Curriculum for Grade 5

Grade Description: Students dig more deeply into place value patterns and operations. Their understanding grows to include decimals in the hundredths and thousandths, operations with fractions and decimals, multi-digit multiplication and division with remainders, area models, properties of multiplication and division, estimation, and measuring volume. We introduce the coordinate plane (quadrant I), which students use to solve problems.

MODULE 1. Place Value and Decimal Fractions

Topic A: Multiplicative Patterns on the Place Value Chart 

Relying on solid understanding of the place value chart and powers of ten, students multiply and divide to solve problems with a decimal number as a factor or quotient.

Multiply by 10 with and without a place value chart

Learn how to quickly multiply a number by 10. Use a place value chart to assist in shifting of the digits using the concept of place value. Then apply the knowledge gained to multiply by 10 without being provided with the place value chart
Multiply by 10 with and without a place value chart

Multiply by 100 with and without a place value chart

Learn how multiplying by 100 is the same as multiplying by 10 twice. Use a place value chart to multiply a number (up to 4 digits) by 100 by shifting of digits using the concept of place value. Then, apply the understanding gained to multiply by 100 witho
Multiply by 100 with and without a place value chart

Multiply by 1,000 with and without a place value chart

Learn that multiplying by 1000 is the same as multiplying by 10 three times. Use a place value chart to multiply a number (up to 4 digits) by 1000 by shifting of digits using the concept of place value. Then, apply the understanding gained to multiply by
Multiply by 1,000 with and without a place value chart

Multiply by 10, 100, and 1,000

Practice multiplying a number by 10, 100, or 1000. Use the understanding of place value to shift the digits to the appropriate location and add the appropriate number of zeros on the end of the product
Multiply by 10, 100, and 1,000

Complete a pattern of multiplication by 10 or 100

Examine a pattern of numbers and insert the number that correctly completes the pattern. Use the understanding of multiplication by 10, 100, or 1000 to identify which factor creates the pattern
Complete a pattern of multiplication by 10 or 100

Divide by 10 with and without a place value chart

Learn how to quickly divide a number by 10. Identify the number shown on a place value chart. Then use the chart to assist in shifting of the digits to model the division. Finally, apply the knowledge gained to divide by 10 without being provided with the
Divide by 10 with and without a place value chart

Divide by 100 with and without a place value chart

Learn how dividing by 100 is the same as dividing by 10 twice. Use a place value chart to divide a number by 100 by shifting of the digits using the concept of place value. Then, apply the understanding gained to divide by 100 without the chart
Divide by 100 with and without a place value chart

Divide by 1,000 with and without a place value chart

Practice dividing a number with 4 or more digits by 1000. Initially, you can choose to use a place value chart to model the division by 10 three times. Then, apply the understanding gained to remove the correct number of zeros from the quotient
Divide by 1,000 with and without a place value chart

Divide by 10, 100, and 1,000

Practice dividing 5-digit 6-digit numbers by 10, 100, and 1000. Use the understanding of place value to shift the digits to the appropriate location and remove the correct number of zeros from the end
Divide by 10, 100, and 1,000

Identify and complete a pattern of division by 10 or 100

Examine a pattern of numbers and insert the number that correctly completes the pattern. Use the understanding of division by 10, 100, or 1000 to identify which divisor creates the pattern
Identify and complete a pattern of division by 10 or 100

Factor out powers of 10 to multiply numbers with a single non-zero digit

Learn how to multiply two numbers that are multiples of 10. First, recognize non-zero digits and practice writing up to 6 digit numbers with one non-zero digit. Then, learn how to multiply two numbers by factoring and rearranging the non-zero digits and p
Factor out powers of 10 to multiply numbers with a single non-zero digit

Multiply numbers with a single non-zero digit

Practice multiplying two numbers that are multiples of powers of 10
Multiply numbers with a single non-zero digit

Record the relationship between hundredths and thousandths using a place value chart

Learn the relationship between the hundredths and thousands place values of decimals. Use decimal counters and their equivalent fractions to reduce fractions
Record the relationship between hundredths and thousandths using a place value chart

Convert between ones, tenths, hundredths, and thousandths

Practice converting between ones, tenths, hundredths, and thousands. Create equivalent expressions by filling in the correct terms
Convert between ones, tenths, hundredths, and thousandths

Multiply a decimal number by 10 with and without a place value chart

Multiply a decimal by 10 quickly. Use a place value chart to assist in shifting of the digits using the concept of place value. Then apply the knowledge gained to multiply by 10 without being provided with the place value chart. Also, learn how to move th
Multiply a decimal number by 10 with and without a place value chart

Multiply a decimal number by 100 with and without a place value chart

Learn how multiplying by 100 is the same as multiplying by 10 twice. Use a place value chart to multiply a decimal by 100 by shifting of digits using the concept of place value. Then, apply the understanding gained to multiply by 100 without the chart. Al
Multiply a decimal number by 100 with and without a place value chart

Multiply a decimal number by 1,000 with and without a place value chart

Learn that multiplying by 1000 is the same as multiplying by 10 three times. Initially, you can choose to use a place value chart to model the multiplication of a decimal by 1000 by shifting of digits using the concept of place value. Then, apply the unde
Multiply a decimal number by 1,000 with and without a place value chart

Multiply a decimal number by 10, 100, and 1,000

Practice multiplying a decimal by 10, 100, or 1000. Use the understanding of place value to shift the digits to the appropriate location. Also, learn the relationship between the zeros of the factor and the movement of the decimal point
Multiply a decimal number by 10, 100, and 1,000

Complete a pattern of multiplication by 10, 100, and 1,000

Examine a pattern of decimal numbers and insert the number that correctly completes the pattern. Use the understanding of multiplying a decimal by 10, 100, or 1000 to identify which factor creates the pattern
Complete a pattern of multiplication by 10, 100, and 1,000

Convert between ones, tenths, hundredths, and thousandths in division problems

Use place value names to assist in division problems. Create equivalent expressions by filling in the correct terms
Convert between ones, tenths, hundredths, and thousandths in division problems

Divide a decimal number by 10 with and without a place value chart

Divide a decimal by 10 quickly. Use a place value chart to assist in shifting of the digits using the concept of place value. Then apply the knowledge gained to divide by 10 without being provided with the place value chart. Also, learn how to move the de
Divide a decimal number by 10 with and without a place value chart

Divide a decimal number by 100 with and without a place value chart

Learn how dividing by 100 is the same as dividing by 10 twice. Use a place value chart to divide a decimal by 100 by shifting of digits using the concept of place value. Then, apply the understanding gained to divide by 100 without the chart. Also, learn
Divide a decimal number by 100 with and without a place value chart

Divide a decimal number by 1,000 with and without a place value chart

Learn that dividing by 1000 is the same as multiplying by 10 three times. Initially, you can choose to use a place value chart to model the division of a decimal by 1000 by shifting of digits using the concept of place value. Then, apply the understanding
Divide a decimal number by 1,000 with and without a place value chart

Divide a number by 10, 100, and 1,000

Practice dividing a decimal by 10, 100, or 1000. Use the understanding of place value to shift the digits to the appropriate location. Also, learn the relationship between the zeros of the divisor and the movement of the decimal point
Divide a number by 10, 100, and 1,000

Complete a pattern of division by 10, 100, and 1,000

Examine a pattern of decimal numbers and insert the number that correctly completes the pattern. Use the understanding of dividing a decimal by 10, 100, or 1000 to identify which factor creates the pattern
Complete a pattern of division by 10, 100, and 1,000

Represent repeated multiplication of 10 as 10 with an exponent

Learn the relationship between repeated multiplication by 10 and the number of zeros in the product. Represent repeated factors of 10 as exponents of 10
Represent repeated multiplication of 10 as 10 with an exponent

Represent 10 with an exponent as repeated multiplication

Learn the relationship between an exponential expression and its multiplication expression. Identify the exponent in an expression. Expand an exponent of 10 into a multiplication expression. Also, practice rewriting a number as an exponent of 10
Represent 10 with an exponent as repeated multiplication

Multiply a decimal number by 10 with an exponent

Learn how to expand numbers that are multiplied by a power of 10. Use the understanding of exponents of 10 and multiplication of decimals to expand the numbers. This skill is often used in science to write very large numbers in scientific notation
Multiply a decimal number by 10 with an exponent

Divide a number by 10 with an exponent

Expand numbers that are divided by a power of 10. Use the understanding of exponents of 10 and division of decimals to expand the numbers
Divide a number by 10 with an exponent

Topic B: Decimal Fractions and Place Value Patterns

Students use familiar symbols (<, =, >) to compare numbers to the thousandths place. They identify, compose, and arrange numbers of equal and unequal length.

Topic C: Place Value and Rounding Decimal Fractions

Using a number line to provide context, students first determine the midway point between two decimal numbers. They then progress to rounding using the number line and the midway point. Finally, students round decimal numbers to any given place value without use of the number line.

Determine the midway point between two decimal numbers on a number line

Learn how to easily identify the halfway point between two decimals. First, use a number line to Identify the midpoint between two decimal numbers marked on that number line. Then, identify the midpoint between two decimals stated as verbal expressions wi
Determine the midway point between two decimal numbers on a number line

Determine whether a decimal number is greater or less than halfway between two points on a number line

Learn how to determine if a decimal number is less than or more than halfway between two given numbers on a number line. First, locate the decimal on the number line. Then, find the point halfway between the two numbers on the numbers line. Finally, ident
Determine whether a decimal number is greater or less than halfway between two points on a number line

Compose and apply a rule for rounding numbers

Learn the rules for rounding decimals. Use a number line to help identify if the given decimal should round up or down, then choose the correct answer. Complete the sentences for the rounding rules
Compose and apply a rule for rounding numbers

Determine whether a decimal number rounds up or down

Practice rounding decimals. Given a decimal number on a basketball, choose which basket the ball should go into to correctly round the number
Determine whether a decimal number rounds up or down

Round a given number by first determining its nearest tenths

Learn to round a decimal by identifying the nearest numbers that the given decimal could round to. Then, determine the midpoint between the nearest numbers. Identify if the given number is less than or greater than the midpoint and round accordingly
Round a given number by first determining its nearest tenths

Round a given number to the hundredths, tenths, and ones place

Practice rounding the same number to the nearest hundreths, tenths, and ones. Enter the correct value rounded to the appropriate place value
Round a given number to the hundredths, tenths, and ones place

Round a decimal number to a given place value (Level 1)

Practice rounding numbers. Choose the correct answer to a rounding questions to complete a picture puzzle
Round a decimal number to a given place value (Level 1)

Round a decimal number to a given place value (Level 2)

Learn how to examine place values to round correctly. Identify the place value to which you want to round and the place value to the right of it. Then, determine whether the value is rounded up or down and type in the correct rounded value
Round a decimal number to a given place value (Level 2)

Round a decimal number to a given place value (Level 3)

Learn how to round to a stated place value. Identify the place value to the right of the value you should round to, then determine whether to round up or down and type in the correct rounded value
Round a decimal number to a given place value (Level 3)

Round a decimal number to a given place value (Level 4)

Practice rounding numbers to the stated place value. Use your understanding of the rounding rules
Round a decimal number to a given place value (Level 4)

Topic D: Adding and Subtracting Decimals

Based on the familiar disk model, students add and subtract numbers to the thousands place. They add and subtract in equations that require regrouping and learn to use the standard algorithm (column addition and column subtraction).

Add numbers to the hundredths place with regrouping using a disk model

Learn how to add two decimal numbers (to the hundredths place). Represent each number with a model of disks for each place value. Then, combine the like place value disks of the two numbers to arrive at the sum. First, work on sums that do not require reg
Add numbers to the hundredths place with regrouping using a disk model

Add numbers to the thousandths place with regrouping using a disk model

Learn how to add two decimal numbers (to the thousandths place). Represent each number with a model of disks for each place value. Then, combine the like place value disks of the two numbers to arrive at the sum. First, work on sums that do not require re
Add numbers to the thousandths place with regrouping using a disk model

Add numbers to the thousandths place with regrouping using column addition and a disk model

Add together two decimal numbers (to the thousands place). Rewrite the addition problem in column form and use disk models to assist in finding the sum with any necessary regrouping
Add numbers to the thousandths place with regrouping using column addition and a disk model

Add numbers to the thousandths place with regrouping using column addition

Learn how to add two decimal numbers (to the thousands place). Rewrite the addition problem in column form to better visualize any necessary regrouping in finding the sum
Add numbers to the thousandths place with regrouping using column addition

Subtract numbers to the hundredths place with regrouping using a disk model

Subtract two decimal numbers (to the hundredths place). Model the subtraction problem with disks, including any needed regrouping
Subtract numbers to the hundredths place with regrouping using a disk model

Subtract numbers to the thousandths place with regrouping using a disk model

Subtract two decimal numbers (to the hundredths place). Model the subtraction problem with disks, including any needed regrouping
Subtract numbers to the thousandths place with regrouping using a disk model

Subtract numbers to the thousandths place with regrouping using column subtraction and a disk model

Learn how to subtract two decimal numbers (to the thousands place). Rewrite the subtraction problem in column form and use disk models to assist in finding the difference with any necessary regrouping
Subtract numbers to the thousandths place with regrouping using column subtraction and a disk model

Subtract numbers of different lengths to the thousandths place with regrouping using column subtraction and a disk model

Learn how to subtract two decimal numbers of different lengths. Rewrite the subtraction problem in column form and use disk models to assist in finding the difference with any necessary regrouping
Subtract numbers of different lengths to the thousandths place with regrouping using column subtraction and a disk model

Subtract numbers to the thousandths place with regrouping using column subtraction

Learn how to subtract two decimal numbers (to the thousands place). Rewrite the subtraction problem in column form to better visualize any necessary regrouping in finding the difference
Subtract numbers to the thousandths place with regrouping using column subtraction

Topic E: Multiplying Decimals

Students take the first steps in understanding multiplication of a decimal number. Working with a single-digit whole number and a decimal number, students work step-by-step through the process using the familiar disk model. They trade disks to model regrouping and explore the importance of decimal point placement.

Topic F: Dividing Decimals

Students rely on familiar models and procedures to apply their division knowledge to decimals. Step-by-step, they learn to correctly work through regrouping, using a new place value, using zeros, and placing a decimal in their quotient.

Divide a decimal number by a single-digit number based on a model

Learn how to divide a decimal by a whole number. Use a disk model to physically find the partial quotients of each place value. Regrouping may be necessary
Divide a decimal number by a single-digit number based on a model

Divide a decimal number by a single-digit number with and without regrouping based on a model

Divide a decimal by a whole number. A disk model is used to represent the decimal and to help find the partial quotients of each place value. Regrouping may be necessary
Divide a decimal number by a single-digit number with and without regrouping based on a model

Divide a decimal number by a single-digit number with and without regrouping based on a model

Learn how to divide a decimal by a whole number. A disk model is used to represent the decimal and to help find the partial quotients of each place value. Regrouping may be necessary
Divide a decimal number by a single-digit number with and without regrouping based on a model

Divide a decimal number by a single-digit number with regrouping to a new place value based on a model

Learn how to divide a decimal by a whole number when the quotient has more decimal places than the dividend. A disk model is used to represent the decimal and to help find the partial quotients of each place value. Regrouping to a new place value will be
Divide a decimal number by a single-digit number with regrouping to a new place value based on a model

Divide a decimal number by a single-digit number with and without regrouping using long division and a model

Use long division with a decimal divided by a whole number. Rewrite the division problem in long division format. A disk model is used to represent the decimal and to help find the partial quotients of each place value. Regrouping may be necessary
Divide a decimal number by a single-digit number with and without regrouping using long division and a model

Use long division to divide a decimal number by a single-digit number with and without regrouping

Learn to divide a decimal by a whole number using long division. Rewrite the division problem in long division format. Find the partial quotients of each place value and record them in the long division. Regrouping may be necessary
Use long division to divide a decimal number by a single-digit number with and without regrouping

Use long division to divide a decimal number by a single-digit number with quotients that include 0

Divide a decimal by a whole number using long division. Rewrite the division problem in long division format. Find the partial quotients of each place value and record them in the long division. Sometimes, the partial quotient may be 0, so regrouping may
Use long division to divide a decimal number by a single-digit number with quotients that include 0

Use long division to divide a decimal number by a single-digit number with regrouping to a new place value

Divide a decimal by a whole number using long division and what to do when the last digit does not divide evenly. Rewrite the division problem in long division format. Find the partial quotients of each place value and record them in the long division. Re
Use long division to divide a decimal number by a single-digit number with regrouping to a new place value

MODULE 2. Multi-Digit Whole Number and Decimal Fraction Operations

Topic A: Mental Strategies for Multi-Digit Whole Number Multiplication

Students work with round numbers in the tens, hundreds, and thousands to see how factoring out can make mental multiplication easier. In doing so, they apply properties of multiplication.

Factor out 10, 100, or 1,000 from a given number

Factor 10, 100, or 1000 out of a number. First, multiply a number by 10, 100, or 1000 and then examine how the two factors create form the product. Then, state the factors for given multiples of 10, 100, or 1000
Factor out 10, 100, or 1,000 from a given number

Solve multiplication problems using the associative and commutative properties

Learn the associative and commutative properties of multiplication. Examine sets of factors to determine whether their arrangement changes the answer. This skill can help you simplify multiplication problems to be able to find the product quickly using me
Solve multiplication problems using the associative and commutative properties

Solve a multi-digit multiplication problem using factoring out and properties of multiplication (Level 1)

Learn how to use factoring of 10, 100, and 1000 and the multiplication properties to multiply large numbers. Factor out 10,100, or 1000 and then group the single digit numbers together and the powers of 10 together. Rearranging the factors allows you to m
Solve a multi-digit multiplication problem using factoring out and properties of multiplication (Level 1)

Solve a multi-digit multiplication problem mentally

Practice using mental math to multiply large numbers together. This skill will allow you to solve problems faster
Solve a multi-digit multiplication problem mentally

Solve a multi-digit multiplication problem using factoring out and properties of multiplication (Level 2)

Use factoring of 10, 100, and 1000 and the multiplication properties to multiply large numbers. Factor out 10,100, or 1000 and then group the single digit numbers together and the powers of 10 together. Rearranging the factors allows you to multiply quick
Solve a multi-digit multiplication problem using factoring out and properties of multiplication (Level 2)

Round multi-digit numbers to estimate the area of a rectangle

Learn how to estimate the area of a rectangle. Round the length and width measurements and then multiply them to estimate the area. This allows you to quickly calculate an approximate area
Round multi-digit numbers to estimate the area of a rectangle

Round multi-digit numbers to estimate the product

Estimate the answer to a multiplication word problem. Round large numbers to their leftmost place. Then, use the understanding of powers of 10 and the properties of multiplication to quickly find the estimate of the answer
Round multi-digit numbers to estimate the product

Topic B: The Standard Algorithm for Multi-Digit Whole Number Multiplication

Students hone their use of the standard algorithm for multiplication, working with multi-digit numbers. They master the use of regrouping and working across zeros. To further their conceptual understanding, the standard algorithm is presented alongside other strategies, such as the area model and factoring out powers of 10.

Identify sum, difference, product, and quotient in equations

Learn the definitions of the words sum, difference, and quotient. Choose the correct word for the type of equation shown. Then, match the type of problem to the word for its result
Identify sum, difference, product, and quotient in equations

Compose simple numerical expressions from text

Learn how to translate verbal expressions into mathematical expressions. From a given statement, write the mathematical expression that represents the words. This skill will help you solve word problems using the correct operations
Compose simple numerical expressions from text

Compose addition and multiplication expressions with multiple addends or factors

Learn how to translate verbal expressions with more than two numbers into mathematical expressions. From a given statement, write the addition or multiplication expression that represents the words. This skill will help you solve word problems using the c
Compose addition and multiplication expressions with multiple addends or factors

Compose complex numerical expressions based on a model (Part 1)

Translate a verbal expression with three numbers into a mathematical expression. Using a diagram, you will choose the correct operations and place the numbers in the appropriate order to form the expression. This understanding will help you solve word pro
Compose complex numerical expressions based on a model (Part 1)

Compose complex numerical expressions based on a model (Part 2)

Learn how to translate a verbal expression with three numbers into a mathematical expression. Using a diagram, you will choose the correct operations and place the numbers in the appropriate order to form the expression. This understanding will help you s
Compose complex numerical expressions based on a model (Part 2)

Compose complex numerical expressions based on a model (Part 3)

Translate a verbal expression with three numbers into a mathematical expression. Using a diagram, you will choose the correct operations and place the numbers in the appropriate order to form the expression. This understanding will help you solve word pro
Compose complex numerical expressions based on a model (Part 3)

Multiply using the standard algorithm (1-digit by 3-digit)

Learn how to multiply a one-digit number by a three-digit number. Rewrite the problem in column form with the larger number on top. Understand how to multiply from right to left, carrying the tens of the partial product to the place value to the left
Multiply using the standard algorithm (1-digit by 3-digit)

Multiply using the standard algorithm (1-digit by 4-digit)

Multiply a one-digit number by a four-digit number. Rewrite the problem in column form with the larger number on top. Understand how to multiply from right to left, carrying the tens of the partial product to the place value to the left
Multiply using the standard algorithm (1-digit by 4-digit)

Factor out powers of 10 to simplify multiplication expressions

Simplify multiplication expressions by factoring out powers of 10. Apply the properties of multiplication to rearrange the factors to be able use mental math to quickly complete the multiplication
Factor out powers of 10 to simplify multiplication expressions

Solve related multiplication expressions after factoring out powers of 10

Learn how to quickly multiply large numbers. Multiply by a related single digit and then used the understanding of the powers of 10 and their number of zeros to find the final product
Solve related multiplication expressions after factoring out powers of 10

Multiply by a number with a power of 10 mentally

Practice mental math techniques to quickly multiply large numbers. Use the understanding of the powers of 10. You may use column form to multiply the related problem before adding the appropriate number of zeros to the final product
Multiply by a number with a power of 10 mentally

Multiply by a number with a power of 10 using the standard algorithm

Learn how to multiply a 2-digit number by a multiple of 10 using column multiplication. Use the guided instructions to find the partial products that form the final answer
Multiply by a number with a power of 10 using the standard algorithm

Multiply using an area model and the standard algorithm

Find the area of a rectangle. Learn how to break the rectangle into piece with an area that is easier to calculate. Notice how the areas of the pieces are represented in the partial products of the standard algorithm
Multiply using an area model and the standard algorithm

Multiply using the standard algorithm (3-digit by 3-digit) (Part 1)

Learn how to multiply two 3-digit numbers. Rewrite the problem in column form. Understand how to multiply from right to left to find the partial products. Then, add the partial products to find the final answer
Multiply using the standard algorithm (3-digit by 3-digit) (Part 1)

Multiply using the standard algorithm (3-digit by 3-digit) (Part 2)

Multiply two 3-digit numbers together. Rewrite the problem in column form. Understand how to multiply from right to left to find the partial products, including the effect of a 0 digit. Then, add the partial products to find the final answer
Multiply using the standard algorithm (3-digit by 3-digit) (Part 2)

Multiply using the standard algorithm (3-digit by 4-digit) (Part 1)

Learn how to multiply a 3-digit number and a 4-digit number together. Rewrite the problem in column form. Understand how to multiply from right to left to find the partial products and how to find the sum of those products for the final answer
Multiply using the standard algorithm (3-digit by 4-digit) (Part 1)

Multiply using the standard algorithm (3-digit by 4-digit) (Part 2)

Multiply a 3-digit number and a 4-digit number together. Rewrite the problem in column form. Understand how to multiply from right to left to find the partial products, including the effect of a 0 digit. Then, find the sum of the partial products for the
Multiply using the standard algorithm (3-digit by 4-digit) (Part 2)

Multiply using the standard algorithm (2-digit by 5-digit)

Learn how to multiply a 5-digit number by a 2-digit number. Rewrite the problem in column form. Understand how to multiply from right to left to find the partial products and how to find the sum of those products for the final answer
Multiply using the standard algorithm (2-digit by 5-digit)

Topic C: Decimal Multi-Digit Multiplication

Students further their understanding multiplication of a decimal number by increasing the number of digits in factors. Working with a 2- or 3-digit whole number and a decimal number in the tenths or hundredths, students work step-by-step through the process using the standard algorithm. They learn how to place a decimal in their answer and how to estimate to check the reasonableness of their answer.

Multiply a 2-digit decimal number by a 2-digit whole number using partial products with an area model

Multiply a 2-digit decimal by a 2-digit whole number. Use a segmented rectangle to represent the partial products in the related whole number times whole number multiplication. Apply an understanding of place value to find the product of the decimal times
Multiply a 2-digit decimal number by a 2-digit whole number using partial products with an area model

Multiply a 2-digit decimal number by a 2-digit whole number using the standard algorithm (Level 1)

Use the related multiplication of two whole numbers to learn how to multiply a 2-digit decimal by a 2-digit whole number. Multiply the decimal by 10, then use the standard algorithm to find product of the whole numbers. Convert the whole number product ba
Multiply a 2-digit decimal number by a 2-digit whole number using the standard algorithm (Level 1)

Multiply a 3-digit decimal number by a 2-digit whole number using the standard algorithm (Level 1)

Learn how to multiply a 3-digit decimal by a 2-digit whole number by using the related multiplication of two whole numbers. Multiply the decimal by 100, then use the standard algorithm to find product of the whole numbers. Convert the whole number product
Multiply a 3-digit decimal number by a 2-digit whole number using the standard algorithm (Level 1)

Multiply a 2- or 3-digit decimal number by a 2-digit whole number using the standard algorithm (Level 2)

Multiply a 2-digit or 3-digit decimal by a 2-digit whole number by using the related multiplication of two whole numbers. Temporarily, ignore the decimal point and use the standard algorithm to find product of the whole numbers. Convert the whole number p
Multiply a 2- or 3-digit decimal number by a 2-digit whole number using the standard algorithm (Level 2)

Multiply a 2- or 3-digit decimal number by a 2-digit whole number using the standard algorithm (Level 3)

Practice multiplying a 2-digit or 3-digit decimal by a 2-digit whole number. Use the standard algorithm to find product and determine the location of the decimal point based on the understanding of decimal multiplication
Multiply a 2- or 3-digit decimal number by a 2-digit whole number using the standard algorithm (Level 3)

Multiply a decimal number by a round number by factoring out powers of 10

Learn how to use round numbers in the multiplication of a decimal times a whole number. Factor a power of 10 out of the whole number. The, rearrange the factors to simplify the multiplication
Multiply a decimal number by a round number by factoring out powers of 10

Multiply a decimal number by a round number

Practice multiplying a decimal times a round number
Multiply a decimal number by a round number

Estimate the product of a decimal number and a 3-digit whole number (Part 1)

Use rounding to estimate the product of a decimal and a 3-digit whole number. Round each of the factors to their left-most place value. Multiply the rounded numbers to approximate the answer
Estimate the product of a decimal number and a 3-digit whole number (Part 1)

Estimate the product of a decimal number and a 3-digit whole number (Part 2)

Practice estimate the product of a decimal and a 3-digit whole number. Round each of the factors to their left-most place value. Multiply the rounded numbers to approximate the answer
Estimate the product of a decimal number and a 3-digit whole number (Part 2)

Estimate the product of a decimal number and a 3-digit whole number then solve using the standard algorithm

Estimate the product of a decimal and a 3-digit whole number and then compare the estimate to the actual product. Round each of the factors to their left-most place value. Multiply the rounded numbers to approximate the answer. Then, find use the standard
Estimate the product of a decimal number and a 3-digit whole number then solve using the standard algorithm

Topic D: Mental Strategies for Multi-Digit Whole Number Division

Students rely on their understanding of powers of 10, division, place value, and rounding to divide multi-digit whole numbers mentally.

Divide round numbers by powers of 10

Learn how to quickly divide a round number by a power of ten. Reduce the number of zeros on the quotient by the number of zeros on the divisor
Divide round numbers by powers of 10

Divide by factoring out powers of 10 from the divisor

Simplify division problems by factoring out powers of 10. Factor a power of ten out of the divisor. Then, divide the dividend first by that power of 10 and then by the other factor
Divide by factoring out powers of 10 from the divisor

Divide multi-digit round numbers mentally

Practice dividing multi-digit round numbers using mental math. Complete a picture puzzle by solving the problems correctly
Divide multi-digit round numbers mentally

Round a multi-digit number to a given place (Level 1)

Learn how to round multi-digit numbers to a given place value. Select the value to the right of the place you want to round to, then determine whether you should round up or down
Round a multi-digit number to a given place (Level 1)

Round a multi-digit number to a given place (Level 2)

Practice rounding multi-digit numbers to the given place
Round a multi-digit number to a given place (Level 2)

List the multiples of a given 2-digit round number

Skip count by listing several multiples of a given number. This skill can help with solving division problems
List the multiples of a given 2-digit round number

Round a 3-digit number to the nearest multiple of a given 2-digit round number (Level 1)

Learn to round a 3-digit number to the closest multiple of a given 2-digit number. List the multiples of the 2-digit number. Determine the which of the multiples has the smallest difference to the 3-digit number
Round a 3-digit number to the nearest multiple of a given 2-digit round number (Level 1)

Round a 3-digit number to the nearest multiple of a given 2-digit round number (Level 2)

Round a 3-digit number to the closest multiple of a given 2-digit number. Identify the multiples of the 2-digit number that are on either side of the 3-digit number. Determine the which of the multiples has the smallest difference to the 3-digit number. T
Round a 3-digit number to the nearest multiple of a given 2-digit round number (Level 2)

Estimate a quotient by finding the nearest multiple

Learn how to estimate a quotient. Round the divisor to its leftmost place. Then, round the dividend to the nearest multiple of the rounded divisor. Find the approximate quotient
Estimate a quotient by finding the nearest multiple

Estimate a quotient of a multi-digit division equation (Level 1)

Estimate the quotient of a multi-digit division problem. Round both the divisor and the dividend to their left-most places. Use powers of 10 to simplify the problem. Divide the rounded value to find the approximate quotient
Estimate a quotient of a multi-digit division equation (Level 1)

Estimate a quotient of a multi-digit division equation (Level 2)

Estimate the quotient of a multi-digit division problem. Round both the divisor and the dividend to their left-most places. Use powers of 10 and place values to simplify the problem. Divide the rounded value to find the approximate quotient. Regrouping ma
Estimate a quotient of a multi-digit division equation (Level 2)

Topic E: Partial Quotients and Multi-Digit Whole Number Division

Students look under the hood of division to really understand the concept of a remainder as well as the steps involved in long division. Students work with one- or two- and three-digit dividends and one- and two-digit divisors. They use the standard algorithm for long division, but approach it in different ways to build math flexibility.

Divide a group of objects into groups of given size with a remainder

Learn how divide with a remainder. Translate the verbal problem into a mathematical expression. Use the model to create the necessary groups. Identify the quotient and the remainder
Divide a group of objects into groups of given size with a remainder

Find the quotient and remainder by using multiples of the divisor

Learn how to divide with a remainder. Use the closest multiple of the divisor that is less than the dividend to find the quotient. Then, determine the remainder
Find the quotient and remainder by using multiples of the divisor

Find the quotient and remainder by subtracting the divisor from the dividend (Part 1)

Use repeated subtraction to find the remainder of a division problem. Estimate the quotient, then subtract the divisor from the dividend as many times as possible to find the remainder
Find the quotient and remainder by subtracting the divisor from the dividend (Part 1)

Find the quotient and remainder by subtracting the divisor from the dividend (Part 2)

Determine the quotient and the remainder of a division problem through repeated subtraction. Subtract the divisor as many times as possible. Count how many times it was subtracted to find the quotient. The number left over after the subtractions is the re
Find the quotient and remainder by subtracting the divisor from the dividend (Part 2)

Estimate the quotient, then solve using long division with a 1-digit quotient (Part 1)

Use estimation to learn how to do long division. Round the dividend to the nearest multiple of the divisor, then use factors of 10 to simplify the division estimate. Use the estimate to complete the long division, including finding the remainder
Estimate the quotient, then solve using long division with a 1-digit quotient (Part 1)

Estimate the quotient, then solve using long division with a 1-digit quotient (Part 2)

Use estimation to learn how to do long division. Round the dividend to the nearest multiple of the divisor to estimate the quotient. Rewrite the division problem in long division form. Use the estimate to complete the long division, including finding the
Estimate the quotient, then solve using long division with a 1-digit quotient (Part 2)

Solve using long division with a 1-digit quotient

Find a quotient using long division. Rewrite the division problem in long division form. Use estimation, then complete the partial products in the long division. Column multiplication and subtraction can be used, if necessary
Solve using long division with a 1-digit quotient

Solve using long division with a 1-digit quotient (overestimate)

Learn what to do if the estimated quotient is too high. Rewrite the division problem in long division form. Round the divisor and the dividend. If the partial product in the long division is too large to subtract, reduce the estimate by 1. Column multipli
Solve using long division with a 1-digit quotient (overestimate)

Solve using long division with a 1-digit quotient (underestimate)

Recognize when the estimated quotient is too low. Rewrite the division problem in long division form. Round the divisor and the dividend. If the remainder after subtraction in the long division is greater or equal to the divisor, increase the estimate by
Solve using long division with a 1-digit quotient (underestimate)

Solve using long division with a 1-digit quotient

Practice long division with a 1-digit quotient. Rewrite the problem in long division form. If you choose to fill in the quotient, you can work out the problem on your own. Choosing to estimate the quotient guides you through the problem
Solve using long division with a 1-digit quotient

Solve using long division with a 2-digit quotient (Part 1)

Find a 2-digit quotient using long division. Rewrite the division problem in long division form. Use estimation, then complete the partial quotient in the long division. Column multiplication and subtraction can be used, if necessary
Solve using long division with a 2-digit quotient (Part 1)

Solve using long division with a 2-digit quotient (over and underestimate)

Learn what do do if the estimated quotient is too high or low low. Rewrite the division problem in long division form. Use estimation, then complete the partial quotients in the long division. Revise the estimates if the subtraction cannot be completed or
Solve using long division with a 2-digit quotient (over and underestimate)

Solve using long division with a 2-digit quotient (Part 2)

Practice long division with a 2-digit quotient. Rewrite the problem in long division form. If you choose to fill in the quotient, you can work out the problem on your own. Choosing to estimate the quotient guides you through the problem
Solve using long division with a 2-digit quotient (Part 2)

Solve using long division with a 3-digit quotient

Find a 3-digit quotient using long division. Rewrite the division problem in long division form. Use estimation to find the partial quotients. Column multiplication and subtraction can be used, if necessary
Solve using long division with a 3-digit quotient

Solve using long division with a 3-digit quotient (over and underestimate) (Part 1)

Learn what do do if the estimated quotient is too high or low low. Rewrite the division problem in long division form. Use estimation, then complete the partial quotients in the long division. Revise the estimates if the subtraction cannot be completed or
Solve using long division with a 3-digit quotient (over and underestimate) (Part 1)

Solve using long division with a 3-digit quotient (over and underestimate) (Part 2)

Practice long division with a 2-digit quotient. Rewrite the problem in long division form. If you choose to fill in the quotient, you can work out the problem on your own. Choosing to estimate the quotient guides you through the problem
Solve using long division with a 3-digit quotient (over and underestimate) (Part 2)

Topic F: Partial Quotients and Multi-Digit Decimal Division

Students look under the hood of division to really understand the concept of a remainder as well as the steps involved in long division. Students work with one- or two- and three-digit dividends and one- and two-digit divisors. They use the standard algorithm for long division, but approach it in different ways to build math flexibility.

Rename decimal numbers in unit form

Rename a decimal number in terms of tenths, hundreths, or thousandths. First, fill in the blank with the number of given units. Then, select the correct unit for the given number
Rename decimal numbers in unit form

Rename a number in unit form as a decimal number

Write a number in place value units as a decimal. The given numbers have an increasing numbers of digits
Rename a number in unit form as a decimal number

Rename a whole number in unit form and decimal form

Rename a whole number in place value unit form. Add the appropriate number of zeros to each whole number to write it in terms of tenths or hundredths. Write the correct number of zeros after the decimal to rewrite a whole number to the given place value
Rename a whole number in unit form and decimal form

Divide a decimal by a whole number (with and without using unit form)

Divide a decimal by a whole number using place values. First, the decimal is stated in place value unit form. Then, choose the place value unit. Divide and then rewrite the answer as a decimal number. Finally, practice dividing a decimal by a whole number
Divide a decimal by a whole number (with and without using unit form)

Divide a decimal number by 10 or 100

Divide a decimal by a power of 10. Learn how to shift the decimal point based on the number of zeros in the divisor. Then, practice this division skill
Divide a decimal number by 10 or 100

Divide a decimal number by a multiple of 10 or 100

Use factors of 10 to divide a decimal number by a 2-digit or 3-digit round number. Factor out a power of 10 from the divisor. Then, divide in two steps, simplifying the division
Divide a decimal number by a multiple of 10 or 100

Estimate the quotient of a decimal number divided by a 2-digit number (Level 1)

Estimate the quotient of a decimal number divided by a 2-digit whole number. Round each number to its leftmost place. Then, identify the multiple of the divisor that is closest to the dividend and determine the approximate quotient. This skill will help y
Estimate the quotient of a decimal number divided by a 2-digit number (Level 1)

Estimate the quotient of a decimal number divided by a 2-digit number (Level 2)

Estimate the quotient of a decimal number divided by a 2-digit whole number. Round the divisor to its leftmost place and the dividend to the closest multiple of the rounded divisor. Then, determine the approximate quotient. This skill will help you in lon
Estimate the quotient of a decimal number divided by a 2-digit number (Level 2)

Solve long division to the tenths place

Learn how to find the quotient of two whole numbers to the tenth place instead of writing the remainder. Rewrite the problem in long division form, then perform the division. Extend the dividend by adding a decimal point followed by a 0 to continue dividi
Solve long division to the tenths place

Solve long division to the hundredths place

Find the quotient of two whole numbers to the hundredth place instead of writing the remainder. Rewrite the problem in long division form, then perform the division. Extend the dividend by adding a decimal point followed by zeros to continue dividing
Solve long division to the hundredths place

Solve long division of a decimal number (Level 1)

Practice long division of a decimal number divided by a 2-digit whole number. Estimate the partial quotients, adjusting the estimates as necessary. Adding zeros is not necessary for these problems. Column multiplication and subtraction can be used, if nec
Solve long division of a decimal number (Level 1)

Solve long division of a decimal number (Level 2)

Practice long division of a decimal number divided by a 2-digit whole number. Estimate the partial quotients, adjusting the estimates as necessary. Zeros may have to be added for addition place values to extend the division. Column multiplication and subt
Solve long division of a decimal number (Level 2)

Solve long division of a decimal number (over and underestimate)

Use long division with a decimal divided by a 2-digit whole number. Rewrite the division problem in long division format. Estimate the partial quotients, learning when to adjust the estimates
Solve long division of a decimal number (over and underestimate)

Solve long division of a decimal number (Level 3)

Practice long division of a decimal number divided by a 2-digit whole number. At each step, you can choose to fill in the quotient or to be guided through the estimate of the quotient. Column multiplication and subtraction can be used, if necessary
Solve long division of a decimal number (Level 3)

Use long division to solve a word problem with a decimal quotient

Solve word problems using long division. Use a model to represent the situation and write the long division problem. At each step, you can choose to fill in the quotient or to be guided through the estimate of the quotient. Zeros may have to be added for
Use long division to solve a word problem with a decimal quotient

Use long division to solve area problems with a decimal quotient

Solve area word problems using long division. Label a diagram with the given information and write the long division problem. At each step, you can choose to fill in the quotient or to be guided through the estimate of the quotient. Zeros may have to be a
Use long division to solve area problems with a decimal quotient

MODULE 3. Addition and Subtraction of Fractions

Topic A: Equivalent Fractions

Students are introduced to the basics of fraction equivalency. They learn to multiply to find an equivalent fraction and to divide to reduce a fraction. The concepts of common factors and greatest common factor are also introduced and applied.

Label the numerator and denominator in a fraction

Write the fraction represented by a model. Learn the names for the parts of a fraction
Label the numerator and denominator in a fraction

Write an equivalent fraction (larger) based on a given multiple or denominator

Learn how to write equivalent fractions. First, use a model. Then, use multiplication to create equivalent fractions. Finally, complete the missing part of a set of equivalent fractions
Write an equivalent fraction (larger) based on a given multiple or denominator

Write an equivalent fraction (smaller) based on a given divisor, numerator, or denominator

Write reduced equivalent fractions. FIrst, use a model. Then, use division to create equivalent fractions. Finally, complete the missing part of a set of equivalent fractions
Write an equivalent fraction (smaller) based on a given divisor, numerator, or denominator

Complete equivalent fractions

Practice equivalent fractions. irst, identify the operation that created equivalent fractions. Then, complete the missing part of a pair of equivalent fractions. Finally, match the equivalent fractions in a memory game
Complete equivalent fractions

Identify common factors of two given numbers

Find the common factors of two numbers. List all of the factor pairs of both numbers, then select the common factors. Then, learn to identify the common factors of two numbers without listing all factor pairs of both
Identify common factors of two given numbers

Identify a common factor of two given numbers and divide both by the common factor

Identify a common factor of a pair of numbers. Divide both numbers by that factor and analyze whether those quotients still have a common factor. This skill can help you find the greatest common factor and reduce fractions completely
Identify a common factor of two given numbers and divide both by the common factor

Reduce a fraction to its simplest form by dividing by the greatest common factor

Reduce a fraction to its simplest form. Select a number that can be divided into both the numerator and the denominator. Perform the division and determine if the parts of the fraction have another common factor. Continue until the fraction is in simplest
Reduce a fraction to its simplest form by dividing by the greatest common factor

Topic B: Making Like Units Pictorially

Students rely on their knowledge of fraction equivalence to work through all aspects of adding and subtracting with fractions and mixed numbers. With plenty of visual support and step-by-step prompting, they work with like and unlike denominators. Students learn to convert between mixed numbers and fractions to solve problems, write their answer in simplest form, and solve word problems.

Add fractions with like denominators

Learn how to add fractions with like denominators. Use the model to perform the addition and then type the answer. Then, find the sum without a model
Add fractions with like denominators

Rewrite an improper fraction as a mixed number

Rewrite an improper fraction as a mixed number. Write the improper fraction shown in the model. Then, use the model to find the whole number and fraction. Rewrite the improper fraction as the sum of a whole number and a fraction. Progress to writing the m
Rewrite an improper fraction as a mixed number

Add fractions with like denominators and rewrite the sum as a mixed number

Practice adding two fractions with like denominators. The sum will have to be rewritten as a mixed number
Add fractions with like denominators and rewrite the sum as a mixed number

Divide shapes into an equal number of parts (precursor to finding common denominators)

Divide two rectangles into an equal number of equal pieces. Drag two divided shapes on top of each other to find the total number of pieces. This skill will help you find common denominators of fractions
Divide shapes into an equal number of parts (precursor to finding common denominators)

Add fractions with unlike denominators (multiply denominators to find a common denominator)

Learn how to add fractions with unlike denominators. Use a model of rectangles divided into equal pieces to help find the like denominator. Multiply to create equivalent fractions with the same denominator
Add fractions with unlike denominators (multiply denominators to find a common denominator)

Rename fractions with unlike denominators (Level 1)

Rename two fractions so that they have a common denominator. Multiply the denominators together, then write equivalent fractions with those denominators
Rename fractions with unlike denominators (Level 1)

Rename fractions with unlike denominators (Level 2)

Identify the common denominator of two fractions. Rewrite equivalent fractions with the common denominator
Rename fractions with unlike denominators (Level 2)

Add fractions with unlike denominators and rewrite the sum as a mixed number

Learn how to add fractions with unlike denominators. Multiply the denominators together to find the common denominator, then create equivalent fractions with the same denominator. Add the renamed fractions. If the sum is an improper fraction, rewrite it a
Add fractions with unlike denominators and rewrite the sum as a mixed number

Add fractions with unlike denominators and rewrite the sum in simplest form (Part 1)

Add fractions with unlike denominators. Create equivalent fractions with the same denominator. Add the renamed fractions. Reduce the sum if it is not in simplest terms. Rewrite the sum as a mixed number if it is an improper fraction
Add fractions with unlike denominators and rewrite the sum in simplest form (Part 1)

Add fractions with unlike denominators and rewrite the sum in simplest form (Part 2)

Practice adding fractions with unlike denominators. Multiply the denominators together to find the common denominator, then create equivalent fractions with the same denominator. Add the renamed fractions. If the sum is an improper fraction, rewrite it as
Add fractions with unlike denominators and rewrite the sum in simplest form (Part 2)

Subtract fractions with like denominators

Learn how to subtract fractions with like denominators. Use the model to perform the subtraction and then type the answer. Then, find the difference without a model
Subtract fractions with like denominators

Subtract fractions with unlike denominators (multiply denominators to find a common denominator)

Use models of rectangles with equal parts to learn to subtract fractions with unlike denominators. Multiply the denominators and then create equivalent fractions with the same denominator. Then subtract the fractions
Subtract fractions with unlike denominators (multiply denominators to find a common denominator)

Subtract fractions with unlike denominators

Subtract fractions with unlike denominators. Create equivalent fractions with the same denominator. Subtract the renamed fractions
Subtract fractions with unlike denominators

Rewrite a mixed number as an improper fraction

Learn how to change a mixed number into an improper fraction. Write the whole number as a fraction and add it to the fractional part. Then practice this skill without being guided through the steps
Rewrite a mixed number as an improper fraction

Subtract a fraction from a mixed number with like denominators (rename the mixed number as a fraction)

Practice subtracting a fraction from a mixed number. The fractions have like denominators, but the mixed numbers may have to be rewritten as improper fractions
Subtract a fraction from a mixed number with like denominators (rename the mixed number as a fraction)

Subtract a fraction from a mixed number with unlike denominators (rename the mixed number as a fraction)

Subtract a fraction from a mixed number with unlike denominators. Rewrite the fractions with common denominators. If necessary, change the mixed number to an improper fraction. Then, subtract
Subtract a fraction from a mixed number with unlike denominators (rename the mixed number as a fraction)

Subtract a fraction from a mixed number with unlike denominators and rewrite the difference in simplest form

Practice subtracting a fraction from a mixed number. Find the common denominator and rewrite the mixed number as an improper fractions, if necessary. Write the answer in simplest form
Subtract a fraction from a mixed number with unlike denominators and rewrite the difference in simplest form

Subtract a fraction from a mixed number with unlike denominators to solve a word problem

Solve word problems that involve the difference of a mixed number and a fraction. Label a diagram to identify the parts of the problem and to help compose the expression to solve. Find the common denominator and rewrite the mixed number as an improper fra
Subtract a fraction from a mixed number with unlike denominators to solve a word problem

Subtract a fraction from 1 whole to solve a word problem

Learn how to solve word problems that involve part of a whole having been completed or used. Label a diagram to identify the parts of the problem and to help compose the expression to solve. Then subtract to answer the question
Subtract a fraction from 1 whole to solve a word problem

Subtract two fractions from 1 whole to solve a word problem

Solve word problems that involve subtracting two fractions from a whole. Use a diagram to organize the information. Find the common denominator and then add the two fractions. Subtract that sum from 1
Subtract two fractions from 1 whole to solve a word problem

Add fractions to solve a word problem

Solve word problems that involve adding fractions. Use a diagram to organize the information. Find the common denominator and then add the two fractions
Add fractions to solve a word problem

Topic C: Making Like Units Numerically

Students increase the complexity of the addition and subtraction operations they can solve by using mixed numbers. They reinforce and apply their understanding of number equivalence as they rename numbers to solve problems.

Add a mixed number and a whole number with like denominators

Find the sum of a mixed number and a whole number. Add the whole number parts together. Then add the fractional part
Add a mixed number and a whole number with like denominators

Subtract a fraction or a mixed number from a whole number with like denominators with and without a number line

Find the difference of a whole number and a fraction or mixed number. First, use a number line to help with the subtraction. Then, practice without the assistance of the number line
Subtract a fraction or a mixed number from a whole number with like denominators with and without a number line

Add a mixed number and a fraction with like denominators

Add a mixed number and a fraction. First, find the sum of the fractional parts, then add those to the whole number. No simplifying is required for these problems
Add a mixed number and a fraction with like denominators

Add mixed numbers with like denominators

Learn how to add two mixed numbers. First, add the whole number parts and then, add the fractional parts. Rename the sum of the fractional parts if it equals 1 or if it is an improper fraction
Add mixed numbers with like denominators

Add mixed numbers with unlike denominators (Level 1)

Find the sum of two mixed numbers with unlike denominators. Add the whole number parts. Then, find the common denominator for the fractional parts and rename them before adding them
Add mixed numbers with unlike denominators (Level 1)

Add mixed numbers with unlike denominators (Level 2)

Add two mixed numbers with unlike denominators. Add the whole number parts. Then, find the common denominator for the fractional parts and rename them before adding them. If the sum of the fractional parts is an improper fraction, rewrite it as a mixed nu
Add mixed numbers with unlike denominators (Level 2)

Subtract mixed numbers with like denominators

Subtract two mixed numbers with like denominators. Subtract the whole number parts from each other, then subtract the fractional parts from each other. No regrouping or simplifying is necessary for these problems
Subtract mixed numbers with like denominators

Subtract mixed numbers with unlike denominators (Level 1)

Subtract two mixed numbers with unlike denominators. Subtract the whole number parts from each other. Then, find the common denominator for the fractional parts and rename them before subtracting them.. No regrouping or simplifying is necessary for these
Subtract mixed numbers with unlike denominators (Level 1)

Subtract a fraction from a mixed number with like denominators (rename the mixed number)

Learn how to subtract a fraction from a mixed number when the fraction is larger than the fractional part of the mixed number. Rename the mixed number by reassigning 1 from the whole number part to the fractional part. Then subtract the fractions
Subtract a fraction from a mixed number with like denominators (rename the mixed number)

Subtract mixed numbers with unlike denominators (Level 2)

Subtract mixed numbers with unlike denominators. First, subtract the whole numbers. Then, rename the fractional parts of the mixed numbers with common denominators. If necessary, rename the mixed number by reassigning 1 from the whole number part to the f
Subtract mixed numbers with unlike denominators (Level 2)

Subtract mixed numbers with unlike denominators (Level 3)

Practice subtracting mixed numbers with unlike denominators. First, subtract the whole numbers. Then, rename the fractional parts of the mixed numbers with common denominators. If necessary, rename the mixed number by reassigning 1 from the whole number p
Subtract mixed numbers with unlike denominators (Level 3)

Topic D: Further Applications

To support more complex understanding of operations with fractions, students are supported by visual models, the number line, and diagrams. They apply their knowledge of fractions to estimate sums and differences and solve multi-step word problems with mixed numbers.

Compare fractions with unlike denominators to ½ to estimate the sum

Determine whether each fraction is greater than, less than, or equal to 1/2. Then, determine if the sum of two fractions is greater than, less than, or equal to 1. At first, use models to help visualize the fractions. Then, practice without models
Compare fractions with unlike denominators to ½ to estimate the sum

Compare fractions with unlike denominators to a missing unit to estimate the sum

Estimate the sum of two fractions with unlike denominators. First, use a number line to represent the larger fraction and determine how close it is to 1. Then, compare the difference to the other fraction to determine if the sum will be greater or less th
Compare fractions with unlike denominators to a missing unit to estimate the sum

Compare fractions with unlike denominators to estimate the difference of a mixed number minus a fraction

Estimate the difference of two fractions with unlike denominators. First, determine what fraction must be subtracted from the mixed number to result in 1. Then, compare that fraction to the fraction that is supposed to be subtracted from the mixed number
Compare fractions with unlike denominators to estimate the difference of a mixed number minus a fraction

Add multiple mixed numbers and fractions

Practice adding several fractions and mixed numbers together. Rearrange the terms so that fractions with common denominators are next to each other and find those partial sums first. Then, add the partial sums together
Add multiple mixed numbers and fractions

Solve a multi-step word problem with mixed numbers with unlike denominators (Part 1)

Learn how to solve word problems that involve several fractions with unlike denominators. Use a diagram to organize the information given in the problem. Then, write and solve an expression for each step of the problem
Solve a multi-step word problem with mixed numbers with unlike denominators (Part 1)

Solve a multi-step word problem with mixed numbers with unlike denominators (Part 2)

Solve word problems that involve several fractions with unlike denominators. Use a diagram to organize the information given in the problem. Then, write and solve an expression for each step of the problem
Solve a multi-step word problem with mixed numbers with unlike denominators (Part 2)

MODULE 4. Multiplication and Division of Fractions and Decimal Fractions

Topic A: Line Plots of Fraction Measurements

Students combine their knowledge of measurement, rounding, and mixed numbers to create line plots. They then analyze the data, requiring them to perform operations with mixed numbers.

Round to the nearest half inch on a ruler

Use a ruler to measure to the nearest half inch. Identify the increments on the ruler. Then, use the halfway points between increments to determine whether an object's length should be rounded up or down. Select the correct rounded length on the ruler
Round to the nearest half inch on a ruler

Round to the nearest half inch on a ruler to create a line plot and analyze the data

Create a line plot from the length measurements of several objects, rounding to the nearest half inch. Analyze the data for minimum and maximum measurement. Identify the most frequent measurement, as well as the range
Round to the nearest half inch on a ruler to create a line plot and analyze the data

Round to the nearest quarter inch on a ruler

Use a ruler to measure to the nearest quarter of an inch. Identify the increments on the ruler. Then, use the halfway points between increments to determine whether an object's length should be rounded up or down. Select the correct rounded length on the
Round to the nearest quarter inch on a ruler

Round to the nearest quarter inch on a ruler to create a line plot and analyze the data

Measure the length of several objects to the nearest quarter of an inch, creating a line plot of the measurements. Analyze the data for minimum and maximum measurement. Identify the most frequent measurement, as well as the difference between two measurem
Round to the nearest quarter inch on a ruler to create a line plot and analyze the data

Round to the nearest eighth of a foot on a ruler

Use a ruler to measure to the nearest eighth of a foot. Identify the increments on the ruler. Then, use the halfway points between increments to determine whether an object's length should be rounded up or down. Select the correct rounded length on the ru
Round to the nearest eighth of a foot on a ruler

Round to the nearest eighth of an inch on a ruler to create a line plot and analyze the data

Measure the length of several objects to the nearest eighth of an inch, creating a line plot of the measurements. Analyze the data for minimum and maximum measurement. Identify the most frequent measurement, as well as the difference between two measureme
Round to the nearest eighth of an inch on a ruler to create a line plot and analyze the data

Topic B: Fractions as Division

To solidify their understanding of fractions as division, students work to convert between the two, using fractions greater than and less than one. They then work step by step to make sense of the remainder of a division problem as a fraction. Equipped with this understanding, students solve increasingly complex division word problems.

Rewrite division of whole numbers as a fraction based on a model

Learn the relationship between dividing a quantity and writing the amount as a fraction. Represent the division as a whole number of foods split between greater whole number of plates. The foods will be cut into the number of pieces represented by the pla
Rewrite division of whole numbers as a fraction based on a model

Rewrite division of whole numbers as a fraction and match a fraction to its related division equation

Rewrite the division of two whole numbers as a fraction. The dividend becomes the numerator and the divisor becomes the denominator. Practice the concept by matching fractions to their related division expression
Rewrite division of whole numbers as a fraction and match a fraction to its related division equation

Relate division to fractions

Practice rewriting division expressions as fractions. Fill in the missing number in the equation
Relate division to fractions

Relate division to fractions greater than one

Represent a division as an improper fractions. First, a model of food and plates are used to visualize the quotient. Then practice rewriting division expressions as fractions. Fill in the missing number in the equation
Relate division to fractions greater than one

Divide and report the remainder as a fraction based on a model

Learn how to divide two whole numbers with a fraction remainder. A model of food and plates is used to physically represent the division. Write the quotient as an improper fraction and a mixed number
Divide and report the remainder as a fraction based on a model

Rename a fraction greater than one as a mixed number (Level 1)

Rewrite an improper fraction as a mixed number. Write the fraction as a division expression. Then, find the quotient and remainder of a division problem to write the answer as a mixed number
Rename a fraction greater than one as a mixed number (Level 1)

Rename a fraction greater than one as a mixed number (Level 2)

Use long division to rewrite an improper fraction as a mixed number. Write the fraction as in long division form, then perform the division. The quotient becomes the whole number part and the remainder becomes the numerator of the fractional part
Rename a fraction greater than one as a mixed number (Level 2)

Solve fraction word problems based on a model (Level 1)

Learn to solve word problems involving fractions. Identify the fraction of a bar that is shaded. Then, use a bar to model a word problem and answer the question
Solve fraction word problems based on a model (Level 1)

Solve fraction word problems based on a model (Level 2)

Use a model to represent a word problem that involves fractions. Label the diagram with the given information. Rewrite the required division as a fraction. Then, change it to a mixed number and answer the question
Solve fraction word problems based on a model (Level 2)

Solve fraction word problems based on a model (Level 3)

Represent a word problem that involves fractions using a model. Label the diagram with the given information. Rewrite the required division as a mixed number in simplest terms and answer the question
Solve fraction word problems based on a model (Level 3)

Solve fraction word problems based on a model (Level 4)

Solve a word problem that involves fractions using a model. Label the diagram with the given information. Rewrite the required division as a fraction. Then, use long division to change the fraction to a mixed number and answer the question
Solve fraction word problems based on a model (Level 4)

Solve fraction word problems based on a model (Level 5)

Practice solving word problems involving fractions. Write the appropriate division expression for the problem. Then, rewrite it as a fraction or mixed number, as necessary
Solve fraction word problems based on a model (Level 5)

Topic C: Multiplication of a Whole Number by a Fraction

Students begin by finding a unit fraction of a whole number and other fractions of a whole number using familiar models. They then relate that process to multiplication. To multiply a whole number by a fraction, students learn to find common factors and reduce either before or after multiplying.

Determine fractions of a whole number based on a model (Level 1)

Find the number that is a fraction of a whole number. Use a model to help find the answer. Then, match a fraction to a model
Determine fractions of a whole number based on a model (Level 1)

Determine fractions of a whole number based on a model to solve a word problem

Represent a word problem with a model. Select how many groups to divide the whole number into, based on the information in the problem. Find the fraction of the whole number using the model, then answer the questions
Determine fractions of a whole number based on a model to solve a word problem

Determine fractions of a whole number based on a model (Level 2)

Find the fraction of a whole number with the help of a model. Represent the information given in the problem with the model by selecting the number of parts. Then, write an expression for the model and solve. If the solution is an improper fraction, rewri
Determine fractions of a whole number based on a model (Level 2)

Determine fractions of a whole number based on a model (Level 3)

Calculate the fraction of a whole number with the help of a model. Represent the information given in the problem with the model by selecting the number of parts. Calculate the value of one part, then highlight how many parts are represented by the fracti
Determine fractions of a whole number based on a model (Level 3)

Determine a whole number given a fraction of that number based on a model

Find the whole number if you know a fraction of that number. Use a model to represent the given information. Identify the value of one part, then use that information to calculate the total
Determine a whole number given a fraction of that number based on a model

Multiply a whole number by a fraction

Learn how to multiply a whole number by a fraction. Write the multiplication as a repeated addition of the fraction. Notice these relationship of the repeated addition and the parts of the fraction. Then, practice this concept without rewriting as additio
Multiply a whole number by a fraction

Relate a fraction of a whole number to multiplication and solve

Find the fraction of a whole number through multiplication. Use a model to represent one part of the whole number, then write a necessary multiplication expression. Then, find the product
Relate a fraction of a whole number to multiplication and solve

Determine a fraction of a measurement by converting units and multiplying

Determine the fraction of a measurement. First, convert the measurement to smaller units. Then, multiply by the fraction and simplify the answer
Determine a fraction of a measurement by converting units and multiplying

Determine common factors of two whole numbers

Find the common factors of two numbers. List all of the factor pairs of both numbers, then select the common factors. Then, identify the common factors of two numbers without listing all factor pairs of both
Determine common factors of two whole numbers

Divide whole numbers by a common factor

Identify a common factor of a pair of numbers. Divide both numbers by that factor and analyze whether those quotients still have a common factor. This skill can help you find the greatest common factor and reduce fractions completely
Divide whole numbers by a common factor

Reduce a fraction by dividing by a common factor

Learn to how to reduce a fraction to simplest terms. Find a common factor of the numerator and denominator. Then divide both numbers by the common factor. Continue dividing by common factors until the numerator and denominator no longer have any more comm
Reduce a fraction by dividing by a common factor

Reduce factors before multiplying a whole number by a fraction (Level 1)

Multiply a fraction times a whole number. Examine how reducing a common factor before multiplying can simplify the multiplication. Select the numbers that share a common factor and identify that factor. Then, divide out the common factor and multiply the
Reduce factors before multiplying a whole number by a fraction (Level 1)

Reduce factors before multiplying a whole number by a fraction (Level 2)

Practice reducing common factors before multiplying in the denominator of a fraction. Select the two numbers that have a common factor and divide them by their common factor. Repeat if necessary. Then, multiply the remaining numbers in the numerator. If t
Reduce factors before multiplying a whole number by a fraction (Level 2)

Multiply a whole number by a fraction by reducing before or after multiplying

Choose whether to reduce before or after multiplying in the numerator of a fraction. Learn to make a wise choice to be able to use mental math
Multiply a whole number by a fraction by reducing before or after multiplying

Topic D: Fraction Expressions and Word Problems

Students synthesize their understanding of fractions and operations to build and solve expressions. Familiar models support their learning, and word problems put the skills in context.

Match operations to the terms sum, difference, product, and quotient

Practice the vocabulary terms used for the addition, subtraction, multiplication, and division. Match a verbal expression to the correct mathematical expression
Match operations to the terms sum, difference, product, and quotient

Compose an expression based on text

Write a mathematical expression for the verbal expression given. Select the correct operation to use between two numbers. Also, put the numbers in the correct order, if necessary
Compose an expression based on text

Compose a compound expression based on text (Part 1)

Compose a mathematical expression involving three values and addition and multiplication. Identify the operations represented by words in the verbal expression. Then, place the numbers into the expression with the correct operations, inserting parentheses
Compose a compound expression based on text (Part 1)

Compose a compound expression based on text (Part 2)

Create a mathematical expression involving three values and multiplication of whole numbers and a fraction. Identify the operations represented by words in the verbal expression. Then, place the numbers into the expression with the correct operations, ins
Compose a compound expression based on text (Part 2)

Compose a compound expression based on text (Part 3)

Write a mathematical expression involving three values and multiplication and subtraction of whole numbers and a fraction. Identify the operations represented by words in the verbal expression. Then, place the numbers into the expression with the correct
Compose a compound expression based on text (Part 3)

Compose a compound equation based on a model and solve (Part 1)

Write and solve a compound equation based on the model shown. Identify the fraction of the bar that is labeled and the expression that represents the full length of the bar. Then, organize the numbers and necessary operations in the expression. Find the s
Compose a compound equation based on a model and solve (Part 1)

Compose a compound equation based on a model and solve (Part 2)

Write and solve a compound equation based on the model shown. Identify the number of sections on the bar.and the expression that represents each section. Then, organize the numbers and necessary operations in the expression. Find the solution, rewriting i
Compose a compound equation based on a model and solve (Part 2)

Solve compound equations with parentheses and fractions

Find the solution to a compound equation involving fractions and parentheses. Rewrite division expressions as fractions. Follow order of operations to solve. Write the solution as simplified fractions or mixed numbers
Solve compound equations with parentheses and fractions

Solve a word problem by multiplying a whole number by a fraction (Level 1)

Solve a word problem requiring the multiplication of a whole number by a fraction. Compose expressions that answer each question. Then solve the expressions, simplifying before multiplying. Answer all of the questions
Solve a word problem by multiplying a whole number by a fraction (Level 1)

Solve a word problem by multiplying a whole number by a fraction (Level 2)

Solve a word problem requiring the multiplication of a whole number by a fraction. Use a diagram to model the problem. Compose expressions that answer each question. Then solve the expressions, simplifying before multiplying
Solve a word problem by multiplying a whole number by a fraction (Level 2)

Topic E: Multiplication of a Fraction by a Fraction

Students learn to multiply fractions by starting with unit fractions and the support of an area model. They then progress to multiplication that involves mixed numbers, reducing, and units of measure.

Multiply unit fractions using an area model

Use the area of a rectangle to model the product of two unit fractions. Label the diagram with the lengths of the sides of the rectangles. Then, find the area equation and relate it to the multiplication of the fractions
Multiply unit fractions using an area model

Multiply fractions using an area model

Model the product of two fractions using a the area of a rectangle. Label the diagram with the lengths of the sides of the rectangles. Then, find the area equation and relate it to the multiplication of the fractions
Multiply fractions using an area model

Multiply fractions (reduce before multiplying)

Practice multiplying two fractions. Reduce common all factors from the numerator and denominator before multiplying, if possible. Also, practice writing fraction of a fraction expressions and simplifying them before finding the product
Multiply fractions (reduce before multiplying)

Multiply fractions (reduce before or after multiplying)

Multiply two fractions together. Decide whether to multiply or reduce at each step. Find the simplified product
Multiply fractions (reduce before or after multiplying)

Solve word problems by multiplying fractions using an area model

Solve word problems by modeling the product of two fractions using a the area of a rectangle. Label the diagram with the information given in the problem. Then, write the resulting expression and solve it to answer the question
Solve word problems by multiplying fractions using an area model

Rename a mixed number as a fraction to multiply by a fraction

Change a mixed number into an improper fraction before multiplying. Then, reduce the common factors from the multiplication before finding the product
Rename a mixed number as a fraction to multiply by a fraction

Convert measurements by multiplying a whole number by a fraction

Convert measurement units. Determine the relationship between the smaller and the larger units. Then, multiply the whole number and the fraction to convert the units. Write the answer in simplest form or as a mixed number, as appropriate
Convert measurements by multiplying a whole number by a fraction

Convert measurements by multiplying fractions

Convert measurement units. Determine the relationship between the smaller and the larger units. Then, multiply to convert the units. Mixed numbers may need to be rewritten as improper fractions and common factors should be divided out before multiplying
Convert measurements by multiplying fractions

Convert multiplication by a decimal to multiplication by a fraction and solve

Learn the relationship between multiplying by 0.1 or 0.01 and multiplying by the equivalent fraction. Convert between decimals and fractions. Notice that multiplying by a decimal can be rewritten as division
Convert multiplication by a decimal to multiplication by a fraction and solve

Multiply by 0.1 using a place value chart

Use a place value chart to multiply a number by 0.1. Identify the number shown on the chart. Then, shift the digits to the correct location for the given multiplication. Learn how to move the decimal point for quick mental math
Multiply by 0.1 using a place value chart

Multiply by 0.01 using a place value chart

Use a place value chart to multiply a number by 0.01. Identify the number shown on the chart. Then, shift the digits to the correct location for the given multiplication. Learn how to move the decimal point for quick mental math
Multiply by 0.01 using a place value chart

Multiply by 0.1 or 0.01

Practice multiplying a number by 0.1 or 0.01
Multiply by 0.1 or 0.01

Decompose a decimal number to multiply

Decompose a decimal number to easily multiply. Write the decimal as the product of a whole number and 0.1 or 0.01. Then, rearrange the factors to simplify the multiplication. Find the product
Decompose a decimal number to multiply

Determine the placement of the decimal point in the product of two decimal numbers

Learn how to find the placement of the decimal point in the product of two decimal numbers. Drag the decimal to the correct location
Determine the placement of the decimal point in the product of two decimal numbers

Multiply two decimal numbers using column multiplication (Part 1)

Use column multiplication to find the product of two decimal numbers. Rewrite the problem in column form. Then, find the partial products without the decimal point. Add the partial products and insert the decimal point at the correct location for the fina
Multiply two decimal numbers using column multiplication (Part 1)

Multiply two decimal numbers using column multiplication (Part 2)

Find the product of two decimal numbers using column multiplication. Rewrite the problem in column form. Then, find the partial products without the decimal point. Add the partial products and insert the decimal point at the correct location for the final
Multiply two decimal numbers using column multiplication (Part 2)

Multiply two decimal numbers using column multiplication (Part 3)

Use column multiplication to find the product of two decimal numbers. Rewrite the problem in column form. Then, find the partial products without the decimal point. Add the partial products and insert the decimal point at the correct location for the fina
Multiply two decimal numbers using column multiplication (Part 3)

Topic F: Multiplication with Fractions and Decimals as Scaling and Word Problems

Students explore the effects of multiplying by less than, equal to, and greater than 1. They solve multiplication problems, provide missing factors, and complete inequalities to solidify their understanding.

Multiply a fraction by a fraction equal to 1

Find equivalent fractions by multiplying a fraction by a fraction equaling 1. Learn that a fraction with the same number for the numerator and denominator is equal to 1. This skill is helpful when renaming fractions with common denominators for addition o
Multiply a fraction by a fraction equal to 1

Identify a missing factor as a fraction equal to 1

Practice multiplying a fraction by another fraction that is equivalent to 1. First, create fractions that are equal to 1 by filling in the missing numerator or denominator. Then, choose the correct fraction that is equal to 1. Finally, write any fraction
Identify a missing factor as a fraction equal to 1

Identify patterns in multiplying by fractions less than, equal to, and greater than 1

Learn the effect of multiplying by fractions less than, equal to, or greater than 1. Identify a fraction as less than, equal to, or greater than 1. Then, determine if the product of that fraction and a whole number is less than, equal to, or greater than
Identify patterns in multiplying by fractions less than, equal to, and greater than 1

Use <, =, and > to compare the result of multiplying by fractions less than, equal to, and greater than 1

Use inequality symbols to compare a fraction to 1. Then, compare the product of that fraction and another fraction to the value of the second fraction
Use <, =, and > to compare the result of multiplying by fractions less than, equal to, and greater than 1

Identify a fraction that will complete a multiplication inequality

Practice determining the relationship between the product of two fractions and the value of one of those fractions. First, given the choice of three fractions, choose the one that makes the inequality statement true. Then, complete the missing part of the
Identify a fraction that will complete a multiplication inequality

Convert a fraction less than one to decimal form (Level 1)

Learn how to rewrite a fraction as a decimal. Determine what factor would change the denominator to a power of 10, then multiply to create an equivalent fraction. Then, write that fraction as a decimal
Convert a fraction less than one to decimal form (Level 1)

Convert a fraction greater than one to decimal form

Rewrite an improper fraction as a decimal. Determine what factor would change the denominator to a power of 10, then multiply to create an equivalent fraction. Then, write that fraction as a decimal
Convert a fraction greater than one to decimal form

Convert a fraction less than one to decimal form (Level 2)

Rewrite a fraction as a decimal. Complete the factor that would create an equivalent fraction with the given power of 10 denominator. Then, multiply the numerators and rewrite the fraction as a decimal
Convert a fraction less than one to decimal form (Level 2)

Convert a fraction less than one to decimal form using division

Use long division to rewrite a fraction as a decimal. Divide the numerator by the denominator, adding zeros to continue dividing without a remainder
Convert a fraction less than one to decimal form using division

Convert a fraction greater than one to decimal form using division

Use long division to rewrite an improper fraction as a decimal. Divide the numerator by the denominator, adding zeros to continue dividing without a remainder
Convert a fraction greater than one to decimal form using division

Determine the outcome of multiplication using <, =, or > (Part 1)

Learn the effect of multiplying by a decimal less than, equal to, or greater than 1. Identify a decimal as less than, equal to, or greater than 1. Then, determine if the product of that decimal and a whole number is less than, equal to, or greater than th
Determine the outcome of multiplication using <, =, or > (Part 1)

Complete inequalities involving multiplication by a decimal number

Practice determining the relationship between the product of two decimals and the value of one of those decimals. First, given the choice of three decimals, choose the one that makes the inequality statement true. Then, complete the missing part of the de
Complete inequalities involving multiplication by a decimal number

Determine the outcome of multiplication using <, =, or > (Part 2)

Multiply by a fraction or decimal greater than 1. Determine if the product is less than or greater than one of the factors, using inequality symbols.Demonstrate understanding of the concept by placing the correct inequality into a formula expression
Determine the outcome of multiplication using <, =, or > (Part 2)

Determine the outcome of multiplication using <, =, or > (Part 3)

Multiply by a fraction or decimal less than 1. Determine if the product is less than or greater than one of the factors, using inequality symbols.Demonstrate understanding of the concept by placing the correct inequality into a formula expression
Determine the outcome of multiplication using <, =, or > (Part 3)

Topic G: Division of Fractions and Decimal Fractions

Students rely upon their understanding of multiplying fractions to learn how to divide fractions. With the assistance of familiar models such as tape diagrams and area models, they learn different ways to approach dividing with fractions. At this stage, they use unit fractions with whole numbers and unit fractions with unit fractions.

Rewrite an equation with multiplication by a fraction as a division equation based on a model

Learn the relationship between multiplying by a fraction and division. Using a given model cut into equal pieces, state how many pieces make a whole. Then, complete multiplication and division expressions about the model
Rewrite an equation with multiplication by a fraction as a division equation based on a model

Compose a division equation with a fraction based on a model

Write division expressions based on a model. Using a given model cut into equal pieces, state how many pieces make a whole. Then, complete a division expressions about the model
Compose a division equation with a fraction based on a model

Divide a whole number by a unit fraction based on a tape diagram

Use a tape diagram to divide a whole number by a unit fraction. Label the whole number and the fraction sections on the diagram. Use a number line to skip count the fraction sections. Then, determine the total number of sections
Divide a whole number by a unit fraction based on a tape diagram

Relate division by a unit fraction to multiplication by the denominator

Learn the relationship between dividing by a unit fraction and multiplying by the denominator. Using a tape diagram, label the whole number and the fraction sections on the diagram. Use a number line to skip count the fraction sections. Then, write the mu
Relate division by a unit fraction to multiplication by the denominator

Divide a whole number by a unit fraction by multiplying by the denominator

Rewrite division by a fraction as multiplication. Multiply the whole number by the denominator of the fraction and write the resulting product
Divide a whole number by a unit fraction by multiplying by the denominator

Divide a whole number by a unit fraction

Divide a whole number by a unit fraction in the context of a word problem. Rewrite the division as a multiplication and find the product
Divide a whole number by a unit fraction

Divide a unit fraction by a whole number based on a tape diagram (Part 1)

Learn how to divide a fraction by a whole number. Use a tape model to represent the fraction as equal parts. Then divide each part in the number of sections indicated by the whole number. Answer how many sections there are in total
Divide a unit fraction by a whole number based on a tape diagram (Part 1)

Divide a unit fraction by a whole number based on a tape diagram (Part 2)

Divide a fraction by a whole number using a tape diagram. Use the model to represent the fraction as equal parts. Then divide each part in the number of sections indicated by the whole number. Rewrite the fraction to represent all of the sections shown on
Divide a unit fraction by a whole number based on a tape diagram (Part 2)

Divide a unit fraction by a whole number

Practice dividing a unit fraction by a whole number. Rename the fraction by filling in the missing denominator. Then, divide and reduce the fraction to simplest form
Divide a unit fraction by a whole number

Multiply a unit fraction by a unit fraction with and without an area model (Part 1)

Multiply two unit fractions together. Use an area model to represent both fractions on one rectangle. Find the shaded area that represents the product of the two fractions. Then apply this concept to multiplication problems without the use of an area mode
Multiply a unit fraction by a unit fraction with and without an area model (Part 1)

Multiply a unit fraction by a unit fraction with and without an area model (Part 2)

Use an area model to represent the division of a unit fraction by a whole number. Rewrite the division as multiplication by a fraction. Use the resulting shaded area to find the product of the two fractions
Multiply a unit fraction by a unit fraction with and without an area model (Part 2)

Relate division by a whole number to multiplication by a unit fraction

Use a tape diagram to discover the relationship between division by a whole number and multiplication by a unit fraction. Split the diagram in sections according to the values given in the problem. Rewrite the resulting division expression as a multiplica
Relate division by a whole number to multiplication by a unit fraction

Solve division equations with unit fractions and whole numbers

Practice dividing unit fractions by whole numbers. Rewrite the division expression as multiplication and find the product
Solve division equations with unit fractions and whole numbers

Multiply a decimal number by a power of ten

Find the product of a decimal and a power of ten. Learn how to shift the decimal point for quick mental math
Multiply a decimal number by a power of ten

Simplify a fraction using the basic property of fractions

Use the basic property of fractions to simplify fractions. First, reduce a common factor out of a fraction. Then, select fraction equations that show the basic property of fractions. Finally, complete the missing number in a basic property of fractions eq
Simplify a fraction using the basic property of fractions

Convert a fraction to a given denominator using the basic property of fractions

Write equivalent equations using the basic property of fractions. Given a fraction and a new value for the denominator, determine which number you must multiply by to get that denominator. Then, write the equivalent fraction
Convert a fraction to a given denominator using the basic property of fractions

Convert between division expressions and fractions

Rewrite a division expression as a fraction. Write the dividend as the numerator and the divisor as the denominator. Also, practice writing the division expression from the fraction
Convert between division expressions and fractions

Complete fraction expressions using the basic property of fractions

Use the basic property of fractions to simplify fractions. First, reduce a common factor out of a fraction. Then, complete the missing number in a basic property of fractions equation
Complete fraction expressions using the basic property of fractions

Convert fractions with decimal denominators to fractions with whole number denominators (Level 1)

Use the basic property of fractions to convert fractions containing decimals to fractions containing only whole numbers. Change a division expression to a fraction. Then, choose the correct factor that makes the denominator a whole number. Simplify the fr
Convert fractions with decimal denominators to fractions with whole number denominators (Level 1)

Convert fractions with decimal denominators to fractions with whole number denominators (Level 2)

Convert fractions containing decimals to fractions containing only whole numbers. Change a division expression to a fraction. Then, choose the correct factor that makes the denominator a whole number. Simplify the fraction
Convert fractions with decimal denominators to fractions with whole number denominators (Level 2)

Convert fractions with decimal denominators to fractions with whole number denominators (Level 3)

Convert fractions containing decimals to fractions containing only whole numbers. Rewrite a division expression as a fraction. Then, choose the correct factor that makes the denominator a whole number. Find the quotient, using long division if necessary
Convert fractions with decimal denominators to fractions with whole number denominators (Level 3)

Convert fractions with decimal denominators to fractions with whole number denominators (Level 4)

Use the basic property of fractions to convert fractions containing decimals to fractions containing only whole numbers. Choose the correct factor that makes the denominator a whole number. Then, multiply and simplify the fraction
Convert fractions with decimal denominators to fractions with whole number denominators (Level 4)

Convert division expressions with decimal divisors to expressions with whole number divisors (Level 1)

Learn how to rewrite division of decimals to a division expression containing whole numbers. Shift the decimal point of the divisor as many places to the right as necessary to make it a whole number. Shift the decimal point of the dividend by the same num
Convert division expressions with decimal divisors to expressions with whole number divisors (Level 1)

Convert division expressions with decimal divisors to expressions with whole number divisors (Level 2)

Rewrite division of decimals to a division expression containing whole numbers. Shift the decimal point as many places to the right as necessary to make it a whole number. Shift the decimal point of the dividend by the same number of places. Then, find th
Convert division expressions with decimal divisors to expressions with whole number divisors (Level 2)

MODULE 5: Algebraic Expressions

Topic A: Solving Complex Missing Addend Equations

Topic Description: Students solve increasingly complex missing addend equations. In these pre-algebra equations, the challenge is not in the number values but in the logic of how numbers and equations can be combined to solve for numbers represented by symbols.