Curriculum for Grade 4

As students develop a more abstract understanding of numbers, we stretch their skills in both directions - with multi-digit whole numbers as well as decimals and fractions. Students learn traditional algorithms as well as other approaches that build math flexibility and fluency. In addition to performing operations with these numbers, students learn new ways to measure, convert units, round numbers, and compare numbers. A firm understanding of place value is the common thread running through all topics.

MODULE 1. Place Value, Rounding, and Algorithms for Addition and Subtraction

Topic A: Place Value of Multi-Digit Whole Numbers  

Students work with whole numbers to 1,000,000 using number disks and the place value chart. They develop understanding of magnitudes of 10, as well as how multiplication and division relate to place value. Students also master the skill of recording large numbers, both in standard form with the appropriate commas and in expanded form.

Model multiplication by 10 using a disk model (Level 1)

Learn how to multiply a number by 10 using disks in a place value chart. This activity allows you to see why multiplying a number by 10 shifts the digits one place to the left
Model multiplication by 10 using a disk model (Level 1)

Model multiplication by 10 using a disk model (Level 2)

Practice multiplying by 10 by moving disks on a place value chart to model the multiplication. Use the idea that multiplying by 10 can be modeled by shifting the digits one place to the left on the place value chart
Model multiplication by 10 using a disk model (Level 2)

Solve multiplication by 10 in unit form and number form

Practice multiplying by 10 without the use of a place value chart. First show the answer using units, then show the answer in number form
Solve multiplication by 10 in unit form and number form

Solve multiplication by 10 in unit form and number form and model on a place value chart

Practice multiplying multi-digit numbers by 10. First model the multiplication on a place value chart, then write the answer using unit form, then write the answer in number form
Solve multiplication by 10 in unit form and number form and model on a place value chart

Model division by 10 using a disk model (Level 1)

Learn how to divide a number by 10 by using disks in a place value chart. This activity shows step by step why dividing a number by 10 shifts the digits one place to the right
Model division by 10 using a disk model (Level 1)

Model division by 10 using a disk model (Level 2)

Practice dividing by 10 using a place value chart. First show the answer using units, then show the answer in number form
Model division by 10 using a disk model (Level 2)

Solve division by 10 in unit form and number form

Divide by 10 without the use of a place value chart. First show the answer using units, then show the answer in number form
Solve division by 10 in unit form and number form

Solve division by 10 in unit form and number form and model on a place value chart

Practice dividing by 10. First, solve the division problem using numbers in unit form. Then model the division on the place value chart, focusing on the fact that the digits move one place to the right when a number is divided by 10
Solve division by 10 in unit form and number form and model on a place value chart

Topic B: Comparing Multi-Digit Whole Numbers

Students work with numbers in the thousands, ten thousands, and hundred thousands. Building upon previous knowledge, such as use of inequality symbols, they deepen their understanding of how to compare large numbers to several place values or numbers of different place value. As part of this understanding, they build their fluency in the base-10 system by finding 1,000, 10,000 and 100,000 more or less than a number.

Compare numbers in a place value chart (at their highest place value)

Compare four- and five-digit numbers using place value concepts. The numbers in this activity have different digits in the greatest place value. Show the comparison using the symbols <, =, or >
Compare numbers in a place value chart (at their highest place value)

Compare numbers in a place value chart (at a place value other than their highest)

Compare two four-digit numbers shown in place value charts by comparing digits from left to right until a pair of digits is found that are not equal. Compare these digits and use the result to compare the original numbers
Compare numbers in a place value chart (at a place value other than their highest)

Compare numbers in a place value chart (at different place values)

Compare four- and five-digit numbers shown in a place value chart and complete the inequalities using the symbols >, +, and <
Compare numbers in a place value chart (at different place values)

Complete inequalities comparing multi-digit numbers

Compare four- and five-digit numbers by completing inequalities using the symbols >, =, and <. Then, fill in a missing digit to make an inequality true
Complete inequalities comparing multi-digit numbers

Order numbers in ascending and descending order using < and > (Part 1)

Put three numbers in order from least to greatest or greatest to least, and write an inequality statement using the symbols < or > to show the results. The numbers being compared are four- and five digit numbers
Order numbers in ascending and descending order using < and > (Part 1)

Order numbers in ascending and descending order using < and > (Part 2)

Rearrange four or five numbers from least to greatest or greatest to least using the symbols < or > to show the results. The numbers being compared have four or five digits
Order numbers in ascending and descending order using < and > (Part 2)

Order numbers in ascending and descending order using < and > (Part 3)

Rearrange four or five numbers from least to greatest or greatest to least using the symbols < or > to show the results. The numbers being compared have four, five, or six digits
Order numbers in ascending and descending order using < and > (Part 3)

Determine 1,000 more or less than a number using a place value chart

Look at a four- or five-digit number in expanded form and in a place value chart, and write the number in standard form. Then add or subtract 1,000
Determine 1,000 more or less than a number using a place value chart

Determine 10,000 more or less than a number using a place value chart

Look at a five- or six-digit number in expanded form and in a place value chart, and write the number in standard form. Then add or subtract 10,000
Determine 10,000 more or less than a number using a place value chart

Determine 100,000 more or less than a number using a place value chart

Look at a six-digit number in expanded form and in a place value chart, and write the number in standard form. Then add or subtract 100,000
Determine 100,000 more or less than a number using a place value chart

Complete a statement comparing numbers with and without a place value chart (1,000 or 10,000 more or less)

Adjust disks on a place value chart to show a given number, then tell whether the new number is 1,000 or 10,000 more or less than the original number
Complete a statement comparing numbers with and without a place value chart (1,000 or 10,000 more or less)

Determine 1,000/10,000/100,000 more or less than a given number

Practice adding and subtracting 1,000, 10,000, and 100,000 to or from a given number
Determine 1,000/10,000/100,000 more or less than a given number

Order numbers in a pattern increasing or decreasing by 1,000 or 10,000 (Level 1)

Complete a number pattern by adding or subtracting 1,000 or 10,000 to or from the previous term in the pattern. The pattern is completed by dragging given numbers to the correct position
Order numbers in a pattern increasing or decreasing by 1,000 or 10,000 (Level 1)

Order numbers in a pattern increasing or decreasing by 1,000 or 10,000 (Level 2)

Complete a number pattern by adding or subtracting 1,000 or 10,000 to or from the previous term in the pattern. The pattern is completed by typing the correct numbers
Order numbers in a pattern increasing or decreasing by 1,000 or 10,000 (Level 2)

Topic C: Rounding Multi-Digit Whole Numbers

Using a number line to provide context, students first determine the midway point between two multi-digit numbers. They then progress to rounding using the number line and the midway point. Finally, students round 4-, 5-, and 6-digit numbers to any given place value without use of the number line.

Determine the midway point between two multi-digit numbers using a number line

Prepare to round numbers by using a number line to find the point midway between multi-digit numbers that are multiples of 10, 100, or 1,000, and determine the digit in the ones, tens, or hundreds place
Determine the midway point between two multi-digit numbers using a number line

Determine whether a number is greater or less than the midway point between two multi-digit numbers using a number line

Prepare to round numbers by placing given numbers on a number line and determining if they are more or less than half way between two given multiples of 10, 100, 1,000, or 10,000
Determine whether a number is greater or less than the midway point between two multi-digit numbers using a number line

Determine whether a multi-digit number rounds up or down to a given place value using a number line (Part 1)

Place multi-digit numbers on a number line, say if the number is less or greater than half-way between the two multiples of 1,000 or 10,000. Name the closest 1,000 or 10,000. Use the equal symbol to show the relationship between the two numbers
Determine whether a multi-digit number rounds up or down to a given place value using a number line (Part 1)

Determine the round numbers nearest a given multi-digit number and whether that number rounds up or down using a number line (Part 1)

Find the nearest thousand or ten thousand to a given number, name the halfway point between the nearest thousands or ten thousands, and determine whether the given number rounds up or down. Practice stating the rules for rounding
Determine the round numbers nearest a given multi-digit number and whether that number rounds up or down using a number line (Part 1)

Determine whether a multi-digit number rounds up or down to a given place value using a number line (Part 2)

Practice rounding 4- and 5-digit numbers to the nearest thousand or ten thousand. The numbers appear on basketballs. Use a number line to help you place the basketballs into the correct hoop to show how to round the number
Determine whether a multi-digit number rounds up or down to a given place value using a number line (Part 2)

Round a multi-digit number to the nearest thousand

Practice rounding to the nearest thousand and ten thousand. First, name the thousands or ten thousands that are nearest to the given number. Name the halfway point between those two numbers. Use this information to round the given number up or down to the
Round a multi-digit number to the nearest thousand

Determine the round numbers nearest a given multi-digit number and whether that number rounds up or down using a number line (Part 2)

Practice rounding to the nearest thousand and ten thousand. First, name the thousands or ten thousands that are nearest to the given number. Name the halfway point between those two numbers. Use this information to round the given number up or down to the
Determine the round numbers nearest a given multi-digit number and whether that number rounds up or down using a number line (Part 2)

Determine whether a multi-digit number rounds up or down to a given place value (Part 1)

Practice rounding 4- and 5-digit numbers to the nearest thousand or ten thousand. The numbers appear on basketballs. Place the basketballs into the correct hoop to show how to round the number. If you lose your two lives, you start again!
Determine whether a multi-digit number rounds up or down to a given place value (Part 1)

Determine whether a multi-digit number rounds up or down to a given place value (Part 2)

Practice rounding 4- and 5-digit numbers to the nearest thousand or ten thousand. The numbers appear on basketballs. Place the basketballs into the correct hoop to show how to round the number. Then complete the rule that explains how to round numbers
Determine whether a multi-digit number rounds up or down to a given place value (Part 2)

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

Round given numbers to the nearest thousand or ten thousand. Determine the digit in the place you would like to round to. Then look at the digit to its right. Compare this digit to 5 to decide whether to round up or down. Then write the rounded number
Round a multi-digit number to a given place value (Level 1)

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

Round given numbers to the nearest thousand or ten thousand. Determine the digit to the right of the place you would like to round to. Compare this digit to 5 to decide whether to round up or down. Then write the rounded number
Round a multi-digit number to a given place value (Level 2)

Round a multi-digit number to a given place value (Level 3)

Round numbers to the nearest ten, hundred, or thousand without any guidance
Round a multi-digit number to a given place value (Level 3)

Round a multi-digit number to various place values

Practice rounding by rounding the same number to the nearest ten, the nearest hundred, nearest thousand, and nearest ten thousand. Notice the pattern involving the number of zeros based on the place you round to
Round a multi-digit number to various place values

Topic D: Multi-Digit Whole Number Addition

Students use column addition to add multi-digit numbers. They begin with the support of a disk model to illustrate the underlying concepts. They learn to record addition problems as column addition, how to regroup and record this action, how to line up numbers of varying length, and how to regroup to a place value higher than the original numbers.

Topic E: Multi-Digit Whole Number Subtraction

Students use column subtraction to subtract multi-digit numbers. They begin with the support of a disk model to illustrate the underlying concepts. They learn to record subtraction problems as column subtraction, how to regroup and record this action, how to line up numbers of varying length, and how to regroup across zeros.

MODULE 2. Multi-Digit Multiplication and Division

Topic A: Finding Area and Perimeter of a Rectangle

Students apply their understanding of measurement and area models to use the formulas for area and perimeter of a rectangle. They use the area model to find both the area and a missing side length. Students identify different ways of writing the same formula for both area and perimeter.

Determine the area of a rectangle by multiplying the lengths of its sides

Find the area of two rectangles by determining the dimensions and multiplying to find area
Determine the area of a rectangle by multiplying the lengths of its sides

Identify the formula for area of a rectangle and use it to solve a problem

Practice recognizing the formula for the area of a rectangle by first applying the formula to find the area of a rectangle, and then by choosing the correct formula from several choices, and then displaying the formula
Identify the formula for area of a rectangle and use it to solve a problem

Determine the area of a rectangle using the formula A = l x w

Practice finding the area of rectangles by using the formula Area = length x width
Determine the area of a rectangle using the formula A = l x w

Determine the side length of a rectangle based on its area and width using the formula

Find the length of the unknown side of a rectangle by using the area formula. Substitute the area and the known side length into the formula, and solve the equation for the missing side length by dividing the area by the given side
Determine the side length of a rectangle based on its area and width using the formula

Identify the formula for perimeter of a rectangle and use it to solve a problem

Find the perimeter of a rectangle by measuring and adding the lengths of the sides, and then explore three different formulas that can be used to find the perimeter of a rectangle
Identify the formula for perimeter of a rectangle and use it to solve a problem

Identify the formula for perimeter of a rectangle

Practice recognizing the formulas for the perimeter of a rectangle by selecting the correct formula from the given choices
Identify the formula for perimeter of a rectangle

Determine the perimeter of a rectangle using the formula P = 2 x (l + w)

Practice finding the perimeter of a rectangle using the formula P = 2 x (l + w). Substitute known values into the formula, and then simplify to find the perimeter
Determine the perimeter of a rectangle using the formula P = 2 x (l + w)

Determine the area and perimeter of the same rectangle

Find both the area and the perimeter of the same rectangles using the formulas A = l x w and P = 2 x (l + w)
Determine the area and perimeter of the same rectangle

Topic B: Multiplication by 10, 100, and 1,000

Students extend their understanding of multiplication to include powers of ten. They begin each exercise with the assistance of a place value chart, which illustrates the meaning behind the operation. Then, they build their fact fluency by solving equations mentally.

Multiply by 10 with and without a disk model

Practice multiplying one-, two-, and three-digit numbers by 10. Begin by using a disk model in a place value chart to see that multiplying by ten shifts each disk one place to the left. Then, practice multiplying by 10 without the disk model
Multiply by 10 with and without a disk model

Multiply by 100 with and without a disk model

Practice multiplying one-, two-, and three-digit numbers by 100. Begin by using a disk model in a place value chart to see that multiplying by one hundred shifts each disk two places to the left. Then, practice multiplying by 100 without the disk model
Multiply by 100 with and without a disk model

Multiply by 1,000 with and without a disk model

Practice multiplying 1-, 2- and 3-digit numbers by 1,000. You have a choice of solving a problem using the disk model or giving the answer without the model
Multiply by 1,000 with and without a disk model

Divide by 10 with and without a disk model

Practice dividing three- and four-digit numbers by 10, first using a disk model in a place value chart to see that each digit shifts one place to the right, and then without the model
Divide by 10 with and without a disk model

Divide by 100 with and without a disk model

Practice dividing multi-digit numbers by 100, first using a disk model in a place value chart to see that each digit shifts two places to the right, and then without the use of the disk model
Divide by 100 with and without a disk model

Divide by 1,000 with and without a disk model

Practice dividing five- and six-digit numbers by 1,000. To begin, you have a choice of solving a problem using the disk model or giving the answer without the model
Divide by 1,000 with and without a disk model

Multiply a 1-, 2-, or 3-digit number by 10, 100, or 1,000

Multiply one-, two-, and three-digit numbers by 10, 100, and 1,000 in this skateboarder game. Each time you enter an incorrect answer, your skateboarder loses a life. Can you win without losing all three lives?
Multiply a 1-, 2-, or 3-digit number by 10, 100, or 1,000

Multiply a 1-digit number by a round 2-digit number (Level 1)

Learn a strategy for multiplying single-digit numbers by a multiple of 10 by decomposing the multiple of 10. First, there is the strategy applied in the place value chart with the disk model, then decompose and multiply the numbers without the model
Multiply a 1-digit number by a round 2-digit number (Level 1)

Multiply a 1-digit number by a round 3-digit number (Level 1)

Learn a strategy for multiplying single-digit numbers by a 3-digit multiple of 100 by decomposing the multiple of 100. First, there is the strategy applied in the place value chart with the model, then decompose and multiply the numbers without the model
Multiply a 1-digit number by a round 3-digit number (Level 1)

Multiply a 1-digit number by a round 2-digit number (Level 2)

Practice multiplying single-digit numbers by three-digit multiples of 100 by first visualizing the multiplication in a place value chart, and then multiplying without the help of the chart. Combine factors as a strategy to multiply
Multiply a 1-digit number by a round 2-digit number (Level 2)

Multiply a 1-digit number by a round 3-digit number (Level 2)

Multiply 1-digit numbers by 3-digit multiples of 100. First, use a place value chart with the disk model. Then, multiply without the aid of a place value chart. Combine and decompose factors as a strategy for multiplying
Multiply a 1-digit number by a round 3-digit number (Level 2)

Multiply a 1-digit number by a round 2-digit number (Level 3)

Multiply 1-digit numbers by 2-digit multiples of 10. First, use a place value chart with the disk model. Then, multiply without the aid of a place value chart. Combine and decompose factors as a strategy for multiplying
Multiply a 1-digit number by a round 2-digit number (Level 3)

Multiply a 1-digit number by a round 3-digit number (Level 3)

Multiply 1-digit numbers by 3-digit multiples of 100. First, use a place value chart with the disk model. Then, multiply without the aid of a place value chart. Combine and decompose factors as a strategy for multiplying
Multiply a 1-digit number by a round 3-digit number (Level 3)

Solve multiplication equations with a 1-digit factor and a round 2- or 3-digit factor

Practice multiplying one-digit numbers by round two-digit or three-digit numbers in this skateboarder game. Each time you enter an incorrect answer, your skateboarder loses a life. Can you win without losing all three lives?
Solve multiplication equations with a 1-digit factor and a round 2- or 3-digit factor

Multiply a 2-digit round number by a 2-digit round number

Practice multiplying two a two-digit multiple of 10 by another two-digit multiple of 10, without the use of place value charts or scaffolding
Multiply a 2-digit round number by a 2-digit round number

Topic C: Multiplication of up to Four Digits by Single-Digit Numbers

Students are gradually scaffolded through the steps of multiplying a multi-digit number by a single-digit number using the standard algorithm. They begin using a concrete disk model and a partial products method of recording. As they begin to work with the standard algorithm, they become more skilled and independent by regrouping, using zeros, using larger numbers, and receiving fewer prompts.

Solve a multiplication equation using partial products with and without and a disk model

Multiply one-digit numbers by two- and three-digit numbers using partial products and no regrouping. The first problems have a place-value model, and then the multiplication is done without the model
Solve a multiplication equation using partial products with and without and a disk model

Solve a multiplication equation with regrouping using partial products with and without and a disk model

Multiply 1-digit numbers by 3-digit numbers using the partial products method. The first two problems have a disk model in a place value chart to show the result of multiplying each place of the 3-digit number by the 1-digit number
Solve a multiplication equation with regrouping using partial products with and without and a disk model

Solve a multiplication equation including a zero using partial products with and without and a disk model

Multiply 1-digit numbers by 3-digit numbers that have a zero in the tens place. Use partial products to do the multiplication. The first few problems have a disk model to show the multiplication and to check the answer by trading disks in the chart
Solve a multiplication equation including a zero using partial products with and without and a disk model

Solve a multiplication equation using the standard algorithm with and without and a disk model

Multiply one-digit numbers by three-digit numbers using the standard algorithm with no regrouping. Each problem demonstrates the multiplication using disks in a place value chart
Solve a multiplication equation using the standard algorithm with and without and a disk model

Solve a multiplication equation with regrouping using the standard algorithm using a disk model

Use the standard algorithm and disks in a place value chart to multiply three-digit numbers by one-digit numbers with regrouping
Solve a multiplication equation with regrouping using the standard algorithm using a disk model

Solve a multiplication equation with regrouping using the standard algorithm (Level 1)

Practice multiplying one-digit numbers by three-digit numbers using the standard algorithm with regrouping. No place value chart is used for these problems
Solve a multiplication equation with regrouping using the standard algorithm (Level 1)

Solve a multiplication equation with regrouping using the standard algorithm (Level 2)

Practice multiplying one-digit numbers by three-digit numbers using the standard algorithm with regrouping. Name the method used. No place value chart is used for these problems
Solve a multiplication equation with regrouping using the standard algorithm (Level 2)

Solve a multiplication equation with regrouping using the standard algorithm (Level 3)

Practice multiplying one-digit numbers by three-digit numbers using the standard algorithm with regrouping. Begin by setting up the problem. No place value chart is used for these problems
Solve a multiplication equation with regrouping using the standard algorithm (Level 3)

Solve a multiplication equation with regrouping using the standard algorithm (Level 4)

Practice multiplying 1-digit numbers by 3- and 4-digit numbers using the standard algorithm with regrouping. Begin by setting up the problem. The steps of the standard algorithm are explained as the problem is completed
Solve a multiplication equation with regrouping using the standard algorithm (Level 4)

Solve a multiplication equation with regrouping while identifying steps of the standard algorithm

Multiply three- and four-digit numbers by one-digit numbers using the standard algorithm with regrouping. Begin by setting up the problem and identifying the steps
Solve a multiplication equation with regrouping while identifying steps of the standard algorithm

Solve a multiplication equation with regrouping using the standard algorithm (Level 5)

Practice multiplying four-digit numbers by one-digit numbers with regrouping. Set up each problem for the standard algorithm, then multiply
Solve a multiplication equation with regrouping using the standard algorithm (Level 5)

Solve a single multiplication equation using both partial products and the standard algorithm

Multiply a three-digit number by a one-digit number using two different methods: partial products and the standard algorithm
Solve a single multiplication equation using both partial products and the standard algorithm

Multiply to find the area of a rectangle

Multiply 2- and 3-digit numbers by 1-digit numbers. Rewrite the larger factor in expanded form, break the rectangle into smaller rectangles, and use the distributive property to find the area of each smaller piece. Add the results to find the total area
Multiply to find the area of a rectangle

Multiply to find the area of a rectangle using partial products (Level 1)

Multiply three-digit numbers by one-digit numbers using an area model, and then connect the area model to the partial products method
Multiply to find the area of a rectangle using partial products (Level 1)

Multiply to find the area of a rectangle using partial products (Level 2)

Multiply four-digit numbers by one-digit numbers using an area model, and then connect the area model to the partial products method
Multiply to find the area of a rectangle using partial products (Level 2)

Topic D: Division of Tens and Ones with Successive Remainders

Students divide 1- and 2-digit numbers to determine the number in each group or the number of groups. They use models to illustrate a word problem and equations to record their work. Students are introduced to the term "quotient" and a method for checking their answer. Students move from simple division to division with a remainder in this topic, and they learn to use long division notation.

Solve a division problem (number in each group) with a remainder based on a model

Practice dividing objects into equal groups as a way to solve a division problem, where the number in each group is the solution to the problem, and review the meaning of the words quotient and remainder
Solve a division problem (number in each group) with a remainder based on a model

Solve a division problem (number of groups) with a remainder based on a model

Practice division by creating equal sized groups, so the solution to the division problem is the number of groups
Solve a division problem (number of groups) with a remainder based on a model

Solve a division problem (number in each group) with a remainder using an array model

Practice division by using an array model, and identify the remainder. The solution is the number in each row. Then check the answer by multiplying the quotient by the divisor and adding the remainder - the result should be the dividend
Solve a division problem (number in each group) with a remainder using an array model

Solve a division problem (number of groups) with a remainder using an array model

Practice division by using an array model, and identify the remainder. The solution is the number of rows. Then check the answer by multiplying the quotient by the divisor and adding the remainder - the result should be the dividend
Solve a division problem (number of groups) with a remainder using an array model

Multiply to find multiples of a given number

Practice finding multiples of a number and review the idea that multiples of a number have that number as a factor
Multiply to find multiples of a given number

List and identify multiples of a given number

Practice finding multiples by skip-counting. Then identify multiples of given numbers
List and identify multiples of a given number

Use multiples to find the quotient and remainder of a division problem

Divide using the concept of multiples. If the dividend isn't a multiple of the divisor, use the multiple of the divisor that is closest to but less than the dividend and then find the remainder
Use multiples to find the quotient and remainder of a division problem

Model division (number in each group) with a remainder using a tape diagram

Find the solution to division problems by thinking of multiples and finding the remainder, and then model the division on a tape diagram, where the divisor shows the number in each group and the quotient tells the number of groups
Model division (number in each group) with a remainder using a tape diagram

Model division (number of groups) with a remainder using a tape diagram

Find the solution to division problems by thinking of multiples and finding the remainder, and then model the division on a tape diagram, where the divisor shows the number of groups and the quotient tells the number in each group
Model division (number of groups) with a remainder using a tape diagram

Solve a division problem with a remainder using the closest multiplication fact

Divide 2-digit numbers by 1-digit numbers. Find the multiple of the divisor that is closest to the dividend and divide that number, then calculate the remainder. The first few problems have hints and directions, but the last few problems do not have them
Solve a division problem with a remainder using the closest multiplication fact

Solve a division problem with a remainder

Practice dividing two-digit numbers by one-digit numbers with remainders
Solve a division problem with a remainder

Solve a division word problem (number of groups) with a remainder using a tape diagram and an equation

Solve word problems using division with remainders. The problems involve determining the number of groups. Write the division expression, model the problem with a tape diagram, solve the division problem, and answer the question in the word problem
Solve a division word problem (number of groups) with a remainder using a tape diagram and an equation

Solve a division word problem (number in each group) with a remainder using a tape diagram and an equation

Solve word problems using division with remainders. The problems involve determining the number of items in each group. Write the division expression, model the problem with a tape diagram, solve the division problem, and answer the question
Solve a division word problem (number in each group) with a remainder using a tape diagram and an equation

Model and solve a division problem, and identify the divisor

Practice dividing one-digit numbers by one-digit numbers using a place value model, and identify the divisor and the remainder
Model and solve a division problem, and identify the divisor

Model and solve a division problem using long division (single-digit quotient)

Divide one-digit numbers by one-digit numbers using the standard algorithm, both with and without remainders. Model the first problems with a place value chart, then divide without the place value chart
Model and solve a division problem using long division (single-digit quotient)

Solve a division problem (number in each group) with a remainder using a disk model

Divide two-digit numbers by one-digit numbers, both with and without remainders. Use a place-value chart to model the division
Solve a division problem (number in each group) with a remainder using a disk model

Model and solve a division problem using long division (two-digit quotient)

Use the standard algorithm to divide two-digit numbers by one-digit numbers, both with and without remainders. Use a place-value chart to model the division
Model and solve a division problem using long division (two-digit quotient)

Model and solve a division problem that involves regrouping

Model dividing a two-digit number by a one-digit number with regrouping using a place value chart, both with and without a remainder
Model and solve a division problem that involves regrouping

Model and solve a division problem that involves regrouping using long division (two-digit quotient)

Model dividing a two-digit number by a one-digit number with regrouping using a place value chart, both with and without a remainder, and show the division using the standard algorithm
Model and solve a division problem that involves regrouping using long division (two-digit quotient)

Model and solve a division problem that involves regrouping using long division (two-digit quotient) (Level 2)

Model dividing a two-digit number by a one-digit number with regrouping using a place value chart, both with and without a remainder and with and without regrouping, and show the division using the standard algorithm
Model and solve a division problem that involves regrouping using long division (two-digit quotient) (Level 2)

Model and solve a division problem using long division by recording partial quotients

Model dividing a two-digit number by a one-digit number with regrouping using a place value chart, both with and without a remainder and with and without regrouping, and show the division using the standard algorithm
Model and solve a division problem using long division by recording partial quotients

Use long division to solve problems with a 2-digit quotient

Divide two-digit numbers by one-digit numbers using the standard algorithm. Problems include regrouping and no regrouping, and remainder and no remainder
Use long division to solve problems with a 2-digit quotient

Topic E: Reasoning with Divisibility

Students build a firm understanding of the concepts of factor, multiple, and divisible by, as well as the relationship among those concepts. They explore divisibility patterns/rules for 2, 3, 5, 6, 9, and 10. To build this understanding, students use manipulatives, arrays, long division, and the hundred chart.

Solve single-digit multiplication problems

Practice multiplication. Find the missing factor or the product. Each correct answer helps the creature clear an obstacle. You have two lives, and you lose a life with each incorrect answer. Can you help him reach his destination?
Solve single-digit multiplication problems

Find factors of a given number by labeling arrays (Level 1)

Find the factors of a given number by finding the dimensions of arrays that contain that number of circles. Then, list the factors
Find factors of a given number by labeling arrays (Level 1)

Find factors of a given number by labeling arrays (Level 2)

Find the factors of a given number by finding the dimensions of arrays that contain that number of circles. Then, list the factors
Find factors of a given number by labeling arrays (Level 2)

Find factors of a given number by building and labeling arrays

Find all factors of a number by building and labeling arrays. Identify a number as prime based on the number of factors
Find factors of a given number by building and labeling arrays

List factor pairs for a given number and identify the number as prime or composite

Find the missing factor to identify all factor pairs of a given number. Then, identify the number as prime or composite
List factor pairs for a given number and identify the number as prime or composite

Determine whether a given number is a factor of another given number

Look at a division problem and determine whether the divisor is a factor of the dividend based on whether or not there is a remainder. Decide whether the dividend is divisible by the divisor
Determine whether a given number is a factor of another given number

Use long division to determine whether a given number is a factor of another given number

Divide using the standard algorithm for division, then tell whether the divisor is a factor of the dividend, and whether the dividend is a multiple of the divisor, based on whether or not there is a remainder
Use long division to determine whether a given number is a factor of another given number

Use long division to show that if a number is a factor of another number, its factors are also factors of that number

Find the missing factor in a multiplication problem, and then discover that factors of the factors are also factors of the initial product
Use long division to show that if a number is a factor of another number, its factors are also factors of that number

Use properties of multiplication to show that if a number is a factor of another number, its factors are also factors of that number

Find the missing factor in a multiplication problem. Then use the associative property of multiplication to show that factors of the factors are also factors of the original product
Use properties of multiplication to show that if a number is a factor of another number, its factors are also factors of that number

Determine multiples of a given factor

Explore multiples of a given number and state that multiples of a number have that number as a factor. Then, find multiples of a given number by skip-counting
Determine multiples of a given factor

Identify the relationship between factors, multiples, and divisible by

Place numbers into statements that show the relationship between factors and multiples and "divisible by." Then match statements to show the relationship among these terms
Identify the relationship between factors, multiples, and divisible by

Identify factors or multiples of a list of given numbers

Identify factors and multiples of given numbers and place them in a table
Identify factors or multiples of a list of given numbers

Use long division to determine whether a given number is a multiple of another given number

Use division (both with and without the standard algorithm) to determine if a number is a multiple of another number and if a number is divisible by another number
Use long division to determine whether a given number is a multiple of another given number

Use long division to show that if a number is a multiple of another number, it is also a multiple of that number's factors

Use the standard algorithm for division to show that if a number is a multiple of another number, it is also a multiple of that number's factors
Use long division to show that if a number is a multiple of another number, it is also a multiple of that number's factors

Use properties of multiplication to show that if a number is a multiple of another number, it is also a multiple of that number's factors

Use the associative property of multiplication to show that if a number is a multiple of another number, it is also a multiple of that number's factors
Use properties of multiplication to show that if a number is a multiple of another number, it is also a multiple of that number's factors

Identify multiples of 2, 5, and 10 on a hundred chart and identify patterns in the ones place of the multiples

Place multiples of 2, 5, and 10 on a hundreds chart and identify possible ones digits for each set of multiples
Identify multiples of 2, 5, and 10 on a hundred chart and identify patterns in the ones place of the multiples

Determine whether a given number is a multiple of 2, 5, or 10

Click on a number machine to get a number, then determine whether the number is a multiple of 2, 5, or 10. You have three lives - try to answer all of the questions before you lose your lives!
Determine whether a given number is a multiple of 2, 5, or 10

Determine whether a given number is even or odd

Explore the idea that multiples of 2 are called even numbers, and all other numbers are odd. Play a game where you ride a motorbike. In order to dodge obstacles, identify 2-digit numbers as even or odd. You have three lives to reach your destination
Determine whether a given number is even or odd

Identify multiples of 3 and 9 on a hundred chart and identify patterns in the multiples

Identify multiples of 3 and 9 on a hundreds chart, then learn the divisibility rule for 3 and 9
Identify multiples of 3 and 9 on a hundred chart and identify patterns in the multiples

Determine whether a given number is a multiple of 3 or 9

Play a game to determine whether or not a given number is a multiple of 3 or 9. Click on a rocketship to get a random number, and say whether the number is a multiple of 3 or 9. You have three lives - try to finish the game before you lose all your lives!
Determine whether a given number is a multiple of 3 or 9

Identify factors (2, 3, 5, 10) of a given multiple

Play a game to determine whether or not a given number is a multiple of 2, 3, 5, or 10. For each correct answer, the motorbike rider avoids an obstacle. You have three lives - try to reach the end before you lose your lives!
Identify factors (2, 3, 5, 10) of a given multiple

Use a hundred chart to show that multiples of 2 and 3 are multiples of 6, and that multiples of 2 and 5 are multiples of 10

Identify multiples of 2 and 3 on the hundred chart, and see that numbers that are multiples of both 2 and 3 are also multiples of 6. Then repeat with multiples of 2 and 5, to see that numbers that are multiples of both 2 and 5 are also multiples of 10
Use a hundred chart to show that multiples of 2 and 3 are multiples of 6, and that multiples of 2 and 5 are multiples of 10

Topic F: Division of Thousands, Hundreds, Tens, and Ones

Students divide numbers in the hundreds and thousands by single-digit numbers. They move from unit notation to standard notation to help facilitate mental math with large numbers. Understanding of the standard algorithm is supported by familiar models - a disk model and tape diagrams. Students are supported in dealing with various division challenges from regrouping to remainders to working with zero.

Multiply using unit notation and standard notation

Practice multiplying one-digit numbers by a given number of tens, hundreds, or thousands and write the answer in both unit notation and standard notation
Multiply using unit notation and standard notation

Divide using a disk model

Divide a given number of ones, tens or hundreds using a disk model in a place value chart. First write the problem and the answer in unit notation, and then write the problem and answer using standard notation
Divide using a disk model

Divide using a disk model (with regrouping)

Divide using the disk model in a place value chart, trading in tens as ones, hundreds as tens, or thousands as hundreds in order to complete the division. Write the problem and answer in both unit notation and standard notation
Divide using a disk model (with regrouping)

Divide using unit notation and standard notation (Level 1)

Divide a given number of tens, hundreds, or thousands by a one-digit number, using both unit notation and standard notation
Divide using unit notation and standard notation (Level 1)

Divide using unit notation and standard notation (Level 2)

Divide a given number of tens, hundreds, or thousands by a one-digit number, using both unit notation and standard notation
Divide using unit notation and standard notation (Level 2)

Divide using standard notation

Practice dividing a given number of tens, hundreds, or thousands by a one-digit number, using standard notation
Divide using standard notation

Divide using a disk model (with regrouping) (Part 1)

Divide three-digit numbers by one-digit numbers using a disk model in the place value chart. The problems require regrouping
Divide using a disk model (with regrouping) (Part 1)

Divide using long division and a disk model (with regrouping and a remainder) (Part 1)

Divide three-digit numbers by one-digit numbers using the traditional algorithm and a disk model in the place value chart, both with and without regrouping
Divide using long division and a disk model (with regrouping and a remainder) (Part 1)

Divide using long division and a disk model (with regrouping and a remainder) (Part 2)

Divide three-digit numbers by one-digit numbers using the traditional algorithm and a disk model in the place value chart, both with and without regrouping
Divide using long division and a disk model (with regrouping and a remainder) (Part 2)

Divide using a disk model (with regrouping) (Part 3)

Divide three-digit numbers by one-digit numbers using a disk model in the place value chart, with regrouping
Divide using a disk model (with regrouping) (Part 3)

Divide using long division and a disk model (with regrouping and a remainder) (Part 2)

Divide three-digit numbers by one-digit numbers using the traditional algorithm and a disk model in the place value chart, with regrouping and remainders
Divide using long division and a disk model (with regrouping and a remainder) (Part 2)

Divide using long division and a disk model (with regrouping and a remainder) (Part 3)

Divide three-digit numbers by one-digit numbers using the traditional algorithm and a disk model in the place value chart, with regrouping and remainders
Divide using long division and a disk model (with regrouping and a remainder) (Part 3)

Divide using long division and a disk model (with regrouping and a remainder) (Part 4)

Divide three-digit numbers by one-digit numbers using the traditional algorithm and a disk model in the place value chart, with regrouping and remainders
Divide using long division and a disk model (with regrouping and a remainder) (Part 4)

Divide using long division with partial quotients and a disk model

Divide three-digit numbers by one-digit numbers using the disk model in the place value chart as well as the standard algorithm. Problems require regrouping and remainders
Divide using long division with partial quotients and a disk model

Divide using long division with partial quotients (Level 1)

Divide three-digit numbers by one-digit numbers using the standard algorithm. Problems involve regrouping and remainders
Divide using long division with partial quotients (Level 1)

Divide using long division with partial quotients (Level 2)

Divide four-digit numbers by one-digit numbers using the standard algorithm. Problems involve regrouping and remainders
Divide using long division with partial quotients (Level 2)

Divide across a zero using a disk model (with regrouping and a remainder)

Use a disk model in a place value chart to divide three-digit numbers by one-digit numbers when there is a zero in the tens place, with and without regrouping and with and without a remainder
Divide across a zero using a disk model (with regrouping and a remainder)

Divide across a zero using long division and a disk model (with regrouping and a remainder) (Part 1)

Divide three-digit numbers by one-digit numbers when there is a zero in the tens place using the standard algorithm and the disk model in a place value chart with regrouping
Divide across a zero using long division and a disk model (with regrouping and a remainder) (Part 1)

Divide using a disk model with zero in the quotient (with regrouping)

Divide three-digit numbers by one-digit numbers using the disk model in a place value chart with regrouping. The quotients in these problems contain a zero
Divide using a disk model with zero in the quotient (with regrouping)

Divide using long division and a disk model with zero in the quotient (with regrouping)

Divide three-digit numbers by one-digit numbers using the standard algorithm and the disk model in a place value chart. Problems involve regrouping, and quotients contain a zero
Divide using long division and a disk model with zero in the quotient (with regrouping)

Divide across a zero using long division and a disk model (with regrouping and a remainder) (Part 2)

Divide three-digit numbers by one-digit numbers using the standard algorithm and the disk model in a place value chart, both with and without regrouping and with and without remainders
Divide across a zero using long division and a disk model (with regrouping and a remainder) (Part 2)

Solve division problems with a quotient of zero (with a remainder) (Level 1)

Divide one-digit numbers by one-digit numbers when the dividend is less than the divisor. Express the quotient as 0 with a remainder
Solve division problems with a quotient of zero (with a remainder) (Level 1)

Solve division problems with a quotient of zero (with a remainder) (Level 2)

Practice solving division problems with a quotient of zero and a remainder
Solve division problems with a quotient of zero (with a remainder) (Level 2)

Divide across a zero using long division with partial quotients and a disk model (with regrouping and a remainder) Part 1

Divide three-digit numbers by one-digit numbers when there is a zero in the tens place of the dividend, using both the standard algorithm and the disk model in a place value chart. Problems involve regrouping and remainders
Divide across a zero using long division with partial quotients and a disk model (with regrouping and a remainder) Part 1

Divide across a zero using long division with partial quotients and a disk model (with regrouping and a remainder) Part 2

Divide three-digit numbers by one-digit numbers when there is a zero in the tens place of the dividend, using both the standard algorithm and the disk model in a place value chart. Problems involve regrouping and remainders
Divide across a zero using long division with partial quotients and a disk model (with regrouping and a remainder) Part 2

Divide across a zero using long division with partial quotients (with regrouping and a remainder) Part 1

Divide three-digit numbers by one-digit numbers when there is a zero in the tens place of the dividend, using the standard algorithm. Problems involve regrouping and remainders
Divide across a zero using long division with partial quotients (with regrouping and a remainder) Part 1

Divide across a zero using long division with partial quotients (with regrouping and a remainder) Part 2

Divide four-digit numbers by one-digit numbers using the standard algorithm when there are zeros in the tens and hundreds places of the dividend, both with and without a remainder
Divide across a zero using long division with partial quotients (with regrouping and a remainder) Part 2

Solve division word problems using long division and a tape diagram (with regrouping and a remainder)

Solve word problems that involve dividing a three-digit or four-digit number by a one-digit number with regrouping and remainders. Use both the standard algorithm and a tape diagram
Solve division word problems using long division and a tape diagram (with regrouping and a remainder)

Solve division word problems using long division and a tape diagram (with regrouping)

Solve word problems that involve dividing a three-digit or four-digit number by a one-digit number with regrouping and no remainders. Use both the standard algorithm and a tape diagram
Solve division word problems using long division and a tape diagram (with regrouping)

Divide using long division with partial quotients (Level 3)

Divide three- and four-digit numbers by one-digit numbers using the standard algorithm. These problems have no remainders
Divide using long division with partial quotients (Level 3)

Solve division word problems across zero using long division and a tape diagram (with regrouping)

Solve word problems with division using a tape diagram and the standard algorithm. Problems involve three- and four-digit dividends and one-digit divisors with regrouping
Solve division word problems across zero using long division and a tape diagram (with regrouping)

Solve division word problems using long division and a tape diagram (with a remainder)

Solve word problems with division using a tape diagram and the standard algorithm, both with and without a remainder. Problems involve three-digit dividends and one-digit divisors with regrouping
Solve division word problems using long division and a tape diagram (with a remainder)

Topic G: Multiplication of Two-Digit by Two-Digit Numbers

Students apply their prior knowledge of multiplication to multiply a 2-digit number by a 2-digit number. They use familiar tools and strategies, including a disk model, an area model, partial products, the distributive property, and the standard algorithm. To support their learning, students work extensively with multiples of 10.

Multiply a 2-digit number by 10

Practice multiplying two-digit number by 10
Multiply a 2-digit number by 10

Identify a round number as a multiple of 10

Fill in the missing numbers to count by 10, then fill in the missing numbers in multiplication equations for which one factor is 10, and finally write a multiplication expression that is equal to a given multiple of 10
Identify a round number as a multiple of 10

Solve a word problem two different ways by regrouping factors

Explore a word problem that shows the way in which you group three factors does not change the result, to illustrate a useful property of multiplication
Solve a word problem two different ways by regrouping factors

Multiply by splitting a round number into a multiple of 10 and regrouping factors based on a disk model (multiply by 10 last)

Explore a multiplication strategy that is useful when one of the factors is a multiple of 10. Break that factor apart into 10 and another factor, and then use the associative property so that you multiply by 10 last
Multiply by splitting a round number into a multiple of 10 and regrouping factors based on a disk model (multiply by 10 last)

Multiply by splitting a round number into a multiple of 10 and regrouping factors based on a disk model (multiply by 10 first)

Explore a multiplication strategy that is useful when one of the factors is a multiple of 10. Break that factor apart into 10 and another factor, and then use the associative property so that you multiply by 10 first
Multiply by splitting a round number into a multiple of 10 and regrouping factors based on a disk model (multiply by 10 first)

Multiply by splitting a round number into a multiple of 10 and regrouping factors (Level 1)

Practice multiplying a two-digit number by a multiple of 10 by breaking the multiple of 10 into 10 and another factor and then applying the associative property
Multiply by splitting a round number into a multiple of 10 and regrouping factors (Level 1)

Multiply by splitting a round number into a multiple of 10 and regrouping factors (Level 2)

Practice multiplying a two-digit number by a multiple of 10 by breaking the multiple of 10 into 10 and another factor and then applying the associative property
Multiply by splitting a round number into a multiple of 10 and regrouping factors (Level 2)

Rewrite an area model multiplication equation using the distributive property

Learn about the distributive property by using an area model to multiply two 2-digit numbers when one factor is a multiple of 10. Break the rectangle into two smaller rectangles, one of which has a length multiple of 10. Then add the two areas together
Rewrite an area model multiplication equation using the distributive property

Multiply to find the area of a rectangle using the distributive property

Practice multiplying a two-digit multiple of 10 and another two-digit number together using an area model and the distributive property
Multiply to find the area of a rectangle using the distributive property

Multiply using partial products and the standard algorithm (one round number)

Practice multiplying a two-digit multiple of 10 and another two-digit number together using the distributive property and adding the partial products
Multiply using partial products and the standard algorithm (one round number)

Multiply to find the area of a rectangle using the distributive property and the standard algorithm

Use an area model to multiply two two-digit numbers. Split each factor into tens and ones, multiply to find the area of each smaller rectangle, and add the partial products to find the answer
Multiply to find the area of a rectangle using the distributive property and the standard algorithm

Multiply using partial products and the standard algorithm

Multiply two two-digit numbers together by rewriting each factor in expanded form, multiplying each factor by each other factor, and then finding the sum of all of the partial products
Multiply using partial products and the standard algorithm

Multiply using the standard algorithm (one round number)

Multiply two two-digit numbers, one of which is a multiple of 10, using the standard algorithm. No regrouping is required for these problems
Multiply using the standard algorithm (one round number)

Multiply using the standard algorithm with regrouping (one round number)

Multiply two two-digit numbers, one of which is a multiple of 10, using the standard algorithm with regrouping
Multiply using the standard algorithm with regrouping (one round number)

Multiply using partial products and the standard algorithm with regrouping (Part 1)

Multiply two two-digit numbers with the help of an area model. Break one of the two factors into tens and ones, and multiply each part by the other factor using the standard algorithm. Then add the partial products
Multiply using partial products and the standard algorithm with regrouping (Part 1)

Multiply using partial products and the standard algorithm with regrouping (Part 2)

Multiply two two-digit numbers with the help of an area model. Break one of the two factors into tens and ones, and multiply each part by the other factor using the standard algorithm. Then add the partial products
Multiply using partial products and the standard algorithm with regrouping (Part 2)

Multiply using the standard algorithm (one round number)

Practice multiplying two a two-digit multiple of 10 by a two-digit multiple of 10 using the standard algorithm
Multiply using the standard algorithm (one round number)

MODULE 3. Fraction Equivalence, Ordering, and Operations

Topic A: Decomposition and Fraction Equivalence

Students learn everything about what a fraction is, how it is written, what it represents, and what its parts are called. They work with fractions both less than and greater than 1 as they model, record, and rename fractions. They explore fractions as part of a whole and also as points on a number line.

Label a shaded figure using fraction notation and shade a given fraction of a figure

Identify the fraction that represents the shaded portion of a figure. Then shade a figure to show a given fraction
Label a shaded figure using fraction notation and shade a given fraction of a figure

Label a shaded figure using fraction notation and shade a given fraction of a figure (fractions greater than 1)

Tell what fraction of given figure is shaded when the fractions are greater than one. Then shade figures to show fractions greater than one
Label a shaded figure using fraction notation and shade a given fraction of a figure (fractions greater than 1)

Label a missing fraction on a labeled number line

Divide a number line from 0 to 1 to show pieces of a given fractional size, then label a missing fraction on the number line. Next, divide a number line to show pieces of a given fraction size, and drag the fractions to the correct locations
Label a missing fraction on a labeled number line

Place a fraction on a number line

Place given fractions at the correct location on the number line. All fractions are between 0 and 1. Then, divide a number line from 0 to 1 into the correct number of pieces before placing a fraction at the correct location on the number line
Place a fraction on a number line

Identify numerator and denominator in a fraction

Identify the fraction shown by a shaded figure, and then identify which digit is the numerator and which is the denominator. Practice labeling the numerators and denominators of other fractions. Type a secret number based on the numerator and denominator
Identify numerator and denominator in a fraction

Identify fractions with a given numerator or denominator

Choose all of the fractions in a list that have a given numerator or a given denominator
Identify fractions with a given numerator or denominator

Model a fraction as the sum of its parts and record this as an equation

Drag tiles to show a given fraction as the sum of smaller fractions. The activity shows visually that a fraction is equal to the sum of its parts. Next, write a fraction to represent the shaded part of a figure, and drag fractions to build equations that
Model a fraction as the sum of its parts and record this as an equation

Model a fraction as the sum of its parts and record this as an equation (fractions greater than one)

Drag tiles to show a given fraction as the sum of smaller fractions. The activity shows visually that a fraction is equal to the sum of its parts. Next, write a fraction to represent the shaded part of a figure, and drag fractions to build equations that
Model a fraction as the sum of its parts and record this as an equation (fractions greater than one)

Record a fraction as the sum of its parts

Write a given fraction as the sum of its parts
Record a fraction as the sum of its parts

Record repeated addition of whole numbers as multiplication

Practice the idea that repeated addition can be written as multiplication. Numbers used are whole numbers less than 10
Record repeated addition of whole numbers as multiplication

Record repeated addition of fractions as multiplication

Write a fraction less than 1 as the sum of unit fractions, and then rewrite the sum as a multiplication expression
Record repeated addition of fractions as multiplication

Record repeated addition of fractions as multiplication (fractions greater than 1)

Write a fraction greater than 1 as the sum of unit fractions, and then rewrite the sum as a multiplication expression
Record repeated addition of fractions as multiplication (fractions greater than 1)

Identify the multiplication expression that matches a given fraction

Write a fraction as a multiplication expression. You have two lives. Can you solve all of the problems before you lose both lives?
Identify the multiplication expression that matches a given fraction

Topic B: Fraction Equivalence Using Multiplication and Division

Students compose equivalent fractions based on a model. They then label the fractions and identify the factor or divisor that relates one to the other.

Identify, label, and compare equivalent fractions

Choose two diagrams that have the same amount shaded, identify the fractions shown by the diagrams, compare them, and state if they are equivalent. Then, shade a diagram to show the same amount as another diagram and identify the two equivalent fractions
Identify, label, and compare equivalent fractions

Divide a model in two different ways to show and label equivalent fractions

Click on a shape to divide it into parts, and identify the fraction that represents the shaded portion of the shape. Then, click on the figure again to see another way to divide the shape and write the equivalent fraction
Divide a model in two different ways to show and label equivalent fractions

Multiply to find equivalent fractions based on a model

Explore the idea that you can write an equivalent fraction by multiplying the numerator and denominator by the same non-zero number. The concept is illustrated with diagrams
Multiply to find equivalent fractions based on a model

Multiply to find equivalent fractions with and without a model

Practice finding equivalent fractions by multiplying the numerator and denominator by the same non-zero number. The first few problems provide a model, and the remaining problems have no model
Multiply to find equivalent fractions with and without a model

Complete the numerator or denominator in a larger equivalent fraction

Find equivalent fractions by multiplying the numerator and denominator by the same non-zero number. At first, drag the correct numbers to the correct locations to create the equivalent fraction. Then, find equivalent fractions without guidance
Complete the numerator or denominator in a larger equivalent fraction

Divide to find equivalent fractions based on a model

Explore the idea that you can write an equivalent fraction by dividing the numerator and denominator by the same non-zero number. This is called simplifying the fraction. The concept is illustrated with diagrams
Divide to find equivalent fractions based on a model

Divide to find equivalent fractions with and without a model

Practice finding equivalent fractions by dividing the numerator and denominator by the same non-zero number, to simplify the fractions. The first few problems provide a model, and the remaining problems have no model
Divide to find equivalent fractions with and without a model

Complete the numerator or denominator in a smaller equivalent fraction

Find equivalent fractions by dividing the numerator and denominator by the same non-zero number. At first, drag the correct numbers to the correct locations to create the equivalent fraction. Then, find equivalent fractions without guidance
Complete the numerator or denominator in a smaller equivalent fraction

Solve problems related to equivalent fractions and multiplier

Find what the numerator and denominator of a fraction were multiplied or divided by to get a given equivalent fraction. Then fill in the missing numerator or denominator to show an equivalent fraction. Find all the equivalent fractions before you lose all
Solve problems related to equivalent fractions and multiplier

Topic C: Fraction Comparison

Using familiar models and the number line, along with their ability to find equivalent fractions, students compare fractions. They explore strategies to find a common numerator or denominator, or to compare to a benchmark. Students work with fractions greater than and less than one.

Label and compare fractions with like denominators or like numerators based on a model

Label and compare two fractions when either the numerators are the same or the denominators are the same. A model is given to help you visualize the comparison
Label and compare fractions with like denominators or like numerators based on a model

Place fractions with like denominators or like numerators on a number line and compare

Compare fractions with like numerators or like denominators by placing them on a number line and clicking on the greatest or least fraction. Fractions are both less than and greater than 1
Place fractions with like denominators or like numerators on a number line and compare

Order four fractions with like denominators or like numerators based on a model

Order four fractions from least to greatest by dragging them to the correct position. Fractions have either the same numerator or the same denominator. Determine the order based on whether the numerators or the denominators are the same
Order four fractions with like denominators or like numerators based on a model

Compare fractions with like denominators or like numerators

Compare two fractions that have either the same numerator or the same denominator
Compare fractions with like denominators or like numerators

Compare fractions to ½ with and without a number line

Use a number line to determine whether a given fraction is less than or greater than the benchmark fraction of 1/2. Then compare fractions to 1/2 without the use of a numberline
Compare fractions to ½ with and without a number line

Solve word problems comparing a fraction to ½ using an equivalent fraction

Solve word problems comparing a fraction to 1/2 by rewriting 1/2 with the same denominator as the given fraction
Solve word problems comparing a fraction to ½ using an equivalent fraction

Compare fractions by comparing each one to ½

Compare two fractions by comparing each fraction to 1/2
Compare fractions by comparing each one to ½

Compare fractions by comparing each one to 1

Compare fractions to 1. When the numerator of the fraction is greater than the denominator, the fraction is greater than 1. Then, compare two fractions by comparing each fraction to 1
Compare fractions by comparing each one to 1

Choose a strategy and use it to compare fractions

Four strategies are given for comparing two fractions. Choose the best strategy for comparing the given fractions, and use it to compare
Choose a strategy and use it to compare fractions

Compare fractions by comparing the remaining unit fraction using a number line and model

Compare two fractions using a number line model. Find how far the given fractions are from 1. The fraction that is closest to 1 is the greater fraction. Then, repeat the activity using bar models
Compare fractions by comparing the remaining unit fraction using a number line and model

Compare fractions by finding a common numerator (when one numerator is a multiple of the other)

Compare two fractions shown in a diagram by rewriting one fraction so it has the same numerator as the other fraction, when one numerator is a multiple of the other numerator
Compare fractions by finding a common numerator (when one numerator is a multiple of the other)

Compare fractions by finding a common denominator (when one denominator is a multiple of the other)

Compare two fractions shown in a diagram by rewriting one fraction so it has the same denominator as the other fraction, when one denominator is a multiple of the other denominator. Then compare fractions by finding a common denominator without a diagram
Compare fractions by finding a common denominator (when one denominator is a multiple of the other)

Compare fractions by finding a common denominator (when one denominator is not a multiple of the other)

Compare two fractions by finding a common denominator when one denominator isn't a multiple of the other. Begin by splitting both rectangles into the same number of pieces. Then rewrite the fractions so they have a common denominator and compare. Then, co
Compare fractions by finding a common denominator (when one denominator is not a multiple of the other)

Compare fractions by finding a common numerator or denominator (when one is a multiple of the other)

Compare two fractions by finding a common numerator or common denominator when one numerator or denominator is a multiple of the other
Compare fractions by finding a common numerator or denominator (when one is a multiple of the other)

Topic D: Fraction Addition and Subtraction

Students apply their understanding of fraction basics to add and subtract fractions. They work with familiar models and the number line to build understanding of the concepts behind the operations. In solving addition and subtraction problems, students convert among equivalent fractions, mixed numbers, and improper fractions.

Identify and add fractions with a common denominator based on a model

Add the fractions that have a common denominators using the pie model. For some problems the fractions are given, and for other problems, you write the fractions before adding
Identify and add fractions with a common denominator based on a model

Add fractions with a common denominator with and without a number line

Add fractions that have a common denominator using a number line model. Then, add fractions with like denominators without a number line model
Add fractions with a common denominator with and without a number line

Add fractions with a common denominator

Add fractions with like denominators in this skateboarding game. Each time you answer correctly, the skateboarder avoids an obstacle
Add fractions with a common denominator

Add fractions with a common denominator and convert the sum to a mixed number (Level 1)

First, practice writing 1 as a fraction. Then, add fractions with a common denominator, and write the answer as a mixed number with the help of a number line model
Add fractions with a common denominator and convert the sum to a mixed number (Level 1)

Subtract fractions with a common denominator with and without a number line

Add fractions with a common denominator and with a sum greater than 1, and write the sum as a mixed number
Subtract fractions with a common denominator with and without a number line

Subtract fractions with a common denominator with and without a number line

Subtract fractions with a common denominator. The first problem illustrates the subtraction on a number line, and remaining problems do not have number lines
Subtract fractions with a common denominator with and without a number line

Subtract a fraction from 1

Subtract fractions from 1 by first rewriting the 1 as a fraction with the same denominator as the other fraction
Subtract a fraction from 1

Rename a mixed number as a fraction to subtract a fraction

Practice rewriting a mixed number as a fraction. Then visualize this process using a bar model and use this strategy to subtract fractions from mixed numbers when the fractions have the same denominator
Rename a mixed number as a fraction to subtract a fraction

Subtract a fraction from a mixed number with and without renaming the mixed number as a fraction

Practice subtracting fractions from mixed numbers when the fractions have the same denominator. For some problems, show the step in which the mixed number is rewritten as a fraction. Then, write the answer without showing this step
Subtract a fraction from a mixed number with and without renaming the mixed number as a fraction

Rename a fraction as an equivalent fraction

Practice writing equivalent fractions by multiplying the numerator and denominator by a given number. Then complete the equivalent fraction by writing the missing numerator or denominator
Rename a fraction as an equivalent fraction

Add fractions with different denominators by finding a common denominator

Learn how to add fractions that have different denominators by first rewriting the fractions with the same denominator. For these problems, one denominator is a multiple of the other
Add fractions with different denominators by finding a common denominator

Add fractions with different denominators and rename the sum as a mixed number

Practice adding fractions with different denominators, when one denominator is a multiple of the other. The rewrite then sumes as mixed numbers
Add fractions with different denominators and rename the sum as a mixed number

Topic E: Extending Fraction Equivalence to Fractions Greater Than 1

To prepare for more complex work with addition and subtraction, students establish a firm understanding of mixed numbers and fractions greater than 1. They convert fractions to mixed numbers and vice versa. They find common denominators when one denominator is a factor of the other and when it is not.

Identify fractions as greater than, less than, or equal to 1

Place fractions in three bins, based on whether the denominator is greater than the numerator, the numerator is greater than the denominator, or the numerator is equal to the denominator. Then identify fractions as less than, greater than, or equal to 1
Identify fractions as greater than, less than, or equal to 1

Label a model with a mixed number and identify its written form

Write the mixed number that represents a fraction model greater than one. Understand that a mixed number represents the sum of a whole number and a fraction, but the plus sign isn't written. Practice reading mixed numbers
Label a model with a mixed number and identify its written form

Identify a mixed number on a number line

Label mixed numbers on a number line. Then, place mixed numbers on a number line
Identify a mixed number on a number line

Label a model with a mixed number and a fraction greater than 1

Look at a model showing a value greater than 1. Use the model to write the value both as a mixed number and as a fraction
Label a model with a mixed number and a fraction greater than 1

Rename a mixed number as a fraction greater than 1 based on a model

Use a model to write a mixed number, and then write the mixed number as a fraction
Rename a mixed number as a fraction greater than 1 based on a model

Rename a mixed number as a fraction greater than 1

Practice a strategy for renaming mixed numbers as fractions
Rename a mixed number as a fraction greater than 1

Rename a fraction greater than 1 as a mixed number based on a model

Learn a strategy for rewriting a fraction greater than 1 as a mixed number using a fraction bar model
Rename a fraction greater than 1 as a mixed number based on a model

Rename a fraction greater than 1 as a mixed number

Practice renaming fractions greater than 1 as mixed numbers
Rename a fraction greater than 1 as a mixed number

Match fraction addition to a mixed number and a fraction greater than 1

Match a given fraction addition problem to the answer. Locate the answer as both a fraction and as a mixed number
Match fraction addition to a mixed number and a fraction greater than 1

Identify a fraction greater than 1 and rename it as a mixed number

Identify the fraction greater than one from a list of fractions, and then rewrite the fraction as a mixed number. Then play a concentration-style matching game, matching fractions greater than 1 with the equivalent mixed numbers
Identify a fraction greater than 1 and rename it as a mixed number

Label models with mixed numbers and compare using <, =, or >

Label to mixed numbers shown in diagrams. Then compare the two mixed numbers using <, =, or >. First compare two mixed numbers that have different numbers of ones, then compare two mixed numbers that have the same number of ones
Label models with mixed numbers and compare using <, =, or >

Compare mixed numbers with different denominators (Part 1)

Compare two mixed numbers that have different denominators. First compare the number of ones and then compare the fractions. Recall how to compare fractions when the numerators are the same, or by comparing each fraction to 1/2
Compare mixed numbers with different denominators (Part 1)

Compare fractions greater than 1 by renaming them as mixed numbers

Learn how to compare fractions greater than one by first rewriting them as mixed numbers, because mixed numbers are often easier to compare. First compare the ones. If the ones are the same, compare the fractions
Compare fractions greater than 1 by renaming them as mixed numbers

Compare a fraction greater than 1 with a mixed number or a fraction greater than 1

Compare fractions greater than 1 with either mixed numbers or fractions greater than 1. You have four lives - can you solve all of the problems correctly before you lose all of your lives?
Compare a fraction greater than 1 with a mixed number or a fraction greater than 1

Compare mixed numbers with different denominators (Part 2)

Compare mixed numbers with different denominators. Begin with the aid of visual fraction models, the compare without the models
Compare mixed numbers with different denominators (Part 2)

Compare mixed numbers with different denominators (Part 3)

Compare mixed numbers with different denominators. Rewrite both fractions with a common denominator by finding a common denominator with visual models. Then compare mixed numbers without the models. Try to solve the problems before you run out of lives!
Compare mixed numbers with different denominators (Part 3)

Compare fractions greater than 1

Compare two fractions greater than 1. For each problem, you have a choice between solving the problem with no assistance or solving the problem with help and guidance through the steps
Compare fractions greater than 1

Topic F: Addition and Subtraction of Fractions by Decomposition

Students rely heavily on their understanding of fractions and mixed numbers to complete operations. To add and subtract, they break apart, regroup, and rename numbers. They gradually move from a step-by-step guided strategy to solving problems mentally.

Round a mixed number to the nearest whole with and without a number line

Place a mixed number on the number line, and say which whole number it is closest to. Write a number sentence for the mixed number and the nearest whole number using the "approximately equal" symbol ≈. Then round mixed numbers to the nearest whole number
Round a mixed number to the nearest whole with and without a number line

Estimate the sum or difference of two mixed numbers by rounding them to the nearest whole

Estimate the sum or difference of two mixed numbers by first rounding each number to the nearest whole number and adding or subtracting the results. Problems include word problems
Estimate the sum or difference of two mixed numbers by rounding them to the nearest whole

Round an improper fraction to the nearest whole by converting it to a mixed number

Round a fraction greater than 1 to the nearest whole number by first rewriting it as a mixed number
Round an improper fraction to the nearest whole by converting it to a mixed number

Round mixed numbers and improper fractions to the nearest whole

Play a game to practice rounding mixed numbers and fractions greater than 1 to the nearest whole number. Each correct answer is a digit in the combination to a safe. Can you get the safe open before you lost all three lives?
Round mixed numbers and improper fractions to the nearest whole

Estimate the sum or difference of a mixed number and an improper fraction by converting the fraction to a mixed number

Estimate the sum or difference of a fraction greater than 1 and a mixed number by first converting the fraction to a mixed number and rounding each mixed number to the nearest whole number
Estimate the sum or difference of a mixed number and an improper fraction by converting the fraction to a mixed number

Add a whole number to a mixed number

Add a whole number to a mixed number by adding the two whole number parts together. Remember that a mixed number represents the sum of a whole number and a fraction, and then apply the associative property to add the whole numbers
Add a whole number to a mixed number

Add a mixed number to a fraction with the same denominator

Add a mixed number to a fraction that has the same denominator. Remember that a mixed number represents the sum of a whole number and a fraction, and then apply the associative property to add the whole fractions
Add a mixed number to a fraction with the same denominator

Add a mixed number to a fraction with the same denominator and write the sum without an improper fraction

Add a mixed number to a fraction with the same denominator by first adding the fractions. If the sum is a fraction greater than 1, rewrite it as a mixed number and add the remaining whole number
Add a mixed number to a fraction with the same denominator and write the sum without an improper fraction

Add a mixed number to a fraction with the same denominator by completing the whole (Level 1)

Add a mixed number and a fraction that have the same denominator. Using fraction models, drag parts of the second fraction to complete the whole with the first fraction. Then add without the model by breaking apart the second fraction to complete the whol
Add a mixed number to a fraction with the same denominator by completing the whole (Level 1)

Add a mixed number to a fraction with the same denominator by completing the whole (Level 2)

Add a mixed number and a fraction that have the same denominator. Add by breaking apart the second fraction to complete the whole with the first fraction
Add a mixed number to a fraction with the same denominator by completing the whole (Level 2)

Add two mixed numbers with the same denominator and write the sum without an improper fraction (Level 1)

Add two mixed numbers with the same denominator. If the fractional part is greater than 1, you will be guided to rewrite answer so that the fractional part is less than 1
Add two mixed numbers with the same denominator and write the sum without an improper fraction (Level 1)

Add two mixed numbers with the same denominator and write the sum without an improper fraction (Level 2)

Add two mixed numbers with the same denominator. If necessary, rewrite answers so that the fractional part is less than 1
Add two mixed numbers with the same denominator and write the sum without an improper fraction (Level 2)

Subtract a fraction from a mixed number with the same denominator (without converting to an improper fraction)

Subtract a fraction from a mixed number with the same denominator. For these problems, you don't have to write the mixed number as a fraction
Subtract a fraction from a mixed number with the same denominator (without converting to an improper fraction)

Subtract a fraction from a mixed number with the same denominator by converting to an improper fraction (Level 1)

Subtract a fraction from a mixed number with the same denominator. Convert the mixed number to a fraction in order to do the subtraction
Subtract a fraction from a mixed number with the same denominator by converting to an improper fraction (Level 1)

Subtract a fraction from a mixed number with the same denominator by converting to an improper fraction (Level 2)

Subtract a fraction from a mixed number with the same denominator by rewriting one whole from the mixed number as a fraction, so that you have enough fractional parts to do the subtraction
Subtract a fraction from a mixed number with the same denominator by converting to an improper fraction (Level 2)

Subtract mixed numbers with the same denominator

Subtract mixed numbers with the same denominator. Begin by subtracting the whole numbers. Then rewrite one whole as a fraction in order to have enough fractional parts to do the subtraction
Subtract mixed numbers with the same denominator

Add and subtract mixed numbers with the same denominator

Add and subtract mixed numbers with the same denominator. Can you solve all of the problems before losing your three lives?
Add and subtract mixed numbers with the same denominator

Topic G: Repeated Addition of Fractions as Multiplication

Students translate their understanding of addition of fractions to multiplication. They transition from work with unit fractions to other fractions and mixed numbers. In solving equations and word problems, students rename solutions as mixed numbers without a fraction greater than 1.

Write a fraction as a sum of unit fractions

Begin exploring multiplication of fractions. Write a fraction as the sum of unit fractions, and then rewrite the sum as a multiplication problem. See that with fractions, just like with whole numbers, repeated addition can be written as multiplication
Write a fraction as a sum of unit fractions

Identify multiplication of a unit fraction by a whole number that matches a given fraction

Play a game to find which multiplication problem is equal to a given fraction. If you are correct, a rocket will blast the multiplication problem. Try to solve all of the problems before you lose your lives!
Identify multiplication of a unit fraction by a whole number that matches a given fraction

Multiply a whole number by a fraction by splitting it into a multiple of a unit fraction

Multiply a whole number by splitting the fraction into a whole number. Then use the associative property to multiply the whole numbers first. Then, multiply a whole number by multiplying the whole number by the numerator and keeping the denominator
Multiply a whole number by a fraction by splitting it into a multiple of a unit fraction

Multiply a whole number by a fraction

Practice multiplying a whole number by a fraction. Enter the product
Multiply a whole number by a fraction

Write repeated addition of fractions as a multiplication statement and rename the product as a mixed number

Write repeated addition as a multiplication problem. If the answer is a fraction greater than 1, rewrite the answer as a mixed number
Write repeated addition of fractions as a multiplication statement and rename the product as a mixed number

Multiply a whole number by a mixed number

Use fraction models and the distributive property to learn how to multiply a whole number by a mixed number. First, multiply the whole number. Then multiply the whole number by the fractional part of the mixed number. Then add the results
Multiply a whole number by a mixed number

Multiply a whole number by a mixed number and rename without a fraction greater than 1

Multiply a whole number by a mixed number. If the fraction in the answer is greater than 1, rewrite the answer so that the fraction is less than one
Multiply a whole number by a mixed number and rename without a fraction greater than 1

Solve a word problem by multiplying a whole number by a mixed number

Solve word problems by multiplying whole numbers by mixed numbers. If the fraction in the answer is greater than 1, rewrite the answer so that the fraction is less than one
Solve a word problem by multiplying a whole number by a mixed number

MODULE 4. Decimal Fractions

Topic A: Exploration of Tenths

Students develop their understanding of the decimal form of fractions in the tenths. The rely on familiar representations such as the number line, place value chart, and fraction models to support understanding. Students convert fractions less than and greater than one from fraction form to decimal form and word form.

Relate fractions in tenths to decimals with and without a number line

Identify a fraction in tenths on a number line, and then learn that fractions in tenths can be written as decimals. Label all tenths between 0 and 1 with both fraction notation and decimal notation. Drag digits to the correct positions to rewrite fraction
Relate fractions in tenths to decimals with and without a number line

Rewrite a fraction in tenths as a decimal, and vice versa

Rewrite fractions in tenths as decimals. If the fraction is less than one, be sure to put a zero to the left of the decimal point. Then rewrite decimals as fractions. Finally, write fractions in tenths in both decimal form and unit form
Rewrite a fraction in tenths as a decimal, and vice versa

Match fractions in tenths to their decimal form and word form

Complete picture puzzles by matching fractions given in tenths to both their decimal form and word form. Then complete tables by completing the fraction form, decimal form, and unit form
Match fractions in tenths to their decimal form and word form

Determine how many more tenths to make a whole using a number line

Use a number line to find how many more tenths are needed to make one whole
Determine how many more tenths to make a whole using a number line

Represent mixed numbers in decimal form using a number line

Represent mixed numbers with the fraction in tenths as decimals. Use a number line to make the connection between fraction and decimal form. Identify decimal values that are greater than 1. Finally, place decimal values at the correct position
Represent mixed numbers in decimal form using a number line

Rewrite a mixed number with tenths as a decimal, and vice versa

Write mixed numbers that have the fraction in tenths as decimals, and write decimals in tenths as mixed numbers. For the final problems, write the value in unit form as well
Rewrite a mixed number with tenths as a decimal, and vice versa

Convert between fraction form, decimal form, and word form with mixed numbers with tenths

Practice with tenths by filling in tables to convert between fraction form, decimal form, and word form
Convert between fraction form, decimal form, and word form with mixed numbers with tenths

Determine how many more tenths to make the next whole using a number line

Use a number line to find how many more tenths are needed to make the next whole number
Determine how many more tenths to make the next whole using a number line

Record a fraction model as a mixed number or a decimal with tenths

Make the connection between a fraction model showing tenths, the decimal representation, and the mixed number or fraction representation
Record a fraction model as a mixed number or a decimal with tenths

Relate tenths to one whole using a place value chart

Relate tenths to one whole using a place value chart. See that ten tenths have the same value as one whole. Represent numbers with tens, ones, and tenths as decimal numbers. Finally, represent given decimal numbers using the disk model
Relate tenths to one whole using a place value chart

Represent numbers greater than 10 tenths in decimal form

Represent numbers greater than 10 tenths as a number of tenths. Use the disk model in a place value chart to see how to trade in 10 tenths for one whole, and write the result as a decimal. Then match the unit form in tenths to the correct decimal form
Represent numbers greater than 10 tenths in decimal form

Topic B: Tenths and Hundredths

Students hone their understanding of tenths, hundredths, and the relationship between the two. Beginning with fractional parts only, students convert between fraction, decimal, and unit form. After mastering this, they work with mixed numbers. Along the way, their understanding is supported by area models, disk models, and number lines.

Identify hundredths using fraction and decimal notation

Learn how to write one hundredth as both a fraction and a decimal, and relate this quantity to centimeters and meters. Label fractions and decimals in hundredths. Match numbers in hundredths written as decimals and fractions. Finally, write fractions in h
Identify hundredths using fraction and decimal notation

Match hundredths decimals to unit form and rewrite a hundredths decimal in unit form

Match hundredths decimals to word form. Then write hundredths decimals in word form and hundredths fractions in decimal and word form
Match hundredths decimals to unit form and rewrite a hundredths decimal in unit form

Label tenths and hundredths on an area model using fraction and decimal form

Label fraction models in tenths and hundredths using fraction form and decimal form
Label tenths and hundredths on an area model using fraction and decimal form

Compare equivalent tenths and hundredths in decimal form

Use fraction models to compare decimals in tenths and hundredths, and identify equivalent decimals. Write the comparison in decimal form and word form
Compare equivalent tenths and hundredths in decimal form

Match equivalent tenths and hundredths in decimal and unit form

Match a decimal in tenths to the equivalent decimal in hundredths and vice versa. Complete tables showing equivalent fractions in hundredths, word forms, and the decimal form in tenths or hundredths. Finally, write fractions in hundredths as decimals
Match equivalent tenths and hundredths in decimal and unit form

Show tenths and hundredths equivalencies using a disk model

Relate hundredths to tenths using a place value chart. See that ten hundredths has the same value as one tenth. Then represent numbers shown in a place value chart with ones, tenths, and hundredths as decimal numbers
Show tenths and hundredths equivalencies using a disk model

Represent a hundredths number using a disk model

Represent decimal numbers to hundredths using disks in a place value chart
Represent a hundredths number using a disk model

Identify points in the hundredths on a number line

Name points on a number line with hundredths decimals. Then place given hundredths decimals on a number line
Identify points in the hundredths on a number line

Label a mixed number on an area model using fraction and decimal form

Label a mixed number to hundredths on an area model using fraction form and decimal form
Label a mixed number on an area model using fraction and decimal form

Match mixed numbers in fraction and decimal form, and rewrite a mixed number fraction in decimal form

Write mixed numbers with the fraction in hundredths as decimals, and then write decimals to hundredths in unit form
Match mixed numbers in fraction and decimal form, and rewrite a mixed number fraction in decimal form

Label a mixed number based on a disk model

Write the decimal form of a number shown in a place value chart with the disk model. Then show how to represent a decimal number to hundredths in the place value chart using the disk model
Label a mixed number based on a disk model

Topic C: Decimal Comparison

Students compare decimals in the hundredths using inequality signs and ordering. They rely on familiar representations of the area model, number line, and place value chart to build understanding. They also compare decimals to fractional numbers in unit form and fraction form.

Use <, =, and > to compare decimal measurements of length, mass, and volume

Compare decimals to hundredths by comparing length, mass, and liquid volume
Use <, =, and > to compare decimal measurements of length, mass, and volume

Use <, =, and > to compare decimal numbers based on an area model

Compare decimals to hundredths by comparing the shaded portions of area models
Use <, =, and > to compare decimal numbers based on an area model

Use <, =, and > to compare decimal numbers based on a number line

Compare decimals to hundredths by placing them on a number line. The number farthest to the right is greatest
Use <, =, and > to compare decimal numbers based on a number line

Use <, =, and > to compare decimal numbers based on a place value chart

Compare decimals to hundredths by writing them in a place value chart and comparing the values of the digits. Compare decimal numbers without the use of a place value chart. Finally, compare decimal numbers to a mixed number and a decimal in unit form
Use <, =, and > to compare decimal numbers based on a place value chart

Complete an inequality by choosing a mixed number, decimal, or decimal in unit form

Complete an inequality by dragging a value in decimal form, fraction form, or decimal in unit form. Then type missing digits in an inequality so that the inequality is true
Complete an inequality by choosing a mixed number, decimal, or decimal in unit form

Complete a double inequality statement based on measurements of length, mass, and volume

Compare three decimal numbers by comparing lengths, mass, and liquid volume. Write a double inequality statement to show the comparison
Complete a double inequality statement based on measurements of length, mass, and volume

Order decimal numbers in a double inequality statement based on a number line

Compare three decimal numbers by placing them on a number line to determine the order of the numbers from least to greatest or greatest to least. Then arrange the numbers to form a double inequality statement to show the comparison
Order decimal numbers in a double inequality statement based on a number line

Order decimal numbers in a double inequality statement

Order three decimal numbers from least to greatest or greatest to least using inequality symbols
Order decimal numbers in a double inequality statement

Order four decimal numbers in ascending order

Order four decimal numbers from least to greatest. Can you find the order before losing all three lives?
Order four decimal numbers in ascending order

Order decimals, fractions, and decimal numbers in unit form in a double inequality statement based on a number line

Place three decimals, fractions, or decimals in unit form on a number line, and use the number line to help you order the numbers from least to greatest using inequality symbols
Order decimals, fractions, and decimal numbers in unit form in a double inequality statement based on a number line

Order decimals, mixed numbers, and decimal numbers in unit form in a double inequality statement

Order three decimals, fractions, or decimals in unit form from least to greatest or greatest to least using inequality symbols
Order decimals, mixed numbers, and decimal numbers in unit form in a double inequality statement

Order four decimals, mixed numbers, and decimal numbers in unit form in ascending order

Order four or five numbers written in decimal form, fraction form, or unit form from least to greatest by dragging the numbers to the correct positions
Order four decimals, mixed numbers, and decimal numbers in unit form in ascending order

Topic D: Addition with Tenths and Hundredths

Students rely on their mastery of converting between decimals, fractions, and mixed numbers in order to add tenths and hundredths. They learn how to add different units (tenths to hundredths) in both fraction and decimal form. They also learn to record their sum without improper fractions.