Courses of Study : Mathematics (Grade 4)

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.