Courses of Study : Mathematics (Grade 2)

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 three–digit 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).