Curriculum for Grade 5

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

Multiply by 10 with and without a place value chart

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

Multiply by 100 with and without a place value chart

Learn how multiplying by 100 is the same as multiplying by 10 twice. Use a place value chart to multiply a number (up to 4 digits) by 100 by shifting of digits using the concept of place value. Then, apply the understanding gained to multiply by 100

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

Learn that multiplying by 1000 is the same as multiplying by 10 three times. Use a place value chart to multiply a number (up to 4 digits) by 1000 by shifting of digits using the concept of place value

Multiply by 10, 100, and 1,000

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

Complete a pattern of multiplication by 10 or 100

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

Divide by 10 with and without a place value chart

Learn how to quickly divide a number by 10. Identify the number shown on a place value chart. Then use the chart to assist in shifting of the digits to model the division. Finally, apply the knowledge gained to divide by 10

Divide by 100 with and without a place value chart

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

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

Practice dividing a number with 4 or more digits by 1000. Initially, you can choose to use a place value chart to model the division by 10 three times. Then, apply the understanding gained to remove the correct number of zeros from the quotient

Divide by 10, 100, and 1,000

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

Identify and complete a pattern of division by 10 or 100

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

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

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

Multiply numbers with a single non-zero digit

Practice multiplying two numbers that are multiples of powers of 10

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

Learn the relationship between the hundredths and thousands place values of decimals. Use decimal counters and their equivalent fractions to reduce fractions

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

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

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

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

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

Learn that multiplying by 1000 is the same as multiplying by 10 three times. Initially, you can choose to use a place value chart to model the multiplication of a decimal by 1000 by shifting of digits using the concept of place value

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

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

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

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

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

Divide a decimal by 10 quickly. Use a place value chart to assist in shifting of the digits using the concept of place value. Then apply the knowledge gained to divide by 10 without being provided with the place value chart

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

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

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

Learn that dividing by 1000 is the same as multiplying by 10 three times. Initially, you can choose to use a place value chart to model the division of a decimal by 1000 by shifting of digits using the concept of place value. Then, apply the understanding

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

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

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

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

Represent repeated multiplication of 10 as 10 with an exponent

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

Represent 10 with an exponent as repeated multiplication

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

Multiply a decimal number by 10 with an exponent

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

Divide a number by 10 with an exponent

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

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

Record a decimal number in expanded notation

Learn how to expand a decimal number into the sum of its place value components. Identify the place value of each digit in a decimal. Then, show the expanded sum that produced the number

Compare numbers to the hundredths place with and without a place value chart

Learn how to compare decimals. Use a place value chart to help compare each set of place values from left to right. Then use the understanding gained to compare two decimals without the help of the chart

Complete inequalities that compare numbers to the hundredths place

Practice comparing decimals. First, insert the correct inequality symbol to compare two numbers. Then, choose the correct number to create a true inequality statement. Then, test your understanding by inserting a digit to make the inequality statement of

Arrange decimal numbers in order from smallest to greatest (Level 1)

Learn how to put decimal numbers in order from least to greatest. Put three numbers in order with the correct inequality symbol between them. Also, practice rearrange numbers so that the order is correct

Arrange decimal numbers in order from smallest to greatest (Level 2)

Practice putting decimal numbers in order. Rearrange 4 numbers from least to greatest

Arrange decimal numbers in order from smallest to greatest (Level 3)

Practice putting decimal numbers in order. Rearrange 4 numbers from least to greatest

Students review the place value of decimal numbers. They use the basic algorithm for rounding whole numbers to round decimals to the ones, tenths, and hundredths place.

Review decimal place value

Students review the place value of decimal numbers and identify digits in the tenths and hundredths place

Use the basic algorithm to round decimals to the ones

Students use the basic algorithm for rounding whole numbers to round decimal numbers to the ones place

Use the basic algorithm to round decimals to the tenths

Students use the basic algorithm to round decimal numbers to the tenths place

Round decimal numbers to the tenths place (Level 1)

Students practice rounding decimal numbers to the tenths place

Round decimal numbers to the tenths place (Level 2)

Given a decimal number and two options, students select the number that has been correctly rounded to the tenths place

Round decimal numbers to the tenths place (Level 3)

Students build fluency in rounding decimal numbers to the tenths place

Use the basic algorithm to round decimals to the hundredths

Students use the basic algorithm to round decimal numbers to the hundredths place

Round decimal numbers to the hundredths place (Level 1)

Given a decimal number and two options, students select the number that has been correctly rounded to the hundredths place

Round decimal numbers to the hundredths place (Level 2)

Students build fluency in rounding decimal numbers to the hundredths place

Round the same decimal number to different place values (Level 1)

Students match pairs to show the same decimal number rounded to different place values

Round the same decimal number to different place values (Level 2)

Students practice rounding the same decimal number to different place values

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

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

Learn how to add two decimal numbers (to the hundredths place). Represent each number with a model of disks for each place value. Then, combine the like place value disks of the two numbers to arrive at the sum

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

Learn how to add two decimal numbers (to the thousandths place). Represent each number with a model of disks for each place value. Then, combine the like place value disks of the two numbers to arrive at the sum

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

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

Add numbers to the thousandths place with regrouping using column addition

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

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

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

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

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

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

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

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

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

Subtract numbers to the thousandths place with regrouping using column subtraction

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

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

Multiply a decimal number with regrouping using a disk model

Learn how to multiply a whole number times a decimal. Use a disk model to help represent the decimal and its multiplication

Multiply a decimal number with regrouping using a disk model and the standard algorithm

Multiply a whole number times a decimal. Use a disk model to help represent the decimal and its multiplication and rewrite the problem in column form

Compare multiplying a whole number with multiplying a decimal number with the same digits

Learn how to use multiplication of whole numbers to help with multiplication of a decimal times a whole number. Identify whether a decimal and a related whole number use the same digits.Compare the product of the decimal and a whole number to the product

Multiply a decimal number by converting it to a whole number and converting the product back to a decimal

Convert a decimal to a whole number to aid in solving a multiplication problem. Identify the appropriate factor to change the decimal to a whole number. Then find the product. Finally, convert the answer back to a decimal

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

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

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

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

Divide a decimal by a whole number. A disk model is used to represent the decimal and to help find the partial quotients of each place value. Regrouping may be necessary

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

Learn how to divide a decimal by a whole number. A disk model is used to represent the decimal and to help find the partial quotients of each place value. Regrouping may be necessary

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

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

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

Use long division with a decimal divided by a whole number. Rewrite the division problem in long division format. A disk model is used to represent the decimal and to help find the partial quotients of each place value. Regrouping may be necessary

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

Learn to divide a decimal by a whole number using long division. Rewrite the division problem in long division format. Find the partial quotients of each place value and record them in the long division. Regrouping may be necessary

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

Divide a decimal by a whole number using long division. Rewrite the division problem in long division format. Find the partial quotients of each place value and record them in the long division. Sometimes, the partial quotient may be 0, so regrouping may

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

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

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

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

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

Solve multiplication problems using the associative and commutative properties

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

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

Learn how to use factoring of 10, 100, and 1000 and the multiplication properties to multiply large numbers. Factor out 10,100, or 1000 and then group the single digit numbers together and the powers of 10 together

Solve a multi-digit multiplication problem mentally

Practice using mental math to multiply large numbers together. This skill will allow you to solve problems faster

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

Use factoring of 10, 100, and 1000 and the multiplication properties to multiply large numbers. Factor out 10,100, or 1000 and then group the single digit numbers together and the powers of 10 together. Rearranging the factors allows you to multiply quick

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

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

Round multi-digit numbers to estimate the product

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

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

Solve multiplication problems using the standard algorithm (Level 1)

Students will multiply a multi- and single-digit number using the standard algorithm to work digit by digit, including regrouping and working across zeros

Solve multiplication problems using the standard algorithm (Level 2)

Students will multiply multi- and single-digit number using the standard algorithm, remembering to regroup and add from the previous step without prompting

Multiply multi-digit numbers by factoring out powers of 10 and using the associative property

Students will multiply multi-digit numbers by factoring out powers of ten, then using the associative property to simplify the equation. They will learn to associate the factors of ten with the number of zeroes added to the end of the solution

Develop and test an algorithm for multiplying by a factor with a single non-zero digit

Students will develop an algorithm for solving multi-digit multiplication problems with a factor ending in zero. Students will test the algorithm in column form

Use the strategy of factoring out powers of 10 to solve multi-digit multiplication problems

Students will use the strategy of factoring out powers of 10 to solve multi-digit multiplication problems

Multiply two 2-digit numbers using the standard algorithm and the strategy of factoring out powers of ten (Level 1)

Students will solve multiplication problems with two 2-digit factors using the standard algorithm and the strategy of factoring out powers of ten and adding the appropriate number of zeros to the final product

Multiply two 2-digit numbers using the standard algorithm and the strategy of factoring out powers of ten (Level 2)

Students will solve multiplication problems with two 2-digit factors using the standard algorithm and the strategy of factoring out powers of ten, with instances of regrouping

Multiply two 2-digit numbers using the standard algorithm and the strategy of factoring out powers of ten (Level 3)

Students will solve multiplication problems with two 2-digit factors using the standard algorithm and the strategy of factoring out powers of ten, including instances of regrouping. Students will solve equations without additional supports

Use the area model to multiply two 2-digit numbers

Students will use the area models to solve multi-digit multiplication problems. Students will use the associative property and standard algorithm of multiplication to solve for partial products, then add them to find the total area

Multiply two 2-digit numbers using the concept of partial products

Students will multiply two 2-digit numbers by first breaking problems into partial products requiring multiplication by ones, then tens. Students will solve for each partial product, then add them to solve for the total product

Multiply multi-digit numbers using the concept of partial products (Level 1)

Students will use the strategy of partial products to multiply larger numbers. Students will solve for each partial product, then add them to solve for the total product

Multiply multi-digit numbers using the concept of partial products (Level 2)

Students will use the strategy of partial products to multiply multi-digit numbers

Multiply multi-digit numbers using the concept of partial products (Level 3)

Students will use the strategy of partial products to multiply multi-digit numbers

Multiply two 3-digit numbers using the concept of partial products (Level 1)

Students will multiply two 3-digit numbers by first breaking the problems into partial products, requiring them to multiply by ones, tens, and hundreds. Students will solve for each partial product, then add them to solve for the total product

Multiply two 3-digit numbers using the concept of partial products (Level 2)

Students will multiply two 3-digit numbers by breaking the problems into partial products. They will learn that partial products of zero do not need to be recorded in column addition

Multiply 3- and 4-digit numbers using the concept of partial products

Students will use the strategy of partial products to solve multiplication problems with 3- and 4-digit numbers. Multiple instances of regrouping occur

Multiply up to 5-digit numbers using the concept of partial products

Students will use the strategy of partial products to solve multiplication problems with up to 5-digit numbers. Multiple instances of regrouping occur

Students begin to multiply decimals in the tenths or hundredths by 2- or 3-digit whole numbers. They learn how to accurately place a decimal in their answer and how to estimate to check the reasonableness of their answer.

Multiply decimal numbers by powers of 10 and solve for missing factors

Students multiply decimal numbers by powers of 10, moving the digits the appropriate number of places to the left. When given a product, they also find the missing factor

Multiply decimal numbers in the tenths by a whole number (Level 1)

Students learn to multiply a decimal number in the tenths by a whole number. They use the standard algorithm to solve

Multiply decimal numbers in the hundredths by a whole number (Level 1)

Students learn to multiply a decimal number in the hundredths by a whole number, using the standard algorithm to solve. They develop a rule for solving multiplication problems with whole number and decimal factors

Multiply decimal numbers in the tenths by a whole number (Level 2)

Students use the previously-developed rule to multiply decimal numbers in the tenths by a whole number

Multiply decimal numbers in the hundredths by a whole number (Level 2)

Students use the previously-developed rule to multiply decimal numbers in the hundredths by a whole number

Factor out a power of 10 to multiply a decimal number by a tens or hundreds number (Level 1)

Students multiply a decimal number by a tens or hundreds number. They first factor out a power of 10, then use the associative property to regroup factors and solve

Factor out a power of 10 to multiply a decimal number by a tens or hundreds number (Level 2)

Students build fluency in multiplying a decimal number by a tens or hundreds number. They factor out a power of 10, then use the associative property to regroup factors and solve

Round numbers to the leftmost place with a non-zero digit (Level 1)

Students round whole and decimal numbers to the leftmost place with a non-zero digit. This involves rounding to the hundreds, tens, and ones places

Round numbers to the leftmost place with a non-zero digit (Level 2)

Students round whole and decimal numbers to the leftmost place with a non-zero digit. This involves rounding to the ones, tenths, and hundredths places

Estimate the product of a whole and decimal number by rounding (Level 1)

Students round whole number and decimal factors to the leftmost place with a non-zero digit in order to estimate their product

Estimate the product of a whole and decimal number by rounding (Level 2)

Students practice rounding whole number and decimal factors to the leftmost place with a non-zero digit in order to estimate their product

Find the estimated and actual products of a whole and decimal number

Students estimate and find the actual product of multiplying a whole number by a decimal number. They use the estimate to check for the correct placement of the decimal point in the actual product

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

Divide round numbers by powers of 10

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

Divide by factoring out powers of 10 from the divisor

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

Divide multi-digit round numbers mentally

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

List the multiples of a given 2-digit round number

Skip count by listing several multiples of a given number. This skill can help with solving division problems

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

Learn to round a 3-digit number to the closest multiple of a given 2-digit number. List the multiples of the 2-digit number. Determine the which of the multiples has the smallest difference to the 3-digit number

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

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

Estimate a quotient by finding the nearest multiple

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

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

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

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

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

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

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

Learn how divide with a remainder. Translate the verbal problem into a mathematical expression. Use the model to create the necessary groups. Identify the quotient and the remainder

Find the quotient and remainder by using multiples of the divisor

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

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

Use repeated subtraction to find the remainder of a division problem. Estimate the quotient, then subtract the divisor from the dividend as many times as possible to find the remainder

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

Determine the quotient and the remainder of a division problem through repeated subtraction. Subtract the divisor as many times as possible. Count how many times it was subtracted to find the quotient. The number left over after the subtractions is the re

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

Use estimation to learn how to do long division. Round the dividend to the nearest multiple of the divisor, then use factors of 10 to simplify the division estimate. Use the estimate to complete the long division, including finding the remainder

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

Use estimation to learn how to do long division. Round the dividend to the nearest multiple of the divisor to estimate the quotient. Rewrite the division problem in long division form. Use the estimate to complete the long division, including finding the

Solve using long division with a 1-digit quotient

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

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

Learn what to do if the estimated quotient is too high. Rewrite the division problem in long division form. Round the divisor and the dividend. If the partial product in the long division is too large to subtract, reduce the estimate by 1. Column multipli

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

Recognize when the estimated quotient is too low. Rewrite the division problem in long division form. Round the divisor and the dividend. If the remainder after subtraction in the long division is greater or equal to the divisor, increase the estimate by

Solve using long division with a 1-digit quotient

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

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

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

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

Learn what do do if the estimated quotient is too high or low low. Rewrite the division problem in long division form. Use estimation, then complete the partial quotients in the long division. Revise the estimates if the subtraction cannot be completed or

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

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

Solve using long division with a 3-digit quotient

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

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

Learn what do do if the estimated quotient is too high or low low. Rewrite the division problem in long division form. Use estimation, then complete the partial quotients in the long division. Revise the estimates if the subtraction cannot be completed or

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

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

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

Rename decimal numbers in unit form

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

Rename a number in unit form as a decimal number

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

Rename a whole number in unit form and decimal form

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

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

Divide a decimal by a whole number using place values. First, the decimal is stated in place value unit form. Then, choose the place value unit. Divide and then rewrite the answer as a decimal number. Finally, practice dividing a decimal by a whole number

Divide a decimal number by 10 or 100

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

Divide a decimal number by a multiple of 10 or 100

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

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

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

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

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

Solve long division to the tenths place

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

Solve long division to the hundredths place

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

Solve long division of a decimal number (Level 1)

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

Solve long division of a decimal number (Level 2)

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

Solve long division of a decimal number (Level 3)

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

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

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

Use long division to solve area problems with a decimal quotient

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

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

Label the numerator and denominator in a fraction

Write the fraction represented by a model. Learn the names for the parts of a fraction

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

Learn how to write equivalent fractions. First, use a model. Then, use multiplication to create equivalent fractions. Finally, complete the missing part of a set of equivalent fractions

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

Write reduced equivalent fractions. FIrst, use a model. Then, use division to create equivalent fractions. Finally, complete the missing part of a set of equivalent fractions

Complete equivalent fractions

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

Identify common factors of two given numbers

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

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

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

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

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

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

Add fractions with like denominators

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

Rewrite an improper fraction as a mixed number

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

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

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

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

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

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

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

Rename fractions with unlike denominators (Level 1)

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

Rename fractions with unlike denominators (Level 2)

Identify the common denominator of two fractions. Rewrite equivalent fractions with the common denominator

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

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

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

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

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

Practice adding fractions with unlike denominators. Multiply the denominators together to find the common denominator, then create equivalent fractions with the same denominator. Add the renamed fractions. If the sum is an improper fraction, rewrite it as

Subtract fractions with like denominators

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

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

Use models of rectangles with equal parts to learn to subtract fractions with unlike denominators. Multiply the denominators and then create equivalent fractions with the same denominator. Then subtract the fractions

Subtract fractions with unlike denominators

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

Rewrite a mixed number as an improper fraction

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

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

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

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

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

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

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

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

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

Subtract a fraction from 1 whole to solve a word problem

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

Subtract two fractions from 1 whole to solve a word problem

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

Add fractions to solve a word problem

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

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

Add a mixed number and a whole number with like denominators

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

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

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

Add a mixed number and a fraction with like denominators

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

Add mixed numbers with like denominators

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

Add mixed numbers with unlike denominators (Level 1)

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

Add mixed numbers with unlike denominators (Level 2)

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

Subtract mixed numbers with like denominators

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

Subtract mixed numbers with unlike denominators (Level 1)

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

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

Learn how to subtract a fraction from a mixed number when the fraction is larger than the fractional part of the mixed number. Rename the mixed number by reassigning 1 from the whole number part to the fractional part. Then subtract the fractions

Subtract mixed numbers with unlike denominators (Level 2)

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

Subtract mixed numbers with unlike denominators (Level 3)

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

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

Compare fractions with unlike denominators to 1/2 to estimate the sum

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

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

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

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

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

Add multiple mixed numbers and fractions

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

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

Learn how to solve word problems that involve several fractions with unlike denominators. Use a diagram to organize the information given in the problem. Then, write and solve an expression for each step of the problem

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

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

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

Round to the nearest half inch on a ruler

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

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

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

Round to the nearest quarter inch on a ruler

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

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

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

Round to the nearest eighth of a foot on a ruler

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

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

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

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

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

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

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

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

Relate division to fractions

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

Relate division to fractions greater than one

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

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

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

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

Rewrite an improper fraction as a mixed number. Write the fraction as a division expression. Then, find the quotient and remainder of a division problem to write the answer as a mixed number

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

Use long division to rewrite an improper fraction as a mixed number. Write the fraction as in long division form, then perform the division. The quotient becomes the whole number part and the remainder becomes the numerator of the fractional part

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

Learn to solve word problems involving fractions. Identify the fraction of a bar that is shaded. Then, use a bar to model a word problem and answer the question

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

Use a model to represent a word problem that involves fractions. Label the diagram with the given information. Rewrite the required division as a fraction. Then, change it to a mixed number and answer the question

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

Represent a word problem that involves fractions using a model. Label the diagram with the given information. Rewrite the required division as a mixed number in simplest terms and answer the question

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

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

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

Practice solving word problems involving fractions. Write the appropriate division expression for the problem. Then, rewrite it as a fraction or mixed number, as necessary

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

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

Find the number that is a fraction of a whole number. Use a model to help find the answer. Then, match a fraction to a model

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

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

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

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

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

Calculate the fraction of a whole number with the help of a model. Represent the information given in the problem with the model by selecting the number of parts. Calculate the value of one part, then highlight how many parts are represented by the fracti

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

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

Multiply a whole number by a fraction

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

Relate a fraction of a whole number to multiplication and solve

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

Determine a fraction of a measurement by converting units and multiplying

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

Determine common factors of two whole numbers

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

Divide whole numbers by a common factor

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

Reduce a fraction by dividing by a common factor

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

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

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

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

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

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

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

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

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

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

Compose an expression based on text

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

Compose a compound expression based on text (Part 1)

Compose a mathematical expression involving three values and addition and multiplication. Identify the operations represented by words in the verbal expression. Then, place the numbers into the expression with the correct operations, inserting parentheses

Compose a compound expression based on text (Part 2)

Create a mathematical expression involving three values and multiplication of whole numbers and a fraction. Identify the operations represented by words in the verbal expression. Then, place the numbers into the expression with the correct operations, ins

Compose a compound expression based on text (Part 3)

Write a mathematical expression involving three values and multiplication and subtraction of whole numbers and a fraction. Identify the operations represented by words in the verbal expression. Then, place the numbers into the expression with the correct

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

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

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

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

Solve compound equations with parentheses and fractions

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

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

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

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

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

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

Multiply unit fractions using an area model

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

Multiply fractions using an area model

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

Multiply fractions (reduce before multiplying)

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

Multiply fractions (reduce before or after multiplying)

Multiply two fractions together. Decide whether to multiply or reduce at each step. Find the simplified product

Solve word problems by multiplying fractions using an area model

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

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

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

Convert measurements by multiplying a whole number by a fraction

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

Convert measurements by multiplying fractions

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

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

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

Multiply by 0.1 using a place value chart

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

Multiply by 0.01 using a place value chart

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

Multiply by 0.1 or 0.01

Practice multiplying a number by 0.1 or 0.01

Decompose a decimal number to multiply

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

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

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

Multiply two decimal numbers using column multiplication (Part 1)

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

Multiply two decimal numbers using column multiplication (Part 2)

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

Multiply two decimal numbers using column multiplication (Part 3)

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

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

Multiply a fraction by a fraction equal to 1

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

Identify a missing factor as a fraction equal to 1

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

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

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

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

Use inequality symbols to compare a fraction to 1. Then, compare the product of that fraction and another fraction to the value of the second fraction

Identify a fraction that will complete a multiplication inequality

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

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

Learn how to rewrite a fraction as a decimal. Determine what factor would change the denominator to a power of 10, then multiply to create an equivalent fraction. Then, write that fraction as a decimal

Convert a fraction greater than one to decimal form

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

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

Rewrite a fraction as a decimal. Complete the factor that would create an equivalent fraction with the given power of 10 denominator. Then, multiply the numerators and rewrite the fraction as a decimal

Convert a fraction less than one to decimal form using division

Use long division to rewrite a fraction as a decimal. Divide the numerator by the denominator, adding zeros to continue dividing without a remainder

Convert a fraction greater than one to decimal form using division

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

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

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

Complete inequalities involving multiplication by a decimal number

Practice determining the relationship between the product of two decimals and the value of one of those decimals. First, given the choice of three decimals, choose the one that makes the inequality statement true. Then, complete the missing part of the de

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

Multiply by a fraction or decimal greater than 1. Determine if the product is less than or greater than one of the factors, using inequality symbols.Demonstrate understanding of the concept by placing the correct inequality into a formula expression

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

Multiply by a fraction or decimal less than 1. Determine if the product is less than or greater than one of the factors, using inequality symbols.Demonstrate understanding of the concept by placing the correct inequality into a formula expression

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

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

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

Compose a division equation with a fraction based on a model

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

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

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

Relate division by a unit fraction to multiplication by the denominator

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

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

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

Divide a whole number by a unit fraction

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

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

Learn how to divide a fraction by a whole number. Use a tape model to represent the fraction as equal parts. Then divide each part in the number of sections indicated by the whole number. Answer how many sections there are in total

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

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

Divide a unit fraction by a whole number

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

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

Multiply two unit fractions together. Use an area model to represent both fractions on one rectangle. Find the shaded area that represents the product of the two fractions. Then apply this concept to multiplication problems without the use of an area mode

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

Use an area model to represent the division of a unit fraction by a whole number. Rewrite the division as multiplication by a fraction. Use the resulting shaded area to find the product of the two fractions

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

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

Solve division equations with unit fractions and whole numbers

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

Multiply a decimal number by a power of ten

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

Simplify a fraction using the basic property of fractions

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

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

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

Convert between division expressions and fractions

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

Complete fraction expressions using the basic property of fractions

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

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

Use the basic property of fractions to convert fractions containing decimals to fractions containing only whole numbers. Change a division expression to a fraction. Then, choose the correct factor that makes the denominator a whole number. Simplify the fr

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

Convert fractions containing decimals to fractions containing only whole numbers. Change a division expression to a fraction. Then, choose the correct factor that makes the denominator a whole number. Simplify the fraction

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

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

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

Use the basic property of fractions to convert fractions containing decimals to fractions containing only whole numbers. Choose the correct factor that makes the denominator a whole number. Then, multiply and simplify the fraction

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

Learn how to rewrite division of decimals to a division expression containing whole numbers. Shift the decimal point of the divisor as many places to the right as necessary to make it a whole number. Shift the decimal point of the dividend by the same num

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

Rewrite division of decimals to a division expression containing whole numbers. Shift the decimal point as many places to the right as necessary to make it a whole number. Shift the decimal point of the dividend by the same number of places. Then, find th

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

Solve missing addend equations

Find the missing term in an addition or subtraction equation. Each equation has a symbol in place of one of the terms. Find the missing number

Solve multi-step missing addend equations

Solve equations with more than one missing term. Each equation will have the same symbol in place of two or three of the terms. Find the missing number

Solve for missing addends in paired equations (Level 1)

Find two missing terms in a pair of equations. Each equation has one or two symbols in place of a term. Find the missing numbers

Solve for missing addends in a set of three equations

Solve for three missing terms in a set of three equations. Each equation has one or two symbols in place of a term. Find the missing numbers

Solve for missing addends in paired equations (Level 2)

Find the missing terms in a pair of equations. Each equation has one or two symbols in place of a term. Learn how to replace a set of terms if the combined value is known. Find the missing numbers

Solve missing addend equations containing a 0

Solve for two missing terms in a pair of equations. Each equation has a symbols in place of a term. Find the missing numbers. Learn the effect of adding 0 in an equation

Solve for missing addends in paired equations containing a 0

Practice solving equations with more than one missing term. Each equation has symbols in place of two or three of the terms. Find the missing numbers