Curriculum for Grade 3

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.

Solve and re-write repeated addition equations

Students compose and solve a repeated addition equation based on a model of real-world objects in equal groups. Students learn to write repeated addition as the statement "X groups of X make X."

Complete statements describing equal groups and their totals

Students complete statements "X groups of X make X" based on models and match such statements to repeated addition equations

Use the multiplication sign

Students learn to use the multiplication and equal signs to replace the statement "X groups of X make X" with an equation. They determine whether or not a multiplication expression matches a model of real-world objects

Express multiplication equations based on a model

Students identify which multiplication equation matches a model of real-world objects

Solve and express multiplication equations based on a model

Students complete a repeated addition equation to match a model of real-world objects. Then, students express the repeated addition equation as a multiplication statement and a multiplication equation

Compose and solve multiplication equations based on a model

Students create a model of real-world objects based on a given multiplication equation

Multiply based on a model of objects in rows

Students compose and solve multiplication equations based on objects in rows

Compose and solve multiplication equations based on an array

Students identify which multiplication equation matches an array of real-world objects. They represent one array as repeated addition, a multiplication statement, and a multiplication equation

Compose expressions and equations based on a model

Students complete repeated addition, a multiplication statement, or a multiplication equation based on a model

Students work with models of real-world objects to solve equal sharing problems. They are introduced to the division symbol. They use the "dealing" method to 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.

Use the division symbol

Students determine the number of groups and number of objects in each group in equal sharing problems based on a model. Represent such problems as an equation using the division symbol. Identify the division symbol

Compose and solve division equations based on a model

Students solve for any of three numbers in equal sharing problems based on a model. They write and solve equations based on models. They determine whether a given model matches a given equation

Model division equations and solve

Students identify the equation that matches a given model. They create a model based on a division expression and solve. They solve for any of three numbers in a division equation based on a model

Divide objects into groups

Students distribute objects into equal groups of given size and then determine the number of groups

Compose division equations

Students compose a division equation based on a model. They solve for any of three numbers in a division equation with and without a model

Solve division word problems

Students solve division word problems

Students deepen and expand their understanding of multiplication by 2 and 3 with new ways of visualizing the concept. The topic focuses on skip counting and arrays which helps students begin to see patterns as they multiply and solve equations. Students also discover and explore the commutative and distributive properties of multiplication.

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 3 (Level 1)

Practice skip counting by 3s. Fill in the missing numbers on a number line when skip counting from 3 to 15

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 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 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 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

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 3

Practice visualizing multiplication using arrays. This activity shows students the commutative property of multiplication-- reversing the factors results in the same product

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 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

Solve x2 multiplication equations (Level 1, Part 1)

Play a game practicing the multiplication facts involving the numbers 1-5 multiplied by 2

Solve x3 multiplication equations (Level 1, Part 1)

Play a game practicing the multiplication facts involving the numbers 1-5 multiplied by 3

Solve x2 multiplication equations (Level 1, Part 2)

Play a game practicing the multiplication facts involving the numbers 1-5 multiplied by 2

Solve x3 multiplication equations (Level 1, Part 2)

Play a game practicing the multiplication facts involving the numbers 1-5 multiplied by 3

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 3 (Level 2)

Practice skip counting by 3s. Fill in the missing numbers on a number line when skip counting from 3 to 30

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 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 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 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

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 3 (Level 2)

Practice using the commutative property of multiplication to fill in missing factors or products in multiplication sentences

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 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 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 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 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

Solve x2 multiplication equations (Level 2, Part 1)

Play a game practicing the multiplication facts involving the numbers 1-10 multiplied by 2

Solve x3 multiplication equations (Level 2, Part 1)

Play a game practicing the multiplication facts involving the numbers 1-10 multiplied by 3

Solve x2 multiplication equations (Level 2, Part 2)

Play a game practicing the multiplication facts involving the numbers 1-10 multiplied by 2

Solve x3 multiplication equations (Level 2, Part 2)

Play a game practicing the multiplication facts involving the numbers 1-10 multiplied 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

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

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

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

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 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

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

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 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 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 2 or 3

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 (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 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 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 3)

Practice solving more difficult division equations with divisors of 3. In this activity, students aren't given any hints

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

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 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

Solve x4 multiplication equations

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

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 2)

Practice completing a multiplication sentence to match a tape diagram. In this activity, students are working with the x4 multiplication facts

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

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

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 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 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

Solve multiplication equations based on the commutative property

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

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 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 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 2)

Practice solving division equations with a divisor of 4

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

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 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

Solve x5 multiplication equations

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

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 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 2)

Practice solving division equations with a divisor of 5

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

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

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 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

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

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

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

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 2)

Practice multiplying by 10 to complete a pattern of equations

Solve x10 multiplication equations

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

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 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

Students review telling time on an analog clock and learn to write time as hours and minutes. They also learn how to use addition and subtraction skills to calculate start and end times and time intervals and apply this to word problems.

Review telling time to five minutes

Students type the hour and minutes to tell the time shown on an analog clock

Tell time to the minute (Level 1)

Students learn to tell time to the minute by first counting by fives, then by ones to calculate the minutes shown on an analog clock

Tell time to the minute (Level 2)

Students continue to practice telling time to the minute, applying the strategies of counting by fives and ones from the previous lesson without scaffolding

Identify the start and end times of a scenario

Given a scenario, students identify the start and end times and place them on a timeline

Calculate the time interval

Students learn what is a time interval. They calculate the length of a time interval by subtracting the start time from the end time

Calculate time intervals using a timeline

Students solidify their understanding of calculating the time interval in a scenario by subtracting the start time from the end time. Students use a timeline to visualize the time interval

Calculate time intervals, without a timeline

Students calculate the time interval of a task by subtracting the start time from the end time, this time without a timeline for support

Rewrite time as hr and min

Students learn that any time can be rewritten as hr and min. They match a digital time to the same time written in hr and min

Calculate the end time using addition

Students determine the end time of a word problem by adding the time interval to the start time. Students use a timeline to visualize the time interval

Calculate the end time using column addition (Level 1)

Students determine the end time of a word problem by adding the time interval and start time with column addition. They solve without using a timeline

Calculate the end time using column addition (Level 2)

Students rewrite word problems involving time as column addition. They use the column addition equation to add the start time and time interval to find the end time. Time intervals are written in minutes

Calculate the end time using column addition (Level 3)

Students rewrite word problem involving time as column addition. The time interval in this scenario is written in hours

Calculate the start time using subtraction

Students determine the start time of a word problem by subtracting the time interval from the end time. Students use a timeline to visualize the time interval

Calculate the start time using column subtraction (Level 1)

Students rewrite a word problem involving time as column subtraction. They subtract the time interval from the end time to find the start time. Time intervals are written in minutes

Calculate the start time using column subtraction (Level 2)

Students rewrite word problem involving time as column subtraction and solve for the start time

Find the time a certain number of minutes earlier than a given time

Students subtract times along a number line. Then, students use column subtraction to find x minutes earlier than a given time

Calculate the start time when the end time and time intervals are known (Level 1)

Students calculate the start time for a word problem by subtracting a time interval from the end time

Calculate start time when the end time and time interval are known (Level 2)

Students calculate the start time by subtracting the time interval from the end time

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 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 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

Compare grams and kilograms

Students compare grams and kilograms using a pan balance. They choose the inequality symbol to compare measurements in kg with measurements in g

Tutorial: Drag the lace to match objects

Learn how to match two objects using laces to connect the cards

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

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

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

Tutorial: Click on highlighted words to access definition

Learn how to click a highlighted word to see the definition of that word

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

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 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 milliliters

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

Learn about the relationship between liters and milliliters, and compare the two units of measure

Discover how many milliliters make a liter and deepen knowledge about how much each unit represents

Compare measures in liters and milliliters to determine which is greater or if they are equal

Compare measures in liters and milliliters to determine which is greater. Then, use greater than, less than, or equal to symbols to compare measure in liters and milliliters

Measure capacity in milliliters

Match containers to their appropriate capacity measurements and units

Using a number line to provide context, they learn the rule for rounding up or down to the nearest ten and hundred. Finally, students round 2-, and 3-digit numbers to any given place value.

Identify numbers in the tens, hundreds, or thousands place

Click on the correct place value of a given number

Identify the neighboring tens of a given number on a number line

Play a game in which you click on the neighboring tens of an identified number on the number line

Discover the concept of rounding

In the context of a recipe, learn whether an amount of flour is close enough without being exact. Explore the concept of rounding

Round to the nearest ten using a number line and learn about the approximation symbol

Round to the nearest ten on a number line by determining which ten is closest to the given number. Students are also introduced to the approximation symbol

Use the approximation symbol when rounding to the nearest ten using a number line for reference

Play a game in which you round to the nearest ten on a number line and use the approximation symbol

Round to the nearest ten and learn the language "round up" or "round down."

Practice rounding to the nearest ten with a numberline for reference and learn the language "round up" and "round down."

Round to the nearest ten using the language "round up" or "round down."

Practice rounding to the nearest ten with a numberline for reference and use the language "round up" and "round down."

Learn the rule for rounding numbers that are exactly in the middle of two tens

Students learn the rule for rounding numbers that are exactly in the middle of two tens and practice rounding these numbers

Round a given number to the nearest ten (Part 1)

Practice rounding numbers to the nearest ten without a numberline

Round a given number to the nearest ten using the rule for rounding

Students learn the rule for rounding up or down. Then, they practice using the rule to round up or down to the nearest ten

Round a given number to the nearest ten (Part 2)

Play a game to practice rounding to the nearest ten

Determine the neighboring hundreds of a given number on a number line

Play a game in which you click on the neighboring hundreds of an identified number on the numberline

Identify the neighboring hundreds of a given number and round to the nearest hundred

On a more detailed number line, identify the neighboring hundreds of a given number and round to the nearest hundred. Note whether the number was rounded up or down

Learn the rule for rounding numbers that are exactly in the middle of two hundreds

Students learn the rule for rounding numbers that are exactly in the middle of two hundreds and practice rounding these numbers

Determine whether a given number rounds up or down to the nearest hundred

Play a game to practice rounding to the nearest hundred

Round a given number to the nearest hundred using the rule for rounding

Students learn the rule for rounding up or down. Then, they practice using the rule to round up or down to the nearest hundred

Round a given number up or down to the nearest hundred

Play a game to practice rounding to the nearest hundred

Round the same number to the tens and hundreds

Students learn that numbers can be rounded to other place values, including the tens and hundreds place. They learn that rounding the same number to different places can change the estimation

Determine the place to which a number was rounded

Students determine if a given number has been rounded to the nearest ten or hundred

Round numbers to the tens or hundreds (Level 1)

Students round a given number to the nearest ten or hundred

Round numbers to the tens or hundreds (Level 2)

Students practice rounding a given number to the nearest ten or hundred

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 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 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 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 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 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 (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 to solve word problems (Level 3)

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

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 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 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 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 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 (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 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 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

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

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

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 (one factor > 5)

Fill in missing products in a multiplication chart where one factor is greater than 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

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

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

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

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

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

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

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 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

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 division equations

Learn how to find the value of an unknown letter in a division equation

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

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

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

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

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

Determine multiples of 6 in a multiplication chart

Practice filling in a multiplication chart with multiples of 6

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

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

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 (Level 1)

Practice solving division problems with divisors of 6

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

Practice solving division problems with divisors of 6

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

Determine multiples of 7 in a multiplication chart

Practice filling in a multiplication chart with multiples of 7

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

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

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 (Level 1)

Practice solving division problems with divisors of 7

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

Practice solving division problems with divisors of 7

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 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 division equations

Practice finding the value of an unknown letter in a division equation

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

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

Determine multiples of 8 in a multiplication chart

Practice filling in a multiplication chart with multiples of 8

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

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

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 (Level 1)

Practice solving division problems with divisors of 8

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

Practice solving division problems with divisors of 8

Identify equal expressions

Students learn that expressions with the same value are called equal expressions. Given one expression, they choose an equal expression

Review operations

Students match the names of the operations to an example. They learn that operations have two numbers with an operation sign between them, then identify and solve operations

Use parentheses to show the order of operations

Students work with expressions with two operations. They learn that parentheses show the order of operations. They identify the first operation or move parentheses to show it

Solve two-operation expressions with parentheses (Level 1)

Students use the order of operations to solve two-operation expressions. They solve the expression in the parentheses, replace it with its value, then solve the second operation

Solve two-operation expressions with parentheses (Level 2)

Given a 2-operation expression, students identify the first operation in parentheses, then drag the numbers to compose and solve the expression. They use the value to compose an expression for the second operation, then solve

Solve two-operation expressions with parentheses (Level 3)

Students continue solving 2-operation expressions with parentheses. They find the value of the first operation, then use this value to compose and solve an expression for the second operation

Solve two-operation expressions with parentheses (Level 4)

Students solve more 2-operation expressions with parentheses using the order of operations. They must select the correct symbol to compose expressions for each operation before solving

Solve two-operation expressions with parentheses (Level 5)

Students solve more 2-operation expressions with parentheses, this time without composing the individual expressions for each operation

Solve three-operation expressions with parentheses

Students solve three-operation expressions. They solve the two operations in parentheses, then use their value to compose the third operation and solve

Solve multi-operation expressions with parentheses

Students solve expressions with two or three operations, denoted by parentheses. They have the choice to give the answer or solve step by step

Solve the same expression with a different order of operations

Students solve the same 2-operation expression with a different placement of the parentheses. They find that changing the order of operations changes the value of the expression

Match equal expressions

Given sets of 2-operation expressions and 1-operation expressions, students match the equal expressions

Determine which expression is true

Given two of the same expression with a different order of operations, students solve to determine which is true

Explore the distributive property of multiplication

Students are introduced to the distributive property of multiplication. They learn that to multiply a sum by a number, you multiply the addends by the number and then add the products

Use the distributive property of multiplication to solve equations (Level 1)

Students build fluency in using the distributive property of multiplication to solve equations

Use the distributive property of multiplication to solve equations (Level 2)

Students build fluency in using the distributive property of multiplication to solve equations

Use the distributive property of multiplication to solve equations (Level 3)

Students build fluency in using the distributive property of multiplication to solve equations

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

Determine multiples of 9 in a multiplication chart

Practice filling in a multiplication chart with multiples of 9

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

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

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 (Level 1)

Practice solving division problems with divisors of 9

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

Practice solving division problems with divisors of 9

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 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

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 1 x n) to represent a mode

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

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 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

Compose a multiplication sentence (including n x 1) 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

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 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 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

Compose a multiplication sentence (including n x 0) 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

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 division problems that use 0 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 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

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

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).

Solve for missing products on a multiplication chart in which 10 is a factor

Practice solving for missing products on a multiplication chart in which 10 is a factor

Relate a product of n tens to the product as a number n0

Learn how to solve multiplication involving tens by using knowledge of basic multiplication. Multiply a number by a tens and then represent this as the actual number, showing how multiplication by multiples of ten is related to simple multiplication

Match numeric products to multiplication equations that use numbers and words (n tens)

Play a game matching multiplication of a single-digit factor by n tens with the correct product

Use properties of multiplication to simplify and solve equations

Practice finding the missing factor in a multiplication problem involving n tens. In this activity, students will break a part a multiple of ten into n tens and use this to solve the equation

Solve multiplication equations that have a single digit and a multiple of ten as factors

Practice solving multiplication equations that have a single digit and a multiple of ten as factors. In this activity, the students are given a hint that the ending digit in the product is 0

Solve for missing products on a multiplication chart that are square numbers

Practice filling in the square numbers on a multiplication chart. In this activity, students are asked to fill in only the numbers that are a number times itself (n^2)

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

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

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

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

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 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 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

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

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 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

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 2)

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 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 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

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.

Multiply to find area by splitting a rectangle into smaller parts

Learn how to find the area of a rectangle by dividing it into smaller parts. In this activity, students find the area of two parts of a rectangle and add these together to find the total area

Use the distributive property of multiplication to find the area of a rectangle split into smaller parts

Practice using the distributive property of multiplication to find the area of a rectangle by splitting it into smaller parts

Subtract to find the area of a covered part of a rectangle

Learn how to find the area of a part of a rectangle. In this activity, part of a rectangle is covered and students find the total area then subtract the area of the uncovered part

Multiply or subtract to find areas of rectangles without gridlines

Practice finding the area of a rectangle without gridlines and the area of the two parts when its divided. In this activity, students learn that the area of the total rectangle is equal to the area of the two parts when the rectangle is divided

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 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 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 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 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

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 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 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

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

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

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

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 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

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

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

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)

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

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 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

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

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

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

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

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

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

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

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

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 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

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

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

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

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

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

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

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.

Compare unit fractions based on a model

Learn how different unit fractions compare to one another by using different models. In this activity, students learn that when a whole is divided into more parts, each part is smaller

Compare unit fractions using <, =, and > with and without a model

Practice using the <, > and = signs to compare two numbers. In this activity, students first compare two whole numbers and then learn how to compare two fractions using a tape diagram. Finally, students will compare fractions without a tape diagram

Identify and label a unit fraction model that is greater or less than a given unit fraction model

Practice using fraction diagram to compare two fractions. In this activity, students will drag the correct figure to make a true statement. Students will compare two figures and then label the figure with the correct fraction

Identify a whole based on a given unit fraction

Indentify how a part of an object relates to a whole. A piece of a figure is given. Write the correct fraction that the piece represents. Then identify the whole object given a piece of the shape and the fractional part of the whole that piece takes up

Build a whole using the correct number of unit fraction tiles

Practice taking one unit fraction piece of an object and building the whole object using the correct number of pieces. In this activity, students drag the correct number of objects to make one whole

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

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 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

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

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

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

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

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

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

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 students must fill in the missing part. Finally, students fill in the entire fraction based on its location on the 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

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

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 labeling the shaded figures with the correct fractions to show that different fractions can be the same shaded part of a figure

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 (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

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 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 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 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

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 (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

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.

Compare fractions with the same numerator or the same denominator based on a model

Practice comparing fractions with either the same numerators or the same denominators. In this activity, students first label tape diagrams with the correct fractions and then use the <, > or = symbol to determine how they fractions are related

Shade and compare fractions with the same numerator based on a model

Learn that if the number of shaded parts of a figure is the same but the shaded parts are smaller, then the fraction is smaller. Two figures divided into a different number of equal parts are given. Shade the same number of pieces in each figure

Label and compare fractions with the same numerator

Practice labeling and comparing equal figures divided into various numbers of pieces that have the same number of pieces shaded. This activity shows that having the same numerator doesn't mean that the fractional pieces that are shaded are equal in size

Compare fractions with the same numerator or the same denominator

Practice comparing two fractions with the same numerators. In this activity, students choose the correct symbol (<, > or =) to show how the fractions are related

Students learn to create picture graphs and bar graphs, both scaled and unscaled. They learn to interpret data from these graphs and use them to solve word problems about the number of objects in categories.

Interpret data from a picture graph

Students represent data on a picture graph. Given a graph, students then find the number of objects in a category, the greatest and least categories, and the total amount represented by the graph

Interpret data from scaled picture graphs (Level 1)

Students learn that in a scaled picture graph, each picture represents more than one object. They learn to identify scaled picture graphs and the number of objects in a category

Interpret data from scaled picture graphs (Level 2)

Students interpret data from a scaled picture graph in which each picture represents 3 items

Solve word problems based on data from a scaled picture graph

Given a scaled picture graph, students interpret data to solve word problems asking, "How many together?"

Interpret data from a horizontal bar graph

Students represent data on a horizontal bar graph. They interpret data from the graph, including the number of objects in a category, which category has more or less, and the category with the fewest objects

Interpret data from a vertical bar graph

Students represent data on a vertical bar graph. They interpret data from the graph, such as identifying the categories with the most or fewest objects and the number of objects in a category

Interpret data from a scaled bar graph (Level 1)

Students learn how to interpret data from a scaled bar graph, labeled in intervals of 2. They identify categories with the most or fewest objects and the number of objects in a category

Interpret data from a scaled bar graph (Level 2)

Students have more practice interpreting data from a scaled bar graph. The bar graph is labeled in intervals of 10

Solve word problems based on data from a bar graph

Given a bar graph, students interpret data to solve word problems asking, "How many together?" and "How many more?"

Solve word problems based on data from a scaled bar graph

Given a scaled bar graph, students interpret data to solve word problems asking, "How many together?" and "How many less?"

Students learn that polygons are made of equal numbers of line segments and angles. They learn the names and attributes of common polygons and instances where the attributes intersect (i.e., squares and rhombuses).

Explore the attributes of a line segment

Students learn about the attributes of line segments-they are straight with two endpoints

Identify common endpoints of line segments

Students learn that line segments can meet at a common endpoint. Given an example, they count the number of line segments with a common endpoint

Identify angles

Students learn that when two line segments share a common endpoint, they make an angle. They discover that shapes have multiple angles and identify them

Identify the number of segments and angles in a triangle

Students build a triangle from line segments. They identify the number of segments and angles that make up triangles

Use a drafting triangle to identify right angles

Students learn about right angles and identify them from sets of angles. They use a drafting triangle to draw and check right angles

Identify the number of segments and angles in a rectangle

Students draw a closed chain of 4 segments to make a rectangle. They learn that a rectangle has 4 right angles

Create polygons with closed segment chains

Students determine if a segment chain is open or closed. They learn that closed segment chains make polygons, where the line segments are the sides. They count the sides of a polygon

Identify polygons

Students identify polygons from a set of figures

Determine the number of sides or angles of a given polygon (Level 1)

Students determine the number of angles and sides of a polygon. They learn that these numbers are equal in any polygon

Determine the number of sides or angles of a given polygon (Level 2)

Given a polygon, students count the number of sides or angles

Determine how many sides a polygon can have

Students learn that polygons can have an infinite number of sides and angles

Identify quadrilaterals

Students discover that polygons have different names depending on the number of sides. They learn that a 4-sided polygon is called a quadrilateral

Identify pentagons

Students learn that a 5-sided polygon is called a pentagon

Identify hexagons

Students learn that a 6-sided polygon is called a hexagon

Sort and label polygons by the number of sides

Students sort and label polygons based on the number of sides. They work with triangles, quadrilaterals, pentagons, and hexagons

Explore attributes of a rectangle

Students learn that a rectangle is a 4-sided polygon in which all angles are right angles

Find opposite sides of a rectangle and their length

Students review that opposite sides of a rectangle have the same length. Given one side of a rectangle, they identify the opposite side and its length

Find the lengths of a rectangle's sides

Given the lengths of two meeting sides of a rectangle, students find the lengths of the missing sides

Solve riddles with the attributes of polygons

Students use scissors to cut corners from polygons. They solve riddles where they must identify the attributes of the resulting polygon

Explore attributes of a square

Students review attributes of squares. They identify squares from a set of figures

Review the attributes of squares, rectangles, and quadrilaterals

Students learn about the similarities and differences in the attributes of squares, rectangles, and quadrilaterals

Explore attributes of a rhombus

Students learn that a rhombus is a polygon with 4 sides of the same length

Determine when a rhombus is also a square

Students learn that a polygon with 4 sides of the same length and 4 right angles is both a square and a polygon

Identify rhombuses and their attributes

Students identify rhombuses from a set of figures.They review the attributes of a rhombus

Review attributes of polygons

Given a polygon, identify all of the figures from a set that do not have the corresponding attributes

Students find the perimeter of a polygon by adding the lengths of its sides. They solve for the length of an unknown side and find the perimeters of equal-sided polygons.

Identify the perimeter of a polygon

Students learn that the perimeter of a polygon is the sum of the lengths of its sides

Measure and add to find the perimeter of a polygon

Students measure the sides of a polygon with a ruler. They add the lengths of each side to find the perimeter

Find the perimeter of a triangle

Students find the perimeter of a triangle by adding the lengths of its sides. They use a model for support

Find the perimeter of a rectangle

Students find the perimeter of a rectangle by adding the lengths of the sides. They simplify the expression into two additions using the associative property, then solve

Find the perimeter of a polygon

Students find the perimeter of a polygon by finding the sum of its sides, with and without using models for support

Find the perimeter of a pentagon

Students find the perimeter of a pentagon by finding the sum of its sides. They simplify the addition expression by using the associative property to solve

Find the length of an unknown side of a triangle

Given the perimeter of a triangle and the lengths of two sides, students compose a missing addend equation to find the length of the unknown side

Find the length of an unknown side of a quadrilateral

Given the perimeter of a quadrilateral and the lengths of three sides, students compose a missing addend equation to find the length of the unknown side

Find the perimeter of a equal-sided polygon using multiplication

Students write and solve multiplication expressions to find the perimeters of polygons with equal sides