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Curriculum for Grade 3

Students' strong foundation of math skills facilitates the shift to multiplication and division, moving from concrete procedures toward abstract thinking and automaticity.

MODULE 1. Properties of Multiplication and Division and Solving Problems with Units of 2-5 and 10

Topic A: Multiplication and the Meaning of the Factors

Students build upon their knowledge of addition to identify factors (how many groups, how many objects in each group) and to compose and solve simple multiplication equations. They work with groups of 2-5 identical objects, beginning with models of identical concrete objects, such as bunches of bananas and fingers on a hand. As students progress, they work with more abstract objects (identical beads) and objects in an array.

Compose and solve a repeated addition equation based on a model

Practice using repeated addition with picture representations to begin to understand multiplication. This activity first gives students the addends, and later requires students to fill in the number of each object and perform the addition
Compose and solve a repeated addition equation based on a model

Compose a repeated addition equation based on a model and identify the number of "groups"

Practice composing an addition sentence with repeated addends. First, count the number of objects in each group. Then, form an addition sentence with the number of objects. Finally, determine how many groups there are
Compose a repeated addition equation based on a model and identify the number of "groups"

Compose and solve a multiplication equation based on a model, a repeated addition equation, and the number of "groups"

Learn how multiplication and repeated addition are related. First perform repeated addition. Then, describe this addition as how many groups of the same number. Finally, fill in a multiplication sentence with the numbers
Compose and solve a multiplication equation based on a model, a repeated addition equation, and the number of "groups"

Compose and solve a multiplication equation based on a model and a repeated addition equation

Practice performing repeated addition and translating this to a multiplication sentence. Students will start to understand the meaning of factors in mutliplication and how they're related to addends in addition
Compose and solve a multiplication equation based on a model and a repeated addition equation

Arrange groups of objects into an array and determine the total

Practice describing a quantity as how many groups of a certain number. This activity helps students understand the idea of factors in multiplication
Arrange groups of objects into an array and determine the total

Compose and solve a multiplication equation based on a model of objects in an array

Learn how to describe a set of objects in terms of the same number of rows and translate this to a multiplication sentence. This activity requires to first find the product and then to fill in the factors of the multiplication sentence
Compose and solve a multiplication equation based on a model of objects in an array

Topic B: Division as an Unknown Factor Problem

Students continue to work with concrete and more abstract objects to build models of division. They use the "dealing" method to create a given number of equal groups and also create groups of a given size. Based on these models, they answer the questions, "How many groups?" and "How many in each group?" They compose and solve division equations and determine the missing factor in multiplication problems.

Divide a set of objects into a given number of equal groups and identify the number of objects in each group

Practice dividing a set of objects into equal groups. This activity shows how you can break up a set of objects into equal groups and then determine the number of objects in each group
Divide a set of objects into a given number of equal groups and identify the number of objects in each group

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

Learn how dividing a set of objects into equal groups is division. This activity teaches students how to take the total number of objects, the number of groups, and the number of objects in each and translate this into a division sentence
Compose and solve a division equation based on a model (Part 1)

Divide a set of objects into equal groups of a given size and identify the number of groups

Practice taking a group of objects and dividing them into a set size of group. The students will first make one group of a given size, then add groups until they have divided up all the objects
Divide a set of objects into equal groups of a given size and identify the number of groups

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

Learn how dividing a set of objects into equal sized groups relates to division. This activity first asks students to create groups of a given size, then asks how many groups there are, and finally shows how this can be written as a division sentence
Compose and solve a division equation based on a model (Part 2)

Arrange a group of objects into an array and compose a division equation based on the model

Practice dealing out a set of objects into a given number of rows, then make a division sentence based on the number of rows and how many objects in each row. You need to make rows of a certain size and make a division sentence from the result
Arrange a group of objects into an array and compose a division equation based on the model

Determine the missing factor in a multiplication equation based on a model

Practice writing multiplication and division sentences based on a group of objects. You need to determine how many objects are in each row and how many objects there are total, and then use this information to write a sentence relating these quantities
Determine the missing factor in a multiplication equation based on a model

Solve a missing factor multiplication equation based on a model

Practice filling in a multiplication sentence using a set of object grouped into rows
Solve a missing factor multiplication equation based on a model

Solve a missing factor multiplication equation and a related division equation based on a model

Practice filling in a multiplication sentence using a set of object grouped into rows and then filling in a division sentence relating the same numbers. This activitiy helps students see how multiplication and division are related
Solve a missing factor multiplication equation and a related division equation based on a model

Topic C: Analyzing Arrays to Multiply Using Units of 2 and 3

Skip count by 2 (Level 1)

Practice skip counting by 2s. Fill in the missing numbers on a number line when skip counting from 2 to 10
Skip count by 2 (Level 1)

Skip count by 3 (Level 1)

Practice skip counting by 3s. Fill in the missing numbers on a number line when skip counting from 3 to 15
Skip count by 3 (Level 1)

Multiply by 2 with and without an array model (Level 1)

Practice performing multiplication facts with products that are the multiples of 2 from 2 to 10. This activity reinforces the idea that skip counting by 2s is also multiplication
Multiply by 2 with and without an array model (Level 1)

Multiply by 3 with and without an array model (Level 1)

Practice performing multiplication facts with products that are multiples of 3 from 3 to 15. This activity reinforces the idea that skip counting by 3s is also multiplication
Multiply by 3 with and without an array model (Level 1)

Multiply by 2 to complete a pattern of equations (Level 1)

Practice performing multiplication facts with products that are the multiplies of 2 from 2 to 10
Multiply by 2 to complete a pattern of equations (Level 1)

Multiply by 3 to complete a pattern of equations (Level 1)

Practice performing multiplication facts with products that are the multiples of 3 from 3 to 15
Multiply by 3 to complete a pattern of equations (Level 1)

Label arrays with equations to show the commutative property of multiplication by 2

Practice visualizing multiplication using arrays. This activity shows students the commutative property of multiplication-- reversing the factors results in the same product
Label arrays with equations to show the commutative property of multiplication by 2

Label arrays with equations to show the commutative property of multiplication by 3

Practice visualizing multiplication using arrays. This activity shows students the commutative property of multiplication-- reversing the factors results in the same product
Label arrays with equations to show the commutative property of multiplication by 3

Complete equations to show the commutative property of multiplication by 2 (Level 1)

Practice the commutative property of multiplication. This activity presents two multiplication sentences that have factors reversed, which result in the same product
Complete equations to show the commutative property of multiplication by 2 (Level 1)

Complete equations to show the commutative property of multiplication by 3 (Level 1)

Practice the commutative property of multiplication. This activity presents two multiplication sentences that have factors reversed, which result in the same product
Complete equations to show the commutative property of multiplication by 3 (Level 1)

Solve x2 multiplication equations (Level 1, Part 1)

Play a game practicing the multiplication facts involving the numbers 1-5 multiplied by 2
Solve x2 multiplication equations (Level 1, Part 1)

Solve x3 multiplication equations (Level 1, Part 1)

Play a game practicing the multiplication facts involving the numbers 1-5 multiplied by 3
Solve x3 multiplication equations (Level 1, Part 1)

Solve x2 multiplication equations (Level 1, Part 2)

Play a game practicing the multiplication facts involving the numbers 1-5 multiplied by 2
Solve x2 multiplication equations (Level 1, Part 2)

Solve x3 multiplication equations (Level 1, Part 2)

Play a game practicing the multiplication facts involving the numbers 1-5 multiplied by 3
Solve x3 multiplication equations (Level 1, Part 2)

Skip count by 2 (Level 2)

Practice skip counting by 2s. Fill in the missing numbers on a number line when skip counting from 2 to 20
Skip count by 2 (Level 2)

Skip count by 3 (Level 2)

Practice skip counting by 3s. Fill in the missing numbers on a number line when skip counting from 3 to 30
Skip count by 3 (Level 2)

Multiply by 2 with and without an array model (Level 2)

Use arrays to start at 10 and perform the x2 multiplication facts up to 20. This activity shows students how multiplying by 2 is related to repeated addition
Multiply by 2 with and without an array model (Level 2)

Multiply by 3 with and without an array model (Level 2)

Use arrays to start at 15 and perform the x3 multiplication facts up to 30. This activity shows students how multiplying by 3 is related to repeated addition
Multiply by 3 with and without an array model (Level 2)

Multiply by 2 to complete a pattern of equations (Level 2)

Practice the 2x multiplication facts from 1 to 10. This activity gives one multiplication fact and asks students to find the next one in succession, which can be done by adding 2 to the previous product
Multiply by 2 to complete a pattern of equations (Level 2)

Multiply by 3 to complete a pattern of equations (Level 2)

Practice the 3x multiplication facts from 1 to 10. This activity gives one multiplication fact and asks students to find the next one in succession, which can be done by adding 3 to the previous product
Multiply by 3 to complete a pattern of equations (Level 2)

Complete equations to show the commutative property of multiplication by 2 (Level 2)

Practice using the commutative property of multiplication to fill in missing factors or products in multiplication sentences
Complete equations to show the commutative property of multiplication by 2 (Level 2)

Complete equations to show the commutative property of multiplication by 3 (Level 2)

Practice using the commutative property of multiplication to fill in missing factors or products in multiplication sentences
Complete equations to show the commutative property of multiplication by 3 (Level 2)

Label arrays with equations to show the distributive property of multiplication by 2 (Part 1)

Practice labeling the number of rows in an array to introduce the idea of the distributive property of multiplication. This activity has the student identify the number of rows before and after adding additional rows to the array
Label arrays with equations to show the distributive property of multiplication by 2 (Part 1)

Label arrays with equations to show the distributive property of multiplication by 2 (Part 2)

Learn how the distributive property applies to multiplication. In this activity, students will label arrays with equations to show the distributive property of multiplication by 2
Label arrays with equations to show the distributive property of multiplication by 2 (Part 2)

Label arrays with equations to show the distributive property of multiplication by 3 (Part 1)

Practice labeling the number of rows in an array to introduce the idea of the distributive property of multiplication. This activity has the student identify the number of rows before and after adding additional rows to the array
Label arrays with equations to show the distributive property of multiplication by 3 (Part 1)

Label arrays with equations to show the distributive property of multiplication by 2 (Part 3)

Practice labeling arrays with equations, then breaking the array into two parts and finding the solutions to all three equations. This activity shows students how the distributive property of multiplication works
Label arrays with equations to show the distributive property of multiplication by 2 (Part 3)

Label arrays with equations to show the distributive property of multiplication by 3 (Part 2)

Practice labeling arrays with equations, then breaking the array into two parts and finding the solutions to all three equations. This activity shows students how the distributive property of multiplication works
Label arrays with equations to show the distributive property of multiplication by 3 (Part 2)

Solve x2 multiplication equations (Level 2, Part 1)

Play a game practicing the multiplication facts involving the numbers 1-10 multiplied by 2
Solve x2 multiplication equations (Level 2, Part 1)

Solve x3 multiplication equations (Level 2, Part 1)

Play a game practicing the multiplication facts involving the numbers 1-10 multiplied by 3
Solve x3 multiplication equations (Level 2, Part 1)

Solve x2 multiplication equations (Level 2, Part 2)

Play a game practicing the multiplication facts involving the numbers 1-10 multiplied by 2
Solve x2 multiplication equations (Level 2, Part 2)

Solve x3 multiplication equations (Level 2, Part 2)

Play a game practicing the multiplication facts involving the numbers 1-10 multiplied by 3
Solve x3 multiplication equations (Level 2, Part 2)

Topic D: Division by 2 and by 3

Students use concrete and abstract objects to understand the concept of division. They then relate division to multiplication to help build understanding and fact fluency. Students begin by solving simple division equations (quotients to 5) and then advance to solving equations with quotients to 10.

Distribute objects equally to create a tape diagram (How many in each group?)

Learn how to distribute objects evenly to create a tape diagram. This activity requires students to understand the number of groups, number of objects in each group, and total number of objects
Distribute objects equally to create a tape diagram (How many in each group?)

Represent a tape diagram as a division equation (How many in each group?)

Practice taking a tape diagram that represents a real life situation and writing a division equation from it. This activity requires the students to identify the parts of the tape diagram first before writing the division equation
Represent a tape diagram as a division equation (How many in each group?)

Distribute objects equally to create a tape diagram (How many groups?)

Practice distributing objects evenly to create a tape diagram. This activity requires students to understand the number of groups, number of objects in each group, and total number of objects
Distribute objects equally to create a tape diagram (How many groups?)

Represent a tape diagram as a division equation (How many groups?)

Learn how to represent a tape diagram as a division equation. This activity requires students to create the tape diagram, locate its parts, then write the division equation
Represent a tape diagram as a division equation (How many groups?)

Complete equations to relate multiplication to division (Part 1)

Learn how division and multiplication are related. This activity requries students to complete multiplication and division equations to see how the two operations are related
Complete equations to relate multiplication to division (Part 1)

Complete equations to relate multiplication to division (Part 2)

Learn that related multiplication and division facts use the same numbers. This activity requires students to first complete multiplication and division equations that are the opposite of one another, and then locate the same numbers in both equations
Complete equations to relate multiplication to division (Part 2)

Match a division fact to its related multiplication fact

Learn how multiplication and division are related. In this activity, students are given a division equation and asked to find the multiplication equation that is related
Match a division fact to its related multiplication fact

Solve division equations by using the related multiplication fact

Learn how to solve division equations using a related multiplication fact. This activity shows students how division by 2 is related to multiplication by 2
Solve division equations by using the related multiplication fact

Solve division equations with a divisor of 2 (Level 1)

Practice solving division equations with divisors of 2. In this activity, students are given a hint as to how the division equation is related to multiplication to help them solve the equations
Solve division equations with a divisor of 2 (Level 1)

Solve division equations with a divisor of 3 (Level 1)

Practice solving division equations with divisors of 3. In this activity, students are given a hint as to how the division equation is related to multiplication to help them solve the equations
Solve division equations with a divisor of 3 (Level 1)

Solve division equations with a divisor of 2 or 3 (Level 1)

Practice solving division equations with divisors of 2 and 3. In this activity, students are given a hint as to how the division equation is related to multiplication to help them solve the equations
Solve division equations with a divisor of 2 or 3 (Level 1)

Solve division equations with a divisor of 2 (Level 2)

Practice solving division equations with divisors of 2. In this activity, students aren't given any hints
Solve division equations with a divisor of 2 (Level 2)

Solve division equations with a divisor of 2 (Level 3)

Practice solving more difficult division equations with divisors of 2. In this activity, students aren't given any hints
Solve division equations with a divisor of 2 (Level 3)

Solve division equations with a divisor of 3 (Level 2)

Practice solving division equations with divisors of 3. In this activity, students aren't given any hints
Solve division equations with a divisor of 3 (Level 2)

Solve division equations with a divisor of 3 (Level 3)

Practice solving more difficult division equations with divisors of 3. In this activity, students aren't given any hints
Solve division equations with a divisor of 3 (Level 3)

Topic E: Multiplication and Division by 4

Building upon previous learning about multiplication and division, students apply their understanding to facts using 4 as a product or divisor. They work with familiar manipulatives and progression of skills to build understanding and fluency.

Skip count by 4

Practice skip counting by 4s. Fill in the missing numbers on a number line when skip counting from 4 to 40
Skip count by 4

Multiply by 4 with and without an array model

Practice multiplying by 4 by using an array model. This activity shows students an additional group of 4 tiles, then asks for the next multiplication by 4 fact
Multiply by 4 with and without an array model

Multiply by 4 to complete a pattern of equations

Learn how to use one multiplication fact to find the next in a pattern. In this activity, students will be multiplying by 4 using their knowledge of skip counting by 4
Multiply by 4 to complete a pattern of equations

Solve x4 multiplication equations

Play a game practicing the multiplication facts involving the numbers 1-10 multiplied by 4
Solve x4 multiplication equations

Represent a tape diagram as a multiplication equation (Level 1)

Learn how to represent a tape diagram as a multiplication equation. This activity requires students to label the parts of the tape diagram, then write the multiplication equation
Represent a tape diagram as a multiplication equation (Level 1)

Represent a tape diagram as a multiplication equation (Level 2)

Practice completing a multiplication sentence to match a tape diagram. In this activity, students are working with the x4 multiplication facts
Represent a tape diagram as a multiplication equation (Level 2)

Label a tape diagram to represent a multiplication equation

Practice labeling a tape diagram to match a multiplication equation. In this activity, students drag the parts of the multiplication sentence to the corresponding parts of the tape diagram
Label a tape diagram to represent a multiplication equation

Identify factors and product in a multiplication equation

Practice identifying the factors and product in a multiplication sentence. In this activity, students drag the correct terms to the corresponding parts of the multiplication sentence
Identify factors and product in a multiplication equation

Label arrays with equations to show the commutative property of multiplication (Level 1)

Practice writing two multiplication sentences based on one array using the x4 multiplication facts. The array is rotated after students write the first sentence to show how the commutative property of multiplication
Label arrays with equations to show the commutative property of multiplication (Level 1)

Label arrays with equations to show the commutative property of multiplication (Level 2)

Practice labeling tape diagrams to demonstrate the commutative property of multiplication using the x4 multiplication facts. In this activity, students label two tape diagrams that demonstrate how switching the order of factors yields the same product
Label arrays with equations to show the commutative property of multiplication (Level 2)

Label tape diagrams with equations to show the commutative property of multiplication

Practice labeling tape diagrams and corresponding multiplication equations to demonstrate the commutative property of multiplication using the x4 multiplication facts
Label tape diagrams with equations to show the commutative property of multiplication

Solve multiplication equations based on the commutative property

Practice solving multiplication equations based on the commutative property using the x4 multiplication facts
Solve multiplication equations based on the commutative property

Solve word problems using tape diagrams and multiplication equations

Practice solving word problems using tape diagrams and multiplication equations using the x4 multiplication facts
Solve word problems using tape diagrams and multiplication equations

Solve division equations by using the related multiplication fact

Learn how division by 4 is related to multiplication by 4. In this activity, students are given a clue as to how the solution is related to a multiplication fact they already know
Solve division equations by using the related multiplication fact

Solve division equations with a divisor of 4 (Level 2)

Practice solving division equations with a divisor of 4
Solve division equations with a divisor of 4 (Level 2)

Solve division equations with a divisor of 4 (Level 1)

Practice solving division equations with a divisor of 4
Solve division equations with a divisor of 4 (Level 1)

Topic F: Multiplication and Division by 5

Building upon previous learning about multiplication and division, students apply their understanding to facts using 5 as a product or divisor and 10 as a product. They also develop understanding of the distributive property of multiplication and division. Students build connections between equations, arrays, tape diagrams, and word problems.

Skip count by 5

Practice skip counting by 5s. Fill in the missing numbers on a number line when skip counting from 5 to 50
Skip count by 5

Multiply by 5 with and without an array model

Practice multiplying by 5 by using an array model. This activity shows students an additional group of 5 tiles, then asks for the next multiplication by 5 fact
Multiply by 5 with and without an array model

Multiply by 5 to complete a pattern of equations

Learn how to use one multiplication fact to find the next in a pattern. In this activity, students will be multiplying by 5 using their knowledge of skip counting by 5
Multiply by 5 to complete a pattern of equations

Solve x5 multiplication equations

Play a game practicing the multiplication facts involving the numbers 1-10 multiplied by 5
Solve x5 multiplication equations

Solve division equations by using the related multiplication fact

Learn how division by 5 is related to multiplication by 5. In this activity, students are given a clue as to how the solution is related to a multiplication fact they already know
Solve division equations by using the related multiplication fact

Solve division equations with a divisor of 5 (Level 1)

Practice solving division equations with a divisor of 5
Solve division equations with a divisor of 5 (Level 1)

Solve division equations with a divisor of 5 (Level 2)

Practice solving division equations with a divisor of 5
Solve division equations with a divisor of 5 (Level 2)

Label arrays with equations to show the distributive property of multiplication

Practice solving multiplication equations using the break apart and distribute strategy. In this activity, students will label two smaller arrays with multiplication equations to find the product of the larger numbers
Label arrays with equations to show the distributive property of multiplication

Complete expressions based on the distributive property of multiplication

Practice using the break apart and distribute strategy to find a multiplication expression that's equivalent to the sum of two multiplication expressions
Complete expressions based on the distributive property of multiplication

Compose a division equation based on an array

Learn how to use an array with 4 or 5 rows to write a division equation
Compose a division equation based on an array

Compose a division equation based on an array to show the distributive property of division

Learn how to compose a division equation based on an array to show the distributive property of division
Compose a division equation based on an array to show the distributive property of division

Solve a division equation based on an array by using the distributive property of division

Practice solving division equations using the break apart and distribute strategy. In this activity, students will label two smaller arrays with division equations to find the quotient of the larger numbers
Solve a division equation based on an array by using the distributive property of division

Complete expressions based on the distributive property of division

Practice using the break apart and distribute strategy to find a division expression that's equivalent to the sum of two division expressions
Complete expressions based on the distributive property of division

Skip count by 10

Practice skip counting by 10s. Fill in the missing numbers on a number line when skip counting from 10 to 100
Skip count by 10

Multiply by 10 to complete a pattern of equations (Level 1)

Learn how to multiply by 10 to complete a pattern of equations
Multiply by 10 to complete a pattern of equations (Level 1)

Multiply by 10 to complete a pattern of equations (Level 2)

Practice multiplying by 10 to complete a pattern of equations
Multiply by 10 to complete a pattern of equations (Level 2)

Solve x10 multiplication equations

Play a game practicing the multiplication facts involving the numbers 1-10 multiplied by 10
Solve x10 multiplication equations

Solve word problems using tape diagrams and division equations (Level 1)

Learn how to use a tape diagram and division equation to solve a word problem. In this activity, students are given clues to help them label the tape diagram first before filling in the division equation
Solve word problems using tape diagrams and division equations (Level 1)

Solve word problems using tape diagrams and division equations (Level 2)

Learn how to use a tape diagram and division equation to solve a word problem. In this activity, students are given clues to help them label the tape diagram first before filling in the division equation
Solve word problems using tape diagrams and division equations (Level 2)

MODULE 2. Place Value and Problem Solving with Units of Measure

Topic A: Measuring Weight and Liquid Volume in Metric Units

Students use a scale and a pan balance with weights to determine the mass of objects. They learn to read a scale between labeled increments and to add and subtract mass measurements to solve problems. To learn how to measure capacity, students pour liquid into labeled containers. They learn the relationship between kilograms and grams and between liters and milliliters.

Measure the mass of objects in kilograms using a scale

Learn about finding mass in kilograms. Put various animals on a scale and read the dial of the scale to find their mass
Measure the mass of objects in kilograms using a scale

Measure the mass of objects in kilograms using a pan balance

Use a pan balance to find the mass of various animals. The animal is on one pan of the scale. Add 1 kg masses to the other pan until the balance is level.. Enter the total mass of the animal
Measure the mass of objects in kilograms using a pan balance

Measure the mass of objects in grams using a pan balance

Learn the relationship between kilograms and grams. Find the mass on an animal with a pan balance using masses in increments of 100 g and 10 g
Measure the mass of objects in grams using a pan balance

Tutorial: Drag the lace to match objects

Learn how to match two objects using laces to connect the cards
Tutorial: Drag the lace to match objects

Match the estimated mass in grams and kilograms to objects

Estimate the masses of fruits by matching an appropriate value and units. Select the correct value for one fruit from the options. Then, match three pictures of various amounts of one fruit to the appropriate mass values
Match the estimated mass in grams and kilograms to objects

Determine mass measurements on a scale that is only labeled in increments of 10

Read a mass value to the nearest gram from a scale dial that is labeled in increments of 10. Labeled increments have 2 or 3 digits
Determine mass measurements on a scale that is only labeled in increments of 10

Add or subtract to compare or find the total mass of objects measured on a scale

Find the sum or difference between two measured masses. The masses are measured either to the nearest gram on a scale that is labeled in increments of 10 or on a pan scale with the appropriate masses placed to balance
Add or subtract to compare or find the total mass of objects measured on a scale

Tutorial: Click on highlighted words to access definition

Learn how to click a highlighted word to see the definition of that word
Tutorial: Click on highlighted words to access definition

Determine visually which of two objects has a greater capacity

Select the container that has the greater capacity. The containers vary in height, width, and form
Determine visually which of two objects has a greater capacity

Measure capacity using non-standard units and liters

Fill two large containers with a jug. Determine which of the large containers has the greater capacity. Then, learn about the standard capacity unit of liter
Measure capacity using non-standard units and liters

Measure capacity in liters

Use a graduated container to measure the capacity of smaller containers. Pour the liquid from the smaller container into the larger and read off the capacity measurement
Measure capacity in liters

Measure capacity in milliliters

Learn the relationship between liters and milliliters. Use a graduated container to measure capacities of smaller containers in increments of 100 ml
Measure capacity in milliliters

Measure capacity in milliliters

Match containers to their appropriate capacity measurements and units
Measure capacity in milliliters

Topic B: Rounding to the Nearest Ten and Hundred

Using a number line to provide context, students first determine the midway point between two round numbers. They then progress to rounding using the number line and the midway point. Finally, students round 2-, and 3-digit numbers to any given place value.

Determine the halfway point between tens on a number line (Level 1)

Learn what the halfway point of an interval is by first labeling a number line and then locating the middle. In this activity, students will begin with the numbers 1-10 and then move on to higher numbers, finding the halfway point of each set
Determine the halfway point between tens on a number line (Level 1)

Determine the halfway point between tens on a number line (Level 2)

Practice finding the halfway point between tens on a number line. In this activity, students will end with the fact that the number halfway between the nearest tens always has a 5 in the ones place
Determine the halfway point between tens on a number line (Level 2)

Determine whether a given number is greater or less than the halfway point between tens on a number line

Learn how to determine whether a given number is greater or less than the halfway point between tens on a number line
Determine whether a given number is greater or less than the halfway point between tens on a number line

Determine the halfway point between hundreds on a number line (Level 1)

Learn how to find the halfway point between hundreds on a number line. In this activity, students will first determine how many parts the interval is divided into before finding the halfway point
Determine the halfway point between hundreds on a number line (Level 1)

Determine the halfway point between hundreds on a number line (Level 2)

Practice finding the halfway point between hundreds on a number line. In this activity, students will end with the fact that the number halfway between the nearest hundreds always has a 5 in the tens place and a 0 in the ones place
Determine the halfway point between hundreds on a number line (Level 2)

Determine whether a given number is greater or less than the halfway point between hundreds on a number line

Learn how to determine whether a given number is greater or less than the halfway point between hundreds on a number line
Determine whether a given number is greater or less than the halfway point between hundreds on a number line

Use the ~ symbol when rounding a number to the nearest ten or hundred

Learn how to round a number to the nearest tenth and use the ~ symbol to show that two numbers are close
Use the ~ symbol when rounding a number to the nearest ten or hundred

Determine the nearest ten to a given number using a number line

Learn how to find the nearest ten or hundred to a number, compare it to the halfway point of the two closest tens or hundreds, and use this information to determine whether to round up or down
Determine the nearest ten to a given number using a number line

Determine whether a given number rounds up or down to the nearest ten (Level 1)

Play a game to practice rounding up or down when rounding to the nearest ten
Determine whether a given number rounds up or down to the nearest ten (Level 1)

Determine the nearest ten to a given number

Practice finding the nearest tens to a number and using this information to determine whether to round the number up or down
Determine the nearest ten to a given number

Determine the nearest hundred to a given number

Practice finding the nearest hundreds to a number and using this information to determine whether to round the number up or down
Determine the nearest hundred to a given number

Round a given number to the nearest ten and to the nearest hundred

Practice round a number to the nearest ten and the nearest hundred
Round a given number to the nearest ten and to the nearest hundred

Round a given number to the nearest ten or to the nearest hundred

Play a game to practice rounding to the nearest ten or hundred
Round a given number to the nearest ten or to the nearest hundred

Determine whether a given number rounds up or down to the nearest ten (Level 2)

Play a game to practice rounding to the nearest ten
Determine whether a given number rounds up or down to the nearest ten (Level 2)

Topic C: Two- and Three-Digit Measurement Addition Using the Standard Algorithm

Students review the standard algorithm for addition with regrouping and then use it to solve word problems involving measurements. As they progress, they receive fewer prompts to complete the standard algorithm.

Add 2-digit numbers using the standard algorithm with regrouping

Practice addition of two 2-digit numbers with regrouping. First, hints are given about how to complete the addition in column form. Then, additional problems are provided without hints
Add 2-digit numbers using the standard algorithm with regrouping

Add 2-digit numbers using the standard algorithm with regrouping to solve word problems

Complete word problems involving the addition of two 2-digit numbers. Scaffolding is provided for setting up the operation, completing the addition in column format, and giving the answer with correct units
Add 2-digit numbers using the standard algorithm with regrouping to solve word problems

Add 3-digit numbers using the standard algorithm with regrouping (Level 1)

Practice addition of two 3-digit numbers with regrouping. Hints are given about how to complete the addition in column form
Add 3-digit numbers using the standard algorithm with regrouping (Level 1)

Add 3-digit numbers using the standard algorithm with regrouping (Level 2)

Add two 3-digit numbers. The numbers are automatically transferred into column format, but no hints are provided
Add 3-digit numbers using the standard algorithm with regrouping (Level 2)

Add 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 1)

Complete word problems involving the addition of two 3-digit numbers. Scaffolding is provided for setting up the operation, completing the addition in column format, and giving the answer with correct units
Add 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 1)

Add 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 2)

Practice addition of two 3-digit numbers with regrouping twice. Hints are given about how to complete the addition in column form
Add 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 2)

Add 3-digit numbers using the standard algorithm with regrouping (Level 3)

Add two 3-digit numbers that require regrouping twice. The numbers are automatically transferred into column format, but no hints are provided
Add 3-digit numbers using the standard algorithm with regrouping (Level 3)

Add 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 2)

Complete word problems involving the addition of two 3-digit numbers requiring regrouping twice. Scaffolding is provided for setting up the operation, completing the addition in column format, and giving the answer with correct units
Add 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 2)

Topic D: Two- and Three-Digit Measurement Subtraction Using the Standard Algorithm

Students review the standard algorithm for subtraction with regrouping and then use it to solve word problems involving measurements. As they progress, they receive fewer prompts to complete the standard algorithm.

Subtract 2-digit numbers using the standard algorithm with regrouping

Practice subtraction of 2-digit numbers with regrouping. First, hints are given about how to complete the subtraction in column form. Then, additional problems are provided without hints
Subtract 2-digit numbers using the standard algorithm with regrouping

Subtract 2-digit numbers using the standard algorithm with regrouping to solve word problems

Complete word problems involving the subtraction of 2-digit numbers. Scaffolding is provided for setting up the operation, completing the subtraction in column format, and giving the answer with correct units
Subtract 2-digit numbers using the standard algorithm with regrouping to solve word problems

Subtract 3-digit numbers using the standard algorithm with regrouping (Level 1)

Practice subtracting 3-digit numbers with regrouping once. Hints are given about how to complete the subtraction in column form
Subtract 3-digit numbers using the standard algorithm with regrouping (Level 1)

Subtract 3-digit numbers using the standard algorithm with regrouping (Level 2)

Subtract 3-digit numbers requiring regrouping once. Transfer the numbers into column format. No hints are provided
Subtract 3-digit numbers using the standard algorithm with regrouping (Level 2)

Subtract 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 1)

Complete word problems involving the subtraction of 3-digit numbers with regrouping once. Scaffolding is provided for setting up the operation, completing the subtraction in column format, and giving the answer with correct units
Subtract 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 1)

Subtract 3-digit numbers using the standard algorithm with regrouping (Level 3)

Practice subtraction of two 3-digit numbers with regrouping twice. Hints are given about how to complete the subtraction in column form
Subtract 3-digit numbers using the standard algorithm with regrouping (Level 3)

Subtract 3-digit numbers using the standard algorithm with regrouping (Level 4)

Subtract 3-digit numbers requiring regrouping twice. Transfer the numbers into column format. No hints are provided
Subtract 3-digit numbers using the standard algorithm with regrouping (Level 4)

Subtract 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 2)

Complete word problems involving the subtraction of 3-digit numbers with regrouping twice. Scaffolding is provided for setting up the operation, completing the subtraction in column format, and giving the answer with correct units
Subtract 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 2)

MODULE 3. Multiplication and Division with Units of 0, 1, 6-9, and Multiples of 10

Topic A: The Properties of Multiplication and Division

Students enrich their understanding of multiplication and division by introducing the multiplication chart and the commutative property (or 'turnaround facts') of multiplication. They continue to build fact fluency, adding factors 6-9 to their repertoire.

Illustrate the commutative property by labeling arrays and tape diagrams

Practice writing two multiplication sentences based on one array. The array is transformed into a tape diagram to show the same property in a different way
Illustrate the commutative property by labeling arrays and tape diagrams

Solve equations that illustrate the commutative property

Practice finding the product of a multiplication equation with factors in a different order. In this activity, students are first given a multiplication equation and then asked to solve a second equation with the factors reversed
Solve equations that illustrate the commutative property

Determine missing products in a multiplication chart (factors to 5)

Fill in a multiplication chart with facts from 1x1 to 5x5
Determine missing products in a multiplication chart (factors to 5)

Determine missing products in a multiplication chart (one factor > 5)

Fill in missing products in a multiplication chart where one factor is greater than 5
Determine missing products in a multiplication chart (one factor > 5)

Skip count by 6

Practice skip counting by 6 from 6 to 30, then using this information to fill in the missing numbers in a pattern
Skip count by 6

Determine multiples of 6 in a multiplication chart

Practice filling in a multiplication chart with multiples of 6. In this activity, students will use the commutative property and their knowledge of other multiplication facts to fill in the chart
Determine multiples of 6 in a multiplication chart

Skip count by 7

Practice skip counting by 7 from 7 to 35, then using this information to fill in the missing numbers in a pattern
Skip count by 7

Determine multiples of 7 in a multiplication chart

Practice filling in a multiplication chart with multiples of 7. In this activity, students will use the commutative property and their knowledge of other multiplication facts to fill in the chart
Determine multiples of 7 in a multiplication chart

Skip count by 8

Practice skip counting by 8 from 8 to 40, then using this information to fill in the missing numbers in a pattern
Skip count by 8

Determine multiples of 8 in a multiplication chart

Practice filling in a multiplication chart with multiples of 8. In this activity, students will use the commutative property and their knowledge of other multiplication facts to fill in the chart
Determine multiples of 8 in a multiplication chart

Skip count by 9

Practice skip counting by 9 from 9 to 45, then using this information to fill in the missing numbers in a pattern
Skip count by 9

Determine multiples of 9 in a multiplication chart

Practice filling in a multiplication chart with multiples of 9. In this activity, students will use the commutative property and their knowledge of other multiplication facts to fill in the chart
Determine multiples of 9 in a multiplication chart

Determine missing products in a multiplication chart (one factor > 5)

Practice finding the missing products in a multiplication chart where one factor is greater than 5
Determine missing products in a multiplication chart (one factor > 5)

Solve for an unknown represented by a letter in multiplication equations

Learn how to find the value of an unknown letter in a multiplication equation
Solve for an unknown represented by a letter in multiplication equations

Solve for an unknown represented by a letter in division equations

Learn how to find the value of an unknown letter in a division equation
Solve for an unknown represented by a letter in division equations

Match an equation containing an unknown to a statement

Learn how to match an equation containing an unknown to a statement. In this activity, students are given three options and asked to match the correct algebraic equation to the statement
Match an equation containing an unknown to a statement

Solve for an unknown represented by a letter in multiplication and division equations

Practice completing multiplication and division equations to solve for an unknown letter
Solve for an unknown represented by a letter in multiplication and division equations

Compose and solve a multiplication equation based on a tape diagram

Practice completing multiplication equations based on a tape diagram to solve for an unknown letter
Compose and solve a multiplication equation based on a tape diagram

Solve a multiplication word problem using a tape diagram

Learn how to use a tape diagram and multiplication equation to solve a word problem. In this activity, students are given clues to help them label the tape diagram first before filling in the multipication equation
Solve a multiplication word problem using a tape diagram

Topic B: Multiplication and Division Using Units of 6 and 7

Students begin with familiar tasks taken to a more challenging level with higher factors. They deepen their understanding of the relationship between multiplication and division as well as their fact fluency.

Skip count by 6

Practice skip counting by 6 from 6 to 60, then using this information to fill in the missing numbers in a pattern
Skip count by 6

Determine multiples of 6 in a multiplication chart

Practice filling in a multiplication chart with multiples of 6
Determine multiples of 6 in a multiplication chart

Determine products of 6 in a times table with and without an array model

Use arrays to start at 30 and perform the x6 multiplication facts up to 60. This activity shows students how multiplying by 6 is related to repeated addition
Determine products of 6 in a times table with and without an array model

Determine products of 6 in a times table

Practice filling in the products of 6 from 1x6 to 10x6. In this activity, some of the mutliplication facts are filled in and students must fill in the rest
Determine products of 6 in a times table

Solve division problems with a divisor of 6 based on its relationship to multiplication

Practice solving division problems with divisors of 6 based on their relationship to multiplication. In this activity, students are given a hint as to how they can use a related multiplication fact to find the quotient
Solve division problems with a divisor of 6 based on its relationship to multiplication

Solve division problems with a divisor of 6 (Level 1)

Practice solving division problems with divisors of 6
Solve division problems with a divisor of 6 (Level 1)

Solve division problems with a divisor of 6 (Level 2)

Practice solving division problems with divisors of 6
Solve division problems with a divisor of 6 (Level 2)

Skip count by 7

Practice skip counting by 7 from 7 to 70, then using this information to fill in the missing numbers in a pattern
Skip count by 7

Determine multiples of 7 in a multiplication chart

Practice filling in a multiplication chart with multiples of 7
Determine multiples of 7 in a multiplication chart

Determine products of 7 in a times table with and without an array model

Use arrays to start at 35 and perform the x7 multiplication facts up to 70. This activity shows students how multiplying by 7 is related to repeated addition
Determine products of 7 in a times table with and without an array model

Determine products of 7 in a times table

Practice filling in the products of 7 from 1x7 to 10x7. In this activity, some of the mutliplication facts are filled in and students must fill in the rest
Determine products of 7 in a times table

Solve division problems with a divisor of 7 based on its relationship to multiplication

Practice solving division problems with divisors of 7 based on their relationship to multiplication. In this activity, students are given a hint as to how they can use a related multiplication fact to find the quotient
Solve division problems with a divisor of 7 based on its relationship to multiplication

Solve division problems with a divisor of 7 (Level 1)

Practice solving division problems with divisors of 7
Solve division problems with a divisor of 7 (Level 1)

Solve division problems with a divisor of 7 (Level 2)

Practice solving division problems with divisors of 7
Solve division problems with a divisor of 7 (Level 2)

Solve multiplication equations using the break apart and distribute strategy

Learn to solve multiplication equations with units of 7 by using the break apart and distribute strategy. In this activity, students will label parts of a tape diagram to demonstrate the distributive property of multiplication
Solve multiplication equations using the break apart and distribute strategy

Solve for an unknown represented by a letter in multiplication equations

Practice finding the value of an unknown letter in a multiplication equation
Solve for an unknown represented by a letter in multiplication equations

Solve for an unknown represented by a letter in division equations

Practice finding the value of an unknown letter in a division equation
Solve for an unknown represented by a letter in division equations

Solve a word problem using a tape diagram and the relationship between multiplication and division

Learn how to solve a word problem using a tape diagram and the relationship between multiplication and division. You need to label the parts of the tape diagram. Use the relationship between multiplication and division to solve for the variable
Solve a word problem using a tape diagram and the relationship between multiplication and division

Topic C: Multiplication and Division Using Units up to 8

In addition to extending students' mastery of multiplication and division to include 8, they are also introduced to multi-step equations that use parentheses. Using illustrations and step-by-step instruction, students learn that parentheses and order of operations do not affect multiplication-only equations. They also continue to build their mastery of the break apart and distribute strategy.

Skip count by 8

Practice skip counting by 8 from 8 to 80, then using this information to fill in the missing numbers in a pattern
Skip count by 8

Determine multiples of 8 in a multiplication chart

Practice filling in a multiplication chart with multiples of 8
Determine multiples of 8 in a multiplication chart

Determine products of 8 in a times table with and without an array model

Use arrays to start at 40 and perform the x8 multiplication facts up to 80. This activity shows students how multiplying by 8 is related to repeated addition
Determine products of 8 in a times table with and without an array model

Determine products of 8 in a times table

Practice filling in the products of 8 from 1x8 to 10x8. In this activity, some of the mutliplication facts are filled in and students must fill in the rest
Determine products of 8 in a times table

Solve division problems with a divisor of 8 based on its relationship to multiplication

Learn how to solve division problems with divisors of 8 based on their relationship to multiplication. In this activity, students are given a hint as to how they can use a related multiplication fact to find the quotient
Solve division problems with a divisor of 8 based on its relationship to multiplication

Solve division problems with a divisor of 8 (Level 1)

Practice solving division problems with divisors of 8
Solve division problems with a divisor of 8 (Level 1)

Solve division problems with a divisor of 8 (Level 2)

Practice solving division problems with divisors of 8
Solve division problems with a divisor of 8 (Level 2)

Solve multi-step equations that include parentheses (Level 1)

Learn how to solve multi-step equations that include parentheses. In this activity, students learn that operations inside parentheses are always done first
Solve multi-step equations that include parentheses (Level 1)

Compare similar multi-step equations with parentheses in different places

Learn that the placement of parentheses in multi-step equations matters. In this activity, students will compare two equations with the same numbers and operations that have parentheses in different places and see that the solutions are different
Compare similar multi-step equations with parentheses in different places

Solve multi-step equations that include parentheses (Level 2)

Practice solving multi-step equations that include parentheses. This activity requires students to understand that operations inside parentheses are always done first
Solve multi-step equations that include parentheses (Level 2)

Identify a multi-step equation with parentheses that is solved correctly

Practice determining which multi-step equation is correct. In this activity, students are given two choices and asked to find the correct answer using their understanding of order of operations
Identify a multi-step equation with parentheses that is solved correctly

Recognize the effect of parentheses on multi-step multiplication equations (Part 1)

Learn that the order of parentheses in multiplication equations doesn't change the answer. In this activity, students solve two equations with parentheses in different places to prove that the solutions are the same
Recognize the effect of parentheses on multi-step multiplication equations (Part 1)

Recognize the effect of parentheses on multi-step multiplication equations (Part 2)

Learn that the order of parentheses in multiplication equations doesn't change the answer. A real life scenario is given and students need to use it to solve two equations with parentheses in different places to prove that the solutions are the same
Recognize the effect of parentheses on multi-step multiplication equations (Part 2)

Re-group factors with parentheses as a strategy to solve multi-step multiplication equations (Part 1)

Learn how to regroup factors with parentheses as a strategy to solve multi-step multiplication equations. In this activity, students are given a multiplication equation with larger numbers that they will break into factors and regroup in order to solve
Re-group factors with parentheses as a strategy to solve multi-step multiplication equations (Part 1)

Re-group factors with parentheses as a strategy to solve multi-step multiplication equations (Part 2)

Practice regrouping factors with parentheses as a strategy to solve multi-step multiplication equations. In this activity, students are given a multiplication equation with larger numbers that they will break into factors and regroup in order to solve
Re-group factors with parentheses as a strategy to solve multi-step multiplication equations (Part 2)

Solve multiplication equations using the break apart and distribute strategy (Part 1)

Learn to solve multiplication equations with units of 8 by using the break apart and distribute strategy. In this activity, students will label parts of a tape diagram to demonstrate the distributive property of multiplication
Solve multiplication equations using the break apart and distribute strategy (Part 1)

Solve multiplication equations using the break apart and distribute strategy (Part 2)

Learn to solve multiplication equations with units of 8 by using the break apart and distribute strategy. In this activity, students will use parentheses to write two multiplication equations, and then solve
Solve multiplication equations using the break apart and distribute strategy (Part 2)

Solve division equations using the break apart and distribute strategy (Part 1)

Learn to divide using the break apart and distribute strategy and an array. In this activity, students will take the two parts of the array, write two division equations, and then solve
Solve division equations using the break apart and distribute strategy (Part 1)

Solve division equations using the break apart and distribute strategy (Part 2)

Practice dividing using the break apart and distribute strategy to divide a large number by 8. In this activity, students use the distributive property to break apart the larger number into two smaller numbers are divisible by 8
Solve division equations using the break apart and distribute strategy (Part 2)

Topic D: Multiplication and Division Using Units of 9

Students apply and extend previous understanding to include 9 as a factor or divisor. We also introduce a strategy specifically for multiplying by 9.

Skip count by 9

Practice skip counting by 9 from 9 to 90, then using this information to fill in the missing numbers in a pattern
Skip count by 9

Determine multiples of 9 in a multiplication chart

Practice filling in a multiplication chart with multiples of 9
Determine multiples of 9 in a multiplication chart

Determine products of 9 in a times table with and without an array model

Use arrays to start at 45 and perform the x9 multiplication facts up to 80. This activity shows students how multiplying by 9 is related to repeated addition
Determine products of 9 in a times table with and without an array model

Determine products of 9 in a times table

Practice filling in the products of 9 from 1x9 to 10x9. In this activity, some of the mutliplication facts are filled in and students must fill in the rest
Determine products of 9 in a times table

Solve division problems with a divisor of 9 based on its relationship to multiplication

Learn how to solve division problems with divisors of 9 based on their relationship to multiplication. In this activity, students are given a hint as to how they can use a related multiplication fact to find the quotient
Solve division problems with a divisor of 9 based on its relationship to multiplication

Solve division problems with a divisor of 9 (Level 1)

Practice solving division problems with divisors of 9
Solve division problems with a divisor of 9 (Level 1)

Solve division problems with a divisor of 9 (Level 2)

Practice solving division problems with divisors of 9
Solve division problems with a divisor of 9 (Level 2)

Solve multiplication equations using the break apart and distribute strategy

Learn to solve multiplication equations with units of 9 by using the break apart and distribute strategy. In this activity, students will label parts of a tape diagram to demonstrate the distributive property of multiplication
Solve multiplication equations using the break apart and distribute strategy

Solve multiplication equations using the 9 = 10-1 strategy

Learn how to solve multiplication problems using the 9=10-1 strategy. In this activity, students will solve multiplication equations with a factor of 9 by using the break apart and distribute strategy with the fact that 9=10-1
Solve multiplication equations using the 9 = 10-1 strategy

Topic E: Analysis of Patterns and Problem Solving Including Units of 0 and 1

Students dig deeper into concepts of multiplication and division as they work with 1 and 0. In addition to working with these numbers as factors, dividends, and divisors, students use a letter to represent an unknown number in an equation and are introduced to let statements regarding such letters.

Compose a multiplication sentence (including 1x) to represent a model

Learn how to write a multiplication sentence based on a model. In this activity, students will determine the number of groups, how many in each group, and the total number in order to write a multiplication equation
Compose a multiplication sentence (including 1x) to represent a model

Solve multiplication problems that use 1 as a factor (including 1 x n)

Practice solving multiplication problems that use 1 as a factor (including 1 x n). In this activity, students will conclude that 1 times a number is always equal to the number
Solve multiplication problems that use 1 as a factor (including 1 x n)

Solve division problems that use 1 as a divisor (including n ÷ 1)

Practice solving division problems that use 1 as a divisor (including n ÷ 1). In this activity, students will conclude that a number divided by 1 is always equal to the number
Solve division problems that use 1 as a divisor (including n ÷ 1)

Compose a multiplication sentence (including x1) to represent a model

Practice composing a multiplication sentence based on a model. In this activity, students will identify the number of groups, number in each group and total number. They will use this information to compose the multiplication sentences
Compose a multiplication sentence (including x1) to represent a model

Solve multiplication problems that use 1 as a factor (including n x 1)

Practice solving multiplication problems that use 1 as a factor (including n x 1). In this activity, students will complete the multiplication sentence n x 1 = n to reinforce that 1 times a number is always that number
Solve multiplication problems that use 1 as a factor (including n x 1)

Solve division problems in which a number is divided by itself

Learn how to solve division problems in which a number is divided by itself. In this activity, students will conclude that a nonzero number divided by itself is always equal to 1
Solve division problems in which a number is divided by itself

Solve for an unknown (represented by a letter) in multiplication and division problems that include 1

Practice solving multiplication and division problems for an unknown. In this activity, the unknown is represented by a variable and one of the numbers in each equation is 1
Solve for an unknown (represented by a letter) in multiplication and division problems that include 1

Compose a multiplication sentence (including x0) to represent a model

Practice composing a multiplication sentence based on a model. In this activity, students will begin to work with groups that have 0 objects in them
Compose a multiplication sentence (including x0) to represent a model

Solve multiplication problems that use 0 as a factor (including n x 0 and 0 x n)

Learn that a factor of 0 always has a product of 0
Solve multiplication problems that use 0 as a factor (including n x 0 and 0 x n)

Solve division problems that use 1 as a dividend (including 0 ÷ n)

Learn how to compose a multiplication sentence based on a model in which the groups have 0 objects in them. Students will recognize that a number times 0 is always 0
Solve division problems that use 1 as a dividend (including 0 ÷ n)

Solve for an unknown (represented by a letter) in multiplication and division problems that include 0

Practice solving for an unknown represented by a variable in multiplication and division problems that include 0
Solve for an unknown (represented by a letter) in multiplication and division problems that include 0

Determine whether a multiplication or division equation with an unknown represented by a letter is true based on a let statement

Play a game to review multiplication and division questions that include 1 or 0. In this activity, students will determine whether a solution is true or false. The questions in this activity involve unknowns represented as letters
Determine whether a multiplication or division equation with an unknown represented by a letter is true based on a let statement

Topic F: Multiplication of Single-Digit Factors and Multiples of 10

Building upon students' fact fluency with single-digit factors, we introduce multiplying a single-digit factor by a multiple of ten. Students relate word-based multiplication (e.g., 4 x 3 tens = 12 tens) to numeric equations (e.g., 4 x 30 = 120).

MODULE 4. Multiplication and Area

Topic A: Foundations for Understanding Area

Students are introduced to the very basics of area using tiling. They learn to use square units, measure sides of a rectangle, skip count rows of tiles, and rearrange tiles to form a different rectangle with the same area.

Identify 2-dimensional shapes

Practice identifying two-dimensional shapes. In this activity, students will identify squares, rectangles, triangles, rhombuses and trapezoids
Identify 2-dimensional shapes

Tile 2-dimensional shapes to compare their area

Learn how to tile two-dimensional shapes to compare their areas. In this activity, students will learn that the amount of space a shape takes up is an area
Tile 2-dimensional shapes to compare their area

Determine and compare area by tiling with square units

Learn how to tile a figure to find its area. In this activity, students will use tiles that are one square unit each to find the area of the entire figure. Students will also compare areas of two figures
Determine and compare area by tiling with square units

Identify shapes that have a given area

Practice identifying shapes that have a given area. In this activity, students are given multiple figures of different sizes and asked to find all figures with a certain area
Identify shapes that have a given area

Determine area by tiling with square centimeters or inches

Learn how to draw a square of a given size and use this to find the area of a figure. In this activity, students will practice measuring in centimeters and inches
Determine area by tiling with square centimeters or inches

Determine area of a rectangle made by rearranging tiles from another rectangle

Learn how to determine the area of a rectangle made by rearranging tiles from another rectangle. In this activity, students will compare the area of the two figures, finding that the areas are equal
Determine area of a rectangle made by rearranging tiles from another rectangle

Determine area by skip counting tiles in each row

Learn how to find the length of the sides of a rectangle and use this to find the area of the rectangle. In this activity, students can use skip counting to find the areas
Determine area by skip counting tiles in each row

Topic B: Concepts of Area Measurement

Building upon the previous module, students start by skip counting tiles in a rectangle to determine its area. They then progress to multiplication using a tiled rectangle and one with only labeled measurements. Students rearrange tiles to determine the measurements of a different rectangle that has the same area. They also solve for an unknown side represented by a letter.

Tutorial: Click on the book to see the multiplication table

Learn that clicking on the book icon opens a multiplication table
Tutorial: Click on the book to see the multiplication table

Multiply to find the area of a tiled rectangle (Level 1)

Learn how to write a multiplication sentence for the area of a rectangle. Use tiles to find the length and width of the figure and then write a multiplication sentence to show that the area of a rectangle is the product of the lengths of the sides
Multiply to find the area of a tiled rectangle (Level 1)

Multiply to find the area of a tiled rectangle (Level 2)

Practice finding the lengths of the sides of a rectangle and using these to find the area of the rectangle. This activity reinforces the idea that the area is the product of the lengths of the sides
Multiply to find the area of a tiled rectangle (Level 2)

Determine the area of a rectangle by multiplying the lengths of the sides (Level 1)

Practice finding the area of a rectangle by multiplying the lengths of the sides. In this activity, the figure is partially covered so students have to multiply to find the area
Determine the area of a rectangle by multiplying the lengths of the sides (Level 1)

Determine the area of a rectangle by multiplying the lengths of the sides (Level 3)

Practice finding the area of a rectangle by multiplying the lengths of the sides. In this activity, the figure isn't divided to tiles so students must multiply to find the area
Determine the area of a rectangle by multiplying the lengths of the sides (Level 3)

Determine the area of a rectangle based on the equal area of a different rectangle

Practice finding the area of a rectangle based on the equal area of a different rectangle. In this activity, students move tiles from one rectangle to another rectangle to find its area
Determine the area of a rectangle based on the equal area of a different rectangle

Determine the length of a side based on the area of a rectangle

Learn how to use the length of one side of a rectangle and the area of a rectangle to find the length of the missing side of a rectangle. In this activity, students learn that you can find the length of an unknown side using division
Determine the length of a side based on the area of a rectangle

Topic C: Arithmetic Properties Using Area Models

Students dig deeper into their understanding of multiplication and area by using area models of rectangles. They compare parts to the whole, find missing parts, and manipulate equations to demonstrate properties. Exercises begin by using rectangles with gridlines and then advance to using those without.

Topic D: Applications of Area Using Side Lengths of Figures

Students learn two different approaches to finding the area of a composite shape based on side lengths. In the first, they break the shape into smaller rectangles and add those areas together. In the second, they "complete" the shape to find the total area and then subtract the area of the "missing piece". Students begin by using shapes with unit squares shown and then progress to those without.

Determine area of a composite shape by splitting it into two rectangles and adding the areas (Part 1)

Learn how to find the area of a composite figure. In this activity, students will practice finding the areas of the smaller parts and adding them to find the total area of the composite figure
Determine area of a composite shape by splitting it into two rectangles and adding the areas (Part 1)

Determine area of a composite shape by completing the rectangle and subtracting the area of the missing piece (Part 1)

Practice finding the area of a composite figure. In this activity, students will practice finding the areas of the smaller parts and adding them to find the total area of the composite figure
Determine area of a composite shape by completing the rectangle and subtracting the area of the missing piece (Part 1)

Determine area of a composite shape by completing the rectangle and subtracting the area of the missing piece (Part 2)

Learn how to determine area of a composite shape by finding the area of the entire rectangle and subtracting the area of the missing piece. In this activity, the composite shapes are a larger rectangle with a piece cut out of the middle
Determine area of a composite shape by completing the rectangle and subtracting the area of the missing piece (Part 2)

Determine area of a composite shape by splitting it into two rectangles and adding the areas (Part 2)

Learn how to find the area of a composite shape by splitting it into three rectangles. In this activity, students find the area of each of the three rectangles and find their sum to find the total area
Determine area of a composite shape by splitting it into two rectangles and adding the areas (Part 2)

Determine the area of a composite shape using either the "break apart and add" or "complete and subtract" strategy

Practice determining which method to use when finding the area of a composite figure. In this activity, students first choose what method to use and then find the area of the figure
Determine the area of a composite shape using either the "break apart and add" or "complete and subtract" strategy

MODULE 5. Fractions as Numbers on the Number Line

Topic A: Partition a Whole into Equal Parts

Students establish a foundation for understanding fractions by working with equal parts of a whole. They use halves, thirds, fourths, fifths, sixths, sevenths, and eighths of shapes including circles, rectangles, line segments, and other shapes. Students partition shapes, label sections, shade fractions, and even solve word problems involving equal sharing. Throughout the topic, they do not use fraction notation (e.g., 2 thirds).

Identify shapes that are partitioned into equal parts

Practice determining which shapes are divided into equal parts. In this activity, students are given shapes that are divided into two or more parts and asked to decide which are divided into equal parts
Identify shapes that are partitioned into equal parts

Identify and label halves, fourths, and eighths

Practice identifying halves, fourths and eighths. In this activity, students divide a paper into parts and determine whether each part is a half, fourth or eighth
Identify and label halves, fourths, and eighths

Identify and label thirds, fifths, sixths, and sevenths

Practice identifying thirds, fifths, sixths and sevenths. In this activity, students divide a paper into parts and determine what each part is called
Identify and label thirds, fifths, sixths, and sevenths

Determine the number of equal parts needed to partition a shape into a given denominator

Practice determining the number of equal parts needed to partition a shape into a given denominator. In this activity, students choose how many equal parts a figure needs to have based on how it's to be divided
Determine the number of equal parts needed to partition a shape into a given denominator

Identify the shaded portion of a shape as a unit fraction

Practice determining what fraction of a shape is shaded. In this activity, shapes are divided into equal parts and students practice naming the shaded part
Identify the shaded portion of a shape as a unit fraction

Sort shapes based on the unit fraction shaded

Practice sorting shapes based on the fraction shaded in each shape. In this activity, students see that a fourth can look different based on how the figure is divided into fourths
Sort shapes based on the unit fraction shaded

Identify the shaded portion of a shape

Practice identifying the shaded portion of a shape. In this activity, different sizes and shapes of figures are divided into different numbers of groups
Identify the shaded portion of a shape

Identify shapes that have a given portion shaded

Practice identifying shapes that have a given portion shaded. In this activity, students are given four figures and asked to choose the one which correctly fits the given criteria
Identify shapes that have a given portion shaded

Partition and shade a shape to represent a given portion

Practice partitioning and shading a shape to represent a given portion. In this activity, students are asked to shade a specific fraction of each figure, and then first divide the figure into parts before shading
Partition and shade a shape to represent a given portion

Solve word problems involving equal parts of a whole

Practice solving word problems involving equal parts of a whole. In this activity, students have to choose the correct fraction written in words based on the situation given
Solve word problems involving equal parts of a whole

Topic B: Unit Fractions and their Relation to the Whole

Students build upon their knowledge from Topic 5A to transition from word form to standard form in identifying fractions. They begin with unit fractions and advance to more complex fractions, including complements of a whole and improper fractions. Throughout the topic, students are presented with a variety of shapes, sizes, and colors of figures. While they do not use the term "improper fractions," they learn the underlying concept of fractional parts that form more than one whole.

Identify unit fractions written in standard form

Learn how to write a fraction using numbers and a fraction bar. In this activity, students learn to write a fraction based on a shaded figure by using (shaded parts)/(parts in all)
Identify unit fractions written in standard form

Label part of a figure with a unit fraction written in standard form

Learn that a unit fraction is one part of all equal parts of the whole. In this activity, students will identify how many equal parts there are and take this information to write a unit fraction for each part
Label part of a figure with a unit fraction written in standard form

Identify the part of a figure that is shaded with a unit fraction

Practice identifying what unit fraction of a figure is shaded. In this activity, students will choose from different unit fractions to determine which is correct
Identify the part of a figure that is shaded with a unit fraction

Identify figures that have a given unit fraction shaded

Practice identifying the figure with a given unit fraction shaded. In this activity, students will choose from different figures to determine which matches the given unit fraction
Identify figures that have a given unit fraction shaded

Write a unit fraction to identify the shaded part of a figure

Practice writing a unit fraction with numbers being given a shaded figure and words. In this activity, the fraction is written in words and students have to choose the correct numerator and denominator
Write a unit fraction to identify the shaded part of a figure

Identify the shaded part of a figure

Practice naming the shaded part of a fraction with words. In this activity, students first identify how many equal parts there are and how many of those parts are shaded before choosing the correct fraction
Identify the shaded part of a figure

Label the shaded part of a figure with a fraction written in standard form

Practice choosing the correct name of the shaded part of a figure. In this activity, students are given different options in words and asked to choose which represents the figure shown
Label the shaded part of a figure with a fraction written in standard form

Shade parts of a figure to represent a given fraction

Practice shading parts of a figure to represent a given fraction. In this activity, students will click on the correct number of sections of a figure to match the given fraction
Shade parts of a figure to represent a given fraction

Identify figures that have a given fraction shaded and fractions that represent the shaded part of a figure

Practice identifying the figures that have the correct portion shaded that matches a given fraction. In this activity, students will also identify which fraction correctly matches a figure
Identify figures that have a given fraction shaded and fractions that represent the shaded part of a figure

Write a fraction to identify the shaded part of a figure (Level 1)

Practice writing a fraction to identify the shaded portion of a figure. In this activity, students have to fill in either the numerator or denominator first, and then fill in both parts of the fraction
Write a fraction to identify the shaded part of a figure (Level 1)

Label the shaded part of a figure with a fraction written in standard form and word form

Practice labeling a figure with the correct fraction in word form and numeric form. In this activity, students choose from three options for the name of the fraction and three options for the numeric fraction
Label the shaded part of a figure with a fraction written in standard form and word form

Write a fraction to identify the shaded part of a figure (Level 2)

Practice writing a fraction to represent a given figure that is partially shaded. In this activity, students fill in both the numerators and denominators of the fraction
Write a fraction to identify the shaded part of a figure (Level 2)

Label shaded and unshaded parts of a figure (Level 1)

Identify what fraction of a figure is shaded and what fraction is unshaded. First choose the correct fraction of the shaded portion of the figure, and then choose the correct portion of the unshaded portion of the figure
Label shaded and unshaded parts of a figure (Level 1)

Label shaded and unshaded parts of a figure (Level 2)

Choose the correct numeric fraction to represent the shaded and unshaded parts of a figure. The figure is divided into equal parts with some parts shaded. Choose which is the correct fraction shaded and which is the correct fraction unshaded
Label shaded and unshaded parts of a figure (Level 2)

Solve word problems involving complementary fractions

Practice solving word problems involving fractions that add up to 1. In this activity, students are given information on the shaded portion of a figure and asked to find the fraction that represents the unshaded portion
Solve word problems involving complementary fractions

Determine the number of fractional parts in a whole

Practice determining how many fractional parts are in a whole. In this activity, students are given a pie cut into equal parts and asked to determine how many parts makes up the whole
Determine the number of fractional parts in a whole

Solve problems involving multiple wholes and improper fractions

Learn that a fraction can have a numerator greater than a denominator. In this activity, students are given one figure and asked to make more, resulting in an improper fraction. Students must decide how the improper fraction compares to one whole
Solve problems involving multiple wholes and improper fractions

Identify a set of figures whose shading represents an improper fraction

Practice matching a figure or set of figures with a given improper fraction. This activity reinforces the idea that a fraction with a larger numerator than denominator is more than one whole
Identify a set of figures whose shading represents an improper fraction

Label a set of figures whose shading represents an improper fraction

Practice matching a set of figures with the correct fraction. In this activity, students are given three fractions as options for a set of shaded figures that is greater than one
Label a set of figures whose shading represents an improper fraction

Divide and shade a set of figures to represent an improper fraction

Practice shading a set of figures to match a given improper fraction. In this activity, students will decide how many equal parts each figure needs to make the given fraction
Divide and shade a set of figures to represent an improper fraction

Topic C: Comparing Unit Fractions and Specifying the Whole

Based on visual models, students learn that the more parts in a whole, the smaller each unit fraction. They then compare unit fractions using both words and symbols, and they relate the unit fraction to the whole.

Topic D: Fractions on the Number Line

Students apply their understanding of fractions to numbers on a number line. They learn that there are numbers between the whole numbers on a number line and how to identify them. Using this tool, students are able to name equivalent whole number/fraction pairs, label fractions greater than 1, and compare fractions with unlike denominators.

Identify fractions on a number line and write 1 as a fraction

Learn that the numbers 0 and 1 can be written as fractions. In this activity, students will have a grasshopper jump a fractional part of 1 along a number line to learn how many grasshopper jumps make one whole
Identify fractions on a number line and write 1 as a fraction

Label fraction numerators on a number line

Practice dividing a one unit segment into fractional parts. In this activity, students will fill in the missing labels for each fractional part of the whole
Label fraction numerators on a number line

Label fractions on a number line (numerator and denominator)

Practice labeling fractions on a number line. In this activity, none of the fractions are filled in and students have to fill in the correct fraction based on the location of the point on the number line
Label fractions on a number line (numerator and denominator)

Segment a number line into fractions and place a given fraction on the number line

Match a fraction with the correct point on a number line. Drag the fraction to the correct point. Finally, decide how many parts the number line needs based on the initial given fraction
Segment a number line into fractions and place a given fraction on the number line

Place a given fraction on a number line visually (without hashmarks)

Practice placing a fraction on a number line without any hash marks. In this activity, students must estimate how the fraction compares to 0 and 1 to place it correctly
Place a given fraction on a number line visually (without hashmarks)

Label fraction numerators on a number line in numbers greater than 1

Learn how to label fractional points greater than 1 on a number line. In this activity, students are practicing working with improper fractions. Students will practice counting by a fraction to obtain the correct numerators to the improper fractions
Label fraction numerators on a number line in numbers greater than 1

Identify a fraction that is equivalent to a whole number on a number line

Learn how to label fractions that are equivalent to whole numbers. Students learn that the word equivalent means a different way of writing the same amount. Students practice writing fractions that are equivalent to the numbers 0, 1, 2, 3, and 4
Identify a fraction that is equivalent to a whole number on a number line

Place fractions greater than 1 on a number line

Practice placing an improper fraction on a number line. In this activity, the whole number points are labeled with fractions on the number line and students must determine how the improper fraction compares to these
Place fractions greater than 1 on a number line

Segment a number line into fractions and place a given fraction (greater than 1) on the number line

Practice placing an improper fraction on a number line by first determining how many fractional segments the number line needs. Choose the correct number of fractional segments, then drag the improper fraction to the correct place on the number line
Segment a number line into fractions and place a given fraction (greater than 1) on the number line

Label fractions greater than 1 on a number line

Practice labeling fractions greater than 1 on a number line. First either the numerator or denominator is labeled and studets must fill in the missing part. Finally, students fill in the entire fraction based on its location on the number line
Label fractions greater than 1 on a number line

Compare fractions with unlike denominators on a number line

Practice comparing fractions with unlike denominators on a number line. In this activity, students will first place the fractions on separate number lines, and then compare them. Students will conclude that fractions further to the right are greater
Compare fractions with unlike denominators on a number line

Use <, =, or > to compare fractions with unlike denominators on a number line

Practice comparing fractions with unlike denominators using the <, >, or = symbols. In this activity, students first place two fractions on a number line before choosing the correct comparison symbol based on their locations on the number line
Use <, =, or > to compare fractions with unlike denominators on a number line

Topic E: Equivalent Fractions

Using familiar shaded models and the number line, students focus on concepts of equivalent fractions. They extend this understanding to include whole numbers and fractions greater than 1.

Create, label, identify, and compare equivalent fractions

Learn how to create equivalent fractions with unlike denominators. Shade parts of figures to represent the same fraction. Keep abeling the shaded figures with the correct fractions to show that different fractions can be the same shaded part of a figure
Create, label, identify, and compare equivalent fractions

Identify equivalent fractions using the number line (less than 1)

Practice labeling points less than 1 on a number line with different fractions. In this activity, students learn that two fractions that are at the same point on a number line are equivalent
Identify equivalent fractions using the number line (less than 1)

Identify equivalent fractions using the number line (greater than 1)

Practice placing fractions on the number line and identifying which are equivalent. In this activity, students are working with fractions that are greater than 1
Identify equivalent fractions using the number line (greater than 1)

Label equivalent fractions on a number line

Learn how to label a fraction with a different fraction that is equivalent. One fraction is given, and then the number line is divided into more parts. Keep labeling the fraction with a different numerator and denominator to make an equivalent fraction
Label equivalent fractions on a number line

Label two equivalent fractions based on models

Practice choosing what fraction of a shape is shaded before and after the shape is divided into more parts. In this activity, students practice determining whether fractions are equivalent
Label two equivalent fractions based on models

Label three equivalent fractions based on models

Practice filling in the numerators or denominators to make three equivalent fractions. In this activity, students are labeling fractions based how many pieces are shaded in three figures divided into different parts
Label three equivalent fractions based on models

Label fractions equivalent to 1 whole

Practice organizing fraction tiles on a shelf where each shelf is equal to 1. In this activity, students label each fraction that's equal to one with the correct numerator. Students conclude that each fraction equal to 1 uses two of the same number
Label fractions equivalent to 1 whole

Write whole numbers as fractions (denominator of 1)

Learn how to write whole numbers as fractions with a denominator of 1. Students practice writing the numbers 1-13 by filling in the missing parts of either the fraction or the whole number
Write whole numbers as fractions (denominator of 1)

Write whole numbers as fractions (various denominators)

Learn how to rename whole numbers in terms of how many halves or thirds they are. In this activity, students first label the numerators with the denominators of 2. Then students label the numerators with denominators of 3
Write whole numbers as fractions (various denominators)

Topic F: Comparison, Order, and Size of Fractions

Based on visual models, students learn to compare two fractions with the same numerator or two fractions with the same denominator. To do so, they apply their understanding of creating and naming fractions, as well as using the <, =, and > symbols.