measurement tools.
    M.2.19.4: Model measuring using non-standard units.
    M.2.19.5: Use vocabulary related to comparison of length.
    Examples: longer, shorter, longest, shortest, and taller.

    Prior Knowledge Skills:
    • Define more, less, length, width, weight and height.
    • Use vocabulary related to length, width, weight and height.
      Examples: longer, shorter, small, big.
    • Identify objects by length and height.
      Examples: shortest pencil, heaviest rock.
    • Identify objects by length.
      Examples: shortest pencil, heaviest rock.
    • Use comparative language (longer/shorter, taller/shorter) for the attributes of objects related to length.
    • Communicate long, tall, short.
    • Understanding concepts of small, big, tall, short.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.19 Order three objects by length (long/longer/longest; short/shorter/shortest).


    Mathematics (2019)
    Grade(s): 2
    All Resources: 3
    Lesson Plans: 2
    Classroom Resources: 1
    20. Measure to determine how much longer one object is than another, expressing the length difference of the two objects using standard units of length.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • select appropriate tools for measuring.
    • measure lengths of two objects.
    • determine how much longer one object is than another.
    • express the length differences for the two objects using centimeters, inches, meters, or yards.
    Teacher Vocabulary:
    • Standard units of length
    Knowledge:
    Students know:
    • strategies for comparing the length of objects.
    • standard units of length.
    • related tools.
    Skills:
    Students are able to:
    • choose and accurately use appropriate measurement tools and units of measure.
    • explain and justify procedures for determining the difference between the lengths of two objects.
    Understanding:
    Students understand that:
    • comparisons of objects are determined using attributes that are measurable.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.20.1: Measure objects using standard units.
    M.2.20.2: Record lengths with appropriate units.
    M.2.20.3: Use subtraction within 20 to solve problems.
    M.2.20.4: Compare length using non-standard units to determine which is longer.
    M.2.20.5: Use vocabulary related to comparison of length.
    Examples: longer, shorter, longest, shortest, and taller.

    Prior Knowledge Skills:
    • Define more, less, length.
    • Use vocabulary related to length.
      Examples: longer, shorter.
    • Identify objects by length.
      Examples: shortest pencil, heaviest rock.
    • Sort objects according to measurable attributes.
    • Use comparative language (longer/shorter, taller/shorter) for the attributes of objects related to length.
    • Communicate long, tall, short.
    • Recognize the length attributes of objects (long/short, tall/short).
    • Recognize length as the measurement of something from end to end.
    • Understand different forms of measurement (inches, centimeters).
    • Understand ruler.
    • Match numerals to objects or drawings.
    • Identify numerals 0 to 20.
    • Count from 0 to 20.
    • Add and subtract numbers within 20 using objects, pictures and fingers.
    • Take a smaller set out of a larger set.
    • Combine two sets to make a larger set up to twenty.
    • Count items in a set up to twenty.
    • Establish one-to-one correspondence between numbers and objects.
    • Understand one less than a number 2 through 20.
    • Understand one more than a number 1 through 20.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.19 Order three objects by length (long/longer/longest; short/shorter/shortest).


    Relate addition and subtraction to length.
    Mathematics (2019)
    Grade(s): 2
    All Resources: 4
    Learning Activities: 3
    Classroom Resources: 1
    21. Use addition and subtraction within 100 to solve word problems involving same units of length, representing the problem with drawings (such as drawings of rulers) and/or equations with a symbol for the unknown number.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • use concrete models and/or pictures to make sense of a word problem.
    • write an equation with a symbol for the unknown in the problem.
    • explain verbally how the problem was solved.
    Teacher Vocabulary:
    • Units of length
    • Drawings
    • Equations
    • Symbol
    Knowledge:
    Students know:
    • Students know strategies for solving addition and subtraction word problems involving length.
    Skills:
    Students are able to:
    • represent quantities and operations physically, pictorially, or symbolically.
    • strategically use a variety of representations to solve problems with all addition and subtraction contexts.
    • use symbols to represent unknown quantities in equations.
    Understanding:
    Students understand that:
    • that they can apply the concept of length to solve addition and subtraction word problems for numbers within 100.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.21.1: Solve one-step addition and subtraction word problems with an unknown by using drawings and equations with a symbol for the unknown number to represent the problem.
    Examples: question mark, blank, box, or letter.
    M.2.21.2: Demonstrate the understanding of terms in addition and subtraction word problems involving length.
    Examples: adding to, taking from, putting together, taking apart, sum, difference, all together, how many more, how many are left, in all, inches, feet, yards, longer, shorter, nearer, farther, closer.
    M.2.21.3: Locate the unknown number regardless of position.
    M.2.21.4: Add and subtract within 50, e.g., by using objects or drawings to represent the problem.
    M.2.21.5: Model writing equations from word problems.
    M.2.21.6: Apply signs +, -, = to actions of joining and separating sets.
    M.2.21.7: Identify units of measurement for length.
    Examples: inches, feet, yard; centimeter, meters.

    Prior Knowledge Skills:
    • Establish one-to-one correspondence between numbers and objects.
    • Point to matching or similar objects.
    • Add and subtract numbers within 20 using objects, pictures and fingers.
    • Pair "taking away" with subtraction.
    • Take a smaller set out of a larger set.
    • Pair putting together with adding.
    • Combine two sets to make a larger set up to twenty.
    • Count items in a set up to twenty.
    • Using counting, find one less than a number 2 through 20.
    • Using counting, find one more than a number 1 through 20.
    • Understand +, -, = and what they represent.
    • Define more, less, length, width, weight and height.
    • Use vocabulary related to length, width, weight and height.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.21 Increase or decrease length by adding or subtracting nonstandard unit(s).


    Mathematics (2019)
    Grade(s): 2
    All Resources: 4
    Lesson Plans: 3
    Unit Plans: 1
    22. Create a number line diagram using whole numbers and use it to represent whole-number sums and differences within 100.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • create number line(s) with equally spaced points and a scale of one.
    • represent the quantities as lengths from 0.
    • explain and justify the solutions using representations on number lines (may include open number lines).
    Teacher Vocabulary:
    • Number line
    • Whole numbers
    • Sum
    • Difference
    Knowledge:
    Students know:
    • how to create a number line.
    • how to count forwards and backwards on a number line.
    • how to use addition and subtraction to solve equations using the number line.
    Skills:
    Students are able to:
    • represent quantities and addition/subtraction on number line diagrams.
    • create and use number line models to represent, solve, and justify solutions to addition and subtraction problems within 100.
    Understanding:
    Students understand that:
    • quantities can be represented as distances from zero on a number line.
    • a variety of models, including number lines, can be used to represent and solve addition and subtraction problems.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.22.1: Recognize that each successive number name refers to a quantity that is one larger; and each previous number name refers to a quantity that is one less.
    M.2.22.2: Use a number line to add and subtract within 10.
    M.2.22.3: Write numerals 0 to 100.
    M.2.22.4: Trace numerals 0 to 100.

    Prior Knowledge Skills:
    • Represent addition and subtraction with objects, pictures, fingers, or sounds within twenty.
    • Understand addition as putting together and subtraction as taking from.
    • Establish one-to-one correspondence between numbers and objects.
    • Rote count to 25.
    • Notice same/different and some/all.
    • Point to matching or similar objects.
    • Add and subtract numbers within 20 using objects, pictures and fingers.
    • Pair "taking away" with subtraction.
    • Take a smaller set out of a larger set.
    • Pair putting together with adding.
    • Combine two sets to make a larger set up to twenty.
    • Count items in a set up to twenty.
    • Using counting, find one less than a number 2 through 20.
    • Using counting, find one more than a number 1 through 20.
    • Understand +, -, = and what they represent.
    • Count forward to 50 by tens.
    • Count backwards from 50 by tens.
    • Mimic counting to 50 by tens.
    • Trace numerals 0- 50.
    • Mimic creating a number line with equally spaced points from 0 to 20.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.22 Represent whole-number sums within 20 using a number line.


    Work with time and money.
    Mathematics (2019)
    Grade(s): 2
    All Resources: 2
    Learning Activities: 1
    Classroom Resources: 1
    23. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

    a. Express an understanding of common terms such as, but not limited to, quarter past, half past, and quarter to.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • tell time to the nearest five minutes using analog and digital clocks.
    • write time to the nearest five minutes using analog and digital clocks.
    • use descriptive terms such as five after, half past, quarter past, and quarter to.
    • delineate between a.m. and p.m.
    Teacher Vocabulary:
    • Analog
    • Digital
    Knowledge:
    Students know:
    • how tell and write time to the nearest 5 minutes using analog and digital clocks.
    • how to explain the difference between a.m. and p.m.
    Skills:
    Students are able to:
    • accurately read and write time to the nearest five minutes from analog and digital clocks.
    Understanding:
    Students understand that:
    • analog and digital clocks represent the time at any particular moment.
    • clocks show the passage of time with the movement of the hands or the changing of the digits.
    • time is an attribute that can be measured.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.23.1: Tell and write time in hours and half-hours using analog and digital clocks.
    M.2.23.2: Recognize vocabulary terms related to time measurements.
    Examples: minute, hour, half hour, o'clock, morning, evening, a.m., p.m.
    M.2.23.3: Illustrate time to hour and half hour.
    Example: Given the time 3:00, illustrate long hand and short hand positions on a clock.
    M.2.23.4: Identify the short hand as the hour hand, and the long hand as the minute hand on an analog clock.
    M.2.23.5: Identify the first number as the hour, and the numbers after the colon as the minutes on a digital clock.
    M.2.23.6: Write numerals 0 to 59.
    M.2.23.7: Recognize numerals 0 to 59.
    M.2.23.8: Count to 60 by fives.
    M.2.23.9: Distinguish between analog and digital clocks.

    Prior Knowledge Skills:
    • Identify numerals 0 to 12.
    • Count by 5s.
    • Identify activities on a daily schedule that come before, next, after other activities.
    • Know before, next and after.
    • Use a daily schedule containing times (in hours) and activities (in pictures).
    • Understand differences with analog and digital clocks.
    • Understand hour is the same as 60 minutes.
    • Know the hours, minutes, seconds on a clock.
    • Tell time in hours on an analog clock.
    • Demonstrate an understanding of yesterday, today, tomorrow, morning, afternoon, day, and night.
    • Recognize yesterday, today, tomorrow.
    • Recognize morning, afternoon, evening/night.
    • Recognize day and night.
    • Understand the concept of time.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.23 Using vocalization, sign language, augmentative communication, or assistive technology, identify the time that matches a routine activity using a clock (limited to hour).


    Mathematics (2019)
    Grade(s): 2
    All Resources: 5
    Learning Activities: 2
    Lesson Plans: 2
    Classroom Resources: 1
    24. Solve problems with money.

    a. Identify nickels and quarters by name and value.

    b. Find the value of a collection of quarters, dimes, nickels, and pennies.

    c. Solve word problems by adding and subtracting within one dollar, using the $ and ¢ symbols appropriately (not including decimal notation).

    Example: 24¢ + 26¢ = 50¢
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • identify nickels and quarters.
    • find the value of a combination of coins.
    • solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using dollar and cent symbols appropriately.
    Knowledge:
    Students know:
    • the value of pennies, nickels, dimes, and quarters.
    • ccounting sequence and skip counting by 1s, 5s, and 10s.
    • strategies for solving word problems.
    Skills:
    Students are able to:
    • use problem solving strategies to solve word problems involving a variety of coins.
    Understanding:
    Students understand that:
    • a variety of strategies can be used to model and solve problems involving money.
    • mathematics procedures can be used to answer questions involving daily life situations.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.24.1: Determine the monetary value of a set of like and unlike bills.
    M.2.24.2: Determine the monetary value of a set of like and unlike coins.
    M.2.24.3: Apply addition and subtraction strategies.
    M.2.24.4: Understand key words in addition and subtraction word problems involving money.
    Examples: adding to, taking from, putting together, taking apart, sum, difference, all together, how much more, how much is left, in all, cents, dollar, change, paid, total.
    M.2.24.5: Count forward from a given number by ones, fives, tens, and twenty-fives.
    M.2.24.6: Identify coins and bills and their value.
    M.2.24.7: Identify symbols for dollar ($), cent (¢).
    M.2.24.8: Identify coins by name including penny, nickel, dime and quarter.
    M.2.24.9: Sort pennies, nickels, dimes, and quarters.
    M.2.24.10: Count 10 objects.
    Examples: pennies and dollar bills.

    Prior Knowledge Skills:
    • Count to 1-25.
    • Understand the concept of amount.
    • Pair the number of objects counted with "how many?"
    • Understand that the last number name tells the number of objects counted.
    • Pair a group of objects with a number representing the total number of objects in the group.
    • Count objects one-by-one using only one number per object.
    • Recognize that numbers have meaning.
    • Recognize numerals 1-25.
    • Communicate number words.
    • Point to matching or similar objects.
    • Identify a penny, dime, nickels, quarters by attributes (color, size).

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.24 Using vocalization, sign language, augmentative communication, or assistive technology, identify and demonstrate knowledge that money has value; limited to penny = 1 cent, nickel = 5 cents, dime = 10 cents.


    Geometry
    Reason with shapes and their attributes.
    Mathematics (2019)
    Grade(s): 2
    All Resources: 2
    Classroom Resources: 2
    25. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

    a. Recognize and draw shapes having specified attributes.

    Examples: a given number of angles or a given number of equal faces
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
    • recognize shapes with specified attributes.
    • draw shapes having specified attributes.
    • determine shapes based on their attributes.
    Teacher Vocabulary:
    • Attributes
    Knowledge:
    Students know:
    • defining characteristics of basic shapes (triangles, rectangles, squares, circles).
    Skills:
    Students are able to:
    • identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
    • recognize shapes with specified attributes.
    • draw shapes having specified attributes.
    • determine shapes based on their attributes.
    Understanding:
    Students understand that:
    • shapes may be sorted by many sets of attributes, but their geometric classification is based on certain defining attributes.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.25.1: Define side, angle, face, closed, and open.
    M.2.25.2: Use vocabulary related to shape attributes.
    Examples: sides, angles, face, closed, open.
    M.2.25.3: Trace shapes.
    M.2.25.4: Sort triangles, quadrilaterals, pentagons, hexagons, and cubes.
    M.2.25.5: Explore triangles, quadrilaterals, pentagons, hexagons, and cubes.

    Prior Knowledge Skills:
    • Notice same/different and some/all.
    • Begin to name and match sizes and shapes.
    • Enjoy playing with all kinds of objects.
    • Point to matching or similar objects.
    • Understand that words can label sameness and differences.
    • Sort objects on the basis of shape or color.
    • Understand and point to a triangle, a circle, a square and rectangle.
    • Understand the concept of same shape and size.
    • Understand that some have more, and some have less.
    • Sort objects on the basis of shape.
    • Sort a variety of objects in a group that have one thing in common.
    • Recognize and sort familiar objects with the same color, shape, or size.
    • Understand and point to a triangle, a circle, a square and rectangle.
    • Understand a line and a point, angle.
    • Count 1-6 for sides.
    • Understand the different shapes.
    • Draw basic shapes.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.25 Using vocalization, sign language, augmentative communication, or assistive technology, identify two-dimensional shapes (limited to square, circle, triangle, and rectangle).


    Mathematics (2019)
    Grade(s): 2
    All Resources: 1
    Classroom Resources: 1
    26. Partition a rectangle into rows and columns of same-size squares, and count to find the total number of squares.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • partition a rectangle into rows and columns and use repeated addition to tell the number of squares.
    Teacher Vocabulary:
    • Partition
    Knowledge:
    Students know:
    • how to partition a rectangle into equal-size squares and count those squares.
    Skills:
    Students are able to:
    • use repeated addition to tell how many total squares in an equally partitioned rectangle.
    Understanding:
    Students understand that:
    • repeated addition connects to the conceptual understanding of multiplication.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.26.1: Define rows, columns, and total.
    M.2.26.2: Identify rectangle.
    M.2.26.3: Count to 20 by ones.
    M.2.26.4: Trace partitions in a rectangle.

    Prior Knowledge Skills:
    • Notice same/different and some/all.
    • Begin to name and match sizes and shapes.
    • Enjoy playing with all kinds of objects.
    • Point to matching or similar objects.
    • Understand that words can label sameness and differences.
    • Sort objects on the basis of shape or color.
    • Understand and point to a square or rectangle.
    • Understand the concept of same shape and size.
    • Understand that some have more, and some have less.
    • Sort objects on the basis of shape.
    • Sort a variety of objects in a group that have one thing in common.
    • Recognize and sort familiar objects with the same color, shape, or size.
    • Understand and point to a square and rectangle.
    • Understand a line and a point, row, column.
    • Identify more and less when given two groups of objects of 10 or fewer.
    • Count objects up to 25.
    • Count to 10 by ones.
    • Understand categories.
    • Count to 0-25.
    • Mimic counting by ones.
    • Recognize numerals 0-20.
    • Understand the concept of amount.
    • Pair the number of objects counted with "how many?"
    • Understand that the last number name tells the number of objects counted.
    • Pair a group of objects with a number representing the total number of objects in the group (up to ten objects).
    • Count objects one-by-one using only one number per object (up to ten objects).
    • Recognize that numbers have meaning.
    • Recognize numerals 0-10.
    • Add one to a set of objects (up to 10 objects).
    • Put together two small groups of objects to create a larger group to represent adding.
    • Separate smaller groups from a larger group of objects to represent subtraction.
    • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
    • Understand number words.
    • Rote counting to 20.
    • Sort objects on the basis of both color and shape.
    • Sort a variety of objects in a group that have one thing in common.
    • Understand that words can label sameness and differences.
    • Sort objects on the basis of shape or color.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.27 Using vocalization, sign language, augmentative communication, or assistive technology, identify half as being two equal parts of a shape (limited to circle, square, rectangle, and triangle).


    Mathematics (2019)
    Grade(s): 2
    All Resources: 1
    Learning Activities: 1
    27. Partition circles and rectangles into two, three, or four equal shares. Describe the shares using such terms as halves, thirds, half of, or a third of, and describe the whole as two halves, three thirds, or four fourths.

    a. Explain that equal shares of identical wholes need not have the same shape.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • cut or draw lines to divide shapes into two, three, or four equal shares.
    • describe the whole as cut into halves, thirds, fourths, and quarters.
    • describe a set of like pieces as halves, thirds, fourths, and quarters.
    • describe a single piece as half of, third of, fourth of, or quarter of.
    • describe the whole as two halves, three thirds, or four fourths.
    • recognize that equal shares may be different shapes within the same whole.
    Teacher Vocabulary:
    • Partition
    Knowledge:
    Students know:
    • strategies for partitioning shapes into two, three, or four equal shares and reason about these shares.
    Skills:
    Students are able to:
    • decompose circles and rectangles into halves, thirds, and fourths.
    • communicate the size of pieces using the appropriate fraction terminology.
    • recognize that equal shares may be different shapes within the same whole.
    Understanding:
    Students understand that:
    • shapes can be equally partitioned into halves, thirds, and fourths.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.2.27.1: Define halves, thirds, fourths, quarters, whole, parts (shares) and equal.
    M.2.27.2: Distinguish between equal and non-equal parts.
    M.2.27.3: Model partitioning circles and rectangles.
    M.2.27.4: Decompose pictures made of simple shapes.
    M.2.27.5: Identify squares, circles, triangles and rectangles.
    M.2.27.6: Explore shapes or figures that can be decomposed into smaller equal parts.

    Prior Knowledge Skills:
    • Notice same/different and some/all.
    • Begin to name and match sizes and shapes.
    • Enjoy playing with all kinds of objects.
    • Point to matching or similar objects.
    • Understand that words can label same and differences.
    • Sort objects on the basis of shape.
    • Recognize and sort familiar objects with the same shape or size.
    • Understand and point to a triangle, a circle, a square and rectangle.
    • Understand the concept of same shape and size.
    • Interact with shapes.
    • Understand a whole and half from one object.
    • Understand grouping of objects also equal a whole.
    • Separate whole group into 2 equal groups to show halves.
    • Separate 2 halves into 4 equal groups to show fourths (quarters).
    • Understand the term of equal.
    • Understand that separating shapes can create other shapes.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.2.27 Using vocalization, sign language, augmentative communication, or assistive technology, identify half as being two equal parts of a shape (limited to circle, square, rectangle, and triangle).


    Operations and Algebraic Thinking
    Represent and solve problems involving multiplication and division.
    Mathematics (2019)
    Grade(s): 3
    All Resources: 4
    Learning Activities: 2
    Classroom Resources: 2
    1. Illustrate the product of two whole numbers as equal groups by identifying the number of groups and the number in each group and represent as a written expression.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given any multiplication problem in the form a x b = c,
  • Interpret the equation as a groups of b objects equals the product c, the total number of items.

  • Example: Given 5 x 7 = 35, students explain that 35 represents the total, 5 is the number of groups and 7 is the number in each group.
  • Use concrete materials/pictorial representations to model multiplication situations.
  • Write expressions and equations illustrated by models and drawings.
  • Write word problems to represent a multiplication situation.
  • Teacher Vocabulary:
    • Equal groups
    • Equation
    • Expression
    • Factor
    • Product
    • Array
    • Row
    • Column
    • Skip count
    Knowledge:
    Students know:
    • that in multiplication, one factor represents the number of groups and the other factor represents the number of items in each group, and the product represents the total number of items in all of the groups.
    Skills:
    Students are able to:
    • Use a model or drawing to illustrate the product of two whole numbers.
    • Write an expression or equation to represent the product of two whole numbers identifying the number of equal groups and the group size.
    Understanding:
    Students understand that:
    • a multiplication problem can be interpreted as x groups of y objects.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.1.1: Identify and define the parts of a multiplication problem including factors, multiplier, multiplicand and product.
    M.3.1.2: Use multiplication to find the total number of objects arranged in rectangular arrays based on columns and rows.
    M.3.1.3: Write an equation to express the product of the multipliers (factors).
    M.3.1.4: Relate multiplication to repeated addition and skip counting.
    M.3.1.5: Apply concepts of multiplication through the use of manipulatives, number stories, skip counting arrays, area of a rectangle, or repeated addition.
    M.3.1.6: Apply basic multiplication facts through 9 x 9 using manipulatives, solving problems, and writing number stories.
    M.3.1.7: Solve addition problems with multiple addends.
    M.3.1.8: Represent addition using manipulatives.

    Prior Knowledge Skills:
    • Recall doubles addition facts.
    • Use repeated addition to solve problems with multiple addends.
    • Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
    • Understand key words in addition and subtraction word problems.
      Examples: sum, difference, all together, how many more, how many are left, in all.
    • Define subtraction as separating groups of objects, taking from, or taking apart.
    • Define addition as combining groups of objects, adding to, or putting together.
    • Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
    • Represent numbers with objects or drawings.
    • Use objects to combine and separate groups.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.1 Using vocalization, sign language, augmentative communication, or assistive technology, model finding the sum of equal groups using repeated addition (sums within 30).


    Mathematics (2019)
    Grade(s): 3
    All Resources: 6
    Learning Activities: 4
    Classroom Resources: 2
    2. Illustrate and interpret the quotient of two whole numbers as the number of objects in each group or the number of groups when the whole is partitioned into equal shares.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given any division problem (including word situations) in the form a ÷ b = c,
  • Use concrete materials/pictorial representations to model various division situations.
  • Identify and explain the meanings of the quantities given as well as the meaning and quantity of the missing information.

  • Example: Given 35 ÷ 5, depending on context, students explain that 35 is the number of objects partitioned into 5 equal shares, and 7 is the size of each share, or that 35 is the number of objects partitioned into groups of 5 objects each, and 7 is the number of groups shared.
  • Explain the strategy or reasoning used to find a quotient (or missing factor).
  • Write expressions and equations illustrated by models and drawings.
  • Write word problems to represent a situation involving division.
  • Teacher Vocabulary:
    • Partitive division
    • Measurement division
    • Missing factor
    • Factor
    • Quotient
    • Partition
    • Product
    • Divisor
    • Dividend
    • Equal share
    Knowledge:
    Students know:
    • that division is related to multiplication in terms of finding a missing factor. The missing factor being either the number of groups or the number of items in each group.
    Skills:
    Students are able to:
    • Interpret quantities in a division situation as the number of objects in each group or the number of equal groups.
    • Use a model or drawing to illustrate a quotient.
    • Write word problems for division context involving equal groups and fair shares.
    Understanding:
    Students understand that:
    • a division expression represents either the number of objects in each group when the total number is partitioned evenly into a given number of groups or the number of groups when the total number is partitioned into groups that each contain a given number.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.2.1: Define the parts of a division problem including divisor, dividend, and quotient.
    M.3.2.2: Write a division equation.
    M.3.2.3: Apply the signs ÷ and = to the action of separating sets.
    M.3.2.4: Recognize division as either repeated subtraction, parts of a set, parts of a whole, or the inverse of multiplication.
    M.3.2.5: Model grouping with basic division facts partitioned equally (e.g. 8/2).
    M.3.2.6: Apply properties of operations as strategies to subtract.
    M.3.2.7: Subtract within 20.
    M.3.2.8: Represent equal groups using manipulatives.

    Prior Knowledge Skills:
    • Putting a larger item into smaller groups
    • Model writing equations from word problems.
    • Apply signs +,
    • , = to actions of joining and separating sets.
    • Use of base 10 blocks to demonstrate making equal sets of a larger whole.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.1 Using vocalization, sign language, augmentative communication, or assistive technology, model finding the sum of equal groups using repeated addition (sums within 30).


    Mathematics (2019)
    Grade(s): 3
    All Resources: 4
    Learning Activities: 2
    Classroom Resources: 2
    3. Solve word situations using multiplication and division within 100 involving equal groups, arrays, and measurement quantities; represent the situation using models, drawings, and equations with a symbol for the unknown number.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given a variety of word problems involving multiplication and division within 100,
    • Write and evaluate multiplication and division expressions to represent the word situation.
    • Explain and justify solutions using a variety of representations (equal groups, arrays, area models, number lines, tape diagrams).
    • Use the relationship between multiplication and division to write equations with an unknown factor.
    Teacher Vocabulary:
    • Equal groups
    • Arrays
    • Measurement division
    • Factor
    • Product
    • Quotient
    • Partitive division
    • Represent
    • Unknown
    Knowledge:
    Students know:
    • Multiplication situations can be related to division contexts by identifying the total number of groups and the number of items in a group.
    • Strategies to solve problems involving multiplication and division.
    Skills:
    Students are able to:
    • Use models, drawings, and equations to represent a multiplication or division situation.
    • Use symbols to represent unknown quantities in equations.
    • Solve word situations with multiplication and division within 100 involving equal groups, arrays, and measurement quantities.
    Understanding:
    Students understand that:
    • a word problem with an unknown product is a multiplication problem, and a word problem with an unknown number of groups or an unknown group size can be thought of as a division problem or a multiplication problem with an unknown factor.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.3.1: Demonstrate computational understanding of multiplication and division by solving authentic problems with multiple representations using drawings, words, and/or numbers.
    M.3.3.2: Identify key vocabulary words to solve multiplication and division word problems.
    M.3.3.3: Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
    M.3.3.4: Recall basic multiplication facts.
    M.3.3.5: Add and subtract within 20.
    M.3.3.6: Represent repeated addition, subtraction, and equal groups using manipulatives.

    Prior Knowledge Skills:
    • Define pair, odd and even.
    • Recall doubles addition facts with sums to 20.
    • Apply signs + and = to actions of joining sets.
    • Model written method for composing equations.
    • Skip count by 2s.
    • Represent addition and subtraction with objects, pictures, fingers, or sounds within twenty.
    • Understand addition as putting together and subtraction as taking from.
    • Establish one-to-one correspondence between numbers and objects.
    • Rote count to 20.
    • Notice same/different and some/all.
    • Establish one-to-one correspondence between numbers and objects.
    • Point to matching or similar objects.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.3 Use strategies (arrays, equal groups, manipulatives, etc.) to model multiplication and division equations to find an unknown number.


    Mathematics (2019)
    Grade(s): 3
    All Resources: 2
    Learning Activities: 1
    Classroom Resources: 1
    4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Relate three whole numbers to determine an unknown number in a multiplication equation.

    • Example: 8 x ? = 48 or ? x 8 = 48.
    • Relate three whole numbers to determine an unknown whole number in a division equation.

    • Example: 5 = ? ÷ 3 or ? ÷ 3 = 5.
    • Relate missing factor multiplication equations to division equations using both symbols ? or ÷ for division.
    Teacher Vocabulary:
    • Unknown
    • Multiplication
    • Division
    • Divisor
    • Dividend
    • Equation
    • Product
    Knowledge:
    Students know:
    • how to use the meaning of multiplication and division and the relationship between the two operations to determine an unknown number in a given equation.
    Skills:
    Students are able to:
    • Relate three whole numbers to determine the unknown factor in a multiplication equation.
    • Relate three whole numbers to determine the unknown whole number in a division equation.
    Understanding:
    Students understand that:
    • the unknown number in a multiplication or division equation is the number that makes the equation true.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.4.1: Use arrays to show equal groups in multiplication and division.
    M.3.4.2: Recall basic multiplication facts.
    M.3.4.3: Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.
    M.3.4.4: Represent repeated addition, repeated subtraction, and equal groups using manipulatives.

    Prior Knowledge Skills:
    • Distinguish between rows and columns.
    • Use repeated addition to solve problems with multiple addends Pulled up from first grade.
    • Represent addition and subtraction with objects, pictures, fingers, or sounds within twenty.
    • Understand addition as putting together and subtraction as taking from.
    • Establish one-to-one correspondence between numbers and objects.
    • Rote count to 20.
    • Notice same/different and some/all.
    • Establish one-to-one correspondence between numbers and objects.
    • Point to matching or similar objects.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.3 Use strategies (arrays, equal groups, manipulatives, etc.) to model multiplication and division equations to find an unknown number.


    Understand properties of multiplication and the relationship between multiplication and division.
    Note: Students need not use formal terms for these properties.
    Mathematics (2019)
    Grade(s): 3
    All Resources: 3
    Classroom Resources: 3
    5. Develop and apply properties of operations as strategies to multiply and divide.
    (Students need not use formal terms for the properties)

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use their understanding of multiplication and division to develop and apply a variety of properties to various situations.

    • Examples: given 4 x 9 = 36 is known, then 9 x 4 = 36 is also known. (commutative property). If 3 x 5 x 2 can be found by 3 x 5 =15, then 15 x 2 = 30 or 5 x 2 = 10, then 3 x 10 = 30. (associative property). If 8 x 5 = 40 and 8 x 2 = 16 are known, then 8 x 7 can be found by 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (distributive property.)
    • Identify an equivalent expression where the properties of operations has been applied.
    • Describe the properties of multiplication related to visual models.
    • Write multiplication equations to represent visual models.
    • Apply properties of operations as strategies to multiply and divide.
    Note: Students need not use formal terms for the properties of operations.
    Teacher Vocabulary:
    • Product
    • Sum
    • Property of operations
    • Multiplication expression
    • Decompose
    • Array
    • Area model
    Knowledge:
    Students know:
    • When any factor, x, is multiplied by a factor of 1, the product is the value of x.
    • If one factor is zero, then there are zero groups or zero items in a group and the product is zero.
    • The commutative property of multiplication shows a x b = c and b x a = c.
    • The associative property of multiplication shows that when multiplying three or more numbers, the product is always the same regardless of the grouping.
    • The distributive property will help in finding products of more difficult multiplication facts.
    Skills:
    Students are able to:
    • Develop properties as strategies for multiplication and division.
    • Apply properties of operations as strategies to multiply and divide.
    Understanding:
    Students understand that:
    • applying properties of operations can help develop strategies to find solutions to multiplication and division problems.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.5.1: Define properties of operations.
    M.3.5.2: Apply basic multiplication facts.
    M.3.5.3: Apply properties of operations as strategies to add and subtract.
    M.3.5.4: Count to answer "how many?" questions about as many as 30 things arranged in a rectangular array.

    Prior Knowledge Skills:
    • Match the numeral in the ones and tens position to a pictorial representation or manipulative of the value.
    • Count forward in multiples from a given number.
    • Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
    • Represent numbers with objects or drawings.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.3 Use strategies (arrays, equal groups, manipulatives, etc.) to model multiplication and division equations to find an unknown number.


    Mathematics (2019)
    Grade(s): 3
    All Resources: 1
    Classroom Resources: 1
    6. Use the relationship between multiplication and division to represent division as an equation with an unknown factor.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given a division problem with an unknown quotient,
    • Use a variety of strategies to solve the division problem and justify the solution.
    • Use the relationship between multiplication and division to write an equation with an unknown factor to represent a division problem.
    • Use symbols to represent the unknown quantities in equations.
    • Use the inverse relationship between multiplication and division to find quotients.
    Teacher Vocabulary:
    • Product
    • Quotient
    • Equation
    • Unknown factor
    • Dividend
    • Divisor
    Knowledge:
    Students know:
    • Multiplication and division are related operations.
    • Using known multiplication facts and the relationship between multiplication and division, will help build fluency with division facts.
    Skills:
    Students are able to:
    • Use the relationship between multiplication and division to find quotients.
    • Write a multiplication equation with a missing factor to represent a division situation.
    • Use symbols to represent an unknown quantity in equations.
    Understanding:
    Students understand that:
    • Multiplication and division are related operations.
    • The dividend in a division equation is the same as the product in a related multiplication equation.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.6.1: Apply divisibility rules for 2, 5, and 10.
    M.3.6.2: Apply basic multiplication facts.
    M.3.6.3: Understand subtraction as an unknown-addend problem.
    M.3.6.4: Recognize division as repeated subtraction, parts of a set, parts of a whole, or the inverse of multiplication.

    Prior Knowledge Skills:
    • Add and subtract within 5.
    • Match the numeral in the ones and tens position to a pictorial representation or manipulative of the value.
    • Count forward in multiples from a given number.
    • Skip count by 2s.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.3 Use strategies (arrays, equal groups, manipulatives, etc.) to model multiplication and division equations to find an unknown number.


    Multiply and divide within 100.
    Mathematics (2019)
    Grade(s): 3
    All Resources: 9
    Learning Activities: 4
    Classroom Resources: 5
    7. Use strategies based on properties and patterns of multiplication to demonstrate fluency with multiplication and division within 100.

    a. Fluently determine all products obtained by multiplying two one-digit numbers.

    b. State automatically all products of two one-digit numbers by the end of third grade

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • When given any single digit multiplication problem, use an efficient strategy (recall, inverse operations, arrays, derived facts, properties of operations, doubling, skip counting, square numbers) to name the product.
    • When given a division problem with a single digit divisor and an unknown single digit quotient, use an efficient strategy (recall, inverse operations, arrays, derived facts, properties of operations, doubling, skip counting, square numbers) to name the quotient.
    Teacher Vocabulary:
    • Fluently
    • Properties of operations
    • Product
    • Digit
    • Divisor
    • Dividend
    • Inverse operation
    • Derived fact
    Knowledge:
    Students know:
    • Strategies for finding products and quotients.
    • How to use multiplication facts in terms of a missing factor to learn division facts.
    Skills:
    Students are able to:
    • Use strategies based on properties of operations and patterns of multiplication to find products and quotients.
    • Use efficient multiplication and division strategies based on the numbers in the problems. -Use multiplication facts in terms of a missing factor to learn division facts.
    Understanding:
    Students understand that:
    • they can use the meaning of the numbers in multiplication and division situations to determine strategies to become fluent with multiplication and division facts.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.7.1: Name the first 10 multiples of each one-digit natural number.
    M.3.7.2: Recognize multiplication as repeated addition, and division as repeated subtraction.
    M.3.7.3: Apply properties of operations as strategies to add and subtract.
    M.3.7.4: Recall basic addition and subtraction facts.

    Prior Knowledge Skills:
    • Recall single-digit subtraction facts.
    • Recall single-digit addition facts.
    • Add and subtract two two-digit numbers with and without regrouping.
    • Determine the value of the number in the ones, tens, hundreds and thousands place using concrete models or drawings and strategies based on place value.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.7 Demonstrate fluency of multiplication using skip counting, multiples of numbers, number charts, arrays, etc.


    Solve problems involving the four operations and identify and explain patterns in arithmetic.
    Mathematics (2019)
    Grade(s): 3
    All Resources: 6
    Learning Activities: 1
    Lesson Plans: 1
    Classroom Resources: 4
    8. Determine and justify solutions for two-step word problems using the four operations and write an equation with a letter standing for the unknown quantity. Determine reasonableness of answers using number sense, context, mental computation, and estimation strategies including rounding.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given a variety of two-step word problems involving all four operations,
    • Apply understanding of operations to find solutions.
    • Use a model to represent the problem situation.
    • Write an equation to represent the problem using a symbol for the unknown quantity.
    • Explain and justify strategies and solutions.
    • Apply understanding of operations and estimation strategies including rounding to evaluate reasonableness of the solution.
    Teacher Vocabulary:
    • Unknown quantity
    • Mental computation
    • Estimation
    • Variable
    • Reasonableness
    • Rounding
    • Expression
    • Equation
    Knowledge:
    Students know:
    • Characteristics of addition, subtraction, multiplication, and division.
    • Strategies for addition, subtraction, multiplication, and division.
    • Strategies for mental computation and estimating sums, differences, products, and quotients.
    Skills:
    Students are able to:
    • Use a variety of strategies to solve two-step word problems involving all four operations.
    • Write an equation to represent the problem context, and use a symbol for the unknown quantity.
    • Justify strategy and solutions using mathematical vocabulary.
    • Determine and justify reasonableness of solutions using mental computation strategies and estimation strategies.
    Understanding:
    Students understand that:
    • Mathematical problems can be solved using a variety of strategies, models, and representations.
    • Contextual situations represented by multiplication and division.
    • Reasonableness of solutions can be evaluated by using estimation strategies.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.8.1: Define the identity property of addition and multiplication.
    M.3.8.2: Estimating sums and differences using multiple methods, including compatible numbers and rounding, to judge the reasonableness of an answer.
    M.3.8.3: Apply commutative, associative, and identity properties for all operations to solve problems.
    M.3.8.4: Identify a rule when given a pattern.
    M.3.8.5: Solve addition and subtraction problems, including word problems, involving one-and two digit numbers with and without regrouping, using multiple strategies. M 3.8.6: Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
    M.3.8.7: Represent multiplication and division with manipulatives.
    M.3.8.8: Recall basic addition and subtraction facts.

    Prior Knowledge Skills:
    • Explain addition and subtraction problems using concrete objects, pictures.
    • Use multiple strategies to add and subtract including counting on, counting back and using doubles.
    • Create a number pattern.
    • Use multiple strategies to add and subtract including counting on, counting back and using doubles.
    • Recall single-digit subtraction facts.
    • Recall single-digit addition facts.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.7 Demonstrate fluency of multiplication using skip counting, multiples of numbers, number charts, arrays, etc.


    Mathematics (2019)
    Grade(s): 3
    All Resources: 4
    Learning Activities: 1
    Classroom Resources: 3
    9. Recognize and explain arithmetic patterns using properties of operations.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Recognize, describe, and explain arithmetic patterns.
    • Given a number pattern, find the next number or numbers in the pattern.
    • Given a number pattern, find a characteristic of the next number or numbers in the pattern.
    • Given an addition table or multiplication table, find the missing values in the table.
    • Given an addition table or multiplication table, find a characteristic of a row or column of that table.
    Teacher Vocabulary:
    • Arithmetic pattern
    • Starting value
    • Addition table
    • Multiplication table
    • Consecutive
    • Term
    • Decompose
    Knowledge:
    Students know:
    • that mathematical ideas and concepts build on patterns and recognize and identify those patterns to make sense of math, and the ability to make generalizations is the foundation for algebraic reasoning.
    Skills:
    Students are able to:
    • Identify arithmetic patterns in number sequences, in the addition table, or multiplication table.
    • Use logical reasoning and properties of numbers and operations to explain characteristics of arithmetic patterns.
    Understanding:
    Students understand that:
    • Mathematical concepts build on patterns.
    • When consecutive terms always differ by the same amount, an arithmetic pattern is formed.
    • Visual patterns can be found in the multiplication table.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.9.1: Define arithmetic patterns: geometric or numeric.
    M.3.9.2: Explain arithmetic patterns using properties of operations.
    M.3.9.3: Recognize arithmetic patterns (including geometric patterns or patterns in the addition table or multiplication table).
    M.3.9.4: Construct repeating and growing patterns with a variety of representations.
    M.3.9.5: Demonstrate computational fluency, including quick recall, of addition and multiplication facts.
    M.3.9.6: Duplicate an existing pattern.
    M.3.9.7: Skip count.
    M.3.9.8: Represent addition and multiplication with manipulatives.

    Prior Knowledge Skills:
    • Explain addition and subtraction problems using concrete objects, pictures.
    • Use multiple strategies to add and subtract including counting on, counting back and using doubles.
    • Create a number pattern.
    • Use multiple strategies to add and subtract including counting on, counting back and using doubles.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.7 Demonstrate fluency of multiplication using skip counting, multiples of numbers, number charts, arrays, etc.


    Operations with Numbers: Base Ten
    Use place value understanding and properties of operations to perform multi-digit arithmetic.
    Mathematics (2019)
    Grade(s): 3
    All Resources: 3
    Lesson Plans: 1
    Classroom Resources: 2
    10. Identify the nearest 10 or 100 when rounding whole numbers, using place value understanding.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given two-digit or three-digit number to round to the nearest 10 or 100,
    • Identify the ten or hundreds that the number falls between.
    • Plot the number on a number line between the tens or hundreds.
    • Identify the nearest ten or hundred and justify the answer.
    • Identify a possible value of the unknown number when instructed that an unknown number will round to a given number when rounding to the nearest 10 or 100.

    • Example: An unknown number will round to 340 when rounded to the nearest 10. Identify a possible value for the unknown number.
    Teacher Vocabulary:
    • Place value
    • Round
    • Nearest 10
    • Nearest 100
    • Benchmark number
    • Midpoint
    Knowledge:
    Students know:
    • Values of the digits in the ones, tens, and hundreds places.
    • How to determine what is halfway between two multiples of 10 or 100.
    • Strategies for rounding to the nearest 10 or 100.
    • Use place value vocabulary and logical reasoning to justify solutions when rounding.
    Skills:
    Students are able to:
    • Round whole numbers to the nearest 10 or 100.
    • Identify a possible value for a number which will result in a given number rounded to the nearest 10 or 100.
      Example: What value will result in 270 when rounded to the nearest 10? Identify the possible values.
    Understanding:
    Students understand that:
    • rounding is determining which ten or hundred a number is closer to.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.10.1: Define rounding.
    M.3.10.2: Round whole numbers from 100 to 999 using whole numbers from 10 to 99.
    M.3.10.3: Model rounding whole numbers to the nearest 100.
    M.3.10.4: Round whole numbers from 10 to 99 using whole numbers from 1 to 9.
    M.3.10.5: Model rounding whole numbers to the nearest 10.
    M.3.10.6: Identify the steps in rounding two- and three-digit numbers.
    Example: Identify the digit that may change and the number to the right.
    M.3.10.7: Round whole numbers from 1 to 9 and model to show proficiency.
    M.3.10.8: Understand that the two digits of a two-digit number represent amounts of tens and ones.
    M.3.10.9: Match the number in the ones, tens, and hundreds position to a pictorial representation or manipulative of the value.

    Prior Knowledge Skills:
    • Determine the value of the number in the ones, tens and hundreds place.
    • Recognize the place value of ones, tens and hundreds.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.10 Using vocalization, sign language, augmentative communication, or assistive technology use concrete materials and pictorial models to model whole numbers.


    Mathematics (2019)
    Grade(s): 3
    All Resources: 6
    Learning Activities: 1
    Lesson Plans: 2
    Classroom Resources: 3
    11. Use various strategies to add and subtract fluently within 1000.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given problems of addition and subtraction within 1000,
    • Fluently find sums and differences using strategies based on place value, properties of operations, and the relationship between addition and subtraction.
    • Justify strategies and by relating the strategy to a written method and explain reasoning used.
    • Use estimation strategies to check for reasonableness and justify solutions.
    Note: Standard algorithm for addition and subtraction is not a grade 3 expectation.
    Teacher Vocabulary:
    • Fluently
    • Sum
    • Difference
    • Place value
    • Strategy
    Knowledge:
    Students know:
    • The relationship between addition and subtraction operations.
    • How conceptual models support and give understanding to procedures for addition and subtraction.
    Skills:
    Students are able to:
    • Use a variety of strategies to solve addition and subtraction problems within 1000.
    Understanding:
    Students understand that:
    • Strategies for addition and subtraction will vary depending on the problem.
    • Strategies can include place value, properties of operations, and the relationship between addition and subtraction.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.11.1: Define the commutative and associative properties of addition and subtraction.
    M.3.11.2: Subtract within 100 using strategies and algorithms based on the relationship between addition and subtraction.
    M.3.11.3: Subtract within 100 using strategies and algorithms based on properties of operations.
    M.3.11.4: Subtract within 100 using strategies and algorithms based on place value.
    M.3.11.5: Add within 100 using strategies and algorithms based on the relationship between addition and subtraction.
    M.3.11.6: Add within 100 using strategies and algorithms based on properties of operations.
    M.3.11.7: Add within 100 using strategies and algorithms based on place value.
    M.3.11.8: Recall basic addition and subtraction facts.

    Prior Knowledge Skills:
    • Add within 100, including adding a two-digit number and a one-digit number and adding two two-digit numbers.
    • Add within 20, demonstrating fluency for addition within 10.
    • Add and subtract within 20.
    • Identify place value for ones, tens and hundreds.
    • Read number names one through one hundred.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.10 Using vocalization, sign language, augmentative communication, or assistive technology use concrete materials and pictorial models to model whole numbers.


    Mathematics (2019)
    Grade(s): 3
    All Resources: 1
    Classroom Resources: 1
    12. Use concrete materials and pictorial models based on place value and properties of operations to find the product of a one-digit whole number by a multiple of ten (from 10 to 90).
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers.
    Teacher Vocabulary:
    • Multiply
    • One-digit
    • Multiple of ten
    • Place value
    • Properties of operations
    • Product
    Knowledge:
    Students know:
    • a variety of strategies or tools to find products (skip counting, properties of operations, concrete materials, number lines, arrays, etc.).
    Skills:
    Students are able to:
    • Find the product of a 1-digit factor and multiple of 10 (from 10 to 90).
    • Use concrete materials and pictorial models to find the product.
    • Use properties of operations to find the product.
    • Justify products.
    Understanding:
    Students understand that:
    • A one-digit number multiplied by ten gives a multiple of ten. Ex: 6 x 10 = 60 is the same as that number of ones (60) or that number of tens (6 tens).
    • Adding a zero to the product of two non-zero whole numbers does not demonstrate the relationship between the product and its place value.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.12.1: Model place value by multiplying vertically.
    M.3.12.2: Model properties of operations by multiplying horizontally.
    M.3.12.3: Recall basic multiplication facts.
    M.3.12.4: Recall multiplication as repeated addition.
    M.3.12.5: Apply properties of operations as strategies to add.

    Prior Knowledge Skills:
    • Identify place value for ones, tens and hundreds.
    • Recall basic multiplication facts
    • Recognize properties of operations.
    • Demonstrate that multiplication is the same as repeated addition

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.10 Using vocalization, sign language, augmentative communication, or assistive technology use concrete materials and pictorial models to model whole numbers.


    Operations with Numbers: Fractions
    Develop understanding of fractions as numbers.
    Third grade denominators are limited to 2,3,4,6,and 8 only.
    Mathematics (2019)
    Grade(s): 3
    All Resources: 5
    Classroom Resources: 5
    13. Demonstrate that a unit fraction represents one part of an area model or length model of a whole that has been equally partitioned; explain that a numerator greater than one indicates the number of unit pieces represented by the fraction.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given any fraction in form a/b,
    • Create an area model to represent the fraction.
    • Use a number line to represent the fraction.
    • Explain the relationship between the fraction and the model including the corresponding number of unit fractions.
      Example: 3/4 is composed of 3 units of 1/4 or 3/4 is the same as 1/4 + 1/4 + 1/4.
    • Identify a point to represent the fraction when given on a number line labeled with multiple points.
    Note: Set models (parts of a group) are not models used in grade 3.
    Teacher Vocabulary:
    • Unit fraction
    • Area model
    • Interval
    • Length (Linear) model
    • Partition
    • Numerator
    • Denominator
    • Part
    • Point
    • Whole
    Knowledge:
    Students know:
    • Fractional parts of a whole must be of equal size but not necessarily equal shape.
    • Denominators represent the number of equal size parts that make a whole.
    • The more equal pieces in the whole, the smaller the size of the pieces.
    • The numerator represents the number of equal pieces in the whole that are being counted or considered.
    Skills:
    Students are able to:
    • Use an area model and length model to show a unit fraction as one part of an equally partitioned whole.
    • Explain that given a fraction with a numerator greater than one, the numerator indicates the number of unit fraction pieces represented by the fraction.
      Example: 3/4 is the same as 3 units of 1/4 size, or three 1/4 pieces, 3 copies of 1/4, or 3 iterations of 1/4.
    • Identify and describe the fractional name given a visual fraction model.
    • Identify and demonstrate fractional parts of a whole that are the same size but not the same shape using concrete materials.
    Understanding:
    Students understand that:
    • Given the same size whole, the larger the denominator, indicating the number of equal parts in the whole, the smaller the size of the pieces because there are more pieces in the whole.
    • Fractions are numbers that represent a quantity less than, equal to, or greater than 1.
    • Fractions represent equal partitions of a whole.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.13.1: Define fraction, numerator, and denominator.
    M.3.13.2: Identify the parts of a fraction.
    M.3.13.3: Label numerator, denominator, and fraction bar.
    M.3.13.4: Identify parts of a whole with two, three, or four equal parts.
    M.3.13.5: Distinguish between equal and non-equal parts.
    M.3.13.6: Partition circles and rectangles into two and four equal shares; describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.

    Prior Knowledge Skills:
    • Define halves, thirds, fourths, quarters, whole, parts (shares) and equal.
    • Distinguish between equal and non-qual parts.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.15 Compare fractions.
    M.AAS.3.15a Use models to identify two equivalent fractions (limit to fourths and halves).
    M.AAS.3.15b Recognize two equivalent fractions (limit to fourths and halves).
    M.AAS.3.15c Use models of fourths and halves to make a whole.


    Mathematics (2019)
    Grade(s): 3
    All Resources: 5
    Learning Activities: 3
    Classroom Resources: 2
    14. Interpret a fraction as a number on the number line; locate or represent fractions on a number line diagram.

    a. Represent a unit fraction (1/b) on a number line by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts as specified by the denominator.

    b. Represent a fraction (a/b) on a number line by marking off a lengths of size (1/b) from zero.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given a fraction a/b (with denominators of 2, 3, 4, 6, 8),
    • Use a number line and partition the interval between 0 and 1 into b equal parts, specified by the denominator.
    • Use a number line and partition the interval between 0 and 1 into b equal parts and mark off a lengths of 1/b unit fractions.
    • Model a fraction with a point on a number line and recognize the length of the fraction as the distance from the fraction point to 0.
    • Extend the number to include fractions greater than one as a continuation of counting unit fractions.
    • Given a fraction, draw a model to represent the fraction using a number line.
    • Given a fraction and a number line with labeled points, identify the labeled point that represents the fraction.
    • Given a point on a number line, identify the fraction modeled by the point.
    Teacher Vocabulary:
    • Fraction
    • Number line
    • Number line diagram
    • Unit fraction
    • Interval
    • Partition
    • Point
    • Denominator
    • Numerator
    Knowledge:
    Students know:
    • How to use fraction strips as a model to connect to finding fractional parts on a number line.
    • Fractions are numbers that can be represented on a number line.
    • Fractions can be placed on the number line by marking off equal parts between two whole numbers.
    • Fractions equal to 1 have the same numerator and same denominator.
    • Fractions greater than 1 have a numerator that will be greater than the denominator.
    Skills:
    Students are able to:
    • Represent fractions on a number line.
    • Locate fractions on a number line.
    • Use a number line and partition an interval from 0 to 1 into equal parts as specified by the denominator of a fraction.
    • Represent a non unit fraction on a number line by marking off unit fraction lengths as specified by the numerator from zero.
    • Extend the number line to include fractions greater than one as a continuation of counting unit fractions.
    Understanding:
    Students understand that:
    • A number line is a length model.
    • Fractions are numbers that represent a quantity less than, equal to, or greater than 1 and can be placed on a number line.
    • A number line can be partitioned to represent equal parts of a whole.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.14.1: Recognize fractions as lengths from zero to one.
    M.3.14.2: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
    M.3.14.3: Identify a number line.
    M.3.14.4: Recognize whole numbers as lengths from zero to one.
    M.3.14.5: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
    M.3.14.6: Identify a number line.
    M.3.14.7: Label the fractions on a pre-made number line diagram.
    M.3.14.8: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
    M.3.14.9: Recognize a number line diagram with equally spaced points.

    Prior Knowledge Skills:
    • Select numbers on a number line that are more than, less than or equal to a specified number.
    • Count to 20 by ones.
    • Count to 10 by ones.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.15 Compare fractions.
    M.AAS.3.15a Use models to identify two equivalent fractions (limit to fourths and halves).
    M.AAS.3.15b Recognize two equivalent fractions (limit to fourths and halves).
    M.AAS.3.15c Use models of fourths and halves to make a whole.


    Mathematics (2019)
    Grade(s): 3
    All Resources: 1
    Learning Activities: 1
    15. Explain equivalence and compare fractions by reasoning about their size using visual fraction models and number lines.

    a. Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers.

    b. Compare two fractions with the same numerator or with the same denominator by reasoning about their size (recognizing that fractions must refer to the same whole for the comparison to be valid). Record comparisons using < , >, or = and justify conclusions.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use a variety of area models and length models to identify equivalent fractions.
    • Use a variety of area models and length models to illustrate equivalent fractions.
    • Use visual representations to find fractions equal to 1.
    • Illustrate and explain fractions equivalent to whole numbers (limited to 0 through 5).
    • Compare two fractions by reasoning about their size and use <, >, or = to record the comparison.
    • Compare two fractions using visual fraction models.
    • Use symbols <, >, or = to record the comparison between two fractions.
    Note: Tasks in grade 3 are limited to fractions with denominators 2, 3, 4, 6, or 8.
    Teacher Vocabulary:
    • Equivalence
    • Visual fraction model
    • Number line
    • Numerator
    • Denominator
    • Reasoning
    • Conclusions
    • Comparison
    • Point
    Knowledge:
    Students know:
    • Fractions with different names can be equal.
    • Two fractions are equivalent if they are the same size, cover the same area, or are at the same point on a number line.
    • Unit fraction counting continues beyond 1 and whole numbers can be written as fractions.
    • Use a variety of area models and length models to show that a whole number can be expressed as a fraction and to show that fractions can be equivalent to whole numbers.
    • Comparing two fractions is only reasonable if they refer to the same whole.
    • The meaning of comparison symbols <, >, = .
    • Reason about the size of a fraction to help compare fractions.
    • Use a variety of area and length models to represent two fractions that are the same size but have different names.
    • Use a fraction model to explain how equivalent fractions can be found.
    • Use a variety of area models and length models to demonstrate that any fraction that has the same nonzero numerator and denominator is equivalent to 1.
    • Use models to show that the numerator of a fraction indicates the number of parts, so if the denominators of two fractions are the same, the fraction with the greater numerator is the greater fraction.
    • Use models to show that the denominator of a fraction indicates the size of equal parts a whole is partitioned into, and that the greater the denominator, the smaller the parts. -Determine when two fractions can not be compared because they do not refer to the same size whole.
    Skills:
    Students are able to:
    • Explain equivalence of two fractions using visual models and reasoning about their size.
    • Compare two fractions with same numerators or with same denominators using visual models and reasoning about their size.
    • Express whole numbers as fractions.
    • Identify fractions equivalent to whole numbers.
    • Record comparisons of two fractions using <, >, or = and justify conclusion.
    • Explain that the whole must be the same for the comparing of fractions to be valid.
    Understanding:
    Students understand that:
    • A fraction is a quantity which can be illustrated with a length model or an area model.
    • Two fractions can be the same size but have different fraction names.
    • A fraction can be equivalent to a whole number.
    • Any fraction that has the same nonzero numerator and denominator is equivalent to 1.
    • The numerator of a fraction indicates the number of parts, so if the denominators of two fractions are the same, the fraction with the greater number of parts is the greater fraction.
    • The denominator of a fraction indicates the size of equal parts in a whole, so the greater the denominator, the smaller the size of the parts in a whole.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.15.1: Define equivalent.
    M.3.15.2: Recognize pictorial representations of equivalent fractions.
    M.3.15.3: Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.
    M.3.15.4: Recognize that equal shares of identical wholes need not have the same shape.
    M.3.15.5: Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
    M.3.15.6: Label a fraction with multiple representations.
    M.3.15.7: Recognize that a whole can be partitioned into differing equal parts (halves, fourths, eighths, etc.).
    M.3.15.8: Partition circles and rectangles into two and four equal shares; and describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.
    M.3.15.9: Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.
    M.3.15.10: Label a pictorial representation.
    M.3.15.11: Recognize that a fraction is a part of a whole.
    M.3.15.12: Partition circles and rectangles into two and four equal shares; describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.

    Prior Knowledge Skills:
    • Label numerator, denominator, and fraction bar
    • Match the number in the ones, tens, and hundreds position to a pictorial representation or manipulative of the value.
    • Distinguish between equal and non-qual parts.
    • Model partitioning circles and rectangles.
    • Identify two-dimensional shapes.
    • Sort two-dimensional shapes
    • Name shapes.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.15 Compare fractions.
    M.AAS.3.15a Use models to identify two equivalent fractions (limit to fourths and halves).
    M.AAS.3.15b Recognize two equivalent fractions (limit to fourths and halves).
    M.AAS.3.15c Use models of fourths and halves to make a whole.


    Data Analysis
    Represent and interpret data.
    Mathematics (2019)
    Grade(s): 3
    All Resources: 13
    Learning Activities: 2
    Lesson Plans: 4
    Classroom Resources: 5
    Unit Plans: 2
    16. For a given or collected set of data, create a scaled (one-to-many) picture graph and scaled bar graph to represent a data set with several categories.

    a. Determine a simple probability from a context that includes a picture.

    b. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled graphs.
    Unpacked Content
    Evidence Of Student Attainment:
    Students
  • Organize data and draw a scaled picture graph (with scales other than 1) to represent a data set with several categories.
  • Organize data and draw a scaled bar graph (with scales other than 1) to represent a data set with several categories.
  • Given a scaled picture graph or bar graph, solve one-And two-step problems using information presented in the graphs.
  • Determine simple probability from a context that includes a picture or information displayed in a graph.

  • Example: A picture graph displays data to represent the type of transportation for students traveling to school as 10 students walk, 8 students ride bikes, 38 ride the bus, and 12 ride in cars. Another student enrolls in school. What is the least likely way they will travel to school? Why?

    Note: Students are expected to reason about probability, not calculate a probability.
    Teacher Vocabulary:
    • Data set
    • Scale
    • Picture graph
    • Scaled bar graph
    • Category
    • Probability
    Knowledge:
    Students know:
    • Strategies for collecting, organizing, and recording data in picture graphs and bar graphs.
    • Describe and interpret data on picture and bar graphs.
    • Strategies for solving addition and subtraction one-And two-step problems.
    Skills:
    Students are able to:
    • Collect and categorize data to display graphically.
    • Draw a scaled picture graph (with scales other than 1) to represent a data set with several categories.
    • Draw a scaled bar graph (with scales other than 1) to represent a data set with several categories.
    • Determine simple probability from a context that includes a picture.
      Example: A bar graph displays data to represent students' favorite colors with data showing 4 students choose red, 11 students choose blue, 2 students choose green, and 4 students choose purple. If Jamal is a student in the class, what do you think his favorite color might be? Why?
    • Solve one-And two-step "how many more" and "how many less" problems using information presented in scaled graphs.
    Understanding:
    Students understand that:
    • Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs.
    • Understand that logical reasoning and connections between representations provide justifications for solutions.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.16.1: Define picture graph, bar graph, and data.
    M.3.16.2: Interpret the data to solve problems.
    M.3.16.3: Identify the parts of a graph (x-axis, y-axis, title, key, equal intervals, labels).
    M.3.16.4: Locate the data on a picture graph and a bar graph.
    M.3.16.5: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
    M.3.16.6: Directly compare two objects, with a measurable attribute in common, to see which object has "more of" or "less of" the attribute, and describe the difference.

    Prior Knowledge Skills:
    • Describe picture graph and bar graph.
    • Use vocabulary related to comparing data.
      Examples: more than, less than, most, least, equal.
    • Recognize attributes of data displays.
    • Locate information on data displays.
    • Classify objects into given categories.
    • Sort the categories by count.
    • Recognize different types of data displays.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.16 Measure lengths of objects using non standard tools (paper clips). Limit to whole numbers.
    M.AAS.3.17 Using vocalization, sign language, augmentative communication or assistive technology, represent and interpret data on a picture or bar graph when given a model or a graph to complete.


    Mathematics (2019)
    Grade(s): 3
    All Resources: 3
    Lesson Plans: 1
    Classroom Resources: 1
    Unit Plans: 1
    17. Measure lengths using rulers marked with halves and fourths of an inch to generate data and create a line plot marked off in appropriate units to display the data.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Measure objects to the nearest 1/2 inch.
    • Measure objects to the nearest 1/4 (quarter) inch.
    • Create a line plot marked off in appropriate units (whole numbers, halves, or quarters) to represent data of several objects.
    • Create a line plot marked off in appropriate units (whole numbers, halves, or quarters) to represent data of repeated measurements.

    • Example: Measuring how far a marble rolls under certain conditions.
    Teacher Vocabulary:
    • Halves
    • Fourths
    • Data
    • Line plot
    • Unit
    • Quarter inch
    • Horizontal
    • Partition
    Knowledge:
    Students know:
    • Nearest half and nearest quarter inch on a ruler.
    • A ruler is a type of number line and shows fraction of 1/2 and 1/4.
    Skills:
    Students are able to:
    • Measure objects to the nearest half and fourth of an inch.
    • Create a line plot to display the data of the objects measured.
    Understanding:
    Students understand that:
    • A line plot is a graph that displays a distribution of data values, including whole numbers, halves and quarters, such that each data value is marked above a horizontal line with an X or dot.
    • A ruler is a type of number line partitioned equally and shows halves and fourths.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.17.1: Define line plot.
    M.3.17.2: Identify the parts of a line plot.
    M.3.17.3: Measure objects to the nearest inch.
    M.3.17.4: Identify one-inch units on a ruler starting with 0.
    M.3.17.5: Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
    M.3.17.6: Directly compare two objects, with a measurable attribute in common, to see which object has "more of" or "less of" the attribute, and describe the difference.

    Prior Knowledge Skills:
    • Define length and line plot.
    • Use vocabulary related to comparison of length.
      Examples: longer, shorter, longest, shortest, taller.
    • Demonstrate rounding up to the nearest whole unit on measurement tools.
    • Demonstrate measuring length using standard units.
    • Describe a line plot.
    • Model measuring length using standard units.
    • Identify the object length.
    • Explore objects in relationship to length.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.16 Measure lengths of objects using non standard tools (paper clips). Limit to whole numbers.
    M.AAS.3.17 Using vocalization, sign language, augmentative communication or assistive technology, represent and interpret data on a picture or bar graph when given a model or a graph to complete.


    Measurement
    Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
    Mathematics (2019)
    Grade(s): 3
    All Resources: 2
    Classroom Resources: 2
    18. Tell and write time to the nearest minute; measure time intervals in minutes (within 90 minutes.)

    a. Solve real-world problems involving addition and subtraction of time intervals in minutes by representing the problem on a number line diagram.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Tell and record time to the nearest minute using an analog clock.
    • Determine elapsed time using a number line.
    • Solve simple word problems using elapsed time in minutes (within 90 minutes) or hours.
    Teacher Vocabulary:
    • Minute
    • Time interval
    • Number line diagram
    • Analog
    • Digital
    • Elapsed time
    • Half-hour
    • Quarter-hour
    Knowledge:
    Students know:
    • Conventions for time notation.
    • Time sequence patterns.
    • Strategies to determine elapsed time.
    Skills:
    Students are able to:
    • Accurately read and write time to the nearest minute from analog and digital clocks.
    • Measure time intervals in minutes.
    • Illustrate elapsed time using a number line.
    • Solve problems involving elapsed time in minutes (with 90 minutes) or hours.
    Understanding:
    Students understand that:
    • An analog clock is a whole partitioned into 60 parts and each part is one minute.
    • A number line can be partitioned to show time intervals in minutes.
    • A number line can be used to solve word problems that involve time intervals.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.18.1: Compare equivalent units of time using hours and minutes.
    Examples: 60 minutes = one hour, 30 minutes = one half of an hour.
    M.3.18.2: Recognize key vocabulary and/or phrases associated with time.
    M.3.18.3: Compare the lengths of time to complete everyday activities.
    M.3.18.4: Tell and write time in hours and half-hours using analog and digital clocks.
    M.3.18.5: Recognize hour, minute, and second hands on an analog clock.
    M.3.18.6: Count by 5's to 60.

    Prior Knowledge Skills:
    • Write numerals 0 to 59.
    • Recognize numerals 0 to 59.
    • Count to 60 by fives.
    • Distinguish between analog and digital clocks.
    • Identify the short hand as the hour hand, and the long hand as the minute hand on an analog clock.
    • Identify the first number as the hour, and the numbers after the colon as the minutes on a digital clock.
    • Tell and write time in hours and half-hours using analog and digital clocks.
    • Recognize vocabulary terms related to time measurements.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.18 Using vocalization, sign language, augmentative communication, or assistive technology, tell time on a digital clock (to the hour, half-hour, quarter hour).


    Mathematics (2019)
    Grade(s): 3
    All Resources: 4
    Lesson Plans: 2
    Classroom Resources: 2
    19. Estimate and measure liquid volumes and masses of objects using liters (l), grams (g), and kilograms (kg).

    a. Use the four operations to solve one-step word problems involving masses or volumes given in the same metric units.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools (such as balance and spring scales, graduated cylinders, beakers, and measuring cups) to determine measures to the nearest whole unit.
    • Given an image of a measurement device, determine the volume or mass shown in the image.
    • Use the four operations to solve one-step word problems involving liquid volume or mass measurements.
    • Given two measurement quantities or two images of a measuring device, determine the total volume/mass, or find the difference between the two volumes/masses.
    • Given the volume or mass of an object, determine the volume/mass of more than one object using multiplication.
    • Given the total volume or mass of multiple identical objects, determine the volume/mass of a single object using division.
    • Explain and justify solutions using a variety of representations.
    Teacher Vocabulary:
    • Liquid volume
    • Mass
    • Liter
    • Gram
    • Kilogram
    • Metric unit
    • Capacity
    • Matter
    Knowledge:
    Students know:
    • Personal benchmarks for metric standard units of measure, mass (gram & kilogram) and liquid volume (liter), and the use of related tools (such as balance, spring scales, graduated cylinders, beakers, measuring cups) for measurement to those units.
    • Characteristics of addition, subtraction, multiplication, and division contexts that involve measurements.
    • How to represent quantities and operations physically, pictorially, or symbolically.
    • Strategies to solve one-step word problems that involve measurement.
    Skills:
    Students are able to:
    • Measure liquid volume and mass in metric standard units.
    • Choose appropriate measurement tools and units of measure.
    • Represent quantities and operations physically, pictorially, or symbolically,
    • Use a variety of strategies to solve one-step word problems that involve measurement.
    Understanding:
    Students understand that:
    • Capacity indicates the measure of the volume (dry or liquid) in a container.
    • Mass indicates the amount of matter in an object and can be represented with different sized units.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.19.1: Define liquid volume, mass, grams, kilograms, and liters.
    M.3.19.2: Recognize how the standard units of measure compare to one another.
    M.3.19.3: Identify key terms for word problems.
    M.3.19.4: Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
    M.3.19.5: Recall basic addition, subtraction, multiplication, and division facts.
    M.3.19.6: Describe measurable attributes of objects such as length or weight. Describe several measurable attributes of a single object.

    Prior Knowledge Skills:
    • Measure objects using standard units.
    • Recall single-digit subtraction facts.
    • Recall single-digit addition facts.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.19 Identify the appropriate measurement tool to measure liquids and masses of a given object.


    Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
    Mathematics (2019)
    Grade(s): 3
    All Resources: 5
    Classroom Resources: 5
    20. Find the area of a rectangle with whole number side lengths by tiling without gaps or overlays and counting unit squares.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use manipulatives to tile a rectangle with unit squares to find the area.
    • Given a rectangle drawn on a coordinate grid, determine the area of the rectangle.
    • Given a rectangle tiled with unit squares, determine the area of the rectangle.
    Teacher Vocabulary:
    • Area
    • Rectangle
    • Tiling
    • Gap
    • Overlay
    • Unit square
    Knowledge:
    Students know:
    • area is a measurable attribute of two-dimensional figures.
    Skills:
    Students are able to:
    • Find the area of a rectangle by tiling it without gaps or overlaps.
    • Measure the area of a rectangle by counting the number of unit squares needed to cover the shape.
    Understanding:
    Students understand that:
    • Area is the number of unit squares needed to cover a surface.
    • Multiple unit squares can be combined to measure the area of rectangles so long as the unit squares completely cover the figure without overlapping each other or extending beyond the edge of the figure.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.20.1: Define length.
    M.3.20.2: Recognize that units of measure must be equal.
    M.3.20.3: Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end.
    M.3.20.4: Recognize that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.

    Prior Knowledge Skills:
    • Identify units of measurement for length.
      Examples: inches, feet, yard; centimeter, meters.
    • Demonstrate how to use measurement tools.
      Example: avoiding gaps and overlaps.
    • Identify units of measure on measurement tools.
    • Use vocabulary related to comparison of length.
      Examples: longer, shorter, longest, shortest, taller.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.20 Find the area of a given shape using arrays (unit cubes and tiles) in relationship to multiplication. Limit units to 25.


    Mathematics (2019)
    Grade(s): 3
    All Resources: 5
    Classroom Resources: 5
    21. Count unit squares (square cm, square m, square in, square ft, and improvised or non-standard units) to determine area.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Accurately measure area by counting standard unit squares (square cm, square m, square in, and square ft) and non-standard unit squares (e.g., orange pattern blocks or floor tiles).
    Teacher Vocabulary:
    • Unit square
    • Length
    • Plane figure
    • Square cm
    • Square m
    • Square in
    • Square ft
    • Improvised
    • Non-standard unit
    Knowledge:
    Students know:
    • area is a measurable attribute of two-dimensional figures.
    Skills:
    Students are able to:
    • Determine area of a rectangle by counting unit squares.
    Understanding:
    Students understand that:
    • A unit square is a square with a side length of 1 unit, and that such a square represents a unit of measurement.
    • The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.21.1: Recognize that unit squares are equal.
    M.3.21.2: Define the units of measurement (cm, m, in, ft).
    M.3.21.3: Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.

    Prior Knowledge Skills:
    • Identify units of measurement for length.
    • Order three objects by length.
    • Compare the lengths of two objects indirectly by using a third object.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.20 Find the area of a given shape using arrays (unit cubes and tiles) in relationship to multiplication. Limit units to 25.


    Mathematics (2019)
    Grade(s): 3
    All Resources: 4
    Classroom Resources: 4
    22. Relate area to the operations of multiplication using real-world problems, concrete materials, mathematical reasoning, and the distributive property.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use arrays and area models to represent the distributive property in mathematical reasoning.
    • Given the side lengths of a rectangle, use a multiplication expression to determine the area of the rectangle.
    • Solve real-world problems involving areas of rectangles using concrete materials, reasoning, multiplication, and distributive property.
    Teacher Vocabulary:
    • Area
    • Multiplication
    • Distributive property
    • Mathematical reasoning
    • Expression
    • Square unit
    • Multiplicative
    Knowledge:
    Students know:
    • The area measurement of rectangular regions has a multiplicative relationship of the number of square units in a row and the number of rows.
    • The area of a rectangle with whole number side lengths is the same as the product of multiplying side lengths.
    • How to use an area model to illustrate the distributive property.
    Skills:
    Students are able to:
    • Relate the area of a rectangle with whole number side lengths and show that the area is the same as would be found by multiplying side lengths.
    • Use concrete materials, arrays and area models to illustrate the distributive property.
    • Solve real world problems involving areas of rectangles using concrete materials, reasoning, multiplication, and distributive property.
    Understanding:
    Students understand that:
    • side lengths with unit squares produces rows and columns and that multiplying the number of rows by the number of columns is equivalent to the total number of squares just like arrays.
    • The side length of a rectangle can be rewritten as the sum of two numbers and that when the other side is multiplied by each of those two numbers, then the sum of the products is equal to the area of the rectangle.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.22.1: Recognize arrays as multiplication or repeated addition.
    M.3.22.2: Recall basic addition and multiplication facts.
    M.3.22.3: Build and draw shapes to possess defining attributes.
    M.3.22.4: Compose simple shapes to form larger shapes.

    Prior Knowledge Skills:
    • Recall doubles addition facts with sums to 20.
    • Apply signs + and = to actions of joining sets.
    • Model written method for composing equations.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.20 Find the area of a given shape using arrays (unit cubes and tiles) in relationship to multiplication. Limit units to 25.


    Mathematics (2019)
    Grade(s): 3
    All Resources: 0
    23. Decompose rectilinear figures into smaller rectangles to find the area, using concrete materials.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Will use concrete materials to find areas of rectilinear figures by
    • Decomposing the figure into non overlapping rectangles, finding the area of each, and then finding the sum of the areas.
    • Composing rectilinear figures by joining two rectangles (without overlapping) and determine the area of the composed rectilinear figure is the sum of the areas of the two joined rectangles.
    Teacher Vocabulary:
    • Compose
    • Decompose
    • Area
    • Additive
    • Rectilinear figure
    • Equivalent
    • Non-overlapping
    • Overlapping
    Knowledge:
    Students know:
    • Area is a measurable attribute of two-dimensional figures.
    • The area measurement of rectangular regions has a multiplicative relationship of the number of square units in a row and the number of rows.
    Skills:
    Students are able to:
    • Decompose rectilinear figures as non-overlapping rectangles using concrete materials.
    • Find the area of two rectangles, and create a rectilinear figure by joining the two rectangles (without overlapping), and determine the area of the created rectilinear figure as the sum of the two rectangles.
    Understanding:
    Students understand that:
    • rectilinear shapes can be decomposed into non overlapping rectangles, and the sum of the areas of the nonverlapping rectangles is equivalent to the area of the original rectilinear shape.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.23.1: Label pre-made arrays.
    M.3.23.2: Partition a rectangle into rows and columns of same-size squares, and count to find the total number of them.
    M.3.23.3: Recall basic addition and multiplication facts.
    M.3.23.4: Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles).
    M.3.23.5: Identify a rectangle.

    Prior Knowledge Skills:
    • Define side, angle, face, closed, and open.
    • Use vocabulary related to shape attributes.
      Examples: sides, angles, face, closed, open.
    • Trace shapes.
    • Sort triangles, quadrilaterals, pentagons, hexagons, and cubes.
    • Explore triangles, quadrilaterals, pentagons, hexagons, and cubes.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.20 Find the area of a given shape using arrays (unit cubes and tiles) in relationship to multiplication. Limit units to 25.


    Geometric measurement: Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
    Mathematics (2019)
    Grade(s): 3
    All Resources: 1
    Classroom Resources: 1
    24. Construct rectangles with the same perimeter and different areas or the same area and different perimeters.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Identify rectangles with the same perimeter and different areas or the same area and different perimeters.
    • Construct rectangles with the same perimeter and different areas or the same area and different perimeters.
    Teacher Vocabulary:
    • Perimeter
    • Area
    • Side length
    • Side measure
    Knowledge:
    Students know:
    • Perimeter is a measurable attribute of rectangles.
    • Area is a measurable attribute of rectangles.
    Skills:
    Students are able to:
    • Construct rectangles with a given perimeter.
    • Construct rectangles with a given area.
    • Construct rectangles with the same perimeters but differing areas.
    • Construct rectangles with the same areas but differing perimeters.
    Understanding:
    Students understand that:
    • Perimeter and area are measurable attributes of rectangles.
    • Perimeter is the distance around a figure found by adding side lengths.
    • The area of a plane figure is measured by the number of square units that cover the interior space of the rectangle.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.24.1: Define perimeter.
    M.3.24.2: Recall the formula for perimeter (P= L+L+W+W or P=2L + 2W).
    M.3.24.3: Recall basic addition and multiplication facts.
    M.3.24.4: Build and draw shapes to possess defining attributes.
    M.3.24.5: Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
    M.3.24.6: Describe measurable attributes of objects such as length or weight.

    Prior Knowledge Skills:
    • Recall doubles addition facts.
    • Model written method for composing equations.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.20 Find the area of a given shape using arrays (unit cubes and tiles) in relationship to multiplication. Limit units to 25.


    Measurement
    Mathematics (2019)
    Grade(s): 3
    All Resources: 0
    25. Solve real-world problems involving perimeters of polygons, including finding the perimeter given the side lengths and finding an unknown side length of rectangles.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Measure to find the perimeter of shapes.
    • Given a figure, determine the perimeter of the figure.
    • Given a figure with a missing side length and a given perimeter, determine the missing side length.
    • Solve real-world problems involving perimeters of polygons.
    • Use a multiplication expression to find perimeter of a polygon when all side measures of the polygon are equal.
    Teacher Vocabulary:
    • Attribute
    • Dimension
    • Perimeter
    • Polygon
    • Two-dimensional
    Knowledge:
    Students know:
    • Measurable attributes of objects, specifically perimeter.
    • Strategies for modeling measurement problems involving perimeter.
    • Strategies for representing and computing perimeter.
    Skills:
    The Students are able to:
    • Solve real-world and mathematical problems involving perimeters of polygons.
    • Find the perimeter of a figure given the side lengths.
    • Find an unknown side length of a polygon given the perimeter and one missing side length.
    Understanding:
    Students understand that:
    • Perimeter is measured in length units and is the distance around a two-dimensional figure.
    • If all the sides of a polygon are equal, then the perimeter can be determined by multiplying one side length by the total number of sides.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.25.1: Define perimeter.
    M.3.25.2: Recall the formula for perimeter (P= L+L+W+W or P=2L + 2W).
    M.3.25.3: Recall basic addition and multiplication facts.
    M. 3.23.4: Build and draw shapes to possess defining attributes.
    M.3.25.4: Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
    M.3.25.5: Describe measurable attributes of objects such as length or weight.

    Prior Knowledge Skills:
    • Recall doubles addition facts.
    • Model written method for composing equations.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.20 Find the area of a given shape using arrays (unit cubes and tiles) in relationship to multiplication. Limit units to 25.


    Geometry
    Reason with shapes and their attributes.
    Mathematics (2019)
    Grade(s): 3
    All Resources: 4
    Classroom Resources: 4
    26. Recognize and describe polygons (up to 8 sides), triangles, and quadrilaterals (rhombuses, rectangles, and squares) based on the number of sides and the presence or absence of square corners.

    a. Draw examples of quadrilaterals that are and are not rhombuses, rectangles, and squares.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Describe, analyze, and compare properties of two-dimensional shapes.
    • Identify shapes that are and are not quadrilaterals by examining the properties of geometric shapes.
    • Draw rhombuses, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories.
    • Use geometric terms when describing quadrilaterals.
    • Identify attributes that are needed to belong to the subcategories of rhombuses, rectangles, and squares, and recognize when a shape does not have those attributes.

    • Example: A quadrilateral with all four sides of different lengths will not be a rhombus, rectangle, or square.
    Teacher Vocabulary:
    • Attribute
    • Category
    • Sub-category
    • Opposite sides
    • Angles
    • Quadrilateral
    • Triangle
    • Pentagon
    • Hexagon
    • Septagon
    • Heptagon
    • Octagon
    • Polygon
    • Square
    • Trapezoid
    • Rhombus
    • Rectangle
    • Two-dimensional
    Knowledge:
    Students know:
    • that shapes in different categories may share attributes and that the shared attributes can define a larger category.
    Skills:
    Students are able to:
    • Identify two-dimensional shapes.
    • Sort shapes according to number of sides.
    • Sort quadrilaterals based on the presence or absence of square corners.
    • Draw examples of squares, rectangles, and rhombuses.
    • Draw quadrilaterals that are not rhombuses, rectangles, and squares.
    Understanding:
    Students understand that:
    • Attributes of a shape help make decisions about how to categorize the shape.
    • Certain attributes are needed to belong to the subcategories of rhombuses, rectangles, and squares.
    • Sometimes a shape does not have the attributes needed to belong to the subcategories of rhombuses, rectangles, and squares.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.3.26.1: Recall the vocabulary of shapes (labels, sides, faces, vertices, etc.).
    M.3.26.2: Recognize and draw shapes having specified attributes such as a given number of angles.
    M.3.26.3: Build and draw shapes to possess defining attributes.
    M.3.26.4: Sort shapes into categories.

    Prior Knowledge Skills:
    • Identify squares, circles, triangles and rectangles.
    • Define side, angle, face, closed, and open.
    • Use vocabulary related to shape attributes.
      Examples: sides, angles, face, closed, open.
    • Trace shapes.
    • Sort triangles, quadrilaterals, pentagons, hexagons, and cubes.
    • Explore triangles, quadrilaterals, pentagons, hexagons, and cubes.
    • Name shapes.
    • Recognize shapes.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.3.26 Using vocalization, sign language, augmentative communication, or assistive technology, recognize and sort polygons by their attributes (triangle, rectangle, square).


    Operations and Algebraic Thinking
    Solve problems with whole numbers using the four operations.
    Mathematics (2019)
    Grade(s): 4
    All Resources: 4
    Learning Activities: 3
    Classroom Resources: 1
    1. Interpret and write equations for multiplicative comparisons.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • When given a multiplication equation, create and explain a corresponding verbal multiplicative comparison statement.
      Example: interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 35 is 7 times as many as 5.
    • When given a verbal (written or oral) representation of a multiplicative comparison, write and solve the related multiplication equation.

    • Example: Sue has 7 cards and Joe has 5 times as many cards as Sue. The student will write 5 x 7 and accurately find the number of cards Joe has to be 35.
    Teacher Vocabulary:
    • Multiplicative comparison
    • Multiplier
    • Equation
    • Times as many
    • Times as much
    • Verbal statement
    • Factor
    • Product
    • Quantity
    • Multiple
    • Scale factor
    Knowledge:
    Students know:
    • How to write an equation to represent a word situation.
    • Which quantity is being multiplied and which factor is telling how many times.
    • Varied language that describes multiplicative comparisons.
    Skills:
    Students are able to:
    • Interpret equations for multiplicative comparisons.
    • Write equations for multiplicative comparisons.
    Understanding:
    Students understand that:
    • Multiplicative comparisons relate the size of two quantities and a scale factor.
    • Factors in multiplication problems have different roles from each other in the context of comparison problems.
    • Explanations and drawings show ways multiplicative comparisons are similar to and different from equal groups and arrays.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.1.1: Use arrays to show equal groups in multiplication.
    M.4.1.2: Recall basic multiplication facts.
    M.4.1.4: Demonstrate computational fluency, including quick recall of addition and subtraction facts.
    M.4.1.5: Recognize multiplication as repeated addition.

    Prior Knowledge Skills:
    • Identify and define the parts of a multiplication problem including factors, multiplier, multiplicand and product.
    • Use multiplication to find the total number of objects arranged in rectangular arrays based on columns and rows.
    • Write an equation to express the product of the multipliers (factors).
    • Relate multiplication to repeated addition and skip counting.
    • Apply concepts of multiplication through the use of manipulatives, number stories, skip-counting arrays, area of a rectangle, or repeated addition.
    • Apply basic multiplication facts through 9 x 9 using manipulatives, solving problems, and writing number stories.
    • Solve addition problems with multiple addends.
    • Represent addition using manipulatives.
    • Distinguish between rows and columns.
    • Use repeated addition to solve problems with multiple addends.
    • Count forward in multiples from a given number.
      Examples: 3, 6, 9, 12; 4, 8, 12, 16.
    • Recall doubles addition facts.
    • Model written method for composing equations.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.1 Solve one-step word problems involving real-life situations using the four operations within 100 without regrouping and select the appropriate method of computation when problem solving.


    Mathematics (2019)
    Grade(s): 4
    All Resources: 5
    Classroom Resources: 5
    2. Solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • When given word problems involving multiplicative comparison, will solve using concrete, pictorial representations, and write related equations involving a single unknown.

    • Example: There are 12 children and 3 adults at the playground. How many times as many children are at the playground than adults? Represent the situation with the equation 12 = n × 3 and a tape diagram with a total of 12 and groups of 3, repeating each group 4 times to solve.
    Teacher Vocabulary:
    • Multiplicative comparison
    • Times as many
    • Product
    • Factor
    • Multiplication
    • Equation
    • Symbol
    • Additive comparison
    • Tape diagram
    • Unknown
    Knowledge:
    Students know:
    • how to find products and quotients.
    • Recognize situations represented by multiplicative comparison.
    • Distinguish between multiplicative comparison and additive comparison.
    Skills:
    Students are able to:
    • Solve word problems involving multiplicative comparison.
    • Write equations using a symbol for the unknown to represent word problems involving multiplicative comparison.
    • Use drawings to represent the word situation involving multiplicative comparison.
    Understanding:
    Students understand that:
    • additive comparison focuses on the difference between two quantities and multiplicative comparison focuses on one quantity being some number times larger than another.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.2.1: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
    M.4.2.2: Recognize key terms to solve word problems.
    Examples: in all, how much, how many, in each.
    M.4.2.3: Apply properties of operations as strategies to add.
    M.4.2.4: Recall basic multiplication facts.
    M.4.2.5: Demonstrate computational fluency, including quick recall of addition and subtraction facts.

    Prior Knowledge Skills:
    • Demonstrate computational understanding of multiplication and division by solving authentic problems with multiple representations using drawings, words, and/or numbers.
    • Identify key vocabulary words to solve multiplication and division word problems.
      Examples: times, every, at this rate, each, per, equal/equally, in all, total.
    • Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
    • Recall basic multiplication facts.
    • Add and subtract within 20.
    • Represent repeated addition, subtraction, and equal groups using manipulatives.
    • Distinguish between rows and columns.
    • Use repeated addition to solve problems with multiple addends.
    • Count forward in multiples from a given number.
      Examples: 3, 6, 9, 12; 4, 8, 12, 16.
    • Recall doubles addition facts.
    • Model written method for composing equations.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.1 Solve one-step word problems involving real-life situations using the four operations within 100 without regrouping and select the appropriate method of computation when problem solving.


    Mathematics (2019)
    Grade(s): 4
    All Resources: 10
    Learning Activities: 3
    Classroom Resources: 7
    3. Determine and justify solutions for multi-step word problems, including problems where remainders must be interpreted.

    a. Write equations to show solutions for multi-step word problems with a letter standing for the unknown quantity.

    b. Determine reasonableness of answers for multi-step word problems, using mental computation and estimation strategies including rounding.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given multi step word problems,
    • Solve a variety of multistep word problems involving all four operations on whole numbers including problems where remainders must be interpreted.
    • Explain and justify solutions using connections between the problem and related equations involving a single (letter) unknown.
    • Evaluate the reasonableness of solutions using estimation strategies.
    Note: Multi step problems must have at least 3 steps.
    Teacher Vocabulary:
    • Operation
    • Multi Step problem
    • Remainder
    • Unknown quantity
    • Equation
    • Rounding
    • Mental strategy
    • Partition
    • Estimation
    • Reasonableness
    Knowledge:
    Students know:
    • Context situations represented by the four operations.
    • How to calculate sums, differences, products, and quotients.
    • Estimation strategies to justify solutions as reasonable.
    Skills:
    Students are able to:
    • Solve multi-step word situations using the four operations.
    • Represent quantities and operations physically, pictorially, or symbolically.
    • Write equations to represent the word problem and use symbols to represent unknown quantities.
    • Use context and reasoning to interpret remainders.
    • Use estimation strategies to assess reasonableness of answers by comparing actual answers to estimates.
    Understanding:
    Students understand that:
    • Using problem solving strategies will help them determine which operation to use to solve a problem.
    • Remainders must be interpreted based on the context, and remainders are sometimes ignored, rounded up, or partitioned.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.3.1: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
    M.4.3.2: Solve single-step word problems.
    M.4.3.3: Recognize key terms to solve word problems.
    Examples: in all, how much, how many, in each.
    M.4.3.4: Solve division problems without remainders.
    M.4.3.5: Recall basic addition, subtraction, and multiplication facts.

    Prior Knowledge Skills:
    • Demonstrate computational understanding of multiplication and division by solving authentic problems with multiple representations using drawings, words, and/or numbers.
    • Identify key vocabulary words to solve multiplication and division word problems.
      Examples: times, every, at this rate, each, per, equal/equally, in all, total.
    • Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
    • Recall basic multiplication facts.
    • Add and subtract within 20.
    • Represent repeated addition, subtraction, and equal groups using manipulatives.
    • Distinguish between rows and columns.
    • Use repeated addition to solve problems with multiple addends.
    • Count forward in multiples from a given number.
      Examples: 3, 6, 9, 12; 4, 8, 12, 16.
    • Recall doubles addition facts.
    • Model written method for composing equations.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.1 Solve one-step word problems involving real-life situations using the four operations within 100 without regrouping and select the appropriate method of computation when problem solving.


    Gain familiarity with factors and multiples.
    Mathematics (2019)
    Grade(s): 4
    All Resources: 9
    Learning Activities: 3
    Lesson Plans: 2
    Classroom Resources: 4
    4. For whole numbers in the range 1 to 100, find all factor pairs, identifying a number as a multiple of each of its factors.

    a. Determine whether a whole number in the range 1 to 100 is a multiple of a given one-digit number.

    b. Determine whether a whole number in the range 1 to 100 is prime or composite.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given a number in the range 1-100,
    • Find all factor pairs and recognize that a whole number is a multiple of each of its factors.
    • Determine whether the whole number in the range 1-100 is a multiple of a given one-digit number.
    • Determine whether a whole number in the range 1-100 is prime or composite.
    Teacher Vocabulary:
    • Multiple
    • Factor
    • Prime
    • Composite
    • Whole number
    • Factor pair
    Knowledge:
    Students know:
    • Factor pairs include two numbers that when multiplied result in a particular product.
    • Multiples are the result of multiplying two whole numbers.
    • How to identify a prime or composite number.
    Skills:
    Students are able to:
    • Find all factor pairs of a given number.
    • Identify a number as a multiple of each of its factors.
    • Determine whether a number is prime or composite.
    Understanding:
    Students understand that:
    • A whole number is a multiple of each of its factors.
    • Numbers can be classified as prime, composite, or neither, based on their properties and characteristics.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.4.1: Define factors, prime number, and composite number.
    M.4.4.2: Apply properties of operations as strategies to multiply and divide.
    M.4.4.3: Identify all factor pairs for a whole number in the range 1-20.
    M.4.4.4: Name the first ten multiples of each one-digit natural number.
    M.4.4.5: Recall basic multiplication facts.
    M.4.4.6: Count within 1000; skip-count by 5s, 10s, and 100s.

    Prior Knowledge Skills:
    • Represent equal groups using manipulatives.
    • Identify and define the parts of a multiplication problem including factors, multiplier, multiplicand and product.
    • Use multiplication to find the total number of objects arranged in rectangular arrays based on columns and rows.
    • Write an equation to express the product of the multipliers (factors).
    • Relate multiplication to repeated addition and skip counting.
    • Define pair, odd and even.
    • Recall doubles addition facts with sums to 20.
    • Apply sign+ and = to actions of joining sets.
    • Model written method for composing equations.
    • Skip count by 2s.
    Generate and analyze patterns.
    Mathematics (2019)
    Grade(s): 4
    All Resources: 5
    Learning Activities: 3
    Classroom Resources: 2
    5. Generate and analyze a number or shape pattern that follows a given rule.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given a rule or pattern,
    • Generate a number or shape pattern that follows a given rule.
    • Identify a missing number or shape in the pattern.
    • Identify a feature of the pattern.

    • Example: Given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence, and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers continue to alternate in this way.
    Teacher Vocabulary:
    • Generate
    • Rule
    • Pattern
    • Sequence
    • Term
    • Continue
    • Identify
    • Explicit
    Knowledge:
    Students know:
    • Strategies for generating and recording number or shape patterns from a given rule.
    • Strategies for identifying and communicating shape and number patterns.
    Skills:
    Students are able to:
    • Generate a number or shape pattern that follows a given a rule.
    • Analyze a number or shape pattern that follows a given rule.
    Understanding:
    Students understand that:
    • A pattern is generated from a given rule.
    • The properties of a rule or pattern can be used to extend a pattern.
    • Some features of a given pattern are not explicit in the pattern's rule.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.5.1: Identify arithmetic patterns, including patterns in the addition table or multiplication table; and explain them using properties of operations.
    M.4.5.2: Recognize arithmetic patterns (including geometric patterns or patterns in the addition table or multiplication table).
    M.4.5.3: Construct repeating and growing patterns with a variety of representations.
    M.4.5.4: Continue an existing pattern.
    M.4.5.5: Identify arithmetic patterns.
    M.4.5.6: Demonstrate computational fluency, including quick recall, of addition multiplication facts.

    Prior Knowledge Skills:
    • Identify a rule when given a pattern.
      Examples: multiplication and division—"Input x 3 = Output".
      addition and subtraction—"Input + 8 = Output".
    • Use repeated addition to solve problems with multiple addends.
    • Count forward in multiples from a given number.
      Examples: 3, 6, 9, 12; 4, 8, 12, 16.
    • Define pair, odd and even.
    • Recall doubles addition facts with sums to 20.
    • Skip count by 2s.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.5 Use repeating patterns to make predictions.


    Operations with Numbers: Base Ten
    Generalize place value understanding for multi- digit whole numbers.
    Mathematics (2019)
    Grade(s): 4
    All Resources: 2
    Classroom Resources: 2
    6. Using models and quantitative reasoning, explain that in a multi-digit whole number, a digit in any place represents ten times what it represents in the place to its right.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Will explain the relationship between the value of a digit in two successive place values.
    • Will explain that a digit in one place value is 10 times greater than the same digit in the place value to its right.
    Note: Expectations are limited to whole numbers less than or equal to 1,000,000.
    Teacher Vocabulary:
    • Quantitative reasoning
    • Place value
    • Division
    • Multiplication
    • Multi-digit
    • Represents
    Knowledge:
    Students know:
    • that in a multi-digit whole number, a digit in one place represents ten times what it represents in the the place to its right.
    Skills:
    Students are able to:
    • Use models to explain how a digit in any place is ten times what the digit represents in the place to its right.
    • Use reasoning to explain how a digit in any place is related to what the digit represents in the place to its right.
    Understanding:
    Students understand that:
    • Each place value represents a different sized unit.
    • When comparing the place values of digits in successive place values, the place value of the digit on the left is 10 times the place value of the digit on the right.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.6.1: Use place value understanding to round whole numbers to the nearest 10 or 100.
    M.4.6.2: Add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
    M.4.6.3: Multiply one-digit whole numbers by multiples of 10 in the range 10 - 90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
    M.4.6.4: Recall basic multiplication facts.
    M.4.6.5: Recall that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.
    M.4.6.6: Recognize that the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
    M.4.6.7: Recognize that 100 can be thought of as a bundle of ten tens, called a "hundred".

    Prior Knowledge Skills:
    • Model place value by multiplying vertically.
    • Model properties of operations by multiplying horizontally.
    • Recall basic multiplication facts.
    • Recall multiplication as repeated addition.
    • Represent numbers with multiple concrete models.
      Examples: concrete models— base ten blocks, number lines, linking cubes, straw bundles.
    • Count to 1000 by hundreds.
    • Count to 100 by tens.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.6 Compare whole number values to 50 using symbols (e.g., <, >, =).


    Mathematics (2019)
    Grade(s): 4
    All Resources: 6
    Learning Activities: 1
    Lesson Plans: 1
    Classroom Resources: 4
    7. Read and write multi-digit whole numbers using standard form, word form, and expanded form.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • When given a number in one form (base-ten numerals, words, expanded form), identify the number in another form.
    Note: Expectations are limited to whole numbers less than or equal to 1,000,000.
    Teacher Vocabulary:
    • Base-ten numerals
    • Expanded form
    • Expanded notation
    • Standard form
    • Word form
    • Place value
    • Thousands period
    • Ones period
    Knowledge:
    Students know:
    • the relationship among places in a number and place values.
    Skills:
    Students are able to:
    • Read numbers 1 to 1,000,000 based on place value understanding.
    • Write numbers using base-ten numerals.
    • Write numbers using expanded notation.
    • Write numbers in word form.
    Understanding:
    Students understand that:
    • The same quantity can be represented with mathematical models, words, and expanded form based on the place value of the digits.
    • The value of a digit in a multi-digit number depends on the place value position it holds.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.7.1: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
    M.4.7.2: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
    M.4.7.3: Convert a number written in expanded notation to standard form.

    Prior Knowledge Skills:
    • Define greater than, less than and equal to.
    • Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
    • Arrange two-digit numbers in order from greatest to least or least to greatest.
    • Identify zero as a place holder in two-digit and three-digit numbers.
    • Model using >, =, and < symbols to record the results of comparisons of two two-digit numbers.
    • Select numbers on a number line that are more than, less than or equal to a specified number.
    • Match the words greater than, equal to and less than to the symbols >, =, and <.
    • Determine the value of the digits in the ones and tens place.
    • Identify sets with more, less or equal objects.
    • Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
    • Number & Operations in Base Ten.
    • Use place value understanding and properties of operations to add and subtract.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.6 Compare whole number values to 50 using symbols (e.g., <, >, =).


    Mathematics (2019)
    Grade(s): 4
    All Resources: 0
    8. Use place value understanding to compare two multi-digit numbers using >, =, and < symbols.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given numerical comparisons,
    • Identify comparison using <, >, and = symbols to record the results of comparison.
    • Use reasoning based on place value understanding to explain the comparison.
    Note: Expectations are limited to whole numbers less than or equal to 1,000,000.
    Teacher Vocabulary:
    • Place value
    • Compare
    • Multi-digit
    Knowledge:
    Students know:
    • the relationship among positions of digits in a number and place value.
    Skills:
    Students are able to:
    • Compare numbers using place value understanding.
    • Use <, >, or = symbols to record the comparison.
    Understanding:
    Students understand that:
    • place value strategies can be used for comparing and ordering numbers.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.8.1: Use place value understanding to round whole numbers to the nearest 10 or 100.
    M.4.8.2: Model rounding whole numbers to the nearest 100.
    M.4.8.3: Round whole numbers from 100 to 999 using whole numbers from 10 to 99.
    M.4.8.4: Model rounding whole numbers to the nearest 10.
    M.4.8.5: Round whole numbers from 10 to 99 using whole numbers from 1 to 9.
    M.4.8.6: Round whole numbers from 1 to 9 and model to show proficiency.

    Prior Knowledge Skills:
    • Define rounding.
    • Round whole numbers from 100 to 999 using whole numbers from 10 to 99.
    • Model rounding whole numbers to the nearest 100.
    • Round whole numbers from 10 to 99 using whole numbers from 1 to 9.
    • Model rounding whole numbers to the nearest 10.
    • Identify the steps in rounding two- and three-digit numbers.
      Example: Identify the digit that may change and the number to the right.
    • Round whole numbers from 1 to 9 and model to show proficiency.
    • Understand that the two digits of a two-digit number represent amounts of tens and ones.
    • Match the number in the ones, tens, and hundreds position to a pictorial representation or manipulative of the value.
    Mathematics (2019)
    Grade(s): 4
    All Resources: 2
    Learning Activities: 1
    Classroom Resources: 1
    9. Round multi-digit whole numbers to any place using place value understanding.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • When given any multi-digit whole number, use place value understanding to round to any place.
    • When given a number which is rounded to a place value, identify an unknown number that rounds to that given number.

    • Example: What are all possible numbers that result in 460 when rounded to the nearest ten? Answer: 455, 456, 457, 458, 459, 460, 461, 462, 463, 464.
    • Use rounding in a variety of situations, to include estimating, problem solving, and determining reasonableness of answers.
    Note: Expectations are limited to whole numbers less than or equal to 1,000,000.
    Teacher Vocabulary:
    • Round
    • Place value
    • Ones
    • Tens
    • Hundreds
    • Thousands
    • Ten thousands
    • Approximately
    • Halfway point
    Knowledge:
    Students know:
    • The relationship among positions of digits in a number and place value. They can use that knowledge to round numbers to nay place.
    Skills:
    Students are able to:
    • Use place value strategies to round multi-digit whole numbers to any place.
    Understanding:
    Students understand that:
    • rounding multi-digit numbers is an estimation strategy used when writing the original number as the closest multiple of a power of 10.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.9.1: Add and subtract within 1000.
    M.4.9.2: Apply signs +, -, and = to actions of joining and separating sets.
    M.4.9.3: Add and subtract single-digit numbers.
    M.4.9.4: Recall basic addition and subtraction facts.

    Prior Knowledge Skills:
    • Define the commutative and associative properties of addition and subtraction.
    • Subtract within 100 using strategies and algorithms based on the relationship between addition and subtraction.
    • Subtract within 100 using strategies and algorithms based on properties of operations.
    • Subtract within 100 using strategies and algorithms based on place value.
    • Add within 100 using strategies and algorithms based on the relationship between addition and subtraction. Add within 100 using strategies and algorithms based on properties of operations.
    • Add within 100 using strategies and algorithms based on place value.
    • Recall basic addition and subtraction facts.
    • Define regrouping, total, sum, difference and solve.
    • Add and subtract two two-digit numbers with and without regrouping.
    • Determine the value of the number in the ones, tens, hundreds and thousands place using concrete models or drawings and strategies based on place value.
    • Match the number in the ones, tens, hundreds and thousands position to a pictorial representation or manipulative of the value.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.9 Round a whole number from 1 to 49 to the nearest ten (using a number line and hundreds chart.)


    Use place value understanding and properties of operations to perform multi-digit arithmetic with whole numbers.
    Mathematics (2019)
    Grade(s): 4
    All Resources: 6
    Learning Activities: 2
    Lesson Plans: 1
    Classroom Resources: 3
    10. Use place value strategies to fluently add and subtract multi-digit whole numbers and connect strategies to the standard algorithm.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use place value strategies and properties of operations to build procedural fluency and understanding of the standard algorithm for addition and subtraction.
    Note: Expectations are limited to whole numbers within 1,000,000.
    Teacher Vocabulary:
    • Addition
    • Subtraction
    • Standard algorithm
    • Place value
    • Decompose
    • Compose
    • Fluently
    • Multi-digit
    • Strategy
    • Difference
    • Sum
    Knowledge:
    Students know:
    • a variety of accurate and efficient strategies to find sums and differences and use them when appropriate.
    Skills:
    Students are able to:
    • Use place value strategies to add and subtract multi-digit numbers.
    • Use the standard algorithm for addition and subtraction and connect strategies to the standard algorithm.
    Understanding:
    Students understand that:
    • There are a variety of strategies, models, and representations for solving mathematical problems with addition and subtraction.
    • Efficient application of computation strategies is based on the numbers and operations in the problems.
    • The steps used in the standard algorithm for addition and subtraction can be justified by using the relationship between addition and subtraction and the understanding of place value.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.10.1: Multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations.
    M.4.10.2: Multiply single-digit numbers.
    M.4.10.3: Recall basic multiplication facts.
    M.4.10.4: Apply concepts of multiplication through the use of manipulatives, number stories, skip-counting arrays, area of a rectangle, or repeated addition.

    Prior Knowledge Skills:
    • Define the commutative and associative properties of addition and subtraction.
    • Subtract within 100 using strategies and algorithms based on the relationship between addition and subtraction.
    • Subtract within 100 using strategies and algorithms based on properties of operations.
    • Subtract within 100 using strategies and algorithms based on place value.
    • Add within 100 using strategies and algorithms based on the relationship between addition and subtraction.
    • Add within 100 using strategies and algorithms based on properties of operations.
    • Add within 100 using strategies and algorithms based on place value.
    • Recall basic addition and subtraction facts.
    • Define regrouping, total, sum, difference and solve.
    • Add and subtract two two-digit numbers with and without regrouping.
    • Determine the value of the number in the ones, tens, hundreds and thousands place using concrete models or drawings and strategies based on place value.
    • Match the number in the ones, tens, hundreds and thousands position to a pictorial representation or manipulative of the value.
    • Model written method for recording horizontal and vertical addition and subtraction problems.
    • Represent two- and three-digit numbers with multiple models.
      Examples: models—base ten blocks, number lines, linking cubes, straw bundles.
    • Recall single-digit addition and subtraction facts.
    • Add and subtract within 20, e.g., by using objects or drawings to represent the problem.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.11 Add and subtract one and two-digit numbers up to 49 with regrouping using concrete manipulatives and visual models.


    Mathematics (2019)
    Grade(s): 4
    All Resources: 10
    Learning Activities: 4
    Classroom Resources: 6
    11. Find the product of two factors (up to four digits by a one-digit number and two two-digit numbers), using strategies based on place value and the properties of operations.

    a. Illustrate and explain the product of two factors using equations, rectangular arrays, and area models.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use strategies based on place value, properties of operations, rectangular arrays, area models, and equations to illustrate and explain the product of two factors (up to four digits by a one-digit number and two two-digit numbers).
    Note: Standard algorithm is not an expectation for grade 4.
    Teacher Vocabulary:
    • Product
    • Factor
    • Compose
    • Decompose
    • Digit
    • Strategy
    • Place value
    • Properties of operations
    • Equation
    • Rectangular array
    • Area model
    • Partial product
    • Multiple of 10
    Knowledge:
    Students know:
    • How to compose and decompose numbers in a variety of ways using place value and the properties of operations.
    • How to represent the product of two factors using an area model.
    • Use strategies based on place value (partial products), the properties of operations, arrays and area models to represent a two digit factor times a two digit factor.
    Skills:
    Students are able to:
    • Use strategies based on place value and the properties of operations to find products.
    • Illustrate the product of two factors using rectangular arrays and area models.
    • Explain the product of two factors using equations.
    • Make connections between models and equations.
    Understanding:
    Students understand that:
    • arrays, area models, place value strategies, and the properties of operations can be used to find products of a single digit factor by a multi-digit factor and products of two two-digit factors.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.11.1: Divide within 100, using strategies such as the relationship between multiplication and division (e.g. knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8).
    M.4.11.2: Divide within 100, using strategies such as properties of operations.
    M.4.11.3: Multiply within 100, using strategies such as properties of operations.
    M.4.11.4: Multiply within 100, using strategies such as the relationship between multiplication and division (e.g. knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8).
    M.4.11.5: Recall products of two one-digit numbers.
    M.4.11.6: Name the first 10 multiples of each one-digit natural number.
    Example: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.
    M.4.11.7: Recall basic addition, subtraction, and multiplication facts.

    Prior Knowledge Skills:
    • Apply divisibility rules for 2, 5, and 10.
      Example: Recognizing that 32 is divisible by 2 because the digit in the ones place is even.
    • Apply basic multiplication facts.
    • Understand subtraction as an unknown
    • addend problem.
    • Recognize division as repeated subtraction, parts of a set, parts of a whole, or the inverse of multiplication.
    • Name the first 10 multiples of each one-digit natural number.
      Example: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.
    • Recognize multiplication as repeated addition, and division as repeated subtraction.
    • Apply properties of operations as strategies to add and subtract.
    • Recall basic addition and subtraction facts.
    • Use repeated addition to solve problems with multiple addends.
    • Count forward in multiples from a given number.
      Examples: 3, 6, 9, 12; 4, 8, 12, 16.
    • Recall doubles addition facts.
    • Model written method for composing equations.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.11 Add and subtract one and two-digit numbers up to 49 with regrouping using concrete manipulatives and visual models.


    Mathematics (2019)
    Grade(s): 4
    All Resources: 8
    Learning Activities: 4
    Classroom Resources: 4
    12. Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with one-digit divisors and up to four-digit dividends.

    a. Illustrate and/or explain quotients using equations, rectangular arrays, and/or area models.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given division problems with one-digit divisors and up to four-digit dividends,
    • Find quotients with remainders using strategies based on place value, properties of operations, and the relationship between multiplication and division.
    • Illustrate quotients using a rectangular array and/or area model, and explain the connection of the visual model to the equation.
    Teacher Vocabulary:
    • Quotient
    • Dividend
    • Divisor
    • Divide
    • Multiply
    • Multiple
    • Equation
    • Remainder
    • Area model
    • Greatest multiple
    • Decompose
    • Compose
    • Array
    • Properties of operations
    • Unknown factor
    • Partial quotient
    Knowledge:
    Students know:
    • How to decompose and compose numbers in a variety of ways using place value and the properties of operations to demonstrate a variety of strategies for division.
    • Division can be described as an unknown factor problem.
    • A variety of contextual situations can be represented with a division equation.
    Skills:
    Students are able to:
    • Use strategies based on place value to find whole number quotients and remainders.
    • Use the properties of operations to find whole number quotients and remainders.
    • Use arrays and area models to find whole number quotients and remainders.
    • Illustrate division situations with rectangular arrays and area models.
    • Write an equation to represent a division situation.
    Understanding:
    Students understand that:
    Division expressions represent
    • The number of objects in each group when the total number is partitioned evenly into a given number of groups.
    • The number of groups when the total number is partitioned into groups that each contain a given number.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.12.1: Define fraction, numerator and denominator.
    M.4.12.2: Recognize fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts.
    M.4.12.3: Identify the parts of a fraction a/b as the quantity formed by a parts and size 1/b.
    M.4.12.4: Recognize fractions as numerals that may represent division problems.
    M.4.12.5: Label numerator, denominator, and fraction bar.
    M.4.12.6: Identify parts of a whole with two, three, or four equal parts.
    M.4.12.7: Recognize that equal shares of identical wholes need not have the same shape.
    M.4.12.8: Distinguish between equal and non-equal parts.

    Prior Knowledge Skills:
    • Recognize fractions as lengths from zero to one.
    • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
    • Identify a number line.
    • Recognize whole numbers as lengths from zero to one.
    • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
    • Identify a number line.
    • Label the fractions on a pre-made number line diagram.
    • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
    • Recognize a number line diagram with equally spaced points.
    • Compare length using non
    • standard units to determine which is longer.
    Operations with Numbers: Fractions
    Extend understanding of fraction equivalence and ordering.
    Grade 4 denominators are limited to 2,3,4,5,6,8,10,12,100.
    Mathematics (2019)
    Grade(s): 4
    All Resources: 8
    Learning Activities: 2
    Classroom Resources: 6
    13. Using area and length fraction models, explain why one fraction is equivalent to another, taking into account that the number and size of the parts differ even though the two fractions themselves are the same size.

    a. Apply principles of fraction equivalence to recognize and generate equivalent fractions.

    Example: a/b is equivalent to (n x a)/(n× b).
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use visual models to create equivalent fractions.
    • Explain the generalized pattern, a/b = (n x a) / (n x b).
    • Use the generalized pattern to create equivalent fractions.

    Set models (parts of a group) are not models used in grade 4.
    Teacher Vocabulary:
    • Fraction
    • Numerator
    • Denominator
    • Equivalent
    • Fraction model
    • Area model -Length model
    Knowledge:
    Students know:
    • Fractions can be equivalent even though the number of parts and size of the parts differ.
    • Two fractions are equivalent if they are at the same point on a number line or if they have the same area.
    Skills:
    Students are able to:
    • Use area and length fraction models to explain why fractions are equivalent.
    • Recognize and generate equivalent fractions.
    Understanding:
    Students understand that:
    • equivalent fractions are fractions that represent equal value.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.13.1: Identify fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts and size 1/b.
    M.4.13.2: Identify a fraction as a number on the number line; represent fractions on a number line diagram.
    M.4.13.3: Recognize a fraction as a number on the number line.
    M.4.13.4: Represent fractions on a number line diagram.
    M.4.13.5: Recognize fractions as numerals that may represent division problems.
    M.4.13.6: Label numerator, denominator, and fraction bar.
    M.4.13.7: Identify parts of a whole with two, three, or four equal parts.
    M.4.13.8: Distinguish between equal and non-equal parts.
    M.4.13.9: Define area, length, equivalent, fraction, numerator and denominator.

    Prior Knowledge Skills:
    • Recognize fractions as lengths from zero to one.
    • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
    • Identify a number line.
    • Recognize whole numbers as lengths from zero to one.
    • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
    • Identify a number line.
    • Label the fractions on a pre-made number line diagram.
    • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
    • Recognize a number line diagram with equally spaced points.
    • Compare length using non
    • standard units to determine which is longer.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.13 Identify and compare models of a whole (1), one-half (1/2), one-third (1/3), and one fourth (1/4) using models, manipulatives, numbers lines, and a clock.


    Mathematics (2019)
    Grade(s): 4
    All Resources: 5
    Learning Activities: 3
    Classroom Resources: 2
    14. Compare two fractions with different numerators and different denominators using concrete models, benchmarks (0, ½, 1), common denominators, and/or common numerators, recording the comparisons with symbols >, =, or <, and justifying the conclusions.

    a. Explain that comparison of two fractions is valid only when the two fractions refer to the same whole.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Compare two fractions with different numerators and different denominators using concrete models, drawings, and benchmarks (0, 1/2, 1).
    • Recognize that comparisons are valid only when the two fractions refer to the same whole.
    • Record the comparisons of two fractions using symbols >,<, or =, and justify the conclusions.
    Teacher Vocabulary:
    • Compare
    • Equivalent fraction
    • Numerator
    • Denominator
    • Benchmark fraction
    • Concrete model
    • Visual model
    • Length model
    • Area model
    Knowledge:
    Students know:
    • Comparing two fractions is only valid if they refer to the same whole.
    • Meaning of comparison symbols,<, >, or = .
    • Fractions can be represented by a variety of visual models (length and area).
    Skills:
    Students are able to:
    • Use concrete models, benchmarks, common denominators, and common numerators to compare two fractions and justify their thinking.
    • Explain the comparison of two fractions is valid only when the two fractions refer to the same whole.
    Understanding:
    Students understand that:
    • When comparing fractions they must refer to the same whole.
    • Benchmark fractions can be used to compare fractions.
    • Fractions can be compared by reasoning about their size using part to whole relationship.
    • Fractions can be compared by reasoning about the number of same-sized pieces.
    • Fractions can be compared by reasoning about their size when there are the same number of pieces.
    • Fractions can be compared by reasoning about the number of missing pieces.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.14.1: Identify fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts and size 1/b.
    M.4.14.2: Identify a fraction as a number on the number line; represent fractions on a number line diagram.
    M.4.14.3: Recognize a fraction as a number on the number line.
    M.4.14.4: Represent fractions on a number line diagram.
    M.4.14.5: Recognize fractions as numerals that may represent division problems.
    M.4.14.6: Label numerator, denominator, and fraction bar.
    M.4.14.7: Identify parts of a whole with two, three, or four equal parts.
    M.4.14.8: Distinguish between equal and non-equal parts.

    Prior Knowledge Skills:
    • Recognize fractions as lengths from zero to one.
    • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
    • Identify a number line.
    • Recognize whole numbers as lengths from zero to one.
    • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
    • Identify a number line.
    • Label the fractions on a pre-made number line diagram.
    • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
    • Recognize a number line diagram with equally spaced points.
    • Compare length using non
    • standard units to determine which is longer.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.13 Identify and compare models of a whole (1), one-half (1/2), one-third (1/3), and one fourth (1/4) using models, manipulatives, numbers lines, and a clock.


    Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
    Mathematics (2019)
    Grade(s): 4
    All Resources: 10
    Learning Activities: 3
    Classroom Resources: 7
    15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

    a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

    b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

    c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • When given any fraction or mixed number, apply unit fraction understanding to decompose the given fraction or mixed number into the sum of smaller fractions, including unit fractions.
    • When given a problem solving situation involving addition and subtraction of fractions or mixed numbers with like denominators, explain and justify solutions using unit fractions, visual models, and equations involving a single unknown.
    Teacher Vocabulary:
    • Decomposition
    • Unit fraction
    • Area model
    • Length model
    • Equation
    • Mixed number
    • Visual fraction model
    • Whole
    • Sum
    • Difference
    • Recomposition
    Knowledge:
    Students know:
    • Situation contexts for addition and subtraction problems.
    • A variety of strategies and models to represent addition and subtraction situations.
    • The fraction a/b is equivalent to the unit fraction 1/b being iterated or "copied" the number of times indicated by the numerator, a.
    • A fraction can represent a whole number or fraction greater than 1 and can be illustrated by decomposing the fraction.
      Example: 6/3 = 3/3 + 3/3 = 2 and 5/3 = 3/3 + 2/3 = 1 2/3.
    Skills:
    Students are able to:
    • Decompose fractions as a sum of unit fractions.
    • Model decomposition of fractions as a sum of unit fractions.
    • Add and subtract fractions with like denominators using properties of operations and the relationship between addition and subtraction.
    • Solve word problems involving addition and subtraction using visual models, drawings, and equations to represent the problem.
    Understanding:
    Students understand that:
    • A unit fraction (1/b) names the size of the unit with respect to the whole and that the denominator tells the number of parts the whole is partitioned, and the numerator indicates the number of parts referenced.
    • A variety of models and strategies can be used to represent and solve word situations involving addition and subtraction.
    • The operations of addition and subtraction are performed with quantities expressed in like units, and the sum or difference retains the same unit.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.15.1: Recognize that a whole can be partitioned into differing equal parts (halves, fourths, eighths, etc.).
    M.4.15.2: Identify numerator and denominator.
    M.4.15.3: Recall basic addition and subtraction facts.
    M.4.15.4: Demonstrate an understanding of fractional parts.
    M.4.15.5: Recall basic addition and subtraction facts.
    M.4.15.6: Define mixed numbers.
    M.4.15.7: Recall basic addition and subtraction facts.
    M.4.15.8: Demonstrate an understanding of fractional parts.
    M.4.15.9: Solve basic word problems using whole numbers.
    M.4.15.10: Express parts of a whole as a fraction.
    M.4.15.11: Write number sentences for word problems.
    M.4.15.12: Identify key terms in word problems.
    M.4.15.13: Recall basic addition and subtraction facts.

    Prior Knowledge Skills:
    • Define fraction, numerator, and denominator.
    • Identify the parts of a fraction a/b as the quantity formed by a parts and size 1/b.
    • Label numerator, denominator, and fraction bar.
    • Identify parts of a whole with two, three, or four equal parts.
    • Distinguish between equal and non-qual parts.
    • Partition circles and rectangles into two and four equal shares; describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.
    • Recognize fractions as lengths from zero to one.
    • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.15 Model decomposing fractions having like denominators, using visual fraction models (limit to half and fourths).


    Mathematics (2019)
    Grade(s): 4
    All Resources: 6
    Learning Activities: 4
    Classroom Resources: 2
    16. Apply and extend previous understandings of multiplication to multiply a whole number times a fraction.

    a. Model and explain how a non-unit fraction can be represented by a whole number times the unit fraction.

    Example:
    9/8=9 x 1/8

    b. Extend previous understanding of multiplication to multiply a whole number times any fraction less than one.

    Example: 4 x 2/3= 4 x 2/3= 8/3

    c. Solve word problems involving multiplying a whole number times a fraction using visual fraction models and equations to represent the problem.

    Examples: 3 x 1/2, 6 x 1/8
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Model and explain a fraction as a multiple of a unit fraction.

    • Example: 5/3 = 1/3 + 1/3 + 1/3 + 1/3 + 1/3 or 5 x 1/3 or (5 x 1)/3.
    • Multiply a whole number times any fraction less than 1 and justify the product.

    • Example: 5 x 2/3 is 5 sets of two-thirds, which is ten-thirds. or 5 x 2/3 = 5 x (2 x 1/3) = (5 x 2) x 1/3 = 10 x 1/3 or 10/3.
    • Solve word problems involving multiplying a whole number times a fraction using a visual model and equation to represent the problem.
    Teacher Vocabulary:
    • Whole number
    • Fraction
    • Non-unit fraction
    • Unit fraction
    • Fraction less than one
    • Fraction greater than one
    • Visual fraction model
    • Equation
    • Decompose
    • Recompose
    • Compose
    Knowledge:
    Students know:
    • Models or equations to represent multiplication situations.
    • The fraction a/b is equivalent to the unit fraction 1/b being iterated or "copied" the number of times indicated by the numerator, a.
    Skills:
    Students are able to:
    • Model and explain how a non-unit fraction can be expressed as multiplication.
    • Multiply a whole number times any fraction less than one.
    • Solve word problems involving a whole number times a fraction using a visual fraction model and equation to represent the problem.
    Understanding:
    Students understand that:
    • Previous work involving multiplication with whole numbers can be extended to fractions in showing multiplication as putting together equal-sized fractional groups.
    • Problem solving situations involving multiplication of a whole number times a fraction can be solved using a variety of strategies, models, and representations.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.16.1: Recognize fractions in their simplest forms.
    M.4.16.2: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
    M.4.16.3: Demonstrate an understanding of fractional parts.
    M.4.16.4: Apply properties of operations as strategies to multiply and divide.
    M.4.16.5: Recall basic multiplication facts.
    M.4.16.6: Define multiple.
    M.4.16.7: Compare two fractions with the same numerator or the same denominator by reasoning about their size.
    M.4.16.8: Recognize that comparisons are valid only when the two fractions refer to the same whole.
    M.4.16.9: Record results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
    M.4.16.10: Name the first ten multiples of each one-digit natural number.
    M.4.16.11: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
    M.4.16.12: Solve simple fractions using multiplication strategies.
    M.4.16.13: Recognize equivalent forms of fractions.
    M.4.16.14: Multiply proper fractions with common denominators 2-10.
    M.4.16.15: Solve word problems using whole numbers.
    M.4.16.16: Write number sentences for word problems.
    M.4.16.17: Identify key terms in word problems.
    M.4.16.18: Multiply and divide within 100.
    M.4.16.19: Recall basic multiplication facts.

    Prior Knowledge Skills:
    • Define fraction, numerator, and denominator.
    • Identify the parts of a fraction a/b as the quantity formed by a parts and size 1/b.
    • Label numerator, denominator, and fraction bar.
    • Identify parts of a whole with two, three, or four equal parts.
    • Distinguish between equal and non-qual parts.
    • Partition circles and rectangles into two and four equal shares; describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.
    • Demonstrate conceptual understanding of adding or subtracting 10 using concrete models.
    • Recognize the place value of ones, tens and hundreds.
    • Count forward and backward by 100.
    • Count forward and backward by 10.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.15 Model decomposing fractions having like denominators, using visual fraction models (limit to half and fourths).


    Understand decimal notation for fractions, and compare decimal fractions.
    Denominators are limited to 10 and 100.
    Mathematics (2019)
    Grade(s): 4
    All Resources: 3
    Learning Activities: 3
    17. Express, model, and explain the equivalence between fractions with denominators of 10 and 100.

    a. Use fraction equivalency to add two fractions with denominators of 10 and 100.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this technique to find the sum of two fractions with respective denominators 10 and 100.
    Teacher Vocabulary:
    • Equivalence
    • Denominator
    • Fraction model
    • Tenths
    • Hundredths
    • Sum
    Knowledge:
    Students know:
    • Strategies for generating equivalent fractions.
    • Strategies for adding fractions with like denominators.
    Skills:
    Students are able to:
    • Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100.
    • Use models to illustrate equivalency between fractions with denominators of 10 and 100.
    • Explain equivalency between fractions with denominators of 10 and 100.
    • Use equivalency to add two fractions with denominators of 10 and 100.
    Understanding:
    Students understand that:
    • equivalent fractions are fractions that represent equal value.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.17.1: Recognize equivalent forms of fractions and decimals.
    M.4.17.2: Demonstrate equivalent fractions using concrete objects or pictorial representation.
    M.4.17.3: Recognize pictorial representations of equivalent fractions and decimals in tenths and hundredths.
    M.4.17.4: Define equivalency.
    M.4.17.5: Identify place value of decimals to the tenths and hundredths.
    M.4.17.6: Use place value understanding to round whole numbers to the nearest 10 or 100.

    Prior Knowledge Skills:
    • Define equivalent.
    • Recognize pictorial representations of equivalent fractions.
    • Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.
    • Recognize that equal shares of identical wholes need not have the same shape.
    • Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
    • Label a fraction with multiple representations.
    • Partition circles and rectangles into two and four equal shares; and describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.
    • Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.
    • Label a pictorial representation.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.17 Model equivalence between fractions of a whole, halves and fourths using visual models.


    Mathematics (2019)
    Grade(s): 4
    All Resources: 1
    Classroom Resources: 1
    18. Use models and decimal notation to represent fractions with denominators of 10 and 100.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use models to represent decimal fractions with denominators of 10 and 100.
    • Use decimal notation to represent fractions with a denominator of 10 and an equivalent fraction with a denominator of 100.
    Teacher Vocabulary:
    • Decimal notation
    • Decimal point
    • Place value
    • Tenths
    • Hundredths
    • Fraction
    • Equivalence
    • Visual model
    Knowledge:
    Students know:
    • strategies for finding equivalent fractions.
    Skills:
    Students are able to:
    • Represent fractions with denominators of 10 and 100 using a visual model and decimal notation.
    Understanding:
    Students understand that:
    • Fraction equivalence applies to decimal fractions with denominators of 10 and 100.
    • Decimals can be decomposed and described using place value understanding.
      Example: 0.13 as one-tenth and three-hundredths, or thirteen hundredths.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.18.1: Compare two fractions with the same numerator or the same denominator by reasoning about their size.
    M.4.18.2: Recognize that comparisons are valid only when the two fractions refer to the same whole.
    M.4.18.3: Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
    M.4.18.4: Convert fractions to decimals.
    M.4.18.5: Compare two decimals to tenths.
    M.4.18.6: Compare whole numbers.
    M.4.18.7: Identify comparison symbols.
    Examples: >, <, and =.

    Prior Knowledge Skills:
    • Define equivalent.
    • Recognize pictorial representations of equivalent fractions.
    • Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.
    • Recognize that equal shares of identical wholes need not have the same shape.
    • Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
    • Label a fraction with multiple representations. Recognize that a whole can be partitioned into differing equal parts (halves, fourths, eighths, etc.).
    • Partition circles and rectangles into two and four equal shares; and describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.
    • Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.
    • Label a pictorial representation.
    • Recognize that a fraction is a part of a whole.
    • Partition circles and rectangles into two and four equal shares; describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.
    • Define numerator and denominator.
    • Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds, or four fourths.
    • Recognize that a whole can be partitioned into differing equal parts (halves, fourths, eighths, etc.).
    • Identify parts of a whole.
    • Represent a fraction with a pictorial model.
    • Identify <, >, and = signs.
    • Recognize that equal shares of identical wholes need not have the same shape.
    • Recognize that a whole can be partitioned into equal parts (halves, fourths, eighths, etc.).
    • Order three objects by length; compare the lengths of two objects indirectly by using a third object.
    • Define greater than, less than and equal to.
    • Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
    • Arrange two-digit numbers in order from greatest to least or least to greatest.
    • Identify zero as a place holder in two-digit and three-digit numbers.
    • Model using >, =, and < symbols to record the results of comparisons of two two-digit numbers.
    • Select numbers on a number line that are more than, less than or equal to a specified number.
    • Match the words greater than, equal to and less than to the symbols >, =, and <.
    • Determine the value of the digits in the ones and tens place.
    • Identify sets with more, less or equal objects.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.17 Model equivalence between fractions of a whole, halves and fourths using visual models.


    Mathematics (2019)
    Grade(s): 4
    All Resources: 3
    Classroom Resources: 3
    19. Use visual models and reasoning to compare two decimals to hundredths (referring to the same whole), recording comparisons using symbols >, =, or <, and justifying the conclusions.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given decimals to the hundredths will,
    • Compare two decimals using place value, visual models, and reasoning.
    • Record comparisons of two decimals using <, >, or = and justify the conclusion.
    • Use place value language to describe decimals in different ways to make comparisons.

    • Example: 0.13 as one-tenth and three-hundredths, or thirteen hundredths.
    Teacher Vocabulary:
    • Visual model
    • Compare
    • Reasoning
    • Tenths
    • Hundredths
    • Decimal point
    • Place value
    Knowledge:
    Students know:
    • a variety of strategies for comparing whole numbers and can record comparisons using symbols <, >, or =.
    Skills:
    Students are able to:
    • Use visual models and reasoning to compare two decimals to hundredths.
    • Record comparisons of two decimals to hundredths using symbols <, >, or =, and justify the conclusion.
    Understanding:
    Students understand that:
    • Comparison of decimals are valid only when they refer to the same whole.
    • Two decimals are equivalent if they represent the same area or name the same point on a number line.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.19.1: Compare two fractions with the same numerator or the same denominator by reasoning about their size.
    M.4.19.2: Recognize that comparisons are valid only when the two fractions refer to the same whole.
    M.4.19.3: Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
    M.4.19.4: Convert fractions to decimals.
    M.4.19.5: Compare two decimals to tenths.
    M.4.19.6: Compare whole numbers.
    M.4.19.7: Identify comparison symbols.
    Examples: >, <, and =.

    Prior Knowledge Skills:
    • Define equivalent.
    • Recognize pictorial representations of equivalent fractions.
    • Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.
    • Recognize that equal shares of identical wholes need not have the same shape.
    • Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
    • Label a fraction with multiple representations.
    • Recognize that a whole can be partitioned into differing equal parts (halves, fourths, eighths, etc.).
    • Partition circles and rectangles into two and four equal shares; and describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.
    • Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.19 Compare fractions of a whole, halves and fourths using symbols (>,<,=).


    Data Analysis
    Represent and interpret data.
    Mathematics (2019)
    Grade(s): 4
    All Resources: 1
    Classroom Resources: 1
    20. Interpret data in graphs (picture, bar, and line plots) to solve problems using numbers and operations.

    a. Create a line plot to display a data set of measurements in fractions of a unit (1/2,1/4,1/8).

    b. Solve problems involving addition and subtraction of fractions using information presented in line plots.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Create a line plot to represent a given data set in fractions of a unit (1/2, 1/4, 1/8) and solve problems involving addition and subtraction with the data set.

    • Example: Data on the line plots shows the shortest measurement length of 13 1/2 inches and the longest measurement length of 14 3/4, students may solve problems such as, "What is the difference in length between the longest and shortest measurement shown in the data set?"
    • Generate a data set and create a line plot to represent the data set and solve problems involving addition and subtraction with the data set.
    • Interpret data presented in graphs (picture, bar, and line plots) and use the data set to solve problems.
    Note: Students may need to label the measurement scale in eighths to use equivalence in like units of eighths to solve problems using the data set.
    Teacher Vocabulary:
    • Interpret
    • Data
    • Picture graph
    • Bar graph
    • Line plot
    • Data set
    • Scale
    • Frequency
    • Key
    • Partition
    Knowledge:
    Students know:
    • how to Measure objects to the nearest half, quarter, and eighth of an inch.
    • Partition a number line to show halves, fourths, and eighths.
    • Interpret data displayed in graphs to solve problems related to the data set.
    Skills:
    Students are able to:
    • Interpret data in graphs (picture, bar, and line plots) to solve problems using numbers and operations.
    • Create a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
    • Interpret data in line plots to solve problems involving addition and subtraction of fractions.

    Note: Students need to mark the line plot in eighths to use equivalence with common denominators of eighths before adding or subtracting with data set.
    Understanding:
    Students understand that:
    • data can be collected, organized and analyzed in data displays to generate and answer questions related to the context of the data.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.20.1: Display data by making a line plot where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.
    M.4.20.2: Interpret data using graphs including bar, line, and circle graphs, and Venn diagrams.
    M.4.20.3: Identify the parts of a line plot.
    M.4.20.4: Recognize a line plot.
    M.4.20.5: Draw a scaled picture graph and a scaled bar graph to represent a data set.

    Prior Knowledge Skills:
    • Define picture graph, bar graph, and data.
    • Interpret the data to solve problems.
    • Identify the parts of a graph (x-axis, y-axis, title, key, equal intervals, labels).
    • Locate the data on a picture graph and a bar graph.
    • Directly compare two objects, with a measurable attribute in common, to see which object has "more of" or "less of" the attribute, and describe the difference.
    • Define line plot.
    • Identify the parts of a line plot.
    • Measure objects to the nearest inch.
    • Identify one-inch units on a ruler starting with 0.
    • Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
    • Directly compare two objects, with a measurable attribute in common, to see which object has "more of" or "less of" the attribute, and describe the difference.
    • Use addition and subtraction within 20 to solve addition and subtraction word problems with an unknown number.
    • Describe picture graph and bar graph.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.20 Using vocalization, sign language, augmentative communication or assistive technology, represent and interpret data on a picture or bar graph when given a model or a graph to complete.


    Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
    Mathematics (2019)
    Grade(s): 4
    All Resources: 4
    Classroom Resources: 4
    21. Select and use an appropriate unit of measurement for a given attribute (length, mass, liquid volume, time) within one system of units: metric - km, m, cm; kg, g, l, ml; customary - lb, oz; time - hr, min, sec.

    a. Within one system of units, express measurements of a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use the relationships between measurement units to express larger units of measure in smaller units.

    • Example: Convert 2 feet to 24 inches, 2 hours to 120 minutes, but not smaller units to larger units for instance, converting 150 feet to 50 yards.
    • Use a two-column table to show relationships between larger units and smaller units and/or make conversions.
    Teacher Vocabulary:
    • Appropriate unit of measure
    • Metric
    • Customary
    • Equivalent
    • Conversion table
    • Mass
    • Liquid volume
    • Kilometer
    • Meter
    • Centimeter
    • Kilogram
    • Gram
    • liter
    • Milliliter
    • Ounce
    • Pound
    • Hour
    • Minute
    • Two-column table
    Knowledge:
    Students know:
    • units of measures for given attributes vary in size and are related by multiplicative comparison.
    Skills:
    Students are able to:
    • Select and use appropriate units of measure for a given attribute.
    • Convert larger units of measure to smaller units of measure within the same measurement system.
    • Record measurement equivalents in a two-column table.
    Understanding:
    Students understand that:
    • There is an appropriate unit of customary measurement and metric measurement for a given attribute.
    • Multiplicative relationships exist between customary units of length, mass, liquid volume, and time.
    • Multiplicative relationships exist between metric units of length, mass, liquid volume.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.21.1: Define conversion.
    M.4.21.2: Define length, kilometers, meters and centimeters.
    M.4.21.3: Define weight, kilograms, grams, pounds, ounces, liters and milliliters.
    M.4.21.4: Define hour, minute, second.
    M.4.21.5: Measure and estimate liquid volumes and masses of objects using standard units of grams, kilograms, and liters.
    M.4.21.6: Identify standard units of measurement equivalents.
    Examples: 60 minutes equals 1 hour, 16 ounces equals 1 pound.
    M.4.21.7: Match measurement units to abbreviations.
    Examples: kilometers (km), meters (m), centimeters (cm), kilograms (kg), grams (g), pounds (lb), ounces (oz), liters (l), milliliters (ml)

    Prior Knowledge Skills:
    • Define liquid volume, mass, grams, kilograms, and liters.
    • Recognize how the standard units of measure compare to one another.
    • Identify key terms for word problems.
      Examples: Difference, altogether, in all, between.
    • Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
    • Recall basic addition, subtraction, multiplication, and division facts.
    • Describe measurable attributes of objects such as length or weight. Describe several measurable attributes of a single object.
    • Compare equivalent units of time using hours and minutes.
      Examples: 60 minutes = one hour, 30 minutes = one half of an hour.
    • Recognize key vocabulary and/or phrases associated with time.
      Examples: Quarter 'til = 15 minutes before; half past the hour = 30 minutes after the hour.
    • Compare the lengths of time to complete everyday activities
      Examples: Brushing your teeth = about 2 minutes; riding the bus = about 20 minutes.
    • Tell and write time in hours and half-hours using analog and digital clocks.
    • Recognize hour, minute, and second hands on an analog clock.
    • Count by 5's to 60.
    • Determine the monetary value of a set of like and unlike bills.
    • Determine the monetary value of a set of like and unlike coins.
    • Apply addition and subtraction strategies.
    • Understand key words in addition and subtraction word problems involving money.
      Examples: adding to, taking from, putting together, taking apart, sum, difference, all together, how much more, how much is left, in all, cents, dollar, change, paid, total.
    • Count forward from a given number by ones, fives, tens, and twenty-fives.
    • Identify coins and bills and their value.
    • Identify symbols for dollar ($), cent (¢).
    • Identify coins by name including penny, nickel, dime and quarter.
    • Sort pennies, nickels, dimes, and quarters.
    • Count 10 objects.
      Examples: pennies and dollar bills
    • Tell and write time in hours and half-hours using analog and digital clocks.
    • Recognize vocabulary terms related to time measurements.
      Examples: minute, hour, half hour, o'clock, morning, evening, a.m., p.m.
    • Illustrate time to hour and half hour.
      Example: Given the time 3:00, illustrate long hand and short hand positions on a clock.
    • Identify the short hand as the hour hand, and the long hand as the minute hand on an analog clock.
    • Identify the first number as the hour, and the numbers after the colon as the minutes on a digital clock.
    • Write numerals 0 to 59.
    • Recognize numerals 0 to 59.
    • Count to 60 by fives.
    • Distinguish between analog and digital clocks.
    • Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.21 Given an object determine the appropriate measurement tool and units of measure using vocalization, sign language, augmentative communication or assistive technology.


    Mathematics (2019)
    Grade(s): 4
    All Resources: 6
    Lesson Plans: 1
    Classroom Resources: 5
    22. Use the four operations to solve measurement word problems with distance, intervals of time, liquid volume, mass of objects, and money.

    a. Solve measurement problems involving simple fractions or decimals.

    b. Solve measurement problems that require expressing measurements given in a larger unit in terms of a smaller unit.

    c. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given multistep word problems involving units of measure will,
    • Represent and solve world problems involving whole number measurements and require expressing measurements when given a larger unit in terms of a smaller unit.

    • Example: Given a picture frame which is 2 feet long and 8 inches wide, express the perimeter of the picture frame in inches.
    • Represent and solve word problems involving two measurements given in the same units, one a whole number measurement and the other a non-whole number measurement.

    • Example: Given a picture frame with dimensions 1/2 ft and 8 in, express the perimeter of the picture frame in inches.
    • Use visual representations to illustrate a measurement scale.
    Note: Quantities are limited to expectations in grade 4 standards and operations will not include division of fractions or decimals.
    Teacher Vocabulary:
    • Operations
    • Distance
    • Intervals of time
    • Liquid volume
    • Mass
    • Number line diagram
    • Measurement scale
    Knowledge:
    Students know:
    • Relative sizes of units within one system of measurement.
    • Strategies to solve word problems involving the four operations.
    • Measurement units in the same system are multiplicatively related.
    Skills:
    Students are able to:
    • Solve measurement word problems
    • Involving distance, intervals of time, liquid volume, mass, and money.
    • Involving measurement conversion of larger units to a smaller unit.
    • Involving simple fractions or decimals.
    • Using diagrams to represent measurement quantities and solutions.

    Note: Quantities and operations are limited to grade 4 standard expectations.
    Understanding:
    Students understand that:
    • Relationships among units within a system of measurement are multiplicative comparisons.
    • The size of the unit of measurement and the number of units are inversely related.
    • Addition and subtraction of measurements require measurements in the same unit and that the common unit is maintained in the answer.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.22.1: Define distance, time, elapsed time, volume, mass.
    M.4.22.2: Determine elapsed time to the day with calendars and to the hour with a clock.
    M.4.22.3: Express liquid volumes and masses of objects using standard units of grams, kilograms, and liters.
    M.4.22.4: Use addition, subtraction, multiplication and division to solve one- and two-step word problems.
    M.4.22.5: Recognize key terms to solve word problems.
    M.4.22.6: Recall basic facts for addition, subtraction, multiplication, and division.
    M.4.22.7: Identify monetary equivalents.
    Examples: four quarters equal one dollar, five one-dollar bills equals five dollars.

    Prior Knowledge Skills:
    • Define liquid volume, mass, grams, kilograms, and liters.
    • Recognize how the standard units of measure compare to one another.
    • Identify key terms for word problems.
      Examples: Difference, altogether, in all, between.
    • Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
    • Recall basic addition, subtraction, multiplication, and division facts.
    • Describe measurable attributes of objects such as length or weight. Describe several measurable attributes of a single object.
    • Compare equivalent units of time using hours and minutes.
      Examples: 60 minutes = one hour, 30 minutes = one half of an hour.
    • Recognize key vocabulary and/or phrases associated with time.
      Examples: Quarter 'til = 15 minutes before; half past the hour = 30 minutes after the hour M. 3.16.3: Compare the lengths of time to complete everyday activities.
      Examples: Brushing your teeth = about 2 minutes; riding the bus = about 20 minutes.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.22 Using vocalization, sign language, augmentative communication, or assistive technology, tell time on a digital and analog clock (to the hour, half-hour, quarter hour).
    M.AAS.4.22a Measure mass, volume, or lengths of an object when given a measurement tool.
    M.AAS.4.22b Using vocalization, sign language, augmentative communication, or assistive technology, identify and determine the value of penny, nickel, dime, and quarter.


    Mathematics (2019)
    Grade(s): 4
    All Resources: 2
    Classroom Resources: 2
    23. Apply area and perimeter formulas for rectangles in real-world and mathematical situations.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given real-world situations involving area and perimeter will,
    • Apply area formula to find the area of rectangles.
    • Find one missing dimension of the rectangle if one dimension is known.
    • Apply perimeter formula to find perimeter of rectangles.
    • Find one missing dimension of the rectangle if one dimension is known.
    Teacher Vocabulary:
    • Area
    • Perimeter
    • Formula
    • Equation
    • Dimension
    • Length
    • Width
    Knowledge:
    Students know:
    • The relationship of area to the operations of multiplication and addition.
    • The relationship of three whole numbers in a multiplication or division equation.
    • How to distinguish between linear and area measures.
    Skills:
    Students are able to:
    • Apply area formula for rectangles given real-world situations.
    • Apply perimeter formula for rectangles given real-world situations.
    Understanding:
    Students understand that:
    Given real-world situations involving rectangles,
    • Area formula represents the region inside a rectangle and is used to calculate area, or calculate one missing dimension if one side length is known.
    • Perimeter formula represents the distance around the rectangle and is used to calculate the perimeter, or calculate one missing dimension if one side length is known.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.23.1: Recall the formula for area (L × W).
    M.4.23.2: Recognize that unit squares are equal.
    M.4.23.3: Recall the formula for perimeter (P= L+L+W+W or P=2L + 2W).
    M.4.23.4: Recall basic addition and multiplication facts.

    Prior Knowledge Skills:
    • Define perimeter.
    • Recall the formula for perimeter (P= L+L+W+W or P=2L + 2W).
    • Recall basic addition and multiplication facts.
    • Build and draw shapes to possess defining attributes.
    • Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
    • Describe measurable attributes of objects such as length or weight.
    • Define rows, columns, and total.
    • Identify rectangle.
    • Count to 20 by ones.
    • Trace partitions in a rectangle.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.23 Determine the area of a square or rectangle by counting units of measurement (e.g., unit squares).


    Geometric measurement: understand concepts of angle and measure angles.
    Mathematics (2019)
    Grade(s): 4
    All Resources: 4
    Learning Activities: 1
    Classroom Resources: 3
    24. Identify an angle as a geometric shape formed wherever two rays share a common endpoint.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Describe an angle.
    • Describe an angle's relationship to a circle.
    Teacher Vocabulary:
    • Angle
    • Ray
    • Endpoint
    • Geometric shape
    • Vertex
    • Line
    • Point
    • Line segment
    Knowledge:
    Students know:
    • Angles are geometric shapes formed when two rays share a common endpoint.
    • How to draw points, lines, line segments, and rays
    Skills:
    Students are able to:
    • Identify an angle as two rays with a common endpoint.
    Understanding:
    Students understand that:
    • angles are geometric shapes made of two rays that are infinite in length and are measured with reference to a circle with its center at the common endpoint of the rays.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.24.1: Define degree, angle, ray, and vertices.
    M.4.24.2: Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces.
    M.4.24.3: Estimate angle measures using 45o, 90o, 180o, 270o, or 360o.
    M.4.24.4: Identify angle, ray, and vertices.
    M.4.24.5: Draw shapes to possess defining attributes.

    Prior Knowledge Skills:
    • Build and draw shapes to possess defining attributes.
    • Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles).
    • Model partitioning circles and rectangles.
    • Decompose pictures made of simple shapes.
    • Identify squares, circles, triangles and rectangles.
    • Explore shapes or figures that can be decomposed into smaller equal parts.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.24 Recognize and Identify angles in geometric shapes as larger or smaller.


    Mathematics (2019)
    Grade(s): 4
    All Resources: 5
    Learning Activities: 1
    Lesson Plans: 1
    Classroom Resources: 3
    25. Use a protractor to measure angles in whole-number degrees and sketch angles of specified measure.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Demonstrate using a protractor to measure angles in different orientations to the nearest degree.
      Example: Given an angle, align the vertex of the angle with the correct point on the protractor, align one ray of the angle with the 0o mark on the protractor, and read where the other ray is located on the protractor.
    • Draw an angle of a given size using a variety of tools.
      Example: Draw a ray and use a protractor to construct a 108o angle.
    • Determine the angle measure when given an image of a protractor with angle rays intersecting the protractor scale.

    • Example: Given a protractor showing angle rays intersecting the protractor at 83 degrees and 123 degrees. What is the angle measure? Determine the angle measure is 40 degrees.
    Teacher Vocabulary:
    • Protractor
    • Angle
    • Whole number
    • Degree
    • Center
    • Circle
    • Intersect
    • Arc
    • Point
    • Ray
    • One-degree angle
    • Vertex
    Knowledge:
    Students know:
    • Measurable attributes of geometric shapes, specifically angle size.
    • Units of measurement, specifically one-degree angle (degrees).
    • An angle is measured by the number or iterations of one-degree angles that exactly cover the rotation of the angle.
    Skills:
    Students are able to:
    • Sketch angles given a specified measure.
    • Use appropriate tools to find angle measure.
    Understanding:
    Students understand that:
    • the rotation of an angle is measured by the number of one-degree angles that exactly cover the rotation of the angle.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.25.1: Define symmetry.
    M.4.25.2: Model using a protractor to draw angles.
    M.4.25.3: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
    M.4.25.4: Measure the length of an object by selecting and using appropriate tools such as a ruler.
    M.4.25.5: Measure length using standard and non-standard units of measurement.
    M.4.25.6: Plot points on grids, graphs, and maps using coordinates.
    M.4.25.7: Draw points, lines, line segments, and parallel and perpendicular lines, angles, and rays.
    M.4.25.8: Identify lines of symmetry on one-dimensional figures.

    Prior Knowledge Skills:
    • Build and draw shapes to possess defining attributes.
    • Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
    • Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles).
    • Identify a rectangle.
    • Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
    • Define halves, thirds, fourths, quarters, whole, parts (shares) and equal.
    • Distinguish between equal and non-qual parts.
    • Model partitioning circles and rectangles.
    • Decompose pictures made of simple shapes.
    • Identify squares, circles, triangles and rectangles.
    • Explore shapes or figures that can be decomposed into smaller equal parts.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.24 Recognize and Identify angles in geometric shapes as larger or smaller.


    Mathematics (2019)
    Grade(s): 4
    All Resources: 1
    Learning Activities: 1
    26. Decompose an angle into non-overlapping parts to demonstrate that the angle measure of the whole is the sum of the angle measures of the parts.

    a. Solve addition and subtraction problems on a diagram to find unknown angles in real-world or mathematical problems.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • When given the measures of two adjacent angles, find the measure of the larger angle formed.
    • Given one angle measure, composed of two smaller angles and given the measure of one of the smaller angles, find the second unknown angle measure.
    • Decompose the angle as the sum of two angle parts.
    • Use addition and subtraction equations to represent and solve problems involving angle measurements.
    Teacher Vocabulary:
    • Decompose
    • Angle
    • Non-overlapping
    • Angle measure
    • Sum
    • Diagram
    • Adjacent
    • Compose
    • Degrees
    Knowledge:
    Students know:
    • Angles are measured in degrees from 0 to 360.
    • Protractor orientation does not affect an angle measurement.
    Skills:
    Students are able to:
    • Decompose an angle into non-overlapping parts and demonstrate that the sum of the angle measure parts is the same as the measure of the whole angle.
    • Use addition and subtraction to find unknown angles on a diagram in real-world or mathematical problems.
    Understanding:
    Students understand that:
    • The rotation of an angle is measured by the number of one-degree angles that exactly cover the rotation of the angle.
    • Angle measurement is additive of the non-overlapping parts of a decomposed angle.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.26.1: Identify straight angles.
    M.4.26.2: Recognize angle measures such as 45o, 90o, 180o, 270o, 300o.
    M.4.26.3: Recall basic addition and subtraction facts.
    M.4.26.4: Skip count by fives and tens.

    Prior Knowledge Skills:
    • Build and draw shapes to possess defining attributes.
    • Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
    • Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles).
    • Identify a rectangle.
    • Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
    • Define halves, thirds, fourths, quarters, whole, parts (shares) and equal.
    • Distinguish between equal and non-qual parts.
    • Model partitioning circles and rectangles.
    • Decompose pictures made of simple shapes.
    • Identify squares, circles, triangles and rectangles.
    • Explore shapes or figures that can be decomposed into smaller equal parts.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.24 Recognize and Identify angles in geometric shapes as larger or smaller.


    Geometry
    Draw and identify lines and angles, and identify shapes by properties of their lines and angles.
    Mathematics (2019)
    Grade(s): 4
    All Resources: 6
    Learning Activities: 2
    Lesson Plans: 1
    Classroom Resources: 3
    27. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines, and identify these in two-dimensional figures.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Describe the characteristics of a given figure.
      Example: An obtuse angle is described as two rays that meet at a point called a vertex with an angle measure greater than 90 degrees.
    • Draw a given figure correctly using a variety of tools.

    • Example: Use a ruler, paper, and pencil to draw two points and connect them to create a line segment.
    • Identify the given figures in two-dimensional shapes.

    • Example: Given a rectangle ABCD, identify that angle ABC is a right angle and that lines AB and CD are parallel.
    Teacher Vocabulary:
    • Point
    • Line
    • Line segment
    • Ray
    • Right angle
    • Acute angle
    • Obtuse angle
    • Perpendicular lines
    • Parallel lines
    • Two dimensional figure
    • Vertex
    • Angle measure
    Knowledge:
    Students know:
    • defining characteristics of geometric figures, such as points, lines, line segments, angles (right, acute, and obtuse), parallel lines, and perpendicular lines.
    Skills:
    Students are able to:
    • Draw points, lines, line segments, rays, angles (right, acute, obtuse).
    • Draw parallel and perpendicular lines.
    • Identify points, lines, line segments, rays, angles, parallel lines, and perpendicular lines in two-dimensional figures.
    Understanding:
    Students understand that:
    • points, lines, line segments, angles (right, acute, and obtuse), parallel lines, and perpendicular lines are defining characteristics of two dimensional shapes.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.27.1: Define points, lines, line segments, rays, right angle, acute angle, obtuse angle, perpendicular lines, and parallel lines.
    M.4.27.2: Define two-dimensional figure.
    M.4.27.3: Recognize one-dimensional points, lines, and line segments.
    M.4.27.4: Model shapes in the world by building shapes from components.

    Prior Knowledge Skills:
    • Recall the vocabulary of shapes (labels, sides, faces, vertices, etc.).
    • Recognize and draw shapes having specified attributes such as a given number of angles.
    • Build and draw shapes to possess defining attributes.
    • Sort shapes into categories.
    • Define side, angle, face, closed, and open.
    • Use vocabulary related to shape attributes.
      Examples: sides, angles, face, closed, open
    • Trace shapes.
    • Sort triangles, quadrilaterals, pentagons, hexagons, and cubes.
    • Explore triangles, quadrilaterals, pentagons, hexagons, and cubes.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.27 Recognize parallel lines, intersecting lines, and angles (right, acute, obtuse).


    Mathematics (2019)
    Grade(s): 4
    All Resources: 5
    Learning Activities: 4
    Classroom Resources: 1
    28. Identify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size.

    a. Describe right triangles as a category, and identify right triangles.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Sort two-dimensional figures based on angle sizes or presence of parallel and/or perpendicular lines.

    • Example: Given a group of regular polygons, sort shapes into categories based on angle size as well as presence of parallel lines.
    • Classify and name shapes using more than one characteristic.
    • Identify a right triangle by labeling the right angle.
    Teacher Vocabulary:
    • Two-dimensional figure
    • Parallel lines
    • Perpendicular lines
    • Angle
    • Right triangle
    Knowledge:
    Students know:
    • Two lines are parallel if they never intersect and are an equal distance apart.
    • Two lines are perpendicular if they are at right angles to each other.
    • A right triangle is a triangle that has one right angle.
    Skills:
    Students are able to:
    • Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines.
    • Classify two-dimensional figures based on the presence or absence of angles of a specified size.
    • Identify right triangles.
    Understanding:
    Students understand that:
    • shapes are categorized based on attributes they possess in common such as angle size, side length, side relationships (parallel and perpendicular).
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.28.1: Define right angle.
    M.4.28.2: Recognize that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
    M.4.28.3: Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
    M.4.28.4: Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces.
    M.4.28.5: Identify triangles.

    Prior Knowledge Skills:
    • Recall the vocabulary of shapes (labels, sides, faces, vertices, etc.).
    • Recognize and draw shapes having specified attributes such as a given number of angles.
    • Build and draw shapes to possess defining attributes.
    • Sort shapes into categories.
    • Define side, angle, face, closed, and open.
    • Use vocabulary related to shape attributes.
      Examples: sides, angles, face, closed, open.
    • Trace shapes.
    • Sort triangles, quadrilaterals, pentagons, hexagons, and cubes.
    • Explore triangles, quadrilaterals, pentagons, hexagons, and cubes.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.28 Using vocalization, sign language, augmentative communication or assistive technology, describe the defining attributes of two-dimensional shapes (e.g., number of sides, number of angles).


    Mathematics (2019)
    Grade(s): 4
    All Resources: 3
    Learning Activities: 2
    Classroom Resources: 1
    29. Define a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts.

    a. Identify line-symmetric figures and draw lines of symmetry.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Given a shape, identify a line of symmetry.
    • Given a shape, identify the number of lines of symmetry.
    • Given half of a two-dimensional figure on grid paper, draw the other half so that the two sides are symmetrical and include the line of symmetry that separates the two halves.
    • Justify the existence or non-existence of line symmetry within figures by drawing the lines of symmetry.
    Teacher Vocabulary:
    • Symmetry
    • Two dimensional figure
    • Line of symmetry
    Knowledge:
    Students know:
    • Characteristics of lines of symmetry.
    Skills:
    Students are able to:
    • Define a line of symmetry for a two-dimensional figure.
    • Identify and draw lines of symmetry for two-dimensional figures.
    Understanding:
    Students understand that:
    • a line of symmetry divides a shape into two parts such that when folded on the line, the two parts match.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.4.29.1: Identify line symmetric figures.
    M.4.29.2: Draw lines of symmetry on a one-dimensional figure.
    M.4.29.3: Recognize lines of symmetry on a one-dimensional figure.

    Prior Knowledge Skills:
    • Recognize a fraction as part of a whole.
    • Decompose a large pre-made shape using smaller shapes.
    • Compose a large pre-made shape using smaller shapes.
    • Partition a rectangle into rows and columns of same-size squares, and count to find the total number of them.
    • Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds, or four fourths.
    • Define halves, thirds, fourths, quarters, whole, parts (shares) and equal.
    • Distinguish between equal and non-qual parts.
    • Model partitioning circles and rectangles.
    • Decompose pictures made of simple shapes.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.4.29 Given a drawing of a shape with a line drawn across the shape, identify if it is divided symmetrically.


    Operations and Algebraic Thinking
    Write and interpret numerical expressions.
    Mathematics (2019)
    Grade(s): 5
    All Resources: 6
    Learning Activities: 4
    Classroom Resources: 2
    1. Write, explain, and evaluate simple numerical expressions involving the four operations to solve up to two-step problems. Include expressions involving parentheses, brackets, or braces, using commutative, associative, and distributive properties.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given a mathematical expression in words, will
    • Write numerical expressions to represent the context and evaluate the expression.
    • Explain their thinking as they use the order of operations to evaluate a variety of problems.
    Given a numerical expression involving multiple operations and up to two sets of grouping symbols, will
    • Evaluate the expression.
    • Explain the meaning of the expression without evaluating the expression.
    Note: Expressions should not contain nested grouping symbols, should be limited to expressions found in application of associative or distributive properties, and not always limited to whole numbers.
    Teacher Vocabulary:
    • Expression
    • Calculate
    • Interpret
    • Evaluate
    • Compare
    • Reasoning
    • Grouping symbol
    • Parentheses
    • Braces
    • Brackets
    • Commutative property
    • Associative property
    • Distributive property
    Knowledge:
    Students know:
    • Vocabulary associated with the four operations to write the symbolic notation of the mathematical expression.
      Example: The phrase, "the product of 4 and 3" is written as "4 x 3."
    • Strategies for evaluating a numerical expression and replace it with an equivalent form.
      Example: Given (22 + 16) + 43 can be replaced with 38 + 43 and then further simplified.
    Skills:
    Students are able to:
    • Write, explain, and evaluate numerical expressions representing two-step problems in context.
    • Evaluate numerical expressions with grouping symbols.
    • Translate a numerical expression into words.
    • Write a numerical expression given a mathematical expression in words.
    Understanding:
    Students understand that:
    • multi-step word problems can be represented by numerical expressions using operations and grouping symbols to indicate order of evaluating them.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.1.1: Define parentheses, braces, and brackets.
    M.5.1.2: Distinguish between non-numerical and numerical expression.
    M.5.1.3: Recognize expressions.
    M.5.1.4: Apply properties of operations as strategies to add and subtract.
    M.5.1.5: Represent addition and subtraction with objects, mental images, drawings, expressions, or equations.

    Prior Knowledge Skills:
    • Write, explain, and evaluate numerical expressions representing two-step problems in context.
    • Evaluate numerical expressions with grouping symbols.
    • Translate a numerical expression into words.
    • Write a numerical expression given a mathematical expression in words.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.1 Evaluate simple numerical expressions involving the four operations.


    Analyze patterns and relationships.
    Mathematics (2019)
    Grade(s): 5
    All Resources: 2
    Classroom Resources: 2
    2. Generate two numerical patterns using two given rules and complete an input/output table for the data.

    a. Use data from an input/output table to identify apparent relationships between corresponding terms.

    b. Form ordered pairs from values in an input/output table.

    c. Graph ordered pairs from an input/output table on a coordinate plane.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Use two related rules to
    • Generate numerical patterns and record as ordered pairs.
    • Graph ordered pairs consisting of corresponding terms.
    • Identify and explain relationships between corresponding terms.

    • Example: Given the rule "add 1 starting at 0", and "add 2 starting at 0," explain the terms in one sequence as 1/2 the corresponding terms in the other sequence, or the terms in one sequence are twice the corresponding terms in the other sequence.
    Teacher Vocabulary:
    • Number pattern
    • Graph
    • Coordinate plane
    • X-axis
    • Y-axis
    • Origin
    • X-coordinate
    • Y-coordinate
    • Ordered pair
    • Generate
    • Sequence
    Knowledge:
    Students know:
    • Strategies to identify numerical patterns and recognize the relationship between the terms in the pattern.
    • Reasoning strategies to generate a numerical pattern which follow a given rule.
    Skills:
    Students are able to:
    • Generate two numerical patterns using two given rules.
    • Complete an input/output table for data.
    • Identify relationship between terms in an input/output table.
    • Form ordered pairs from an input/output table.
    • Graph ordered pairs on a coordinate plane.
    Understanding:
    Students understand that:
    • relationships between two numerical patterns can be represented by ordered pairs and graphed in the first quadrant of the coordinate plane.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.2.1: Construct repeating and growing patterns with a variety of representations.
    M.5.2.2: Continue an existing pattern.
    M.5.2.3: Identify arithmetic patterns (including patterns in the addition table or multiplication table).

    Prior Knowledge Skills:
    • Generate two numerical patterns using two given rules.
    • Complete an input/output table for data.
    • Identify relationship between terms in an input/output table.
    • Form ordered pairs from an input/output table.
    • Graph ordered pairs on a coordinate plane.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.2 Given a rule, Identify and extend numerical patterns (e.g., given the rule "Add 3" and the starting number 0).


    Operations with Numbers: Base Ten
    Understand the place value system.
    Mathematics (2019)
    Grade(s): 5
    All Resources: 4
    Classroom Resources: 4
    3. Using models and quantitative reasoning, explain that in a multi-digit number, including decimals, a digit in any place represents ten times what it represents in the place to its right and 1/10 of what it represents in the place to its left.

    a. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, using whole-number exponents to denote powers of 10.

    b. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10, using whole-number exponents to denote powers of 10.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use models to illustrate the relationship between two successive place values in whole numbers and decimals.
    • Explain that a digit in one place represents 1/10 of what it represents to its left or the place value is 10 times the place value on the right.
    • Use strategies to find products and explain patterns when multiplying by powers of 10.
      Example: The product of 420 x 200 = 42 x 10 x 2 x 100 is the same as (42 x 2) x (10 x 100) = 84 x 1000 = 84,000 shows multiplying by three powers of 10 shifts the digits in the product three place values greater (to the left.)
    • Use strategies to find products and quotients and use place value understanding to explain patterns in the placement of the decimal point when involving a power of 10.
    • Write powers of 10 in standard form and using exponential notation.
    Teacher Vocabulary:
    • Digit
    • Decimal
    • Decimal point
    • Thousandths
    • Hundredths
    • Tenths
    • Base-ten
    • Expanded form
    • Place value
    • Power of 10
    • Factor
    • Base
    • Exponent
    • Product
    Knowledge:
    Students know:
    • Each place value position represents 10 times what it represents in the place to its right.
      Example: In 433, the underlined 3 represents 3 tens and has a value of 30 which is ten times the value of the 3 ones to its right.
    • Place value understanding is extended to apply reasoning that a place value position represents 1/10 of what it represents in the place value to its left.
      Example: In 433, the underlined 3 represents 3 ones and has a value of 3 which is one-tenth of the value of the 3 tens or 30 to its left.
    • A given number multiplied by a power of 10 shifts the digits in the given number one place value greater (to the left) for each factor of 10. -A given number divided by a power of 10 shifts the digits in the given number one-tenth of the value (to the right) for each factor of 10.
    Skills:
    Students are able to:
    • Reason and explain the relationship between two successive place values.
    • Explain patterns of zeros of the product when multiplying by powers of 10.
    • Explain patterns in placement of decimals when multiplying or dividing by power of 10.
    • Write powers of 10 using exponential notation.
    Understanding:
    Students understand that:
    • The relationship of adjacent places values in the base ten system extend beyond whole numbers to decimal values.
    • Multiplying or dividing by a power of 10 shifts the digits in a whole number or decimal that many places to the left or right respectively.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.3.1: Use place value understanding to round whole numbers to the nearest 10 or 100.
    M.5.3.2: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
    M.5.3.3: Identify that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.

    Prior Knowledge Skills:
    • Reason and explain the relationship between two successive place values.
    • Explain patterns of zeros of the product when multiplying by powers of 10.
    • Explain patterns in placement of decimals when multiplying or dividing by power of 10.
    • Write powers of 10 using exponential notation.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.3 Compare base-10 models up to 99 and whole numbers up to 100 to determine symbols (<, >, =).


    Mathematics (2019)
    Grade(s): 5
    All Resources: 9
    Lesson Plans: 1
    Classroom Resources: 7
    Unit Plans: 1
    4. Read, write, and compare decimals to thousandths.

    a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.

    Example: 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

    b. Compare two decimals to thousandths based on the meaning of the digits in each place, using >, =, and < to record the results of comparisons.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Given a decimal number in one form (words, base-ten numerals, expanded), identify the number in another form.
    • Read decimals with number names.

    • Example: Read 4.023 as "four and 23 thousandths."
    • Write decimals using base-ten numerals and expanded form.

    • Example: 4.023 as 4 x 1 + 2 x 1/100 + 3 x 1/1000 or 4 x 1 + 2 x 0.01 + 3 x 0.001.
    • Use place value understanding to compare two decimals.
    Teacher Vocabulary:
    • Compare
    • Decimal
    • Thousandths
    • Hundredths
    • Tenths
    • Symbol
    • Greater than
    • Less than
    • Equal
    • Place value strategy
    • Expanded form
    • Expanded notation
    Knowledge:
    Students know:
    • How to read and write whole numbers in standard form, word form, and expanded form.
    • How to compare two whole numbers using place value understanding.
    • Prior place value understanding with whole numbers is extended and applied to decimal values.
    • Recognize and model decimal place value using visual representations to compare.
    Skills:
    Students are able to:
    • Read and write decimal values in word form, standard form, and expanded form.
    • Compare decimals to thousandths using <, >, or = .
    Understanding:
    Students understand that:
    • the adjacent place value relationship in the base ten system extends to decimals and is used to write decimals in expanded form and compare decimals.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.4.1: Recognize decimals as parts of a whole.
    M.5.4.2: Compare whole numbers.
    M.5.4.3: Write whole numbers in words and expanded form.
    M.5.4.4: Read whole numbers.
    M.5.4.5: Define expanded notation and standard form.
    M.5.4.6: Convert a number written in expanded to standard form.
    M.5.4.7: Define hundredths and thousandths.
    M.5.4.8: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
    M.5.4.9: Identify comparison symbols.
    Examples: >, =, and <.

    Prior Knowledge Skills:
    • Read and write decimal values in word form, standard form, and expanded form.
    • Compare decimals to thousandths using <, >, or = .
    • Understand rounding decimals using place value.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.3 Compare base-10 models up to 99 and whole numbers up to 100 to determine symbols (<, >, =).


    Mathematics (2019)
    Grade(s): 5
    All Resources: 5
    Learning Activities: 1
    Lesson Plans: 1
    Classroom Resources: 2
    Unit Plans: 1
    5. Use place value understanding to round decimals to thousandths.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given a decimal number,
    • Use place value vocabulary and models to justify the rounding of the number to a specified place value.
    • Rounded to a specified place value, identify a number that could have resulted in that rounding.
    Teacher Vocabulary:
    • Round
    • Place value
    • Tenths
    • Hundredths
    • Thousandths
    • Decimal
    • Number line
    • Midpoint
    Knowledge:
    Students know:
    • how to use place value understanding to round multi-digit whole numbers to any place.
    Skills:
    Students are able to:
    • Round decimals using place value understanding.
    Understanding:
    Students understand that:
    • in the base ten system, the adjacent place value relationship extends to decimals and is used to round decimals.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.5.1: Round multi-digit whole numbers to any place.
    M.5.5.2: Round whole numbers to the nearest 10 or 100.

    Prior Knowledge Skills:
    • Use the standard algorithm to find a product.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.3 Compare base-10 models up to 99 and whole numbers up to 100 to determine symbols (<, >, =).


    Perform operations with multi-digit whole numbers and decimals to hundredths.
    Mathematics (2019)
    Grade(s): 5
    All Resources: 2
    Classroom Resources: 2
    6. Fluently multiply multi-digit whole numbers using the standard algorithm.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given a context for multiplication of two whole numbers,
    • Choose the most appropriate strategy to find the product.
    • Accurately use standard algorithm when appropriate.
    Teacher Vocabulary:
    • Multiply
    • Multi-digit
    • Standard algorithm
    • Distributive property
    • Partial product
    • Area model
    Knowledge:
    Students know:
    • Strategies based on place value and properties of operations for finding products of two factors including a one-digit and up to a four-digit factor and two two-digit factors.
    • Decomposition of a given number into base ten units.
    • How to illustrate a product of two factors using an area model.
    • Connections between an area model and finding partial products when multiplying.
    Skills:
    Students are able to:
    • Use the standard algorithm to find a product.
    Understanding:
    Students understand that:
    • properties of operations and the base ten system are foundational to the computation of products using the standard algorithm.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.6.1: Demonstrate steps in setting up a long multiplication problem.
    M.5.6.2: Multiply 2-digit numbers by 1-digit multiplier.
    M.5.6.3: Multiply 1-digit numbers by 1-digit multiplier.
    M.5.6.4: Recall basic multiplication facts.
    M.5.6.5: Recall repeated addition facts.

    Prior Knowledge Skills:
    • Find whole number quotients and remainders using a variety of strategies based on place value and properties of operations.
    • Illustrate and explain the calculation using equations, arrays, and area mode.
    • Use concrete models, drawings, and strategies to add, subtract, multiply, and divide decimals.
    • Relate strategies for operations with decimals to a written method and explain reasoning used.
    • Solve real-world context problems involving decimals.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.6 Model multiplication with two digit whole numbers by one digit whole numbers with regrouping using strategies such as arrays, decomposition, and manipulatives.


    Mathematics (2019)
    Grade(s): 5
    All Resources: 4
    Classroom Resources: 4
    7. Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Choose strategies based on place value, partial quotients, properties of operations, or the relationship between multiplication and division to find whole number quotients and remainders.
    • Solve word problem situations involving division.
    • Justify solution path for quotients using equations, arrays or area models.
      • Note: Standard algorithm for division is not an expectation at grade 5.
    Teacher Vocabulary:
    • Quotient
    • Dividend
    • Divisor
    • Divide
    • Multiply
    • Equation
    • Remainder
    • Multiple
    • Area model
    • Decompose
    • Partial quotient
    • Equation
    Knowledge:
    Students know:
    • Efficient strategies to find a whole number quotient when a multi-digit number (up to 4-digit dividend) is divided by a single-digit divisor.
    • How to justify quotients using an illustration or the relationship between multiplication and division.
    Skills:
    Students are able to:
    • Find whole number quotients and remainders using a variety of strategies based on place value and properties of operations.
    • Illustrate and explain the calculation using equations, arrays, and area models.
    Understanding:
    Students understand that:
    • Strategies for division by a one-digit divisor are extended to two-digit divisors.
    • Visual models are used to illustrate division.
    • Remainders may be written as a fraction or decimal and interpreted based on context of the problem situation.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.7.1: Construct a division equation with an example of the division algorithm.
    M.5.7.2: Illustrate the division algorithm using a one-digit divisor and a 2-digit dividend.
    M.5.7.3: Identify the place value of a division problem.
    M.5.7.4: Restate the inverse process of division as multiplication.
    M.5.7.5: Recall basic multiplication facts.

    Prior Knowledge Skills:
    • Use concrete models, drawings, and strategies to add, subtract, multiply, and divide decimals.
    • Relate strategies for operations with decimals to a written method and explain reasoning used.
    • Solve real-world context problems involving decimals.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.6 Model multiplication with two digit whole numbers by one digit whole numbers with regrouping using strategies such as arrays, decomposition, and manipulatives.


    Mathematics (2019)
    Grade(s): 5
    All Resources: 12
    Learning Activities: 2
    Classroom Resources: 10
    8. Add, subtract, multiply, and divide decimals to hundredths using strategies based on place value, properties of operations, and/or the relationships between addition/subtraction and multiplication/division; relate the strategy to a written method, and explain the reasoning used.

    a. Use concrete models and drawings to solve problems with decimals to hundredths.

    b. Solve problems in a real-world context with decimals to hundredths.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use strategies based on place value, properties of operations, and relationship between addition and subtraction to find sums and differences of decimals.
    • Use strategies based on place value, properties of operations, and relationship between multiplication and division to find products and quotients of decimals.
    • Use models to justify the sum, difference, product or quotient of decimals.
    • Solve real-world problems with decimals to hundredths.
    Note: Products are limited to thousandths and quotients are either whole numbers or decimals terminating at the tenths or hundredths place.
    Teacher Vocabulary:
    • Decimal
    • Tenths
    • Hundredths
    • Place value
    Knowledge:
    Students know:
    • Strategies based on place value understanding, properties, and relationship between operations to find the sum, difference, product, and quotient of whole numbers.
    • How to write decimal notation for fractions with denominators of 10 or 100.
    • Use estimation strategies to assess reasonableness of answers.
    Skills:
    Students are able to:
    • Use concrete models, drawings, and strategies to add, subtract, multiply, and divide decimals.
    • Relate strategies for operations with decimals to a written method and explain reasoning used.
    • Solve real-world context problems involving decimals.
    Understanding:
    Students understand that:
    Problems involving operations with decimals
    • Can be solved using a variety of strategies based on place value, properties of operations, or the relationship between the operations.
    • Can be illustrated using concrete models or drawings.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.8.1: Use decimal notation for fractions with denominators 10 or 100.
    M.5.8.2: Multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations.
    M.5.8.3: Add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
    M.5.8.4: Apply properties of operations as strategies to multiply and divide.
    M.5.8.5: Identify that 100 can be thought of as a bundle of ten tens, called a "hundred".
    M.5.8.6: Identify that the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
    M.5.8.7: Recall basic addition, subtraction, multiplication, and division facts.

    Prior Knowledge Skills:
    • Use fraction equivalence to add and subtract fractions and mixed numbers with unlike denominators.
    • Find whole number quotients and remainders using a variety of strategies based on place value and properties of operations.
    • Illustrate and explain the calculation using equations, arrays, and area models.
    • Use concrete models, drawings, and strategies to add, subtract, multiply, and divide decimals.
    • Relate strategies for operations with decimals to a written method and explain reasoning used.
    • Solve real-world context problems involving decimals.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.8 Add decimals to tenths using concrete models, drawings, and manipulatives without regrouping.


    Operations with Numbers: Fractions
    Use equivalent fractions as a strategy to add and subtract fractions.
    Mathematics (2019)
    Grade(s): 5
    All Resources: 4
    Lesson Plans: 1
    Classroom Resources: 3
    9. Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.

    Example: Recognize an incorrect result 2/51/23/7 by observing that 3/7 < 1/2.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Model and solve real-world problems involving sums and differences of fractions (including mixed numbers) with unlike denominators.
    • Use visual models to illustrate the problem situation involving fractions.
    • Use fraction understanding and estimation strategies to assess the reasonableness of answers.
    Teacher Vocabulary:
    • Fraction
    • Benchmark fraction
    • Denominator
    • Fraction model
    • Estimate
    • Reasonableness
    • Equation
    • Unlike denominator
    • Unlike units
    Knowledge:
    Students know:
    • The meaning and magnitude of fractions expressed in units of halves, fourths, eighths, thirds, sixths, twelfths, fifths, tenths, and hundredths.
    • Strategies to find sums of two or more fractions with like denominators.
    • Strategies to find the difference of two fractions with like denominators.
    • How to decompose a fraction greater than 1 and express as a mixed number.
      Example: 7/3 = 3/3 + 3/3 + 1/3 = 2 1/3.
    Skills:
    Students are able to:
    • Solve real-word problems involving addition and subtraction of fractions with unlike denominators.
    • Represent problems using fraction models or equations.
    • Assess reasonableness of answers using estimation and benchmark fractions.
    Understanding:
    Students understand that:
    • solving word problems involving addition and subtraction of fractions with unlike units
    • Require strategies to find equivalent fractions in a common unit, and the sum or difference will be expressed in the common unit.
    • Can be assessed for reasonableness of answers using estimation strategies.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.9.1: Add and subtract mixed numbers with like denominators.
    M.5.9.2: Recognize that comparisons are valid only when the two fractions refer to the same whole.
    M.5.9.3: Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
    M.5.9.4: Recognize a fraction as a number on the number line; represent fractions on a number line diagram.
    M.5.9.5: Recognize key terms to solve word problems.
    M.5.9.6: Apply properties of operations for addition and subtraction.
    M.5.9.7: Recall basic addition and subtraction facts.

    Prior Knowledge Skills:
    • Use fraction equivalence to add and subtract fractions and mixed numbers with unlike denominators.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.9 Illustrate equivalent fractions using models of wholes, halves, thirds, and fourths to add fractions with like denominators.


    Mathematics (2019)
    Grade(s): 5
    All Resources: 6
    Learning Activities: 2
    Lesson Plans: 1
    Classroom Resources: 3
    10. Add and subtract fractions and mixed numbers with unlike denominators, using fraction equivalence to calculate a sum or difference of fractions or mixed numbers with like denominators.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use a variety of strategies and fraction equivalence to find sums and differences of fractions and mixed numbers with unlike denominators.
    Teacher Vocabulary:
    • Fraction
    • Denominator
    • Numerator
    • Visual Model
    • Sum
    • Difference
    • Equivalence
    • Unlike denominators
    • Unlike units
    Knowledge:
    Students know:
    • Strategies to determine if two given fractions are equivalent.
    • How to use a visual model to illustrate fraction equivalency.
    • Contextual situations for addition and subtraction.
    Skills:
    Students are able to:
    • Use fraction equivalence to add and subtract fractions and mixed numbers with unlike denominators.
    Understanding:
    Students understand that:
    Addition and subtraction of fractions and mixed numbers with unlike units,
    • Require strategies to find equivalent fractions in a common unit, and the sum or difference will be expressed in the common unit.
    • Can be assessed for reasonableness of answers using estimation strategies.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.10.1: Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
    M.5.10.2: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
    M.5.10.3: Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
    M.5.10.4: Recognize and generate simple equivalent fractions.
    M.5.10.5: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
    M.5.10.6: Compare two fractions with the same numerator or the same denominator by reasoning about their size.
    M.5.10.7: Recall basic addition, subtraction, multiplication, and division facts.

    Prior Knowledge Skills:
    • Use fraction equivalence to add and subtract fractions and mixed numbers with unlike denominators.
    Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
    Mathematics (2019)
    Grade(s): 5
    All Resources: 3
    Classroom Resources: 3
    11. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

    a. Model and interpret a fraction as division of the numerator by the denominator (a/b= a ÷ b)

    b. Use visual fraction models, drawings, or equations to represent word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Solve problems involving division of whole numbers leading to quotients of a fraction or mixed number.

    • Example: Given that 3 cookies are shared equally with 6 people, find what fraction of the cookies each person receives. Each person receives 3/6 of a cookie or 1/2 of a cookie.
      Example: Given that 3 cookies are shared equally with 2 people, find what fraction of the cookies each person receives. Each person receives 3/2 cookies or 1 1/2 cookies.
    • Model and interpret a fraction as division.
    • Use models, drawings, or equations to represent word problems.
    Teacher Vocabulary:
    • Fraction
    • Numerator
    • Denominator
    • Division
    • Remainder
    • Dividend
    • Divisor
    Knowledge:
    Students know:
    • Contextual situations for division.
    • Strategies to equipartition.
    Skills:
    Students are able to:
    • Solve word problems involving division of whole numbers leading to quotients with fractions.
    • Use fraction models, drawings, equations to represent word problems.
    • Model and interpret a fraction as division.
    Understanding:
    Students understand that:
    • a ÷ b is a division expression and can be written as a/b showing division of the numerator by the denominator (including cases where the value of a < b).
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.11.1: Define a mixed number.
    M.5.11.2: Generate equivalent fractions.
    M.5.11.3: Recognize a fraction as a number on the number line; represent fractions on a number line diagram.

    Prior Knowledge Skills:
    • Find products of a fraction times a whole number and products of a fraction times a fraction.
    • Use area models, linear models or set models to represent products.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.11 Using vocalization, sign language, augmentative communication or assistive technology, identify models of thirds (e.g., 1/3. 2/3, 3/3) and tenths (e.g., 1/10, 2/10, 3/10, 4/10, 5/10, 6/10, 7/10, 8/10, 9/10, 10/10).


    Mathematics (2019)
    Grade(s): 5
    All Resources: 3
    Learning Activities: 3
    12. Apply and extend previous understandings of multiplication to find the product of a fraction times a whole number or a fraction times a fraction.

    a. Use a visual fraction model (area model, set model, or linear model) to show (a/b) x q and create a story context for this equation to interpret the product as a parts of a partition of q into b equal parts.

    b. Use a visual fraction model (area model, set model, or linear model) to show (a/b) x (c/d) and create a story context for this equation to interpret the product.

    c. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

    d. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths to show that the area is the same as would be found by multiplying the side lengths.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a fraction times a whole number,
    • use visual models to illustrate the product to develop the procedure (a/b) × q.
    • Create a story context for the equation (a/b) × q.
    Given a fraction times a fraction,
    • Use visual models to illustrate the product to develop the procedure (a/b) × (c/d).
    • Create a story context for the equation (a/b) × (c/d).
    Given a rectangle with two fractional side lengths,
    • Use an area model to illustrate and find the rectangular area.
    • Find the area by tiling it with unit squares of the appropriate unit fraction.
    Given a rectangle with fractional side lengths including mixed numbers,
    • Use an area model to illustrate and find the rectangular area to lead to answers in the form of whole numbers or mixed numbers.

    • Example: Using an area model, a rectangle with dimensions of 1 1/2 x 1 2/3 will have partial products of 1, 1/2, 1/3, and 1/6 and the sum of the partial products will give an area of 2 sq units.
    • Use an area model to find the area of a rectangle by tiling the rectangle with unit squares.

    • Example: Using an area model, a rectangle with dimensions 1 1/2 x 1 1/3 will be tiled with unit squares of 1/6 size showing the tiled partial products as 6/6, 3/6, 2/6, and 1/6 for a total area of 12/6 sq units, so it would take 12 tiles of size 1/6 units to cover the area of the rectangle.
    Teacher Vocabulary:
    • Fraction
    • Fraction model
    • Whole number
    • Area
    • Area model
    • Linear model
    • Set model
    • Tiling
    • Unit squares
    • Equation
    Knowledge:
    Students know:
    • How to write an equation involving repeated addition with fractions as a multiplication equation of a whole number times the fraction.
      Example: 2/9 + 2/9 + 2/9 + 2/9 = 4 x 2/9 = 8/9.
    • The relationship of partial products to an area model when multiplying by two whole numbers.
    • Area of a rectangle is determined by multiplying side lengths and is found in square units.
    Skills:
    Students are able to:
    • Use previous understandings of multiplication to
    • Find products of a fraction times a whole number and products of a fraction times a fraction.
    • Use area models, linear models or set models to represent products.
    • Create a story context to represent equations (a/b) × q and (a/b) × (c/d) to interpret products.
    • Find area of rectangles with fractional side lengths and represent products as rectangular areas.
    • Find the area of a rectangle by tiling the area of a rectangle with unit squares.
    Understanding:
    Students understand that:
    • Any whole number can be written as a fraction.
    • The general rule for multiplication involving fractions can be justified through visual models.
    • A variety of contextual situations can be represented by multiplication involving fractions.
    • Tiling with unit squares can be used to find the area of a rectangle with fractional side lengths.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.12.1: Define proper fraction.
    M.5.12.2: Multiply fractions using denominators between 2 and 5.
    M.5.12.3: Identify proper and improper fractions.
    M.5.12.4: Recall basic multiplication facts.
    M.5.12.5: Model changing a whole number to a fraction.
    M.5.12.6: Partition a rectangle into rows and columns of same-size squares, and count to find the total number of them.
    M.5.12.7: Label the numerator and denominator of a fraction.
    M.5.12.8: Count the area squares for the length and width.
    M.5.12.9: Identify the width and length of a rectangle.

    Prior Knowledge Skills:
    • Solve real-word problems involving multiplication of fractions and mixed numbers.
    • Write equations to represent the word situation.
    • Use visual fraction models to represent the problem.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.12 Determine the product of unit fractions with unlike denominators (limited to denominators of 2, 3, 4, 10) using visual models.


    Mathematics (2019)
    Grade(s): 5
    All Resources: 0
    13. Interpret multiplication as scaling (resizing).

    a. Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

    Example: Use reasoning to determine which expression is greater? 225 or 3/4 × 225; 11/50 or 3/2 × 11/50

    b. Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and relate the principle of fraction equivalence.

    c. Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number and relate the principle of fraction equivalence.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Reason about the impact of scaling one or both factors on the size of the product before multiplying and justify their thinking.

    • Example: Which is greater? 3/5 x 13 or 13 x 3/4? 13 x 3/4 is greater than 3/5 x 13 because both expressions contain a factor of 13, but the scale factor of 3/4 will result in a greater product than a scale factor of 3/5 because 3/4 > 3/5.
    • Explain the size of the product when multiplying a number by a fraction greater than 1 and when multiplying a number by a fraction less than 1.
    Teacher Vocabulary:
    • Resizing
    • Scaling
    • Product
    • Factor
    Knowledge:
    Students know:
    • How to interpret multiplicative comparisons.
    • Strategies to compare products with whole numbers using reasoning and justification.
      Example: Which is greater? 5 x 2 x 13 or 13 x 9? 10 x 13 is greater than 9 x 13 because both expressions contain a factor of 13, but the scale factor of 10 will result in a greater product than a scale factor of 9.
    • Fraction meaning and magnitude of fractions less than and greater than 1.
    Skills:
    Students are able to:
    • Interpret multiplication as scaling.
    • Use reasoning to compare products of multiplication expressions.
    • Reason and explain when multiplying a given number by a fraction why the product will be greater than or less than the original number.
    Understanding:
    Students understand that:
    • a product reflects the size of its factors.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.13.1: Define scaling.
    M.5.13.2: Define principle of fraction equivalence.
    M.5.13.3: Multiply a fraction by a whole number.
    M.5.13.4: Compare two fractions with the same numerator or the same denominator by reasoning about their size.
    M.5.13.5: Recognize that comparisons are valid only when the two fractions refer to the same whole.
    M.5.13.6: Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
    M.5.13.7: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
    M.5.13.8: Identify factor and product.
    M.5.13.9: Use comparison symbols.
    Examples: >, =, or <.

    Prior Knowledge Skills:
    • Interpret multiplication as scaling.
    • Use reasoning to compare products of multiplication expressions.
    • Reason and explain when multiplying a given number by a fraction why the product will be greater than or less than the original number.
    Mathematics (2019)
    Grade(s): 5
    All Resources: 2
    Learning Activities: 1
    Classroom Resources: 1
    14. Model and solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models, drawings, or equations to represent the problem.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use a variety of strategies, including models, pictures, tables, and patterns to solve problems that provide a context for multiplying fractions and mixed numbers.
    Teacher Vocabulary:
    • Fraction
    • Models
    • Mixed number
    • Multiplication
    Knowledge:
    Students know:
    • Contextual situations for multiplication.
    • How to use an area model to illustrate the product of two whole numbers and its relationship to partial products and extend this knowledge to illustrate products involving fractions and mixed numbers.
    Skills:
    Students are able to:
    • Solve real-word problems involving multiplication of fractions and mixed numbers.
    • Write equations to represent the word situation.
    • Use visual fraction models to represent the problem.
    Understanding:
    Students understand that:
    • A variety of strategies are used to model and solve problems that provide a context for multiplying fractions and mixed numbers.
    • Solutions are interpreted based on the meaning of the quantities and the context of the problem situation.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.14.1: Define improper fraction, mixed number, fraction, equations, numerator, denominator.
    M.5.14.2: Multiply proper fractions with common denominators 2-10.
    M.5.14.3: Solve problems using whole numbers.
    M.5.14.4: Write number sentences for word problems.
    M.5.14.5: Identify key terms to solve multiplication word problems.
    Examples: times, every, at this rate, each, per, equal/equally, in all, total.
    M.5.14.6: Recall basic multiplication facts.

    Prior Knowledge Skills:
    • Divide unit fractions by a whole number and whole numbers by unit fractions.
    • Use visual models to illustrate quotients.
    • Create story contexts for division.
    • Use relationship between multiplication and division to explain quotients.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.14 Use a model to solve multiplying a whole number by a unit fraction of 1/2, 1/3, and 1/4.


    Mathematics (2019)
    Grade(s): 5
    All Resources: 3
    Learning Activities: 2
    Classroom Resources: 1
    15. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

    a. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions and illustrate using visual fraction models, drawings, and equations to represent the problem.

    b. Create a story context for a unit fraction divided by a whole number, and use a visual fraction model to show the quotient.

    c. Create a story context for a whole number divided by a unit fraction, and use a visual fraction model to show the quotient.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Solve real-world problems involving division of a unit fraction by a non-zero whole number, or division of a whole number by a unit fraction.
    • Justify solutions using visual models, drawings, and equations to represent the problem context.
    • Explain quotients using the relationship between multiplication and division.
    • Create a story context for a unit fraction divided by a whole number and use models to illustrate the quotient.
    • Create a story context for a whole number divided by a unit fraction and use models to illustrate the quotient.
    Teacher Vocabulary:
    • Unit fraction
    • Whole number
    • Division
    • Dividend
    • Divisor
    • Quotient
    • Equation
    • Multiplication
    • Factor
    • Fraction models
    Knowledge:
    Students know:
    • Contextual situations involving division with whole numbers and unit fractions.
    • Strategies for representing a division problem with a visual model.
    Skills:
    Students are able to:
    • Use previous understandings of operations to
    • Divide unit fractions by a whole number and whole numbers by unit fractions.
    • Use visual models to illustrate quotients.
    • Create story contexts for division.
    • Use the relationship between multiplication and division to explain quotients.
    Understanding:
    Students understand that:
    • A variety of contextual situations are represented with division of a whole number by a fraction or a fraction by a whole number.
    • Quotients resulting from division of a whole number by a fraction or a fraction by a whole number can be illustrated and justified with a visual model.
    • The relationship between multiplication and division can be used to justify quotients resulting from division of a whole number by a fraction or a fraction by a whole number.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.15.1: Define quotient.
    M.5.15.2: Multiply a fraction by a whole number.
    M.5.15.3: Recognize key terms to solve word problems.
    Examples: times, every, at this rate, each, per, equal/equally, in all, total.
    M.5.15.4: Recall basic multiplication and division facts.
    M.5.15.5: Express whole numbers as fractions.
    M.5.15.6: Recognize fractions that are equivalent to whole numbers.
    M.5.15.7: Recall basic multiplication and division facts.
    M.5.15.8: Solve word problems involving multiplication of a fraction by a whole number.
    M.5.15.9: Recognize key terms to solve word problems.
    M.5.15.10: Recall basic multiplication and division facts.

    Prior Knowledge Skills:
    • Find products of a fraction times a whole number and products of a fraction times a fraction.
    • Use area models, linear models or set models to represent products.
    • Create a story context to represent equations (a/b) × q and (a/b) × (c/d) to interpret products.
    • Find area of rectangles with fractional side lengths and represent products as rectangular areas.
    • Find the area of a rectangle by tiling the area of a rectangle with unit squares.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.15 Use a model to solve dividing a whole number by a unit fraction of 1/2.


    Data Analysis
    Represent and interpret data.
    Mathematics (2019)
    Grade(s): 5
    All Resources: 1
    Classroom Resources: 1
    16. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).

    a. Add, subtract, multiply, and divide fractions to solve problems involving information presented in line plots.

    Note: Division is limited to unit fractions by whole numbers and whole numbers by unit fractions.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Produce a data set by measuring objects to the nearest one-eighth unit and
    • Construct a line plot to display, analyze, and interpret data set.
    • Use the four operations to solve problems involving the data set presented in the line plot.
    • Use the data set to create problems (involving the four operations) and solve them.
    Note: Division is limited to unit fractions by whole numbers and whole numbers by a unit fractions.
    Teacher Vocabulary:
    • Line plot
    • Data
    • Data set
    • Frequency
    • Fraction
    • Operations
    • Number line
    • Fraction intervals
    Knowledge:
    Students know:
    • Strategies to equipartition a length model.
    • Measurement in units of halves, fourths, and eighths using a tool for standard units of measure.
    • Strategies to solve problems using the four operations with fractions.
    Skills:
    Students are able to:
    • Create a line plot with appropriate intervals.
    • Represent data on a line plot.
    • Apply strategies for solving problems involving all four operations with the fractional data.
    Understanding:
    Students understand that:
    • mathematical data can be collected, analyzed, and organized in a data display to solve problems involving the data.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.16.1: Make a line plot to display a data set of measurements in fractions of a unit.
    M.5.16.2: Solve problems involving addition and subtraction of fractions by using information presented in line plots.
    M.5.16.3: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.
    M.5.16.4: Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.
    M.5.16.5: Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories.
    M.5.16.6: Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

    Prior Knowledge Skills:
    • Recall the meaning of a fraction as part of a whole.
    • Identify the location of a fraction on a number line.
    • Compare fractions by finding common denominators
    • Find an unkinown value to complete a number sentence.
    • Read a line plot and bar graph.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.16 Using vocalization, sign language, augmentative communication or assistive technology, represent and interpret data on a picture, bar graph, or line plot when given a model or a graph.


    Measurement
    Convert like measurement units within a given measurement system.
    Mathematics (2019)
    Grade(s): 5
    All Resources: 6
    Learning Activities: 2
    Classroom Resources: 4
    17. Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Convert different-sized measurement units within the same system.
    • Solve multi-step word problems involving conversion of metric or customary units.
    Teacher Vocabulary:
    • Measurement system
    • US Customary
    • Metric
    • Unit
    • Conversion
    • Equivalent measurements
    Knowledge:
    Students know:
    • Strategies for converting a larger unit of measure to a smaller unit in the same system.
    • Relative size of customary and metric units of measure.
    • Strategies for converting between units of measure in the same system.
    Skills:
    Students are able to:
    • Convert measurement units.
    • Solve multi-step word problems involving measurement conversions.
    Understanding:
    Students understand that:
    • the multiplicative relationship between units of measures given in the same measurement system is essential when converting units to a larger or smaller unit.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.17.1: Identify relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec.
    M.5.17.2: Express measurements in a larger unit in terms of a smaller unit.
    M.5.17.3: Solve two-step word problems.
    M.5.17.4: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).
    M.5.17.5: Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
    M.5.17.6: Recall basic addition, subtraction, multiplication, and division facts.

    Prior Knowledge Skills:
    • Create a line plot with appropriate intervals.
    • Represent data on a line plot.
    • Apply strategies for solving problems involving all four operations with the fractional data.
    • Convert measurement units.
    • Solve mulit-step word problems involving measurement conversions.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.17 Using vocalization, sign language, augmentative communication, or assistive technology, to tell time using an analog or digital clock to the half or quarter hour.
    M.AAS.5.17a Use standard units to measure the weight and length of objects.
    M.AAS.5.17b Sort a collection of coin according to their value.


    Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
    Mathematics (2019)
    Grade(s): 5
    All Resources: 0
    18. Identify volume as an attribute of solid figures, and measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised (non-standard) units.

    a. Pack a solid figure without gaps or overlaps using n unit cubes to demonstrate volume as n cubic units.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Measure volume of rectangular solids by packing the figure and counting the number of same-sized unit cubes needed to completely fill the figure.
    Teacher Vocabulary:
    • Volume
    • Cube
    • Cubic unit
    • Unit cube
    • Space
    • Three-dimensional
    • Attribute
    Knowledge:
    Students know:
    • strategies or the formula to find the area of a rectangle.
    Skills:
    Students are able to:
    • Count unit cubes to find volume.
    • Demonstrate volume by packing a solid figure with unit cubes.
    Understanding:
    Students understand that:
    • volume represents the amount of space enclosed in a three-dimensional figure and is measured by the number of same-size cubes that exactly fill the interior space of the object.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.18.1: Define volume including the formulas V = L × W x h, and V = B x h.
    M.5.18.2: Define solid figures.
    M.5.18.3: Define unit cube.
    M.5.18.4: Recognize that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
    M.5.18.5: Describe attributes of three-dimensional figures.
    M.5.18.6: Describe attributes of two-dimensional figures.
    M.5.18.7: Compare the unit size of volume/capacity in the metric system including milliliters and liters.
    M.5.18.8: Define cubic inches, cubic centimeters, and cubic feet.
    M.5.18.9: Compare the unit size of volume/capacity in the customary system including fluid ounces, cups, pints, quarts, gallons.
    M.5.18.10: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
    M.5.18.11: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).
    M.5.18.12: Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
    M.5.18.13: Recall basic multiplication facts.
    M.5.18.14: Fluently add.

    Prior Knowledge Skills:
    • Count unit cubes to find volume.
    • Demonstrate volume by packing a solid figure with unit cubes.
    • Solve word problems involving volume.
    • Use associative property of multiplication to find volume.
    • Relate operations of multiplication and addition to finding volume.
    • Apply formulas to find volume of right rectangular prisms.
    • Find volume of solid figures composed of two rectangular prisms.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.18 Using vocalization, sign language, augmentative communication, or assistive technology, identify cubes, cylinders, and spheres as three-dimensional shapes.


    Mathematics (2019)
    Grade(s): 5
    All Resources: 2
    Lesson Plans: 1
    Classroom Resources: 1
    19. Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume.

    a. Use the associative property of multiplication to find the volume of a right rectangular prism and relate it to packing the prism with unit cubes. Show that the volume can be determined by multiplying the three edge lengths or by multiplying the height by the area of the base.

    b. Apply the formulas V = l x w x h and V = B x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems.

    c. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the two parts, applying this technique to solve real-world problems.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given right rectangular prisms with whole number edge lengths,
    • Use associative property of multiplication to find volume and relate it to packing a solid with unit cubes.
    • Apply formula V = l × w × h, where V represents volume and l, w, and h represent the three dimensions of the prism (length, width, height) and relate the formula to a unit cube filled model.
    • Apply formula V = B × h, where V represents volume, B is the base-area, and h represents the height (number of layers of the base-area) and relate the formula to a unit cube filled model.

    • Given a solid figure composed of two or more right rectangular prisms in real world or mathematical contexts, find the total volume by decomposing the figure into non-overlapping rectangular prisms and find the sum of the volumes.
    Teacher Vocabulary:
    • Volume
    • Unit cube
    • Rectangular prism
    • Base
    • Base-area
    • Dimensions
    • Face
    • Length
    • Width
    • Height
    • Layers
    • Edge
    • Equivalent
    • Conservation of volume
    • Attribute
    • Composition
    • Decomposition
    • Formula
    Knowledge:
    Students know:
    • Measurable attributes of area and how it relates to finding the volume of objects.
    • Units of measurement for volume, specifically unit cubes.
    Skills:
    Students are able to:
    • Solve word problems involving volume.
    • Use associative property of multiplication to find volume.
    • Relate operations of multiplication and addition to finding volume.
    • Apply formulas to find volume of right rectangular prisms.
    • Find volume of solid figures composed of two rectangular prisms.
    Understanding:
    Students understand that:
    • Volume is a derived attribute based on a length unit and can be computed as the product of three length measurements or as the product of one base area and one length measurement.
    • Volume is an extension of area and can be found as the area of the base being repeated for a given number of layers.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.19.1: Define volume.
    M.5.19.2: Recognize angle measure as additive.
    M.5.19.3: Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.
    M.5.19.4: Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
    M.5.19.5: Recognize the formula for volume.
    M.5.19.6: Recall the attributes of three-dimensional solids.
    M.5.19.7: Recall basic multiplication facts.
    M.5.19.8: Fluently add.
    M.5.19.9: Compare the unit size of volume/capacity in the metric system including milliliters and liters.
    M.5.19.10: Measure and estimate liquid volumes.
    M.5.19.11: Recall basic multiplication facts.
    M.5.19.12: Compare the unit size of volume/capacity in the metric system including milliliters and liters.
    M.5.19.13: Recognize the formula for volume.
    M.5.19.14: Recall basic multiplication facts.
    M.5.19.15: Describe attributes of three-dimensional figures.
    M.5.19.16: Describe attributes of two-dimensional figures.
    M.5.19.17: Identify solid figures.

    Prior Knowledge Skills:
    • Count unit cubes to find volume.
    • Demonstrate volume by packing a solid figure with unit cubes.
    • Convert measurement units.
    • Solve mulit-step word problems involving measurement conversions.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.19 Determine the volume of a rectangular prism by counting units of measurement (e.g., unit cubes).


    Geometry
    Graph points on the coordinate plane to solve real-world and mathematical problems.
    Mathematics (2019)
    Grade(s): 5
    All Resources: 5
    Learning Activities: 1
    Lesson Plans: 1
    Classroom Resources: 3
    20. Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points to represent real-world and mathematical problems.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use the first quadrant in a coordinate plane to identify coordinates of a given point.
    • Use the first quadrant in a coordinate plane to explain how the location of an ordered pair is determined.
    • Given a real-world situation involving a relationship between two variables, graph a representation of the situation and interpret coordinate values of the points in the context of the problem.
    • Given a graph representing a real-world situation, interpret the coordinate values of the points in the context of the situation.
    Teacher Vocabulary:
    • Coordinate system
    • Coordinate plane
    • First quadrant
    • Points
    • Lines
    • Perpendicular
    • X-axis
    • Y-axis
    • Origin
    • Ordered pair
    • Coordinate plane
    • Horizontal
    • Vertical
    • Intersection of lines
    Knowledge:
    Students know:
    • Specific directions and vocabulary to explain ordered pair location.
    • The first number of an ordered pair indicates how far to travel from the origin in the direction of one axis and the second number indicates how far to travel in the direction of the second axis.
    Skills:
    Students are able to:
    • Graph points in the first quadrant.
    • Interpret coordinate values in context of the problem.
    Understanding:
    Students understand that:
    • graphing points on a coordinate plane provides a representation of a mathematical context which aids in visualizing situations and solving problems.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.20.1: Define ordered pair of numbers, quadrant one, coordinate plane, and plot points.
    M.5.20.2: Label the horizontal axis (x).
    M.5.20.3: Label the vertical axis (y).
    M.5.20.4: Identify the x- and y- values in ordered pairs.
    M.5.20.5: Model writing ordered pairs.

    Prior Knowledge Skills:
    • Graph points in the first quadrant.
    • Interpret coordinate values in context of the problem.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.20 Identify a point on a horizontal number line representing the horizontal x-axis (no greater than 5) and identify a point on a vertical number line representing the y-axis (no greater than 5).


    Classify two-dimensional figures into categories based on their properties.
    Mathematics (2019)
    Grade(s): 5
    All Resources: 1
    Learning Activities: 1
    21. Classify triangles according to side length (isosceles, equilateral, scalene) and angle measure (acute, obtuse, right, equiangular).
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given a variety of triangles,
    • Measure sides and angles to classify triangles based on side length and angle measure.
    Teacher Vocabulary:
    • Classify
    • Polygon
    • Side measure
    • Angle measure
    • Isosceles
    • Equilateral
    • Scalene
    • Acute
    • Obtuse
    • Right
    • Equiangular
    Knowledge:
    Students know:
    • Measurable attributes of triangles include length of side and angle measures.
    • Appropriate tools and units of measure for length of side and angle measures.
    Skills:
    Students are able to:
    • Classify triangles according to side measures and angle measures.
    Understanding:
    Students understand that:
    • triangles can be described and classified by their properties of side length, angle size, or cross-classify to include both side length and angle size.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.21.1: Define isosceles, equilateral, scalene, right and equiangular triangles; obtuse, acute, and right angle; vertex/vertices.
    M.5.21.2: Identify a right triangle.
    M.5.21.3: Sort and categorize shapes.
    M.5.21.4: Recognize and draw shapes having specified attributes.

    Prior Knowledge Skills:
    • Recall the vocabulary of shapes (labels, sides, faces, vertices, etc.).
    • Recognize and draw shapes having specified attributes such as a given number of angles.
    • Build and draw shapes to possess defining attributes.
    • Sort shapes into categories.
    • Define side, angle, face, closed, and open.
    • Use vocabulary related to shape attributes.
      Examples: sides, angles, face, closed, open.
    • Trace shapes.
    • Sort triangles, quadrilaterals, pentagons, hexagons, and cubes.
    • Explore triangles, quadrilaterals, pentagons, hexagons, and cubes.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.20 Identify a point on a horizontal number line representing the horizontal x-axis (no greater than 5) and identify a point on a vertical number line representing the y-axis (no greater than 5).


    Mathematics (2019)
    Grade(s): 5
    All Resources: 1
    Learning Activities: 1
    22. Classify quadrilaterals in a hierarchy based on properties.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    When given variety of two-dimensional figures,
    • Use attributes of shapes to explain their classification in as many categories and subcategories as possible.
    • Distinguish properties that are more general from those that are more specific and make connections between and within categories of figures.

    • Example: A quadrilateral is a figure with a general property of 4-sides, while a parallelogram is a specific type of quadrilateral with two pairs of opposite sides which are both parallel and congruent. Based on this hierarchy, all parallelograms are quadrilaterals, but not all quadrilaterals are parallelograms.
    Teacher Vocabulary:
    • Quadrilateral
    • Hierarchy
    • Two-dimensional
    • Properties
    • Attributes
    • Polygon
    • Rectangle
    • Rhombus
    • Square
    • Trapezoid
    • Parallelogram
    Knowledge:
    Students know:
    • properties or attributes of two-dimensional shapes.
    Skills:
    Students are able to:
    • Classify quadrilaterals based on properties.
    Understanding:
    Students understand that:
    • Quadrilaterals can be identified by general properties to more specific properties.
    • Properties belonging to a category of two-dimensional figures also belong to all subcategories of that category.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.22.1: Define vertex/vertices and angle.
    M.5.22.2: Identify that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
    M.5.22.3: Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces.
    M.5.22.4: Identify triangles, quadrilaterals, pentagons, hexagons, heptagons, and octagons based on the number of sides, angles, and vertices.

    Prior Knowledge Skills:
    • Classify triangles according to side measures and angle measures.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.5.20 Identify a point on a horizontal number line representing the horizontal x-axis (no greater than 5) and identify a point on a vertical number line representing the y-axis (no greater than 5).


    Mathematics (2019)
    Grade(s): 5
    All Resources: 0
    23. Explain that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

    Example: All rectangles have four right angles, and squares have four right angles, so squares are rectangles.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a variety of two-dimensional figures,
    • Use attributes to classify a shape into categories and subcategories.
    • Use mathematical vocabulary to explain that attributes belonging to one category are also attributes of the subcategory.
    Teacher Vocabulary:
    • Attribute
    • Category
    • Subset
    • Subcategory
    • Two-dimensional
    • Figure
    • Quadrilateral
    • Right angle
    • Parallel
    • Perpendicular
    Knowledge:
    Students know:
    • vocabulary associated with the properties of shapes.
    Skills:
    Students are able to:
    • Explain the relationship between shapes in categories and subcategories.
    Understanding:
    Students understand that:
    • Quadrilaterals can be identified by general properties to more specific properties.
    • Properties belonging to a category of two-dimensional figures also belong to all subcategories of that category.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.5.23.1: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
    M.5.23.2: Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
    M.5.23.3: Recognize attributes of shapes.
    M.5.23.4: Recall the vocabulary of shapes (labels, sides, faces, vertices, etc.).
    M.5.23.5: Sort shapes into categories.

    Prior Knowledge Skills:
    • Classify triangles according to side measures and angle measures.
    • Classify quadrilaterals based on properties.
    • Explain the relationship between shapes in categories and subcategories.
    Proportional Reasoning
    Develop an understanding of ratio concepts and use reasoning about ratios to solve problems.
    Mathematics (2019)
    Grade(s): 6
    All Resources: 8
    Learning Activities: 1
    Lesson Plans: 3
    Classroom Resources: 4
    1. Use appropriate notations [a/b, a to b, a:b] to represent a proportional relationship between quantities and use ratio language to describe the relationship between quantities.
    Unpacked Content
    Evidence Of Student Attainment:
    Students: Given contextual or mathematical situations involving multiplicative comparisons.
    • Communicate the relationship of two or more quantities using ratio language.
    Teacher Vocabulary:
    • Ratio
    • Ratio Language
    • Part-to-Part
    • Part-to-Whole
    • Attributes
    • Quantity
    • Measures
    • Fraction
    Knowledge:
    Students know:
    • Characteristics of additive situations.
    • Characteristics of multiplicative situations
    Skills:
    Students are able to:
    • Compare and contrast additive vs. multiplicative contextual situations.
    • Identify all ratios and describe them using "For every…, there are…"
    • Identify a ratio as a part-to-part or a part-to whole comparison.
    • Represent multiplicative comparisons in ratio notation and language (e.g., using words such as "out of" or "to" before using the symbolic notation of the colon and then the fraction bar. for example, 3 out of 7, 3 to 5, 6:7 and then 4/5).
    Understanding:
    Students understand that:
    • In a multiplicative comparison situation one quantity changes at a constant rate with respect to a second related quantity. -Each ratio when expressed in forms: ie 10/5, 10:5 and/or 10 to 5 can be simplified to equivalent ratios, -Explain the relationships and differences between fractions and ratios.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.1.1: Define quantity, fraction, and ratio.
    M.6.1.2: Identify the units or quantities being compared.
    Example: Read 2/3 as 2 out of 3.
    M.6.1.3: Write a ratio in appropriate notation;[a/b, a to b, a:b].
    M.6.1.4: Draw a model of a given ratio or fraction.
    M.6.1.5: Identify the numerator and denominator of a fraction.

    Prior Knowledge Skills:
    • Compare two fractions with the same numerator or the same denominator by reasoning about their size.
    • Addition and subtraction of fractions as joining and separating parts referring to the same whole.
    • Label numerator, denominator, and fraction bar.
    • Recognize fraction 1 as the quantity formed by 1 part when a whole is partitioned into b equal parts.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.1 Demonstrate a simple ratio relationship using ratio notation given a real-world problem.


    Mathematics (2019)
    Grade(s): 6
    All Resources: 8
    Learning Activities: 2
    Lesson Plans: 1
    Classroom Resources: 5
    2. Use unit rates to represent and describe ratio relationships.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given contextual or mathematical situations involving multiplicative comparisons,
    • Use unit rate to solve missing value problems (e.g., cost per item or distance per time unit).
    • Use rate language to explain the relationships between ratio of two quantities as non-complex fractions and the associated unit rate of one of the quantities in terms of the other.
    Teacher Vocabulary:
    • Unit rate
    • Ratio
    • Rate language
    • Per
    • Quantity
    • Measures
    • Attributes
    Knowledge:
    Students know:
    • Characteristics of multiplicative comparison situations.
    • Rate and ratio language.
    • Techniques for determining unit rates.
    • To use reasoning to find unit rates instead of a rule or using algorithms such as cross-products.
    Skills:
    Students are able to:
    • Explain relationships between ratios and the related unit rates.
    • Use unit rates to name the amount of either quantity in terms of the other quantity flexibly.
    • Represent contextual relationships as ratios.
    Understanding:
    Students understand that:
    • A unit rate is a ratio (a:b) of two measurements in which b is one.
    • A unit rate expresses a ratio as part-to-one or one unit of another quantity.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.2.1: Define unit rate, proportion, and rate.
    M.6.2.2: Create a ratio or proportion from a given word problem.
    M.6.2.3: Calculate unit rate by using ratios or proportions.
    M.6.2.4: Write a ratio as a fraction.

    Prior Knowledge Skills:
    • Recall basic multiplication facts.
    • Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.
    • Recognize key terms to solve word problems.
      Examples: times, every, at this rate, each, per, equal/equally, in all, total.
    • Recognize a fraction as a number on the number line.
    • Label numerator, denominator, and fraction bar.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.1 Demonstrate a simple ratio relationship using ratio notation given a real-world problem.


    Mathematics (2019)
    Grade(s): 6
    All Resources: 8
    Learning Activities: 1
    Lesson Plans: 3
    Classroom Resources: 4
    3. Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given contextual or mathematical situations involving ratio and rate (including those involving unit pricing, constant speed, and measurement conversions),
    • Represent the situations using a variety of strategies (tables of equivalent ratios, changing to unit rate, tape diagrams, double number line diagrams, equations, and plots on coordinate planes) in order to solve problems, find missing values on tables and interpret relationships and results.
    • Change given rates to unit rates in order to find and justify solutions to problems.
    Given contextual or mathematical situations involving percents,
    • Understand the relationship between ratios, fractions, decimals and percents.
    • Interpret the percent as rate per 100.
    • Solve problems and justify solutions when finding the whole, given a part and the percent.
    • Solve problems and justify solutions when finding the part, given the whole and the percent.
    • Solve problems and justify solutions when finding percent, given the whole and the part.
    Teacher Vocabulary:
    • Rate
    • Ratio
    • Rate reasoning
    • Ratio reasoning
    • Transform units
    • Quantities
    • Ratio Tables
    • Double Number Line Diagram
    • Percents
    • Coordinate Plane
    • Ordered Pairs
    • Quadrant I
    • Tape Diagrams
    • Unit Rate
    • Constant Speed
    Knowledge:
    Students know:
    • Strategies for representing contexts involving rates and ratios including. tables of equivalent ratios, changing to unit rate, tape diagrams, double number lines, equations, and plots on coordinate planes.
    • Strategies for finding equivalent ratios,
    • Strategies for using ratio reasoning to convert measurement units.
    • Strategies to recognize that a conversion factor is a fraction equal to 1 since the quantity described in the numerator and denominator is the same.
    • Strategies for converting between fractions, decimals and percents.
    • Strategies for finding the whole when given the part and percent in a mathematical and contextual situation.
    • Strategies for finding the part, given the whole and the percent in mathematical and contextual situation.
    • Strategies for finding the percent, given the whole and the part in mathematical and contextual situation.
    Skills:
    Students are able to:
    • Represent ratio and rate situations using a variety of strategies (e.g., tables of equivalent ratios, changing to unit rate, tape diagrams, double number line diagrams, equations, and plots on coordinate planes).
    • Use ratio, rates, and multiplicative reasoning to explain connections among representations and justify solutions in various contexts, including measurement, prices and geometry.
    • Understand the multiplicative relationship between ratio comparisons in a table by writing an equation.
    • Plot ratios as ordered pairs.
    • Solve and justify solutions for rate problems including unit pricing, constant speed, measurement conversions, and situations involving percents.
    • Solve problems and justify solutions when finding the whole given a part and the percent.
    • Model using an equivalent fraction and decimal to percents.
    • Use ratio reasoning, multiplication, and division to transform and interpret measurements.
    Understanding:
    Students understand that:
    • A unit rate is a ratio (a:b) of two measurements in which b is one.
    • A symbolic representation of relevant features of a real world problem can provide for resolution of the problem and interpretation of the situation.
    • When computing with quantities the transformation and interpretation of the resulting unit is dependent on the particular operation performed.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.3.1: Define ratio, rate, proportion, percent, equivalent, input, output, ordered pairs, diagram, unit rate, and table.
    M.6.3.2: Create a ratio or proportion from a given word problem, diagram, table, or equation.
    M.6.3.3: Calculate unit rate or rate by using ratios or proportions with or without a calculator.
    M.6.3.4: Restate real world problems or mathematical problems.
    M.6.3.5: Construct a graph from a set of ordered pairs given in the table of equivalent ratios.
    M.6.3.6: Calculate missing input and/or output values in a table with or without a calculator.
    M.6.3.7: Draw and label a table of equivalent ratios from given information.
    M.6.3.8: Identify the parts of a table of equivalent ratios (input, output, etc.).
    M.6.3.9: Compute the unit rate, unit price, and constant speed with or without a calculator.
    M.6.3.10: Create a proportion or ratio from a given word problem.
    M.6.3.11: Identify the two units being compared.
    M.6.3.12: Define percent.
    M.6.3.13: Calculate a proportion for missing information with or without a calculator.
    M.6.3.14: Identify a proportion from given information.
    M.6.3.15: Solve a proportion using part over whole equals percent over 100 with or without a calculator.
    M.6.3.16: Form a ratio.
    M.6.3.17: Convert like measurement units within a given system with or without a calculator. (Example: 120 min = 2 hrs).
    M.6.3.18: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec.

    Prior Knowledge Skills:
    • Recognize arithmetic patterns (including geometric patterns or patterns in the addition table or multiplication table).
      Examples: Continued Geometric Pattern by drawing the next three shapes.
    • Complete the numerical pattern for the following chart when given the rule, "Input + 5 = Output".
    • Recognize that comparisons are valid only when the two fractions refer to the same whole.
    • Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.
    • Recognize key terms to solve word problems.
      Examples: times, every, at this rate, each, per, equal/equally, in all, total.
    • Recall basic multiplication facts.
    • Recognize equivalent forms of fractions and decimals.
    • Recognize a fraction as a number on the number line.
    • Label numerator, denominator, and fraction bar.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.1 Demonstrate a simple ratio relationship using ratio notation given a real-world problem.


    Number Systems and Operations
    Use prior knowledge of multiplication and division to divide fractions.
    Mathematics (2019)
    Grade(s): 6
    All Resources: 1
    Classroom Resources: 1
    4. Interpret and compute quotients of fractions using visual models and equations to represent problems.

    a. Use quotients of fractions to analyze and solve problems.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a division problem involving a fraction divided by a fraction,
    • Create an appropriate story context.
    • Solve the problem using visual fraction models and an equation.
    • Explain the relationship between the model and the problem.
    • Interpret the solution.
    • Use the inverse relationship between multiplication and division, or concept of division as repeated subtraction, to explain and justify the solution.
    Teacher Vocabulary:
    • Visual fraction models
    • Dividend
    • Divisor
    • Quotient
    • Equation
    • Numerator
    • Denominator
    • Mixed number
    • Improper fraction
    Knowledge:
    Students know:
    • Strategies for representing fractions and operations on fractions using visual models,
    • The inverse relationship between multiplication and division (a ÷ b = c implies that a = b x c).
    • Strategies to solve mathematical and conceptual problems involving quotients of fractions.
    Skills:
    Students are able to:
    • Represent fractions and operations on fractions using visual models.
    • Interpret quotients resulting from the division of a fraction by a fraction.
    • Accurately determine quotients of fractions by fractions using visual models/equations.
    • Justify solutions to division problems involving fractions using the inverse relationship between multiplication and division.
    Understanding:
    Students understand that:
    • The operation of division is interpreted the same with fractions as with whole numbers.
    • The inverse relationship between the operations of multiplication and division that was true for whole numbers continues to be true for fractions.
    • The relationships between operations can be used to solve problems and justify solutions and solution paths.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.4.1: Define fraction (including numerator and denominator), reciprocal, equation, and quotient.
    M.6.4.2: Construct an equation from a given word problem.
    M.6.4.3: Discuss the process of multiplying by the reciprocal.
    M.6.4.4: Interpret division of fractions by multiplying by the reciprocal.
    M.6.4.5: Demonstrate division of fractions using a visual fraction model.
    M.6.4.6: Demonstrate multiplication of fractions using a visual fraction model.

    Prior Knowledge Skills:
    • Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
    • Write number sentences for word problems.
    • Identify key terms to solve multiplication word problems.
      Examples: times, every, at this rate, each, per, equal/equally, in all, total.
    • Recall basic multiplication facts.
    • Recognize key terms to solve word problems.
      Examples: times, every, at this rate, each, per, equal/equally, in all, total.
    • Label numerator, denominator, and fraction bar.
    • Recognize a fraction as a number on the number line.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.4 Use models to divide fractions (limit to unit fractions).


    Compute multi-digit numbers fluently and determine common factors and multiples.
    Mathematics (2019)
    Grade(s): 6
    All Resources: 1
    Classroom Resources: 1
    5. Fluently divide multi-digit whole numbers using a standard algorithm to solve real-world and mathematical problems.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a context which calls for the division of two whole numbers,
    • Choose the most appropriate strategy for computing the answer.
    • Produce accurate results using a standard algorithm when appropriate.
    Teacher Vocabulary:
    • Standard algorithm
    • Dividend
    • Divisor
    • Quotient
    Knowledge:
    Students know:
    • strategies for computing answers to division mathematical and real-world problems using the standard division algorithm.
    Skills:
    Students are able to:
    • Strategically choose and apply appropriate strategies for dividing.
    • Accurately find quotients using the standard division algorithm.
    Understanding:
    Students understand that:
    • Mathematical problems can be solved using a variety of strategies, models, and representations.
    • Efficient application of computation strategies is based on the numbers and operations in the problems,
    • The steps used in the standard algorithms for division can be justified by using properties of operations and understanding of place value.
    • Among all techniques and algorithms that may be chosen for accurately performing multi-digit computations, some procedures have been chosen with which all should be fluent for efficiency, communication, and use in other mathematics situations.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M. 6.5.1: Define factors and multiples.
    M. 6.5.2: Discuss the steps for solving a division problem.
    M. 6.5.3: Recognize division and multiplication as inverse operations.
    M. 6.5.4: Recall basic division and multiplication facts.
    M. 6.5.5: Solve real-world division problems with and without models or a calculator.

    Prior Knowledge Skills:
    • Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
    • Write number sentences for word problems.
    • Identify key terms to solve multiplication word problems.
      Examples: times, every, at this rate, each, per, equal/equally, in all, total.
    • Recall basic multiplication facts.
    • Recognize key terms to solve word problems.
      Examples: times, every, at this rate, each, per, equal/equally, in all, total.
    • Label numerator, denominator, and fraction bar.
    • Recognize a fraction as a number on the number line.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.5 Apply the concepts of dividing multi-digit numbers without remainders to real-world problems.


    Mathematics (2019)
    Grade(s): 6
    All Resources: 3
    Lesson Plans: 1
    Classroom Resources: 2
    6. Add, subtract, multiply, and divide decimals using a standard algorithm.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a context which calls for complex computation involving multi-digit decimals,
    • Choose the most appropriate strategy for computing the answer.
    • Produce accurate results efficiently using a standard algorithm for each operation when appropriate.
    Teacher Vocabulary:
    • Standard algorithms (addition, subtraction, multiplication, and division)
    • Quotient
    • Sum
    • Product
    • Difference
    • Tenths
    • Hundredths
    • Thousandths
    • Ten thousandths
    • Hundred thousandths
    Knowledge:
    Students know:
    • Place value conventions (i.e., a digit in one place represents 10 times as much as it would represent in the place to its right and 1/10 of what it represents in the place to its left).
    • Strategies for computing answers to complex addition, subtraction, multiplication, and division problems involving multi-digit decimals, including a standard algorithm for each operation.
    Skills:
    Students are able to:
    • Strategically choose and apply appropriate computation strategies.
    • Accurately find sums, differences, products, and quotients using the standard algorithms for each operation.
    Understanding:
    Students understand that:
    • Place value patterns and values continue to the right of the decimal point and allow the standard algorithm for addition and subtraction to be applied in the same manner as with whole numbers.
    • Mathematical problems can be solved using a variety of strategies, models, and representations.
    • Efficient application of computation strategies is based on the numbers and operations in the problem.
    • The steps used in the standard algorithms for the four operations can be justified by using properties of operations and understanding of place value.
    • Among all techniques and algorithms that may be chosen for accurately performing multi-digit computations, some procedures have been chosen with which all should be fluent for efficiency, communication, and use in other mathematics situations.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.6.1: Solve division problems involving multi-digit whole numbers and decimal numbers with or without a calculator.
    M.6.6.2: Solve multiplication problems involving multi-digit whole numbers and decimal numbers with or without a calculator.
    M.6.6.3: Recall basic multiplication and division facts.
    M.6.6.4: Solve addition and subtraction of multi-digit decimal numbers (emphasis on alignment).
    M.6.6.5: Solve addition and subtraction of multi-digit whole numbers.
    M.6.6.6: Recognize place value of whole numbers and decimals.
    M.6.6.7: Demonstrate addition, subtraction, multiplication, and division of whole numbers and decimals using manipulatives.

    Prior Knowledge Skills:
    • Recall basic multiplication facts.
    • Recall basic addition, subtraction, multiplication, and division facts.
    • Use place value understanding to round whole numbers to the nearest 10 or 100.
    • Identify place value of decimals to the tenths and hundredths.
    • Recall basic addition and subtraction facts.
    • Recall basic addition and subtraction facts.
    • Recall basic addition, subtraction, and multiplication facts.
    • Multiply within 100, using strategies such as the relationship between multiplication and division.
    • Multiply within 100, using strategies such as properties of operations.
    • Divide within 100, using strategies such as properties of operations.
    • Divide within 100, using strategies such as the relationship between multiplication and division.
    • Add and subtract within 1000.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.6 Solve two-factor multiplication problems with products up to 100 (whole numbers only).


    Mathematics (2019)
    Grade(s): 6
    All Resources: 4
    Learning Activities: 1
    Classroom Resources: 3
    7. Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use the distributive property to write an equivalent expression for the sum of the two numbers as the product of the greatest common factor of the two numbers, and the sum of two whole numbers with no common factor. [if the two whole numbers are 36 and 8, 36+8 = 4(9+2)].
    Teacher Vocabulary:
    • Greatest common factor
    • Distributive property
    • Parentheses
    • Decompose
    Knowledge:
    Students know:
    • Distributive property of multiplication over addition.
    • Strategies to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor by decomposing the numbers.
    Skills:
    Students are able to:
    • Use and model the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor by decomposing the numbers.
    Understanding:
    Students understand that:
    • Multiplication is distributive over addition.
    • Composing and decomposing numbers provides insights into relationships among numbers.
    • Quantities can be represented using a variety of equivalent expressions.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.7.1: Define greatest common factor, least common multiple, and the distributive property.
    M.6.7.2: Design problems using greatest common factor and the distributive property.
    M.6.7.3: Show an understanding of how to solve a problem using the distributive property, with or without the use of a calculator.

    Prior Knowledge Skills:
    • Identify factor and product.
    • Explain why addition and subtraction strategies work, using place value and the properties of operations.
    • Apply properties of operations as strategies to multiply and divide.
    Mathematics (2019)
    Grade(s): 6
    All Resources: 0
    8. Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.

    a. Use factors and multiples to determine prime factorization.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given any two or more whole numbers,
    • Strategically select and apply strategies for finding the greatest common factor of the two numbers and justify that the strategy used does produce the correct value for the greatest common factor.
    • Strategically select and apply strategies for finding the least common multiple of the two numbers and justify that the strategy used does produce the correct value for the least common multiple.
    • Use the relationship between factors and multiples to determine prime factorization.
    Teacher Vocabulary:
    • Greatest common factor
    • Least common multiple
    • Exponential Form
    • Prime Factorization
    • Factors
    • Multiples
    • Prime
    • Relatively Prime
    • Composite
    Knowledge:
    Students know:
    • Strategies for determining the greatest common factor of two or more numbers,
    • Strategies for determining the least common multiple of two or more numbers,
    • Strategies for determining the prime factorization of a number.
    Skills:
    Students are able to:
    • Apply strategies for determining greatest common factors and least common multiples.
    • Apply strategies for determining the product of a number's prime factors in multiple forms which include exponential form and standard form.
    Understanding:
    Students understand that:
    • Determining when two numbers have no common factors other than one means they are considered relatively prime.
    • Composing and decomposing numbers provides insights into relationships among numbers.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.8.1: Identify the least common multiple of a given set of numbers, with or without the use of a calculator.
    M.6.8.2: List multiples of any given whole number, with or without the use of a calculator.
    M.6.8.3: Identify the greatest common factors of a given set of numbers, with or without the use of a calculator.
    M.6.8.4: Define prime factorization.
    M.6.8.5: List common factors of given whole numbers, with or without the use of a calculator.
    M.6.8.6: Identify the prime factorization of a single digit number, with or without the use of a calculator.
    M.6.8.7: Identify the prime factorization of any two digit whole number, with or without the use of a calculator.

    Prior Knowledge Skills:
    • Define Multiple.
    • Name the first ten multiples of each one-digit natural number.
    • Name the first 10 multiples of each one-digit natural number.
      Example: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.
    • Count within 1000; skip-count by 5s, 10s, and 100s.
    • Recall basic multiplication facts.
    • Name the first ten multiples of each one-digit natural number.
    • Identify all factor pairs for a whole number in the range 1-20.
    • Apply properties of operations as strategies to multiply and divide.
    • Define factors, prime number, and composite number.
    Apply knowledge of the number system to represent and use rational numbers in a variety of forms.
    Mathematics (2019)
    Grade(s): 6
    All Resources: 0
    9. Use signed numbers to describe quantities that have opposite directions or values and to represent quantities in real-world contexts.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Given contextual or mathematical situations containing quantities that have opposite directions or values use positive, negative numbers, and their opposites to represent quantities in the contexts and explain the meaning of 0 in each situation.
    Teacher Vocabulary:
    • Positive Numbers
    • Negative Numbers
    • Opposites
    Knowledge:
    Students know:
    • notation for and meaning of positive and negative numbers, and their opposites in mathematical and real-world situations.
    Skills:
    Students are able to:
    • Use positive, negative numbers, and their opposites to represent quantities in real-world contexts.
    Understanding:
    Students understand that:
    • Positive and negative numbers are used together to describe quantities having opposite directions or values (temperature above/below zero, elevation above/below sea level, credits/debits, or positive/negative electrical charges).
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.9.1: Give examples of positive and negative numbers to represent quantities having opposite directions in real-world contexts.
    M.6.9.2: Discover that the opposite of the opposite of a number is the number itself.
    M.6.9.3: Show on a number line that numbers that are equal distance from 0 and on opposite sides of 0 have opposite signs.

    Prior Knowledge Skills:
    • Locate positive numbers on a horizontal number line.
    • Locate positive numbers on a vertical number line.
      Examples: thermometer, map.
    • Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.
    • Represent fractions on a number line diagram.
    • Recognize a fraction as a number on the number line.
    • Identify a fraction as a number on the number line; represent fractions on a number line diagram.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.9 Describe quantities with positive and negative numbers (e.g. temperature, sea level, etc.).


    Mathematics (2019)
    Grade(s): 6
    All Resources: 5
    Learning Activities: 2
    Lesson Plans: 1
    Classroom Resources: 2
    10. Locate integers and other rational numbers on a horizontal or vertical line diagram.

    a. Define opposites as numbers located on opposite sides of 0 and the same distance from 0 on a number line.

    b. Use rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Create and interpret number line diagram.
    • Given any rational number (positive or negative).
    • Locate the number on a number line.
    • Identify opposite signs of numbers as indicating the same distance from zero on the opposite side of zero, the opposite of the opposite, or a representation of its opposite as the point itself [-(-3) = 3], and zero as its own opposite.
    Teacher Vocabulary:
    • Integers
    • Rational numbers
    • Horizontal line diagram
    • Vertical line diagram
    Knowledge:
    Students know:
    • Strategies for creating number line models of rational numbers (marking off equal lengths by estimation or recursive halving).
    • Strategies for locating numbers on a number line.
    • Notation for positive and negative numbers and zero.
    Skills:
    Students are able to:
    • Represent rational numbers and their opposites on a number line including both positive and negative quantities.
    • Explain and justify the creation of number lines and placement of rational numbers on a number line.
    • Explain the meaning of 0 in a variety of real-world contexts.
    Understanding:
    Students understand that:
    • Representing rational numbers on number lines requires using both a distance and a direction,
    • Locating numbers on a number line provides a representation of a mathematical context which aids in visualizing ideas and solving problems.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.10.1: Define integers, positive and negative numbers.
    M.6.10.2: Demonstrate the location of positive and negative numbers on a vertical and horizontal number line.
    M.6.10.3: Give examples of positive and negative numbers to represent quantities having opposite directions in real-world contexts.
    M.6.10.4: Discuss the measure of centering of 0 in relationship to positive and negative numbers.
    M.6.10.5: Discover that the opposite of the opposite of a number is the number itself.
    M.6.10.6: Show on a number line that numbers that are equal distance from 0 and on opposite sides of 0 have opposite signs.
    M.6.10.7: Define rational number.
    M.6.10.8: Plot pairs of integers and/or rational numbers on a coordinate plane.
    M.6.10.9: Arrange integers and /or rational numbers on a horizontal or vertical number line.
    M.6.10.10: Locate the position of integers and/or rational numbers on a horizontal or vertical number line.
    M.6.10.11: Identify a rational number as a point on the number line.
    M.6.10.12: Name the pairs of integers and /or rational numbers of a point on a coordinate plane.

    Prior Knowledge Skills:
    • Model writing ordered pairs.
    • Identify the x- and y- values in ordered pairs.
    • Label the vertical axis (y).
    • Label the horizontal axis (x).
    • Define ordered pair of numbers, quadrant one, coordinate plane, and plot points.
    • Locate positive numbers on a vertical number line.
      Examples: thermometer, map.
    • Locate positive numbers on a horizontal number line.
    • Locate negative numbers on a horizontal number line.
    • Label x- and y-axis and zero on a coordinate.
    • Illustrate vertical and horizontal number lines.
    • Specify locations on the coordinate system.
    • Define x-axis, y-axis, and zero on a coordinate.
    • Define ordered pair of numbers.
    • Define parentheses, braces, and brackets.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.9 Describe quantities with positive and negative numbers (e.g. temperature, sea level, etc.).


    Mathematics (2019)
    Grade(s): 6
    All Resources: 4
    Learning Activities: 2
    Lesson Plans: 1
    Classroom Resources: 1
    11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

    a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

    b. Identify (a,b) and (a,-b) as reflections across the x-axis.

    c. Identify (a,b) and (-a,b) as reflections across the y-axis.

    d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Create and interpret coordinate axes with positive and negative coordinates.
    • Given ordered pairs made up of rational numbers, locate and explain the placement of the ordered pair on a coordinate plane.
    • Given two ordered pairs that differ only by signs, locate the points on a coordinate plane and explain the relationship of the locations of the points as reflections across one or both axes.
    • Given real world and mathematical problems where a coordinate graph will aid in the solution and given a graph of a real world or mathematical situation, interpret the coordinate values of the points in the context of the situation including finding vertical and horizontal distances.
    Teacher Vocabulary:
    • Coordinate plane
    • Quadrants
    • Coordinate values
    • ordered pairs
    • x axis
    • y axis
    • Reflection
    Knowledge:
    Students know:
    • Strategies for creating coordinate graphs.
    • Strategies for finding vertical and horizontal distance on coordinate graphs.
    Skills:
    Students are able to:
    • Graph points corresponding to ordered pairs,
    • Represent real world and mathematical problems on a coordinate plane.
    • Interpret coordinate values of points in the context of real world/mathematical situations.
    • Determine lengths of line segments on a coordinate plane when the line segment joins points with the same first coordinate (vertical distance) or the same second coordinate (horizontal distance).
    Understanding:
    Students understand that:
    • A graph can be used to illustrate mathematical situations and relationships. These representations help in conceptualizing ideas and in solving problems,
    • Distances on lines parallel to the axes on a coordinate plane are the same as the related distance on the axis (number line).
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.11.1: Define quadrant, coordinate plane, coordinate axes (x-axis and y-axis), horizontal, vertical, and reflection.
    M.6.11.2: Demonstrate an understanding of an extended coordinate plane.
    M.6.11.3: Draw a four-quadrant coordinate plane.
    M.6.11.4: Draw and extend vertical and horizontal number lines.
    M.6.11.5: Interpret graphing points in all four quadrants of the coordinate plane in real-world situations.
    M.6.11.6: Recall how to graph points in all four quadrants of the coordinate plane.
    M.6.11.7: Define ordered pairs.
    M.6.11.8: Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
    M.6.11.9: Demonstrate when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
    M.6.11.10: Identify which signs indicate the location of a point in a coordinate plane.
    M.6.11.11: Recall how to plot ordered pairs on a coordinate plane.
    M.6.11.12: Define reflections.
    M.6.11.13: Calculate the distances between points having the same first or second coordinate using absolute value.

    Prior Knowledge Skills:
    • Model writing ordered pairs.
    • Identify the x- and y- values in ordered pairs.
    • Label the vertical axis (y).
    • Label the horizontal axis (x).
    • Define ordered pair of numbers, quadrant one, coordinate plane, and plot points.
    • Locate positive numbers on a vertical number line.
      Examples: thermometer, map.
    • Locate positive numbers on a horizontal number line.
    • Locate negative numbers on a horizontal number line.
    • Label x- and y-axis and zero on a coordinate.
    • Illustrate vertical and horizontal number lines.
    • Specify locations on the coordinate system.
    • Define x-axis, y-axis, and zero on a coordinate.
    • Define ordered pair of numbers.
    • Locate positive numbers on a horizontal number line.
    • Locate negative numbers on a horizontal number line.
    • Define symmetry.
    • Identify lines of symmetry on one-dimensional figures.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.11 Graph or identify ordered pairs in the first quadrant of the coordinate plane between 0 and 5, limited to whole numbers.


    Mathematics (2019)
    Grade(s): 6
    All Resources: 2
    Classroom Resources: 2
    12. Explain the meaning of absolute value and determine the absolute value of rational numbers in real-world contexts.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Write, interpret, and explain the absolute values of the quantities.
    • Distinguish comparisons of absolute value from statements about order (students will use logical reasoning to explain how an account balance less than $30 represents a debt greater than $30).
    Teacher Vocabulary:
    • Absolute value
    • Inequality
    Knowledge:
    Students know:
    • The meaning of absolute value and determine the absolute value of rational numbers in real-world contexts.
    Skills:
    Students are able to:
    • Understand that the absolute value of a number is the distance from zero in mathematical and real-world situations.
    Understanding:
    Students understand that:
    • the absolute value of a number is its distance from zero.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.12.1: Define absolute value and rational numbers.
    M.6.12.2: Recall how to order numbers.
    M.6.12.3: Give examples of the magnitude for a positive or negative quantity in a real-world situations using absolute value.
    M.6.12.4: Recognize the absolute value of a rational number is its' distance from 0 on a vertical and horizontal number line.

    Prior Knowledge Skills:
    • Model writing ordered pairs.
    • Identify the x- and y- values in ordered pairs.
    • Label the vertical axis (y).
    • Label the horizontal axis (x).
    • Define ordered pair of numbers, quadrant one, coordinate plane, and plot points.
    Mathematics (2019)
    Grade(s): 6
    All Resources: 0
    13. Compare and order rational numbers and absolute value of rational numbers with and without a number line in order to solve real-world and mathematical problems.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Write, interpret, and explain inequalities that show order of the given numbers including absolute values of the quantities.
    • Given contextual and mathematical situations involving quantities that can be represented as positive or negative rational numbers including absolute values of the quantities.
    Teacher Vocabulary:
    • Absolute Value
    • Inequalities
    Knowledge:
    Students know:
    • How to use and interpret inequality notation with rational numbers and absolute value.
    • Strategies for comparing and ordering rational numbers and the absolute value of rational numbers with and without a number line in order to solve real-world and mathematical problems.
    Skills:
    Students are able to:
    • Use mathematical language to communicate the relationship between verbal representations of inequalities and the related number line and algebraic models.
    • Distinguish comparisons of the absolute value of positive and negative rational numbers from statements about order.
    • Use number line models to explain absolute value concepts in order to solve real-world and mathematical problems.
    Understanding:
    Students understand that:
    • The absolute value of a number is its distance from zero on a number line regardless of direction,
    • When using number lines to compare quantities those to the left are less than those to the right.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.13.1: Define rational number.
    M.6.13.2: Plot pairs of integers and/or rational numbers on a coordinate plane.
    M.6.13.3: Arrange integers and/or rational numbers on a horizontal or vertical number line.
    M.6.13.4: Locate the position of integers and/or rational numbers on a horizontal or vertical number line.
    M.6.13.5: Evaluate a statement about order using comparisons of absolute value.
    M.6.13.6: Recall how to order positive and negative numbers. (Use number line if needed.).

    Prior Knowledge Skills:
    • Locate positive numbers on a vertical number line.
      Examples: thermometer, map.
    • Locate positive numbers on a horizontal number line.
    • Locate negative numbers on a horizontal number line.
    • Label x- and y-axis and zero on a coordinate.
    • Illustrate vertical and horizontal number lines.
    • Specify locations on the coordinate system.
    • Define x-axis, y-axis, and zero on a coordinate.
    • Define ordered pair of numbers.
    • Interpret data using graphs including bar, line, and circle graphs, and Venn diagrams.
    • Display data by making a line plot where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.
    Algebra and Functions
    Apply knowledge of arithmetic to read, write, and evaluate algebraic expressions.
    Mathematics (2019)
    Grade(s): 6
    All Resources: 1
    Classroom Resources: 1
    14. Write, evaluate, and compare expressions involving whole number exponents.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Write whole numbers with indicated exponents and their equivalent form without exponents, and justify the equivalence.
    Teacher Vocabulary:
    • Numerical expression
    • Exponent
    Knowledge:
    Students know:
    • Conventions of exponential notation.
    • Factorization strategies for whole numbers.
    Skills:
    Students are able to:
    • Use factorization strategies to write equivalent expressions involving exponents.
    • Accurately find products for repeated multiplication of the same factor in evaluating exponential expressions.
    Understanding:
    Students understand that:
    • The use of exponents is an efficient way to write numbers as repeated multiplication of the same factor and this form reveals features of the number that may not be apparent in multiplied out form, (showing the prime factorization of two numbers with exponents helps determine how many of each factor).
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.14.1: Define exponent, numerical expression, algebraic expression, variable, base, power, square of a number, and cube of a number.
    M.6.14.2: Compute a numerical expression with exponents, with or without a calculator.
    M.6.14.3: Restate exponential numbers as repeated multiplication.
    M.6.14.4: Choose the correct value to replace each variable in the expression (Substitution).
    M.6.14.5: Calculate the multiplication of single or multi-digit whole numbers, with or without a calculator.

    Prior Knowledge Skills:
    • Product, power of 10.
    • Recognize decimal place value using visual representations.
    • Recall multiplication and division facts of 10.
    • Skip count forward and backward by 10.
    • Recognize decimals as parts of a whole.
    • Compare whole numbers.
    • Read whole numbers.
    • Write whole numbers in words and expanded form.
    • Define expanded notation and standard form.
    • Convert a number written in expanded to standard form.
    • Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
    • Recall basic multiplication facts.
    • Recall basic addition, subtraction, multiplication, and division facts.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.14 Match an algebraic expression with one variable to its real-world situation.


    Mathematics (2019)
    Grade(s): 6
    All Resources: 8
    Learning Activities: 2
    Lesson Plans: 1
    Classroom Resources: 5
    15. Write, read, and evaluate expressions in which letters represent numbers in real-world contexts.

    a. Interpret a variable as an unknown value for any number in a specified set, depending on the context.

    b. Write expressions to represent verbal statements and real-world scenarios.

    c. Identify parts of an expression using mathematical terms such as sum, term, product, factor, quotient, and coefficient.

    d. Evaluate expressions (which may include absolute value and whole number exponents) with respect to order of operations.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given contextual or mathematical problems both when known models exist (for example formulas) or algebraic models are unknown,
    • Interpret the parts of the model in the original context.
    • Create the algebraic model of the situation when appropriate.
    • Use appropriate mathematical terminology to communicate the meaning of the expression.
    • Evaluate the expressions for values of the variable including finding values following conventions of parentheses and order of operations.
    Teacher Vocabulary:
    • Expressions
    • Term
    • Coefficient
    • Sum
    • Product
    • Factor
    • Quotient
    • Variable
    • Constant
    • Difference
    • Evaluate
    • Order of Operations
    • Exponent
    • Absolute Value
    Knowledge:
    Students know:
    • Correct usage of mathematical symbolism to model the terms sum, term, product, factor, quotient, variable, difference, constant, and coefficient when they appear in verbally stated contexts.
    • Conventions for order of operations.
    • Convention of using juxtaposition (5A or xy) to indicate multiplication.
    Skills:
    Students are able to:
    • Translate fluently between verbally stated situations and algebraic models of the situation.
    • Use operations (addition, subtraction, multiplication, division, and exponentiation) fluently with the conventions of parentheses and order of operations to evaluate expressions for specific values of variables in expressions.
    • Use terminology related to algebraic expressions such as sum, term, product, factor, quotient, or coefficient, to communicate the meanings of the expression and the parts of the expression.
    Understanding:
    Students understand that:
    • The structure of mathematics allows for terminology and techniques used with numerical expressions to be used in an analogous way with algebraic expressions, (the sum of 3 and 4 is written as 3 + 4, so the sum of 3 and y is written as 3 + y).
    • When language is ambiguous about the meaning of a mathematical expression grouping, symbols and order of operations conventions are used to communicate the meaning clearly.
    • Moving fluently among representations of mathematical situations (words, numbers, symbols, etc.), as needed for a given situation, allows a user of mathematics to make sense of the situation and choose appropriate and efficient paths to solutions.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.15.1: Define algebraic expression and variable.
    M.6.15.2: Convert mathematical terms to mathematical symbols and numbers.
    M.6.15.3: Translate verbal and numerical expression using all operations.
    M.6.15.4: Define coefficient, constant and term.
    M.6.15.5: Match mathematical terms with correct mathematical symbols.
    M.6.15.6: Convert mathematical terms to mathematical symbols and numbers.
    M.6.15.7: Calculate an expression in the correct order. with or without a calculator (Ex. exponents, mult./div. from left to right, and add/sub. from left to right).
    M.6.15.8: Choose the correct value to replace each variable in the algebraic expression (Substitution).
    M.6.15.9: Calculate a numerical expression, with or without a calculator (Ex. V=4x4x4).
    M.6.15.10: Recognize the correct order to solve expressions with more than one operation.

    Prior Knowledge Skills:
    • Recognize key terms to solve word problems.
      Examples: times, every, at this rate, each, per, equal/equally, in all, total.
    • Recognize key terms to solve word problems.
      Examples: times, every, at this rate, each, per, equal/equally, in all, total.
    • Define simple expression.
    • Recall simple equations.
    • Recognize properties of addition and multiplication.
    • Recall addition, subtraction, multiplication, division symbols.
    • Define parentheses, braces, and brackets.
    • Define numerical expression.
    • Recognize expressions.
    • Apply properties of operations as strategies to add and subtract.
    • Recall properties of operations as strategies to add and subtract.
    • Represent addition and subtraction with objects, mental images, drawings, expressions, or equations.
    • Use addition, subtraction, multiplication and division to solve one- and two-step word problems.
    • Recognize key terms to solve word problems.
    • Apply properties of operations as strategies to multiply and divide.
    • Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.
    • Recall the formula for area (L × W).
    • Recognize that unit squares are equal.
    • Recall the formula for perimeter (P= L+L+W+W or P=2L + 2W).
    • Recall basic addition and multiplication facts.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.15 Evaluate algebraic expressions when given specific values for the variables (e.g. x + 2, where x = 4).


    Mathematics (2019)
    Grade(s): 6
    All Resources: 4
    Classroom Resources: 4
    16. Generate equivalent algebraic expressions using the properties of operations, including inverse, identity, commutative, associative, and distributive.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Given contextual or mathematical problems which may be modeled by algebraic expressions, use properties of the operations to produce combined and re-written forms of the expressions that are useful in resolving the problem.
    Teacher Vocabulary:
    • Properties of operations
    • Distributive property
    • Inverse property
    • Identity property
    • Commutative property
    • Associative property
    • Equivalent algebraic expressions
    Knowledge:
    Students know:
    • the properties of operations, including inverse, identity, commutative, associative, and distributive and their appropriate application to be able to generate equivalent algebraic expressions.
    Skills:
    Students are able to:
    • Accurately use the properties of operations on algebraic expressions to produce equivalent expressions useful in a problem solving context.
    Understanding:
    Students understand that:
    • The properties of operations used with numerical expressions are valid to use with algebraic expressions and allow for alternate but still equivalent forms of expressions for use in problem solving situations.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.16.1:Define equivalent, simplify, term, distributive property, associative property of addition and multiplication, and the commutative property of addition and multiplication.
    M.6.16.2: Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
    M.6.16.3: Combine terms that are alike of a given expression.
    M.6.16.4: Recognize the property demonstrated in a given expression.
    M.6.16.5: Simplify an expression by dividing by the greatest common factor.
    Example: 18x + 6y = 6(3x + y).
    M.6.16.6: Determine the greatest common factor in an algebraic expression.

    Prior Knowledge Skills:
    • Define parentheses, braces, and brackets.
    • Define numerical expression.
    • Recognize expressions.
    • Apply properties of operations as strategies to add and subtract.
    • Recall properties of operations as strategies to add and subtract.
    • Represent addition and subtraction with objects, mental images, drawings, expressions, or equations.
    • Define simple expression.
    • Recall simple equations.
    • Recognize properties of addition and multiplication.
    • Recall addition, subtraction, multiplication, division symbols.
    • Use addition, subtraction, multiplication and division to solve one- and two-step word problems.
    • Apply properties of operations as strategies to multiply and divide.
    Mathematics (2019)
    Grade(s): 6
    All Resources: 1
    Classroom Resources: 1
    17. Determine whether two expressions are equivalent and justify the reasoning.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a contextual or mathematical situation that could be represented algebraically,
    • Explain by reasoning from the context why two expressions must be equivalent.
    • Use properties of operations and equality to verify if two algebraic expressions are equivalent or not.
    Teacher Vocabulary:
    • Equivalent
    • Expressions
    Knowledge:
    Students know:
    • The properties of operations, including inverse, identity, commutative, associative, and distributive and their appropriate application to be able to determine whether two expressions are equivalent.
    • Conventions of order of operations.
    Skills:
    Students are able to:
    • Accurately use the properties of operations to produce equivalent forms of an algebraic expression when interpreting mathematical and contextual situations.
    • Use mathematical reasoning to communicate the relationships between equivalent algebraic expressions.
    Understanding:
    Students understand that:
    • Manipulation of expressions via properties of the operations verifies mathematically that two expressions are equivalent.
    • Reasoning about the context from which expressions arise allows for interpretation and meaning to be placed on each of the expressions and their equivalence.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.17.1: Define equivalent expressions.
    M.6.17.2: Recognize equivalent expressions.
    M.6.17.3: Substitute for the variable to find the value of a given expression.
    M.6.17.4: Calculate a numerical expression.
    M.6.17.5: Recognize that a variable without a written coefficient is understood to have a coefficient of one. (Ex. x = 1x).

    Prior Knowledge Skills:
    • Use comparison symbols.
      Examples: >, =, or < .
    • Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
    • Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
    • Comparison symbols.
      Examples: >, =, and < .
    • Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
    • Compare two fractions with the same numerator or the same denominator by reasoning about their size.
    • Recognize that comparisons are valid only when the two fractions refer to the same whole.
    • Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
    • Convert fractions to decimals.
    • Compare two decimals to tenths.
    • Compare whole numbers.
    • Identify comparison symbols.
      Examples: >, <, and = .
    Use equations and inequalities to represent and solve real-world or mathematical problems.
    Mathematics (2019)
    Grade(s): 6
    All Resources: 4
    Lesson Plans: 1
    Classroom Resources: 3
    18. Determine whether a value is a solution to an equation or inequality by using substitution to conclude whether a given value makes the equation or inequality true.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given situations that have been modeled with equations or inequalities:
    • Substitute given specified values for the variables and the evaluate expressions.
    • Determine if the resulting numerical sentence is true when the specified values are substituted for the variables.
    • Explain with mathematical reasoning why a specified value is or is not a solution to a given equation or inequality.
    Teacher Vocabulary:
    • Substitution
    • Equation
    • Inequality
    Knowledge:
    Students know:
    • Conventions of order of operations.
    • The solution is the value of the variable that will make the equation or inequality true.
    • That using various processes to identify the value(s) that when substituted for the variable will make the equation true.
    Skills:
    Students are able to:
    • Substitute specific values into algebraic equation or inequality and accurately perform operations of addition, subtraction, multiplication, division and exponentiation using order of operation.
    Understanding:
    Students understand that:
    • Solving an equation or inequality means finding the value or values (if any) that make the mathematical sentence true.
    • The solution to an inequality is often a range of values rather than a specific value.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.18.1: Define exponent, numerical expression, algebraic expression, variable, base, power, square of a number, and cube of a number.
    M.6.18.2: Compute a numerical expression with exponents, with or without a calculator.
    M.6.18.3: Restate exponential numbers as repeated multiplication.
    M.6.18.4: Choose the correct value to replace each variable in the expression (Substitution).
    M.6.18.5: Calculate the multiplication of single or multi-digit whole numbers, with or without a calculator.

    Prior Knowledge Skills:
    • Use comparison symbols.
      Examples: >, =, or < .
    • Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
    • Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
    • Comparison symbols.
      Examples: >, =, and < .
    • Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
    • Compare two fractions with the same numerator or the same denominator by reasoning about their size.
    • Recognize that comparisons are valid only when the two fractions refer to the same whole.
    • Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
    • Convert fractions to decimals.
    • Compare two decimals to tenths.
    • Compare whole numbers.
    • Identify comparison symbols.
      Examples: >, <, and = .

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.19 Match equations and inequalities to real-world situations.


    Mathematics (2019)
    Grade(s): 6
    All Resources: 3
    Classroom Resources: 3
    19. Write and solve an equation in the form of x+p=q or px=q for cases in which p, q, and x are all non-negative rational numbers to solve real-world and mathematical problems.

    a. Interpret the solution of an equation in the context of the problem.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given contextual or mathematical situations which may be modeled by x + p = q or px = q (p,q, and x are rational and non-negative),
    • Explain the role of the variable as a place holder where the variable stands for a particular number (y + 7 = 12) or a value in a formula (A = L × W) and where values are substituted for one or more variables another variable assumes different values.
    • Write and solve equations modeling the situation, solve the resulting equations, and justify the solutions.
    Teacher Vocabulary:
    • Variable
    • Equation
    • Non-negative rational numbers
    Knowledge:
    Students know:
    • Correct translation between verbally stated situations and mathematical symbols and notation.
    • How to write and solve a simple equation using non-negative rational numbers to solve mathematical and real-world problems.
    Skills:
    Students are able to:
    • Translate fluently between verbally stated situations and algebraic models of the situation.
    • Use inverse operations and properties of equality to produce solutions to equations of the forms x + p = q or px = q.
    • Use logical reasoning and properties of equality to justify solutions, reasonableness of solutions, and solution paths.
    Understanding:
    Students understand that:
    • Variables may be unknown values that we wish to find.
    • The solution to the equation is a value for the variable which, when substituted into the original equation, results in a true mathematical statement.
    • A symbolic representation of relevant features of a real world problem can provide for resolution of the problem and interpretation of the situation.
    • The structure of mathematics present in the properties of the operations and equality can be used to maintain equality while rearranging equations, as well as justify steps in the solutions of equations.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.19.1: Define equation and variable.
    M.6.19.2: Set up an equation to represent the given situation, using correct mathematical operations and variables.
    M.6.19.3: Solve the equation represented by the real-world situation.
    M.6.19.4: Identify the unknown variable in a given situation.
    M.6.19.5: List given information from the problem.
    M.6.19.6: Explain the solution in the context of the problem.

    Prior Knowledge Skills:
    • Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.
    • Recognize key terms to solve word problems.
      Examples: times, every, at this rate, each, per, equal/equally, in all, total.
    • Define simple expression.
    • Recall simple equations.
    • Recognize properties of addition and multiplication.
    • Recall addition, subtraction, multiplication, division symbols.
    • Define parentheses, braces, and brackets.
    • Define numerical expression.
    • Recognize expressions.
    • Apply properties of operations as strategies to add and subtract.
    • Recall properties of operations as strategies to add and subtract.
    • Represent addition and subtraction with objects, mental images, drawings, expressions, or equations.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.19 Match equations and inequalities to real-world situations.


    Mathematics (2019)
    Grade(s): 6
    All Resources: 0
    20. Write and solve inequalities in the form of x>c, x<c, x≥c, or x≤c to represent a constraint or condition in a real-world or mathematical problem.

    a. Interpret the solution of an inequality in the context of a problem.

    b. Represent the solutions of inequalities on a number line and explain that the solution set may contain infinitely many solutions.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given contextual or mathematical situations which may be modeled by x > c or x < c,
    • Write inequalities modeling the situation.
    • Identify the set of values making the resulting inequalities true.
    • Represent the solutions on a number line.
    Teacher Vocabulary:
    • Inequalities
    • Constraint
    • Infinitely many solutions
    Knowledge:
    Students know:
    • Correct translation between verbally stated situations and mathematical symbols and notation,
    • Many real-world situations are represented by inequalities,
    • The number line represents inequalities from various contextual and mathematical situations.
    Skills:
    Students are able to:
    • Translate fluently among verbally stated inequality situations, algebraic models of the situation ( x > c or x < c), and visual models on a number line.
    Understanding:
    Students understand that:
    • Inequalities have infinitely many solutions.
    • A symbolic or visual representation of relevant features of a real world problem can provide for resolution of the problem and interpretation of the situation.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.20.1: Define inequality and solution set of an inequality.
    M.6.20.2: Set up an inequality to represent the given situation, using correct mathematical operations and variable.
    M.6.20.3: Identify solution set for the inequality used to represent the situation.
    M.6.20.4: Recognize the inequality symbols; <, >, < , > , =, >, <, ?, and ?.
    M.6.20.5: Construct and label a number line.
    M.6.20.6: Graph the solution set on a number line for the inequality used to represent the situation.

    Prior Knowledge Skills:
    • Use comparison symbols.
      Examples: >, =, or <.
    • Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
    • Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
    • Comparison symbols.
      Examples: >, =, and < .
    • Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits.
    • Compare using >, =, and < symbols to record the results of comparisons.
    • Compare two fractions with the same numerator or the same denominator by reasoning about their size.
    • Recognize that comparisons are valid only when the two fractions refer to the same whole.
    • Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
    • Convert fractions to decimals.
    • Compare two decimals to tenths.
    • Compare whole numbers.
    • Identify comparison symbols.
      Examples: >, <, and = .

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.19 Match equations and inequalities to real-world situations.


    Identify and analyze relationships between independent and dependent variables.
    Mathematics (2019)
    Grade(s): 6
    All Resources: 1
    Classroom Resources: 1
    21. Identify, represent, and analyze two quantities that change in relationship to one another in real-world or mathematical situations.

    a. Use tables, graphs, and equations to represent the relationship between independent and dependent variables.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a real world problem involving two quantities that change in relationship to one another,
    • Represent the context using graphs, tables, and equations.
    • Explain the connections among the representations using mathematical vocabulary including dependent and independent variables.
    Teacher Vocabulary:
    • Dependent variables
    • Independent variables
    • Equations
    Knowledge:
    Students know:
    • Roles of dependent and independent variables.
    • Correct translation between verbally stated situations and mathematical symbols and notation.
    Skills:
    Students are able to:
    • Represent real world problems involving two quantities that change in relationship to one another using equations, graphs, and tables,
    • Use mathematical vocabulary to explain connections among representations of function contexts.
    • Analyze and interpret the relationship between the independent and the dependent variable in a given situation.
    Understanding:
    Students understand that:
    • Equations with two variables represent mathematical relationships in which the value of the dependent variable varies with changes in the independent variable.
    • A symbolic or visual representation of relevant features of a real world problem can aid in interpretation of the situation.
    • Translating between language, a table, an equation, or a graph represents the same relationship and provides a different perspective on the function.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.21.1: Define dependent variable, independent variable, ordered pairs, input, output, and coordinate plane.
    M.6.21.2: Examine the graph and table to determine any relationship between the variables.
    M.6.21.3: Recall how to draw a number line.
    M.6.21.4: Draw and label a coordinate plane.
    M.6.21.5: Analyze the pattern represented by the values in the table and develop an equation to express the relationship.
    M.6.21.6: Relate the table and graph to the equation.
    M.6.21.7: Plot independent (input) and dependent (output) values on a coordinate plane.
    M.6.21.8: Create a table of independent and dependent values from the equation.

    Prior Knowledge Skills:
    • Model writing ordered pairs.
    • Identify the x- and y- values in ordered pairs.
    • Label the vertical axis (y).
    • Label the horizontal axis (x).
    • Define ordered pair of numbers, quadrant one, coordinate plane, and plot points.
    • Locate positive numbers on a vertical number line.
      Examples: thermometer, map.
    • Locate positive numbers on a horizontal number line.
    • Locate negative numbers on a horizontal number line.
    • Label x- and y-axis and zero on a coordinate.
    • Illustrate vertical and horizontal number lines.
    • Specify locations on the coordinate system.
    • Define x-axis, y-axis, and zero on a coordinate.
    • Define ordered pair of numbers.
    • Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.
    • Recognize key terms to solve word problems.
      Examples: times, every, at this rate, each, per, equal/equally, in all, total.
    • Recognize that comparisons are valid only when the two fractions refer to the same whole.
    • Recognize arithmetic patterns (including geometric patterns or patterns in the addition table or multiplication table).
    • Recall basic multiplication facts.
    • Interpret data using graphs including bar, line, and circle graphs, and Venn diagrams.
    • Identify the parts of a line plot.
    • Recognize a line plot.
    • Draw a scaled picture graph and a scaled bar graph to represent a data set.
    • Recognize a fraction as a number on the number line.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.21 Identify the independent and dependent variables among two quantities that change in relationship to one another in real-world situations (e.g. purchase total depends on number of items purchased).


    Data Analysis, Statistics, and Probability
    Use real-world and mathematical problems to analyze data and demonstrate an understanding of statistical variability and measures of center.
    Mathematics (2019)
    Grade(s): 6
    All Resources: 1
    Lesson Plans: 1
    22. Write examples and non-examples of statistical questions, explaining that a statistical question anticipates variability in the data related to the question.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a variety of mathematical questions,
    • Justify the classification of questions as either statistical or non-statistical.
    • Write statistical and non-statistical questions.
    Teacher Vocabulary:
    • Statistical questions
    • Variability
    Knowledge:
    Students know:
    • Characteristics of statistical and non-statistical questions.
    Skills:
    Students are able to:
    • Justify the classification of mathematical questions as statistical or non-statistical questions.
    Understanding:
    Students understand that:
    • Statistical questions have anticipated variability in the answers.
    • Data are the numbers produced in response to a statistical question.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.22.1: Define statistical question.
    M.6.22.2: Identify examples of statistical questions and non-statistical questions.
    M.6.22.3: Compare and contrast statistical questions and non- statistical questions.

    Prior Knowledge Skills:
    • Identify different types of questions.
    • Recognize questions that produce numerical answers.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.23 Find the range and median (when given an odd number of data points), and mean (involving one or two-digit numbers) in real-world situations.


    Mathematics (2019)
    Grade(s): 6
    All Resources: 7
    Learning Activities: 1
    Classroom Resources: 6
    23. Calculate, interpret, and compare measures of center (mean, median, mode) and variability (range and interquartile range) in real-world data sets.

    a. Determine which measure of center best represents a real-world data set.

    b. Interpret the measures of center and variability in the context of a problem.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a set of numerical data, summarize the data by,
    • Reporting the number of observations (n).
    • Describing the nature of the attribute under investigation.
    • Calculating, interpreting, and comparing the measures of center (median/mean/mode) in a real-world data set,
    • Calculating, interpreting and comparing the measures of variability (interquartile range and range) in a real-world data set.
    • Given a set of numerical data interpret the measures of center and variability in the context of a problem.
    • Justify their choice of measures of center and variability to describe the data based on the data distribution and the context in which the data were gathered.
    Teacher Vocabulary:
    • Data distribution
    • Measures of center
    • Measures of variability
    • Mean
    • Median
    • Mode
    • Interquartile range
    • Range
    Knowledge:
    Students know:
    • Measures of center and how they are affected by the data distribution and context.
    • Measures of variability and how they are affected by the data distribution and context.
    • Methods of determining mean, median, mode, interquartile range, and range.
    Skills:
    Students are able to:
    • Describe the nature of the attribute under investigation including how it was measured and its unit of measure using the context in which the data were collected.
    • Determine measures of center and variability for a set of numerical data.
    • Use characteristics of measures of center and variability to justify choices for summarizing and describing data.
    Understanding:
    Students understand that:
    • Measures of center for a set of data summarize the values in the set in a single number and are affected by the distribution of the data.
    • Measures of variability for a set of data describe how the values vary in a single number and are affected by the distribution of the data.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.23.1: Define numerical data set, measure of variation, and measure of center.
    M.6.23.2: Relate the measure of variation, of a data set, with the concept of range.
    M.6.23.3: Relate the measure of the center for a numerical data set with the concept of measure of center.
    M.6.23.4: Define numerical data set, quantitative, measure of center, median, frequency distribution, and attribute.
    M.6.23.5: Compare and contrast the center and variation.
    M.6.23.6: Collect the data.
    M.6.23.7: Organize the data.
    M.6.23.8: Describe how attribute was measured including units of measurement.
    M.6.23.9: Identify the attribute used to create the numerical set.

    Prior Knowledge Skills:
    • Identify a numerical data set.
    • Calculate the range of data.
    • Organize numbers in a ordered list.
    • Calculate the mean, median, and mean of a data set.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.23 Find the range and median (when given an odd number of data points), and mean (involving one or two-digit numbers) in real-world situations.


    Mathematics (2019)
    Grade(s): 6
    All Resources: 6
    Learning Activities: 2
    Lesson Plans: 1
    Classroom Resources: 3
    24. Represent numerical data graphically, using dot plots, line plots, histograms, stem and leaf plots, and box plots.

    a. Analyze the graphical representation of data by describing the center, spread, shape (including approximately symmetric or skewed), and unusual features (including gaps, peaks, clusters, and extreme values).

    b. Use graphical representations of real-world data to describe the context from which they were collected.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a set of numerical data,
    • Analyze graphical representation of data by describing the center, spread, and shape including approx. symmetric or skewed.
    • Reporting significant features in the shape of data including striking deviations, (e.g., extreme values, outliers, gaps, and clusters).
    • Organize and display the data using plots on line plots, dot plots, stem and leaf plots, histograms, and box plots.
    Teacher Vocabulary:
    • Dot plots
    • Histograms
    • Box plots
    • Stem and leaf plots
    • Line plots
    • Extreme values
    • Outliers
    • Gaps
    • Clusters
    • Symmetric
    • Skewed
    • Center
    • Spread
    • peaks
    • 5 number summary
    • Minimum
    • Maximum
    • Median
    • lower quartile
    • Upper quartile
    Knowledge:
    Students know:
    • How to use graphical representations of real-world data to describe context, center, spread and shape from which they were collected.
    • Techniques for constructing line plots, stem and leaf plots, dot plots, histograms, and box plots.
    Skills:
    Students are able to:
    • Organize and display data using dot plots, line plots, stem and leaf plots, histograms, and box plots.
    • Describe the nature of the attribute under investigation including how it was measured and its unit of measure using the context in which the data were collected.
    • Describe the shape of numerical data distribution including patterns and extreme values.
    • Use graphical representations of real-world data to describe and summarize the context from which they were collected.
    Understanding:
    Students understand that:
    • Sets of data can be organized and displayed in a variety of ways, each of which provides unique perspectives of the data set.
    • Data displays help in conceptualizing ideas and in solving problems.
    • The overall shape and other significant features of a set of data, (e.g., gaps, peaks, clusters and extreme values) are important in summarizing numerical data sets.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.24.1: Define dot plots, line plot, stem and leaf plots, upper quartile, lower quartile, median, histograms, and box plots.
    M.6.24.2: Recall how to read a graph or table.
    M.6.24.3: Calculate upper quartile median, lower quartile median, overall median, greatest value, and lowest value.
    M.6.24.4: Create box plot using calculations.
    M.6.24.5: Plot data on dot plots and histograms.
    M.6.24.6: Construct and label the display.
    M.6.24.7: Recognize the different types of displays.
    M.6.24.8: Define distribution and skew.
    M.6.24.9: Describe the shape of a set of data in a given distribution.
    M.6.24.10: Describe the spread of a set of data in a given distribution.
    M.6.24.11: Describe the center of a set of data in a given distribution.

    Prior Knowledge Skills:
    • Identify different types of graphs.
    • Create a bar graph and box plot.
    • Organize data in an ordered list.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.24 Interpret graphical representations of a data set (e.g. line plot, dot plots, bar graphs, stem and leaf plots, or line graphs).


    Geometry and Measurement
    Graph polygons in the coordinate plane to solve real-world and mathematical problems.
    Mathematics (2019)
    Grade(s): 6
    All Resources: 1
    Classroom Resources: 1
    25. Graph polygons in the coordinate plane given coordinates of the vertices to solve real-world and mathematical problems.

    a. Determine missing vertices of a rectangle with the same x-coordinate or the same y-coordinate when graphed in the coordinate plane.

    b. Use coordinates to find the length of a side between points having the same x-coordinate or the same y-coordinate.

    c. Calculate perimeter and area of a polygon graphed in the coordinate plane (limiting to polygons in which consecutive vertices have the same x-coordinate or the same y-coordinate).
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given real world and mathematical problems involving the mapping of polygons onto a coordinate system,
    • Determine the length of a side joining points with the same first coordinate or the same second coordinate.
    • Determine missing vertices of a rectangle.
    • Graph polygons in coordinate plane given vertices and solve real world problems.
    Teacher Vocabulary:
    • Polygon
    • Coordinate plane
    • Vertices
    • X-coordinate
    • Y-coordinate
    Knowledge:
    Students know:
    • Terminology associated with coordinate systems.
    • Correct construction of coordinate systems.
    Skills:
    Students are able to:
    • Graph points corresponding to ordered pairs.
    • Represent real world and mathematical problems on a coordinate plane.
    • Interpret coordinate values of points in the context of real world and mathematical situations.
    • Determine lengths of line segments on a coordinate plane when the line segment joins points with the same first coordinate or the same second coordinate.
    Understanding:
    Students understand that:
    • A variety of representations such as diagrams, number lines, charts, and graphs can be used to illustrate mathematical situations and relationships.
    • These representations help in conceptualizing ideas and in solving problems.
    • Distances on lines parallel to the axes on a coordinate plane are the same as the related distance on the axis (number line).
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.25.1: Define vertices.
    M.6.25.2: Apply absolute value to find the length of a side joining points with the same first coordinate or the same second coordinate.
    M.6.25.3: Plot points on a coordinate plane., then connect points for the vertices to sketch a polygon.
    M.6.25.4: Identify ordered pairs.
    M.6.25.5: Recognize polygons.
    M.6.25.6: Define perimeter and area.
    M.6.25.7: Identify the length between vertices on a coordinate plane.
    M.6.25.8: Calculate the perimeter and area using the distance between the vertices.

    Prior Knowledge Skills:
    • Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces.
    • Identify triangles, quadrilaterals, pentagons, hexagons, heptagons, and octagons based on the number of sides, angles, and vertices.
    • Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
    • Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
    • Recognize attributes of shapes.
    • Recall the vocabulary of shapes (labels, sides, faces, vertices, etc.). Sort shapes into categories.
    • Define ordered pair of numbers, quadrant one, coordinate plane, and plot points. Label the horizontal axis (x).
    • Label the vertical axis (y).
    • Identify the x- and y- values in ordered pairs.
    • Model writing ordered pairs.
    • Define vertex/vertices and angle.
    • Recall the formula for area (L × W).
    • Recognize that unit squares are equal.
    • Recall the formula for perimeter (P= L+L+W+W or P=2L + 2W).
    • Recall basic addition and multiplication facts.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.25 Graph squares, rectangles, and triangles in the first quadrant of the coordinate plane.


    Solve real-world and mathematical problems to determine area, surface area, and volume.
    Note: Students must select and use the appropriate unit for the attribute being measured when determining length, area, angle, time, or volume.
    Mathematics (2019)
    Grade(s): 6
    All Resources: 3
    Classroom Resources: 3
    26. Calculate the area of triangles, special quadrilaterals, and other polygons by composing and decomposing them into known shapes.

    a. Apply the techniques of composing and decomposing polygons to find area in the context of solving real-world and mathematical problems.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a variety of triangles and quadrilaterals:
    • Find their area.
    • Justify their solutions and solution paths by composing shapes into rectangles and decomposing into triangles or other shapes.
    Given real world and mathematical problems involving area of triangles and other polygons,
    • Compose and decompose shapes to find solutions.
    • Interpret solutions.
    Teacher Vocabulary:
    • Right triangles
    • Special quadrilaterals
    • Polygons
    • Area
    • Decompose
    • Compose
    Knowledge:
    Students know:
    • Appropriate units for measuring area: square inches, square units, square feet, etc..
    • Strategies for composing and decomposing shapes to find area.
    Skills:
    Students are able to:
    • Communicate the relationship between models of area and the associated real world mathematical problems.
    • Use logical reasoning to choose and apply strategies for finding area by composing and decomposing shapes.
    • Accurately compute area of rectangles using multiplication and the formula.
    Understanding:
    Students understand that:
    • The area of a figure is measured by the number of same-size unit squares that exactly cover the interior space of the figure.
    • Shapes can be composed and decomposed into shapes with related properties,
    • Area is additive.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.26.1: Define area, special quadrilaterals, right triangles, and polygons.
    M.6.26.2: Analyze the area of other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.
    M.6.26.3: Apply area formulas to solve real-world mathematical problems.
    M.6.26.4: Demonstrate how the area of a rectangle is equal to the sum of the area of two equal right triangles.
    M.6.26.5: Explain how to find the area for rectangles.
    M.6.26.6: Select manipulatives to demonstrate how to compose and decompose triangles and other shapes.
    M.6.26.7: Recognize and demonstrate that two right triangles make a rectangle.

    Prior Knowledge Skills:
    • Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.
    • Recall the formula for area (L × W).
    • Recognize that unit squares are equal.
    • Recall the formula for perimeter (P= L+L+W+W or P=2L + 2W).
    • Recall basic addition and multiplication facts.
    • Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.
    • Partition a shape into 4 parts with equal area, and describe the area of each part as 1 of the area of the shape.
    • Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds, or four fourths.
    • Recognize that equal shares of identical wholes need not have the same shape.
    • Demonstrate equivalent fractions using concrete objects or pictorial representations.
    • Define right angle.
    • Recognize that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
    • Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
    • Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces.
    • Identify triangles.
    Mathematics (2019)
    Grade(s): 6
    All Resources: 3
    Learning Activities: 1
    Lesson Plans: 1
    Classroom Resources: 1
    27. Determine the surface area of three-dimensional figures by representing them with nets composed of rectangles and triangles to solve real-world and mathematical problems.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given real world and mathematical problems involving surface area,
    • Use models of the relating net of the 3-D figure to explain and justify solutions and solution paths.
    Teacher Vocabulary:
    • Nets
    • Surface area
    • Rectangular prism
    • Triangular prism
    • Square pyramid
    • Rectangular pyramid
    • Triangular pyramid
    Knowledge:
    Students know:
    • Measurable attributes of objects, specifically area and surface area.
    • Strategies for representing the surface area of a 3-D shape as a 2-D net.
    Skills:
    Students are able to:
    • Communicate the relationships between rectangular models of area and multiplication problems.
    • Model the surface area of 3-D shapes using 2-D nets.
    • Accurately measure and compute area of triangles and rectangles.
    • Strategically and fluently choose and apply strategies for finding surface areas of 3-D figures.
    Understanding:
    Students understand that:
    • Area is additive.
    • Surface area of a 3-D shape is represented by the sum of the areas of the faces of the object.
    • Models represent measurable attributes of objects and help to solve problems.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.27.1: Define three-dimensional figures, surface area, and nets.
    M.6.27.2: Identify three-dimensional figures.
    M.6.27.3: Draw nets to find the surface area of a given three-dimensional figure.
    M.6.27.4: Recall how to calculate the area of a rectangle.
    M.6.27.5: Select and create a three-dimensional figure using manipulatives.

    Prior Knowledge Skills:
    • Describe attributes of three-dimensional figures.
    • Describe attributes of two-dimensional figures.
    • Identify solid figures.
    • Recall the formula for area (L × W).
    • Recognize that unit squares are equal.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.27 Calculate problems involving perimeter of squares, triangles, rectangles, and other polygons with sides up to 10 units and calculate problems involving the area of rectangles and squares with sides up to 10 units (whole numbers only).


    Mathematics (2019)
    Grade(s): 6
    All Resources: 3
    Learning Activities: 1
    Classroom Resources: 2
    28. Apply previous understanding of volume of right rectangular prisms to those with fractional edge lengths to solve real-world and mathematical problems.

    a. Use models (cubes or drawings) and the volume formulas (V = lwh and V = Bh) to find and compare volumes of right rectangular prisms.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a right rectangular prism with fractional edge lengths within a real world or mathematical problem context,
    • Find and justify the volume of the prism as part or all of the problem's solution by relating a cube filled model to the corresponding multiplication problem(s).
    Given cubes with appropriate unit fraction edge lengths,
    • Create and explain rectangular prism models to show that the volume of a right rectangular prism with fractional edge lengths l, w, and h is represented by the formulas V = l w h and V = b h.
    Teacher Vocabulary:
    • Right rectangular prism
    • V = b h (Volume of a right rectangular prism = the area of the base x the height)
    Knowledge:
    Students know:
    • Measurable attributes of objects, specifically volume.
    • Units of measurement, specifically unit cubes.
    • Relationships between unit cubes and corresponding cubes with unit fraction edge lengths.
    • Strategies for determining volume.
    • Strategies for finding products of fractions.
    Skills:
    Students are able to:
    • Communicate the relationships between rectangular models of volume and multiplication problems.
    • Model the volume of rectangles using manipulatives.
    • Accurately measure volume using cubes with unit fraction edge lengths.
    • Strategically and fluently choose and apply strategies for finding products of fractions.
    • Accurately compute products of fractions.
    Understanding:
    Students understand that:
    • The volume of a solid object is measured by the number of same-size cubes that exactly fill the interior space of the object.
    • Generalized formulas for determining area and volume of shapes can be applied regardless of the level of accuracy of the shape's measurements (in this case, side lengths).
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.6.28.1: Define volume, rectangular prism, edge, and formula.
    M.6.28.2: Recall how to multiply fractional numbers.
    M.6.28.3: Evaluate the volumes of rectangular prisms in the context of solving real-world and mathematical problems.
    M.6.28.4: Use models and volume formulas (V=lwh and V=Bh) to find volumes in the context of solving real-world and mathematical problems.
    M.6.28.5: Calculate the volume of a rectangular prism using fractional lengths.
    M.6.28.6: Test the formula V= lwh and V=Bh with the experimental findings.
    M.6.28.7: Experiment with finding the volume using a variety of sizes of rectangular prisms manipulatives.

    Prior Knowledge Skills:
    • Define volume.
    • Recognize the formula for volume.
    • Recall the attributes of three-dimensional solids.
    • Compare the unit size of volume/capacity in the metric system including milliliters and liters.
    • Measure and estimate liquid volumes.
    • Describe attributes of three-dimensional figures.
    • Describe attributes of two-dimensional figures.
    • Define volume including the formulas V = L × W × h, and V = B × h.
    • Define solid figures.
    • Define unit cube.
    • Recognize that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
    • Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
    • Describe attributes of three-dimensional figures.
    • Describe attributes of two-dimensional figures.
    • Compare the unit size of volume/capacity in the metric system including milliliters and liters.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.6.28 Solve real-world and mathematical problems involving the volume of cubes and rectangular prisms.


    Proportional Reasoning
    Analyze proportional relationships and use them to solve real-world and mathematical problems.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 2
    Lesson Plans: 1
    Classroom Resources: 1
    1. Calculate unit rates of length, area, and other quantities measured in like or different units that include ratios or fractions.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Compute a unit rate for ratios that compare quantities with different units.
    • Determine the unit rate for a given ratio, including unit rates expressed as a complex fraction.

    • Example: if a runner runs 1/2 mile every 3/4 hour, a student should be able to write the ratio as a complex fraction.)
    Teacher Vocabulary:
    • Unit rate
    • Ratio
    • Unit
    • Complex fractions
    Knowledge:
    Students know:
    • What a unit rate is and how to calculate it given a relationship between quantities.
    • Quantities compared in ratios are not always whole numbers but can be represented by fractions or decimals.
    • A fraction can be used to represent division.
    Skills:
    Students are able to:
    Compute unit rates associated with ratios of fractional
    • lengths.
    • Areas.
    • quantities measured in like or different units.
    Understanding:
    Students understand that:
    • Two measurements that create a unit rate are always different (miles per gallon, dollars per hour)
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.1.1: Define unit rate, proportions, area, length, and ratio.
    M.7.1.2: Recall how to find unit rates using ratios.
    M.7.1.3: Recall the steps used to solve division of fraction problems.

    Prior Knowledge Skills:
    • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
    • Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
    • Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
    • Generate equivalent fractions.
    • Define quantity, fraction, and ratio.
    • Reinterpret a fraction as a ratio.
      Example: Read 2/3 as 2 out of 3.
    • Write a ratio as a fraction.
    • Create a ratio or proportion from a given word problem, diagram, table, or equation.
    • Calculate unit rate or rate by using ratios or proportions.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.1 Calculate a unit rate (limited to whole numbers under 100).


    Mathematics (2019)
    Grade(s): 7
    All Resources: 4
    Learning Activities: 1
    Lesson Plans: 1
    Classroom Resources: 2
    2. Represent a relationship between two quantities and determine whether the two quantities are related proportionally.

    a. Use equivalent ratios displayed in a table or in a graph of the relationship in the coordinate plane to determine whether a relationship between two quantities is proportional.

    b. Identify the constant of proportionality (unit rate) and express the proportional relationship using multiple representations including tables, graphs, equations, diagrams, and verbal descriptions.

    c. Explain in context the meaning of a point (x,y) on the graph of a proportional relationship, with special attention to the points (0,0) and (1, r) where r is the unit rate.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Decide whether a relationship between two quantities is proportional.
    • Recognize that not all relationships are proportional.
    • Use equivalent ratios in a table or a coordinate graph to verify a proportional relationship.
    • Identify the constant of proportionality when a proportional relationship exists between two quantities.
    • Use a variety of models (tables, graphs, equations, diagrams and verbal descriptions) to demonstrate the constant of proportionality.
    • Explain the meaning of a point (x, y) in the context of a real-world problem.
    • Example, if a boy charges $6 per hour to mow lawns, this relationship can be graphed on the coordinate plane. The point (1,6) means that after 1 hour of working the boy makes $6, which shows the unit rate of $6 per hour.
    Teacher Vocabulary:
    • Equivalent ratios
    • proportional
    • Coordinate plane
    • Ratio table
    • Unit rate
    • Constant of proportionality
    • Equation
    • ordered pair
    Knowledge:
    Students know:
    • (2a) how to explain whether a relationship is proportional.
    • (2b) that the constant of proportionality is the same as a unit rate. Students know:
      • where the constant of proportionality can be found in a table, graph, equation or diagram.
      • (2c) that the constant of proportionality or unit rate can be found on a graph of a proportional relationship where the input value or x-coordinate is 1.
    Skills:
    Students are able to:
    • (2a) determine if a proportional relationship exists when given a table of equivalent ratios or a graph of the relationship in the coordinate plane.
    • (2b) identify the constant of proportionality and express the proportional relationship using a variety of representations including tables, graphs, equations, diagrams, and verbal descriptions.
    • (2c) model a proportional relationship using coordinate graphing.
    • Explain the meaning of the point (1, r), where r is the unit rate or constant of proportionality.
    Understanding:
    Students understand that:
    • (2a) A proportional relationship requires equivalent ratios between quantities. Students understand how to decide whether two quantities are proportional.
    • (2b) The constant of proportionality is the unit rate. Students are able to identify the constant of proportionality for a proportional relationship and explain its meaning in a real-world context. (2c) The context of a problem can help them interpret a point on a graph of a proportional relationship.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.2.1: Define proportions and proportional relationships.
    M.7.2.2: Demonstrate how to write ratios as a fraction.
    M.7.2.3: Define equivalent ratios and origin.
    M.7.2.4: Locate the origin on a coordinate plane.
    M.7.2.5 Show how to graph on Cartesian plane.
    M.7.2.6: Determine if the graph is a straight line through the origin.
    M.7.2.7: Use a table or graph to determine whether two quantities are proportional.
    M.7.2.8: Define a constant and equations.
    M.7.2.9: Create a table from a verbal description, diagram, or a graph.
    M.7.2.10: Identify numeric patterns and finding the rule for that pattern.
    M.7.2.11: Recall how to find unit rate.
    M.7.2.12: Recall how to write equations to represent a proportional relationship.
    M.7.2.13: Discuss the use of variables.
    M.7.2.14: Define ordered pairs.
    M.7.2.15: Show how to plot points on a Cartesian plane.
    M.7.2.16: Locate the origin on the coordinate plane.

    Prior Knowledge Skills:
    • Recall basic addition, subtraction, multiplication, and division facts.
    • Define ordered pair of numbers.
    • Define x-axis, y-axis, and zero on a coordinate.
    • Specify locations on the coordinate system.
    • Define ordered pair of numbers, quadrant one, coordinate plane, and plot points.
    • Label the horizontal axis (x).
    • Label the vertical axis (y).
    • Identify the x- and y- values in ordered pairs.
    • Model writing ordered pairs.
    • Define quantity, fraction, and ratio.
    • Reinterpret a fraction as a ratio.
      Example: Read 2/3 as 2 out of 3.
    • Write a ratio as a fraction.
    • Create a ratio or proportion from a given word problem, diagram, table, or equation.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.2 Use a ratio to model or describe a real-world relationship.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 7
    Learning Activities: 1
    Classroom Resources: 6
    3. Solve multi-step percent problems in context using proportional reasoning, including simple interest, tax, gratuities, commissions, fees, markups and markdowns, percent increase, and percent decrease.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use proportional reasoning strategies including setting up and solving proportions to solve problems involving simple interest, tax, gratuities, commissions, fees, markups, percent increase, markdowns or percent decrease.

    • Example: Students might be asked to "order" from a menu for lunch then calculate the tax and gratuities to determine the total cost.
    Teacher Vocabulary:
    • Proportion
    • Simple interest
    • Tax
    • Gratuities
    • Commissions
    • Fees
    • Markups and markdowns
    • percent increase and percent decrease
    Knowledge:
    Students know:
    • how to interpret a real-world problem to determine what is being asked.
    • Techniques for calculating and using percents to solve problems in context.
    • how to interpret the solution in the context of the problem.
    Skills:
    Students are able to:
    • Write and solve proportions to help them solve real-world problems involving percent.
    • Solve problems that require them to calculate: simple interest, tax, gratuities, commission, fees, mark ups, markdowns, percent increase and percent decrease.
    Understanding:
    Students understand that:
    • percents relate to real-world contexts, and how to determine the reasonableness of their answers based on that context.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.3.1: Define interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.
    M.7.3.2: Apply definitions to context in real world problems.
    M.7.3.3: Solve proportional problems.
    M.7.3.4: Recall how to find percent and ratios.
    M.7.3.5: Recall steps for solving multi-step problems.

    Prior Knowledge Skills:
    • Define percent.
    • Calculate a proportion for missing information.
    • Identify a proportion from given information.
    • Solve a proportion using part over whole equals percent over 100.
    • Define equation and variable.
    • Set up an equation to represent the given situation, using correct mathematical operations and variables.
    • Identify the unknown, in a given situation, as the variable.
    • Solve the equation represented by the real-world situation.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.3 Calculate 10%, 20%, 25%, and 50% of a number up to 100.


    Number Systems and Operations
    Apply and extend prior knowledge of addition, subtraction, multiplication, and division to operations with rational numbers.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 11
    Learning Activities: 5
    Classroom Resources: 6
    4. Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals.

    a. Identify and explain situations where the sum of opposite quantities is 0 and opposite quantities are defined as additive inverses.

    b. Interpret the sum of two or more rational numbers, by using a number line and in real-world contexts.

    c. Explain subtraction of rational numbers as addition of additive inverses.

    d. Use a number line to demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

    e. Extend strategies of multiplication to rational numbers to develop rules for multiplying signed numbers, showing that the properties of the operations are preserved.

    f. Divide integers and explain that division by zero is undefined. Interpret the quotient of integers (with a non-zero divisor) as a rational number.

    g. Convert a rational number to a decimal using long division, explaining that the decimal form of a rational number terminates or eventually repeats.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Explain situations where opposite quantities combine to make zero, known as additive inverses.
    • Apply their knowledge of addition and subtraction of rational numbers to describe real-world contexts.
    • Add and subtract rational numbers using number lines to show connection to distance
    • Explain the connection between subtraction and addition of additive inverses.
    • Model multiplication and division of rational numbers (number horizontal and vertical number lines, integer chips, bar models).
    • Use properties of operations to multiply signed numbers.
    • Convert rational numbers to a decimal using long division and determine if the result is terminating or repeating.
    Teacher Vocabulary:
    • Integers
    • Rational numbers
    • Additive inverses
    • opposite quantities
    • Absolute value
    • Terminating decimals
    • Repeating decimals
    Knowledge:
    Students know:
    • a number and its opposite have a sum of 0.
    • A number and its opposite are called additive inverses.
    • Strategies for adding and subtracting two or more numbers.
    • Absolute value represents distance on a number line, therefore it is always non-negative.
    • Strategies for multiplying signed numbers.
    • Every quotient of integers (with non-zero divisor) is a rational number.
    • If p and q are integers, then -(p/q) = (-p)/q = p/(-q).
    • The decimal form of a rational number terminates or eventually repeats.
    Skills:
    Students are able to:
    • add rational numbers.
    • Subtract rational numbers.
    • Represent addition and subtraction on a number line diagram.
    • Describe situations in which opposite quantities combine to make 0.
    • Find the opposite of a number.
    • Interpret sums of rational numbers by describing real-world contexts.
    • Show that the distance between two rational numbers on the number line is the absolute value of their difference.
    • Use absolute value in real-world contexts involving distances.
    • Multiply and divide rational numbers.
    • Convert a rational number to a decimal using long division.
    Understanding:
    Students understand that:
    • finding sums and differences of rational numbers (negative and positive) involves determining direction and distance on the number line.
    • Subtraction of rational numbers is the same as adding the additive inverse, p - q = p + (-q).
    • If a factor is multiplied by a number greater than one, the answer is larger than that factor.
    • If a factor is multiplied by a number between 0 and 1, the answer is smaller than that factor.
    • Multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers.
    • Integers can be divided, provided that the divisor is not zero.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.4.1: Define rational numbers, horizontal, and vertical.
    M.7.4.2: Recall how to extend a horizontal number line.
    M.7.4.3: Recall how to extend a vertical number line.
    M.7.4.4: Demonstrate addition and subtraction of whole numbers using a horizontal or vertical number line.
    M.7.4.5: Give examples of rational numbers.
    M.7.4.6: Define absolute value and additive inverse.
    M.7.4.7: Explain that the sum of a number and its opposite is zero.
    M.7.4.8: Locate positive, negative, and zero numbers on a number line.
    M.7.4.9: Recall properties of addition and subtraction.
    M.7.4.10: Model addition and subtraction using manipulatives.
    M.7.4.11: Show addition and subtraction of 2 or more rational numbers using a number line within real world context.
    M.7.4.12: Define absolute value and additive inverse.
    M.7.4.13: Show subtraction as the additive inverse.
    M.7.4.14: Give examples of the opposite of a given number.
    M.7.4.15: Show addition and subtraction using a number line.
    M.7.4.16: Discuss various strategies for solving real-world and mathematical problems.
    M.7.4.17: Identify properties of operations for addition and subtraction.
    M.7.4.18: Recall the steps for solving addition and subtraction of rational numbers.
    M.7.4.19: Identify the difference between two rational numbers on a number line.
    M.7.4.20: Recall the steps of solving multiplication of rational numbers.
    M.7.4.21: Identify the pattern for multiplying signed numbers.
    M.7.4.22: Recall the steps of solving division of rational numbers.
    M.7.4.23: Explain that dividing a rational number zero is undefined.
    M.7.4.24: Recall that a fraction can be written as a division problem.
    M.7.4.25: Recall the steps to divide two rational numbers.
    M.7.4.26: Identify whether a decimal is terminating or repeating.

    Prior Knowledge Skills:
    • Define parentheses, braces, and brackets.
    • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
    • Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
    • Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
    • Generate equivalent fractions.
    • Show on a number line that numbers that are equal distance from 0 and on opposite sides of 0 have opposite signs.
    • Define rational number.
    • Arrange integers and /or rational numbers on a horizontal or vertical number line.
    • Locate the position of integers and/or rational numbers on a horizontal or vertical number line.
    • Identify a rational number as a point on the number line.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.4 Add and subtract integers up to 15.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 0
    5. Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Apply their knowledge of addition, subtraction, multiplication and division of rational numbers to describe real-world contexts.
    • Solve multi-step problems using numerical expressions that involve addition, subtraction, multiplication, and/or division of rational numbers, including problems that involve complex fractions
    Teacher Vocabulary:
    • Rational numbers
    • Complex fractions
    • properties of operations
    Knowledge:
    Students know:
    • how to model real-world problems to include situations involving elevation, temperature changes, debits and credits, and proportional relationships with negative rates of change.
    • how to evaluate numerical expressions with greater fluency, using the properties of operations when necessary.
    Skills:
    Students are able to:
    • Solve real-world and mathematical problems involving the four operations with rational numbers.
    Understanding:
    Students understand that:
    • rational numbers can represent values in real-world situations.
    • properties of operations learned with whole numbers in elementary apply to rational numbers.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.5.1: Discuss various strategies for solving real-world and mathematical problems.
    M.7.5.2: Recall steps for solving fractional problems.
    M.7.5.3: Identify properties of operations for addition and multiplication.
    M.7.5.4: Recall the rules for multiplication and division of rational numbers.
    M.7.5.5: Recall the rules for addition and subtraction of rational numbers.

    Prior Knowledge Skills:
    • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
    • Define rational number.
    • Arrange integers and /or rational numbers on a horizontal or vertical number line.
    • Locate the position of integers and/or rational numbers on a horizontal or vertical number line.
    • Identify a rational number as a point on the number line.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.5 Solve multiplication problems up to fifteen with whole number factors.


    Algebra and Functions
    Create equivalent expressions using the properties of operations.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 1
    Classroom Resources: 1
    6. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use properties of operations to produce combined and re-written forms of the expressions that are useful in resolving mathematical and contextual problems.
    Teacher Vocabulary:
    Term
  • like terms
  • Constant
  • Factor
  • Expression
  • Rational coefficient
  • Knowledge:
    Students know:
    • how to add, subtract, multiply, and divide rational numbers.
    • A(b + c) = ab + ac.
    • how to find the greatest common factor of two or more terms.
    Skills:
    Students are able to:
    • apply properties of operations as strategies to add and subtract linear expressions with rational coefficients.
    • Apply properties of operations as strategies to factor linear expressions with rational coefficients.
    • Apply properties of operations as strategies to expand linear expressions with rational coefficients.
    Understanding:
    Students understand that:
    • only like terms can be combined, e.g., x + y = x + y but x + x = 2x.
    • To factor an expression, one must factor out the greatest common factor.
    • There are many different ways to write the same expression.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.6.1: Define linear expression, rational, coefficient, and rational coefficient.
    M.7.6.2: Simplify an expression by dividing by the greatest common factor (Ex. 18x + 6y= 6(3x + y).
    M.7.6.3: Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
    M.7.6.4: Recognize the property demonstrated in a given expression.
    M.7.6.5: Combine like terms of a given expression.
    M.7.6.6: Recall how to find the greatest common factor.
    M.7.6.7: Give examples of the properties of operations including distributive, commutative, and associative.

    Prior Knowledge Skills:
    • Apply properties of operations for addition and subtraction.
    • Define equivalent, simplify, term, distributive property, associative property of addition and multiplication, and the commutative property of addition and multiplication.
    • Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
    • Combine terms that are alike of a given expression.
    • Recognize the property demonstrated in a given expression.
    • Simplify an expression by dividing by the greatest common factor.
      Example: 18x + 6y = 6(3x + y).
    • Determine the greatest common factor.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.5 Solve multiplication problems up to fifteen with whole number factors.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 3
    Learning Activities: 1
    Classroom Resources: 2
    7. Generate expressions in equivalent forms based on context and explain how the quantities are related.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Write an expression for a situation and determine equivalent expressions for the same situation.
    Teacher Vocabulary:
    • like terms
    • Equivalent expressions
    • Distributive property
    • Factor
    Knowledge:
    Students know:
    • properties of operations can be used to identify or create equivalent linear expressions.
    • Equivalent expressions can reveal real-world and mathematical relationships, and some forms of equivalent expressions can provide more insight than others.
    Skills:
    Students are able to:
    • determine whether two expressions are equivalent.
    • Rewrite expressions into equivalent forms by combining like terms, using the distributive property, and factoring.
    Understanding:
    Students understand that:
    • rewriting expressions in multiple equivalent forms allows for thinking about problems in different ways and highlights different aspects/relationships of quantities in problems.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.7.1: Define expression, equivalent, and equivalent expressions.
    M.7.7.2: Recall mathematical terms such as sum, difference, etc.
    M.7.7.3: Recognize that a variable without a written coefficient is understood to have a coefficient of one.
    M.7.7.4: Recall how to convert mathematical terms to mathematical symbols and numbers and vice versa.
    M.7.7.5: Restate numerical expressions with words.

    Prior Knowledge Skills:
    • Define equivalent expressions.
    • Recognize equivalent expressions.
    • Recognize that a variable without a written coefficient is understood to be one.
    • Convert mathematical terms to mathematical symbols and numbers (Ex. sum: +, difference: -; product: ·, quotient: ÷).

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.7 Match equivalent expressions using the properties of operations.
    M.AAS.7.7a Identify a pattern in a sequence of whole numbers with a whole number common difference (e.g. when skip counting by 5, the whole number common difference is 5).


    Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 1
    Classroom Resources: 1
    8. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form.
    • Interpret solutions of problems with rational numbers in the context of the problem.
    • Assess the reasonableness of answers using mental computation and estimation strategies.
    • Use variables to represent quantities in a real-world or mathematical problem.
    Teacher Vocabulary:
    • Rational numbers
    • Integers
    • Estimation
    Knowledge:
    Students know:
    • techniques for converting between fractions, decimals, and percents.
    • Techniques for estimation, mental computations, and how to assess the reasonableness of their answers.
    Skills:
    Students are able to:
    • convert between different forms of a rational number.
    • Add, subtract, multiply and divide rational numbers. -translate verbal forms of problems into algebraic symbols, expressions, and equations.
    • Use estimation and mental computation techniques to assess the reasonableness of their answers.
    Understanding:
    Students understand that:
    • One form of a number may be more advantageous than another form, based on the problem context.
    • Using estimation strategies helps to determine the reasonableness of answers.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.8.1: Define estimation, rational numbers, and reasonable.
    M.7.8.2: Recall mental calculation strategies.
    M.7.8.3: Recall estimation strategies.
    M.7.8.4: Analyze the given word problem to set up a mathematical problem.
    M.7.8.5: Recognize the mathematical operations of rational numbers in any form, including converting between forms. (Ex. 0.25=1/4 =25%).
    M.7.8.6: Recognize the rules of operations of positive and negative numbers.
    M.7.8.7: Recognize properties of numbers (Distributive, Associative, Commutative).
    M.7.8.8: Recall problem solving methods.

    Prior Knowledge Skills:
    • Represent addition and subtraction with objects, mental images, drawings, expressions, or equations.
    • Define integers, positive and negative numbers.
    • Define rational number.
    • Define equivalent, simplify, term, distributive property, associative property of addition and multiplication, and the commutative property of addition and multiplication.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.8 Add and subtract integers in a real-world situation.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 2
    Classroom Resources: 2
    9. Use variables to represent quantities in real-world or mathematical problems and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities.

    a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

    b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality, and interpret it in the context of the problem.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Write and solve mathematical equations (or inequalities) to model real world problems.
    • Interpret the solution to an equation in the context of a problem
    • Interpret the solution set of an inequality in the context of a problem.
    • Graph the solution to an inequality on a number line.
    Teacher Vocabulary:
    • Algebraic expressions
    • Equations
    • Inequalities
    • Greater than
    • Greater than or equal to
    • less than
    • less than or equal to
    Knowledge:
    Students know:
    • p(x + q) = px + pq, where p and q are specific rational numbers.
    • When multiplying or dividing both sides of an inequality by a negative number, every term must change signs and the inequality symbol reversed.
    • In the graph of an inequality, the endpoint will be a closed circle indicating the number is included in the solution set (≤ or ≥) or an open circle indicating the number is not included in the solution set ( < or >).
    Skills:
    Students are able to:
    • use variables to represent quantities in a real-world or mathematical problem.
    • Construct equations (px + q = r and p(x + q) = r) to solve problems by reasoning about the quantities.
    • Construct simple inequalities (px + q > r or px + q < r) to solve problems by reasoning about the quantities.
    • Graph the solution set of an inequality.
    Understanding:
    Students understand that:
    • Real-world problems can be represented through algebraic expressions, equations, and inequalities.
    • Why the inequality symbol reverses when multiplying or dividing both sides of an inequality by a negative number.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.9.1: Define equation, inequality, and variable.
    M.7.9.2: Set up equations and inequalities to represent the given situation, using correct mathematical operations and variables.
    M.7.9.3: Calculate a solution or solution set by combining like terms, isolating the variable, and/or using inverse operations.
    M.7.9.4: Test the found number or number set for accuracy by substitution.
    M.7.9.5: Recall solving one step equations and inequalities.
    M.7.9.6: Recognize properties of numbers (Distributive, Associative, Commutative).
    M.7.9.7: Define equation and variable.
    M.7.9.8: Set up an equation to represent the given situation, using correct mathematical operations and variables.
    M.7.9.9: Calculate a solution to an equation by combining like terms, isolating the variable, and/or using inverse operations.
    M.7.9.10: Test the found number for accuracy by substitution.
    Example: Is 5 an accurate solution of 2(x + 5)=12?.
    M.7.9.11: Identify the unknown, in a given situation, as the variable.
    M.7.9.12: List given information from the problem.
    M.7.9.13: Recalling one-step equations.
    M.7.9.14: Explain the distributive property.
    M.7.9.15: Define inequality and variable.
    M.7.9.16: Set up an inequality to represent the given situation, using correct mathematical operations and variables.
    M.7.9.17: Calculate a solution set to an inequality by combining like terms, isolating the variable, and/or using inverse operations.
    M.7.9.18: Test the solution set for accuracy.
    M.7.9.19: Identify the unknown, of a given situation, as the variable.
    M.7.9.20: List information from the problem.
    M.7.9.21: Recall how to graph inequalities on a number line.
    M.7.9.22: Recall how to solve one step inequalities.

    Prior Knowledge Skills:
    • Define inequality.
    • Define equivalent, simplify, term, distributive property, associative property of addition and multiplication, and the commutative property of addition and multiplication.
    • Define equation, solution of an equation, solution of an inequality, and inequality.
    • Compare and contrast equations and inequalities.
    • Determine if an inequality is by replacing the variable with a given number.
    • Determine if an equation is true by replacing the variable with a given number.
    • Simplify a numerical sentence to determine equivalence.
    • Recognize the symbols for =, >, <, ?, and ?.
    • Define equation and variable.
    • Set up an equation to represent the given situation, using correct mathematical operations and variables.
    • Identify the unknown, in a given situation, as the variable.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.9 Use the properties of operations to solve one-step equations and inequalities from real-world and mathematical problems.


    Data Analysis, Statistics, and Probability
    Make inferences about a population using random sampling.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 5
    Learning Activities: 1
    Classroom Resources: 4
    10. Examine a sample of a population to generalize information about the population.

    a. Differentiate between a sample and a population.

    b. Compare sampling techniques to determine whether a sample is random and thus representative of a population, explaining that random sampling tends to produce representative samples and support valid inferences.

    c. Determine whether conclusions and generalizations can be made about a population based on a sample.

    d. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest, generating multiple samples to gauge variation and making predictions or conclusions about the population.

    e. Informally explain situations in which statistical bias may exist.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • distinguish between a population and a sample population, and identify both for statistical questions.
    • Understand that a population characteristic is determined using data from the entire population, whereas a sample statistic is determined using data from a sample of the population.
    • Describe different ways that data can be collected to answer a statistical question.
    • Understand why a sample of a population may be useful or necessary to answer a statistical question.
    Teacher Vocabulary:
    • Population
    • Sample
    • biased
    • Unbiased
    • Sampling techniques
    • Random sampling
    • Representative samples
    • Inferences
    Knowledge:
    Students know:
    • a random sample can be found by various methods, including simulations or a random number generator.
    • Samples should be the same size in order to compare the variation in estimates or predictions.
    Skills:
    Students are able to:
    • determine whether a sample is random or not and justify their reasoning.
    • Use the center and variability of data collected from multiple same-size samples to estimate parameters of a population.
    • Make inferences about a population from random sampling of that population.
    • Informally assess the difference between two data sets by examining the overlap and separation between the graphical representations of two data sets.
    Understanding:
    Students understand that:
    • statistics can be used to gain information about a population by examining a sample of the populations.
    • Generalizations about a population from a sample are valid only if the sample is representative of that population.
    • Random sampling tends to produce representative samples and support valid inferences
    • The way that data is collected, organized and displayed influences interpretation.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.10.1: Recall how to calculate range, outlier, ratio, and proportion.
    M.7.10.2: Define sample, data, variation, prediction, estimation, validity, population, inference, random sampling, statistic, and generalization.
    M.7.10.3: Explain the validity of random sampling.
    M.7.10.4: Differentiate the appropriate sampling method.
    M.7.10.5: Analyze attributes of sample size.
    M.7.10.6: Compare and contrast the random sampling data to the population.
    M.7.10.7: Compare sample size with population to check for validity.
    M.7.10.8: Analyze conclusions of the sample to determine its appropriateness for the population.
    M.7.10.9: Predict an outcome of the entire population based on random samplings.
    M.7.10.10: Discuss real world examples of valid sampling and generalizations.
    M.7.10.11: Recall the nature of the attribute, how it was measured, and its unit of measure.
    M.7.10.12: Collect data from population randomly, choosing same size samples. (Ex. If population is your school, different random samplings should be same number of students).
    M.7.10.13: Define and discuss bias.
    M.7.10.14: Compare and contrast statistical situations to determine if statistical bias exists.

    Prior Knowledge Skills:
    • Define statistical question.
    • Calculate the range, mean, median, and mode of a numerical data set.
    • Recognize the difference between population and sample.
    • Identify bias from real world context.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.10 Find the range and median (when given an odd number of data points), and mean (involving one or two-digit numbers) in real-world situations.


    Make inferences from an informal comparison of two populations.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 1
    Classroom Resources: 1
    11. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Determine which measure of center best represents the typical value in the data set.
    • Calculate measures of variability (range, interquartile range, and mean absolute deviation), noting how larger values indicate that values are more spread out from the center of the distribution.
    Teacher Vocabulary:
    • Visual overlap
    • Measure of variability
    • Data distribution
    • range
    • interquartile range
    • mean absolute deviation
    Knowledge:
    Students know:
    • populations can be compared using measures of center and measures of variability
    Skills:
    Students are able to:
    • informally assess the degree of visual overlap of two numerical data distributions with similar variabilities.
    • Measure the difference between the centers by expressing it as a multiple of a measure of variability.
    Understanding:
    Students understand that:
    • outliers skew data, which in turn affects the display.
    • Measures of center give information about the location of mean, median, and mode, whereas measures of variability give information about how spread out the data is.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.11.1: Define measure of variability, distribution, and measure of center.
    M.7.11.2: Analyze the skew of the distributions and recognize the difference in measure of center and variability.
    M.7.11.3: Compare the measure of center and measure of variability of two distributions.
    M.7.11.4: Relate the measure of variation with the concept of range.
    M.7.11.5: Relate the measure of the center with the concept of mean.
    M.7.11.6: Recall how to calculate measure of center and measure of variability.
    M.7.11.7: Discuss how to read and interpret a graph.

    Prior Knowledge Skills:
    • Describe the center of a set of data in a given distribution.
    • Compare and contrast the center and variation.
    • Interpret graphing points in all four quadrants of the coordinate plane in real-world situations.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.11 Make inferences from graphical representations of a data set (e.g. line plot, dot plots, histograms, bar graphs, stem and leaf plots, or line graphs).


    Mathematics (2019)
    Grade(s): 7
    All Resources: 2
    Classroom Resources: 2
    12. Make informal comparative inferences about two populations using measures of center and variability and/or mean absolute deviation in context.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use measures of center for numerical data from random samples to draw informal comparative inferences about two populations.
    • Use measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
    Teacher Vocabulary:
    • Mean
    • median
    • mode
    • Mean absolute deviation
    • Range
    • Interquartile range
    Knowledge:
    Students know:
    • measures of center are insufficient to compare populations. measures of variability are necessary to assess if data sets are significantly different or not.
    • Mean is the sum of the numerical values divided by the number of values.
    • Median is the number that is the midpoint of an ordered set of numerical data.
    • Mode is the data value or category occurring with the greatest frequency (there can be no mode, one mode, or several modes).
    • Mean absolute deviation of a data set is found by the following steps: 1) calculate the mean 2) determine the deviation of each variable from the mean 3) divide the sum of the absolute value of each deviation by the number of data points.
    • Range is a number found by subtracting the minimum value from the maximum. value.
    Skills:
    Students are able to:
    • find the measures of center of a data set.
    • Find the interquartile range of a data set and use to compare variability between data sets.
    Understanding:
    Students understand that:
    • outliers skew data, which in turn affects the display.
    • Measures of center give information about the location of mean, median and mode, whereas measures of variability give information about how spread out the data is.
    • The mean absolute deviation of a data set describes the average distance that points within a data set are from the mean of the data set.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.12.1: Define measure of variability, measure of center, inference and mean absolute deviation.
    M.7.12.2: Recall how to calculate measure of center and measure of variability.
    M.7.12.3: Recall that center is related to measure of center and measure of variability is related to variation.
    M.7.12.4: Compare and contrast the measure of center and measure of variability of two numerical data sets.
    M.7.12.5: Calculate the mean absolute deviation of a data set in context.

    Prior Knowledge Skills:
    • Describe the center of a set of data in a given distribution.
    • Compare and contrast the center and variation.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.12 Compare two sets of data within a single data display such as a picture graph, line plot, or bar graph.


    Investigate probability models.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 3
    Classroom Resources: 3
    13. Use a number from 0 to 1 to represent the probability of a chance event occurring, explaining that larger numbers indicate greater likelihood of the event occurring, while a number near zero indicates an unlikely event.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Accurately describe the likelihood of an event occurring.
    • Describe the probability of an event occurring on a scale of 0 to 1 and using appropriate vocabulary based on the scale.
    • Categorize and order the probabilities of events by their likelihood.
    • Use words like impossible, very unlikely, unlikely, equally likely/unlikely, likely, very likely, and certain to describe the probabilities of events.
    Teacher Vocabulary:
    • probability
    • Event
    • Chance
    • likely
    • Unlikely
    • very unlikely
    • very likely
    • Equally likely
    • Impossible
    • Certain
    Knowledge:
    Students know:
    • probability is equal to the ratio of favorable number of outcomes to total possible number of outcomes.
    • As a number for probability increases, so does the likelihood of the event occurring.
    • A probability near 0 indicates an unlikely event.
    • A probability around 1/2 indicates an event that is neither unlikely nor likely.
    • A probability near 1 indicates a likely event.
    Skills:
    Students are able to:
    • approximate the probability of a chance event.
    • Use words like impossible, very unlikely, unlikely, equally likely/unlikely, likely, very likely, and certain to describe the probabilities of events.
    Understanding:
    Students understand that:
    • the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.
    • An event that is equally likely or equally unlikely has a probability of about 0.5 or .
    • The sum of the probabilities of an event and its complement must be 1.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.13.1: Define probability and event.
    M.7.13.2: Recall the order of fractions on a number line.
    M.7.13.3: Recall how to compare fractions with like denominators.
    M.7.13.4: Demonstrate how to compare fractions with different denominators.
    M.7.13.5: Determine the likelihood of an event occurring.

    Prior Knowledge Skills:
    • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
    • Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
    • Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
    • Generate equivalent fractions.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 5
    Learning Activities: 2
    Classroom Resources: 3
    14. Define and develop a probability model, including models that may or may not be uniform, where uniform models assign equal probability to all outcomes and non-uniform models involve events that are not equally likely.

    a. Collect and use data to predict probabilities of events.

    b. Compare probabilities from a model to observed frequencies, explaining possible sources of discrepancy.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Develop uniform (all outcomes have the same probability) and non-uniform (outcomes with different probabilities) probability models and use them to find probabilities of simple events.
    • Explain possible sources of discrepancy if the agreement between the probability model and observed frequencies is not good.
    • Estimate the probability of an event happening in an experiment.
    • Compare the accuracy of estimated probabilities from different experiments to the actual probability.
    Teacher Vocabulary:
    • Probability model
    • Uniform model
    • non-uniform model
    • observed frequencies
    Knowledge:
    Students know:
    • the probability of any single event can be expressed using terminology like impossible, unlikely, likely, or certain or as a number between 0 and 1, inclusive, with numbers closer to 1 indicating greater likelihood.
    • A probability model is a visual display of the sample space and each corresponding probability
    • probability models can be used to find the probability of events.
    • A uniform probability model has equally likely probabilities.
    • Sample space and related probabilities should be used to determine an appropriate probability model for a random circumstance.
    Skills:
    Students are able to:
    • make predictions before conducting probability experiments, run trials of the experiment, and refine their conjectures as they run additional trials.
    • Collect data on the chance process that produces an event.
    • Use a developed probability model to find probabilities of events.
    • Compare probabilities from a model to observed frequencies
    • Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
    Understanding:
    Students understand that:
    • long-run frequencies tend to approximate theoretical probability.
    • predictions are reasonable estimates and not exact measures.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.14.1: Define probability of chance, probability of events, outcome, and probability of observed frequency.
    M.7.14.2: Compare and contrast probability of chance and probability of observed frequency.
    M.7.14.3: Display all outcomes in a graphic representation (probability model-tree diagram, organized list, table, etc.).
    M.7.14.4: Demonstrate how to write the probability as a fraction, with likely outcomes as the numerator and possible outcomes as the denominator.
    M.7.14.5: Recall how to simplify fractions to lowest terms.
    M.7.14.6: Recognize equivalent fractions.
    M.7.14.7: Recall how to create a table or graphic display of data.
    M.7.14.8: Define probability of chance, outcome, and event.
    M.7.14.9: List all possible outcomes using a graphic representation (probability model-tree diagram, organized list, table, etc.).
    M.7.14.10: Using the model, count the frequency of the desired outcome.
    M.7.14.11: Demonstrate how to write the probability as a fraction, with likely outcomes as the numerator and possible outcomes as the denominator.
    M.7.14.12: Recall how to simplify fractions to lowest terms.
    M.7.14.13: Recognize equivalent fractions.
    M.7.14.14: Recall how to create a table or graphic display of data.
    M.7.14.15: Analyze collected data to predict probability of events.
    M.7.14.16: Define probability of observed frequency, outcome, discrepancy and event.
    M.7.14.17: List all actual outcomes using a graphic representation (probability model-tree diagram, organized list, table, etc.).
    M.7.14.18: Using the model, count the frequency of the actual outcome.
    M.7.14.19: Demonstrate how to write the probability as a fraction, with likely outcomes as the numerator and possible outcomes as the denominator.
    M.7.14.20: Recall how to simplify fractions in lowest terms.
    M.7.14.21: Recognize equivalent fractions.
    M.7.14.22: Recall how to create a table or graphic display of data.

    Prior Knowledge Skills:
    • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
    • Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
    • Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
    • Generate equivalent fractions.
    • Recall how to read a graph or table.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.14 Describe the probability of events occurring as possible or impossible.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 2
    Classroom Resources: 2
    15. Approximate the probability of an event using data generated by a simulation (experimental probability) and compare it to the theoretical probability.

    a. Observe the relative frequency of an event over the long run, using simulation or technology, and use those results to predict approximate relative frequency.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Predict the approximate relative frequency of an event given the probability.
    • Compare the accuracy of estimated probabilities from different experiments to the actual probability.
    • Describe how a single event can be simulated using an experiment.
    Teacher Vocabulary:
    • Experimental probability
    • Simulation
    • Theoretical probability
    • Relative frequency
    Knowledge:
    Students know:
    • relative frequencies for experimental probabilities become closer to the theoretical probabilities over a large number of trials.
    • Theoretical probability is the likelihood of an event happening based on all possible outcomes.
    • long-run relative frequencies allow one to approximate the probability of a chance event and vice versa.
    Skills:
    Students are able to:
    • approximate the probability of a chance event.
    • observe an event's long-run relative frequency.
    Understanding:
    Students understand that:
    • real-world outcomes can be simulated using probability models and tools.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.15.1: Define probability of chance, outcome, theoretical probability, experimental probability and event.
    M.7.15.2: Recognize the difference between possible outcomes and likely outcomes.
    M.7.15.3: Write the probability as a fraction, with likely outcomes as the numerator and possible outcomes as the denominator.
    M.7.15.4: Recall how to simplify fraction to lowest terms.
    M.7.15.5: Recognize equivalent fractions.
    M.7.15.6: Define relative frequency.

    Prior Knowledge Skills:
    • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
    • Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
    • Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
    • Generate equivalent fractions.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.15 Given a data set that represents a series of events, identify the event most likely to occur.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 5
    Classroom Resources: 5
    16. Find probabilities of simple and compound events through experimentation or simulation and by analyzing the sample space, representing the probabilities as percents, decimals, or fractions.

    a. Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams, and determine the probability of an event by finding the fraction of outcomes in the sample space for which the compound event occurred.

    b. Design and use a simulation to generate frequencies for compound events.

    c. Represent events described in everyday language in terms of outcomes in the sample space which composed the event.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Conduct probability experiments to quantify and interpret likeliness of an event occurring.
    • Design and use a simulation to generate frequencies for compound events
    • Analyze the results from a simulation of a compound event to estimate the probability of the compound event.
    • Represent probabilities as percents, decimals, and fractions.
    Teacher Vocabulary:
    • Tree diagram
    • Compound probability
    • Simulation
    • Sample space
    • Event
    Knowledge:
    Students know:
    • how the sample space is used to find the probability of compound events.
    • A compound event consists of two or more simple events.
    • A sample space is a list of all possible outcomes of an experiment.
    • how to make an organized list.
    • how to create a tree diagram.
    Skills:
    Students are able to:
    • find probabilities of compound events using organized lists, tables, tree diagrams and simulations
    • Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams.
    • For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.
    • Design a simulation to generate frequencies for compound events.
    • Use a designed simulation to generate frequencies for compound events.
    Understanding:
    Students understand that:
    • the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
    • A compound event can be simulated using an experiment.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.16.1: Define simple events and compound events.
    M.7.16.2: Discover when to add or multiply events to find probability of compound events.
    M.7.16.3: Recall how to find the probability of simple events.
    M.7.16.4: Demonstrate adding and multiplying fractions.
    M.7.16.5: Recognize how to obtain a common denominator when adding fractions.
    M.7.16.6: Recall how to add fractions with like denominators.
    M.7.16.7: Define simulation, frequency, and compound events.
    M.7.16.8: Recall how to find the probability of compound events.
    M.7.16.9: Create a tree diagram including all possible outcomes.
    M.7.16.10: Choose appropriate model to display outcomes (tree diagram, organized list, or table).
    M.7.16.11: Identify the desired outcomes in model. M 7.16.12: Create and use a simulation to illustrate compound events.
    M.7.16.13: Recall when to add or multiply events to find probability of compound events.
    M.7.16.14: Recall how to find the probability of simple events.
    M.7.16.15: Demonstrate adding and multiplying fractions.
    M.7.16.16: Recognize how to obtain a common denominator when adding fractions.
    M.7.16.17: Recall how to add fractions with like denominators.
    M.7.16.18: Recall how to construct a table.

    Prior Knowledge Skills:
    • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
    • Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
    • Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
    • Generate equivalent fractions.
    • Recall how to read a graph or table.
    Geometry and Measurement
    Construct and describe geometric figures, analyzing relationships among them.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 2
    Lesson Plans: 1
    Classroom Resources: 1
    17. Solve problems involving scale drawings of geometric figures, including computation of actual lengths and areas from a scale drawing and reproduction of a scale drawing at a different scale.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Solve problems involving scale drawings.
    • Use a scale factor to reproduce a scale drawing at a different scale.
    • Determine the scale factor for a scale drawing.
    Teacher Vocabulary:
    • Scale drawing
    • Reproduction
    • Scale factor
    Knowledge:
    Students know:
    • how to calculate actual measures such as area and perimeter from a scale drawing.
    • Scale factor impacts the length of line segments, but it does not change the angle measurements.
    • There is a proportional relationship between the corresponding sides of similar figures.
    • A proportion can be set up using the appropriate corresponding side lengths of two similar figures.
    • If a side length is unknown, a proportion can be solved to determine the measure of it.
    Skills:
    Students are able to:
    • find missing lengths on a scale drawing.
    • Use scale factors to compute actual lengths, perimeters, and areas in scale drawings.
    • Use a scale factor to reproduce a scale drawing at a different scale.
    Understanding:
    Students understand that:
    • scale factor can enlarge or reduce the size of a figure.
    • Scale drawings are proportional relationships.
    • Applying a scale factor less than one will shrink a figure.
    • Applying a scale factors greater than one will enlarge a figure.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.17.1: Define scale, scale drawings, length, area, and geometric figures.
    M.7.17.2: Locate/use scale on a map.
    M.7.17.3: Identify proportional relationships.
    M.7.17.4: Recognize numeric patterns.
    M.7.17.5: Recall how to solve proportions.

    Prior Knowledge Skills:
    • Construct repeating and growing patterns with a variety of representations.
    • Continue an existing pattern.
    • Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.
    • Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.
    • Define unit rate, proportion, and rate.
    • Create a ratio or proportion from a given word problem.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 1
    Classroom Resources: 1
    18. Construct geometric shapes (freehand, using a ruler and a protractor, and using technology), given a written description or measurement constraints with an emphasis on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Determine if a unique triangle can be made when given three specific conditions of a triangle.
    • Explain why three given conditions about a triangle may result in more than one or no triangles.
    Teacher Vocabulary:
    • Construct
    • protractor
    • Angle measures
    • Constraints
    • Acute triangle right triangle
    • obtuse triangle
    • isosceles triangle
    • Scalene triangle
    • Equilateral triangle
    Knowledge:
    Students know:
    • if three side lengths will create a unique triangle or no triangle.
    Skills:
    Students are able to:
    • freehand, draw geometric shapes with given conditions.
    • Using a ruler and protractor, draw geometric shapes with given conditions.
    • Using technology, draw geometric shapes with given conditions.
    • Construct triangles from three measures of angles or sides.
    • Identify the conditions that determine a unique triangle, more than one triangle, or no triangle.
    Understanding:
    Students understand that:
    • from their experiences with constructions, what conditions are necessary to construct a triangle.
    • only certain combinations of angle and side measures will create triangles.
    • Constructing a triangle requires a specific relationship between the legs of the triangle and a specific sum between the angles of the triangle.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.18.1: Demonstrate how to use a protractor to draw an angle.
    M.7.18.2: Construct segments of a given length using a ruler.
    M.7.18.3: Recognize attributes of geometric shapes.

    Prior Knowledge Skills:
    • Model using a protractor to draw angles.
    • Measure the length of an object by selecting and using appropriate tools such as a ruler.
    • Recognize attributes of shapes.
    • Define vertex/vertices and angle.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.18 Construct and analyze a geometric figure using manipulatives.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 3
    Learning Activities: 1
    Classroom Resources: 2
    19. Describe the two-dimensional figures created by slicing three-dimensional figures into plane sections.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
    Teacher Vocabulary:
    • Two-dimensional figures
    • Three-dimensional solids
    • plane sections
    Knowledge:
    Students know:
    • the difference between a two-dimensional and three-dimensional figure.
    • The names and properties of two-dimensional shapes.
    • The names and properties of three-dimensional solids.
    Skills:
    Students are able to:
    • Discover two-dimensional shapes from slicing three-dimensional figures. For example, students might slice a clay rectangular prism from different perspectives to see what two-dimensional shapes occur from each slice.
    Understanding:
    Students understand that:
    • slicing he prism from different planes may provide a different two-dimensional shape.
    • There are specific two-dimensional shapes resulting from slicing a three-dimensional figure.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.19.1: Define two-dimensional figure, three-dimensional figure, and plane section.
    M.7.19.2: List attributes of three-dimensional figures.
    M.7.19.3: List attributes of two-dimensional figures.
    M.7.19.4: Describe the relationship between two- and three-dimensional figures.
    M.7.19.5: Recognize symmetry.

    Prior Knowledge Skills:
    • Identify that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
    • Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces.
    • Identify triangles, quadrilaterals, pentagons, hexagons, heptagons, and octagons based on the number of sides, angles, and vertices.
    • Define three-dimensional figures, surface area, and nets.
    • Select and create a three-dimensional figure using manipulatives.
    • Identify three-dimensional figures.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.19 Match two similar geometric shapes that are proportional in size and orientation.


    Solve real-world and mathematical problems involving angle measure, circumference, area, surface area, and volume.
    Note: Students must select and use the appropriate unit for the attribute being measured when determining length, area, angle, time, or volume.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 3
    Classroom Resources: 3
    20. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

    a. Informally derive the formula for area of a circle.

    b. Solve area and circumference problems in real-world and mathematical situations involving circles.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Solve problems with the circumference and area of a circle.
    Teacher Vocabulary:
    • Diameter
    • Radius
    • Circle
    • Area
    • Circumference
    • π
    Knowledge:
    Students know:
    • that the ratio of the circumference of a circle and its diameter is always π.
    • The formulas for area and circumference of a circle.
    Skills:
    Students are able to:
    • use the formula for area of a circle to solve problems.
    • Use the formula(s) for circumference of a circle to solve problems.
    • Give an informal derivation of the relationship between the circumference and area of a circle.
    Understanding:
    Students understand that:
    • area is the number of square units needed to cover a two-dimensional figure.
    • Circumference is the number of linear units needed to surround a circle.
    • The circumference of a circle is related to its diameter (and also its radius).
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.20.1: Define diameter, radius, circumference, area of a circle, and formula.
    M.7.20.2: Identify and label parts of a circle.
    M.7.20.3: Recognize the attributes of a circle.
    M.7.20.4: Apply the formula of area and circumference to real world mathematical situations.

    Prior Knowledge Skills:
    • Define center, radius, and diameter of a circle.
    • Identify real-world examples of radius and diameter.
      Examples: bicycle wheel, pizza, pie.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.20 Identify the radius, diameter, and circumference of a circle.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 4
    Lesson Plans: 1
    Classroom Resources: 3
    21. Use facts about supplementary, complementary, vertical, and adjacent angles in multi-step problems to write and solve simple equations for an unknown angle in a figure.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Find the values of angles using complementary and supplementary angle relationships and equations.
    • Identify angle relationships in angle diagrams involving vertical, supplementary, and complementary angles.
    • Write equations to represent relationships between known and unknown angle measurements.
    • Determine the measures of unknown angles and judge the reasonableness of the measures.
    Teacher Vocabulary:
    • Supplementary angles
    • Complementary angles
    • vertical angles
    • Adjacent angles
    Knowledge:
    Students know:
    • supplementary angles are angles whose measures add to 180 degrees.
    • Complementary angles are angles whose measures add to 90 degrees.
    • vertical angles are opposite angles formed when two lines intersect.
    • Adjacent angles are non-overlapping angles which share a common vertex and side.
    Skills:
    Students are able to:
    • write a simple equation to find an unknown angle.
    • Identify and determine values of angles in complementary and supplementary relationships.
    • Identify pairs of vertical angles in angle diagrams.
    • Identify pairs of complementary and supplementary angles in angle diagrams.
    • Use vertical, complementary, and supplementary angle relationships to find missing angles.
    Understanding:
    Students understand that:
    • vertical angles are the pair of angles formed across from one another when two lines intersect, and that the measurements of vertical angles are congruent.
    • Complementary angles are angles whose measures add up to 90o, and supplementary angles are angles whose measures add up to 180o.
    • Relationships between angles depends on where the angles are located.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.21.1: Define supplementary angles, complementary angles, vertical angles, adjacent angles, parallel lines, perpendicular lines, and intersecting lines.
    M.7.21.2: Discuss strategies for solving multi-step problems and equations.
    M.7.21.3: Identify all types of angles.
    M.7.21.4: Identify right angles and straight angles.

    Prior Knowledge Skills:
    • Model using a protractor to draw angles.
    • Draw points, lines, line segments, and parallel and perpendicular lines, angles, and rays.
    • Define vertex/vertices and angle.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.21 Classify angles as acute, obtuse, right, or straight.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 4
    Classroom Resources: 4
    22. Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms.
    Unpacked Content
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