EM2NY_G5_M1_Learn_25A_121424_Updated 10.4

5 A Story of Units® Fractions

Are Numbers

LEARN ▸ Place Value Concepts for Multiplication and Division with Whole Numbers

What does this painting have to do with math?

Color and music fascinated Wassily Kandinsky, an abstract painter and trained musician in piano and cello. Some of his paintings appear to be “composed” in a way that helps us see the art as a musical composition. In math, we compose and decompose numbers to help us become more familiar with the number system. When you look at a number, can you see the parts that make up the total?

On the cover

Thirteen Rectangles, 1930

Wassily Kandinsky, Russian, 1866–1944

Oil on cardboard

Musée des Beaux-Arts, Nantes, France

Wassily Kandinsky (1866–1944), Thirteen Rectangles, 1930. Oil on cardboard, 70 x 60 cm.

Musée des Beaux-Arts, Nantes, France. © 2020 Artists Rights Society (ARS), New York. Image

credit: © RMN-Grand Palais/Art Resource, NY

ISBN 979-8-89012-142-4

Fractions Are Numbers ▸ 5 LEARN

1

Place Value Concepts for Multiplication and Division with Whole Numbers

2

Addition and Subtraction with Fractions

3

Multiplication and Division with Fractions

4

Place Value Concepts for Decimal Operations

5

6

Addition and Multiplication with Area and Volume Foundations to Geometry in the Coordinate Plane

Place Value Concepts for Multiplication and Division with Whole Numbers

by 10, 100, and 1,000

Topic C

Topic B Multiplication of Whole Numbers

Topic D

Name Date

For this counting collection, I am partners with .

We are counting .

We think they have a value of . This is how we organized and counted the collection:

We counted altogether. An equation that describes how we counted is: .

Self-Reflection

Write one thing that worked well for you and your partner. Explain why it worked well.

Write one challenge you had. How did you work through the challenge?

Name

Date

Use the place value chart to complete the statement and equation.

1.

millions hundred thousands ten thousands thousands hundredstens ones

3 ten thousands is 10 times as much as 30,000 = 10 ×

millions hundred thousands ten thousands thousands hundredstens ones

2. is 10 times as much as . = 10 ×

Use the place value chart to complete the equation.

3. 60,000 ÷ 10 =

millions hundred thousands ten thousands thousands hundredstens ones

4. millions hundred thousands ten thousands thousands hundredstens ones

5. Complete each statement by drawing a line to the correct value.

6.

7.

13. Consider the number shown.

8 7 7, 4 8 7

a. Complete the equation to represent the number in expanded form.

877,487 = ( ) + ( ) + ( ) + ( ) + ( ) + ( )

b. Draw a box around the digit that represents 10 times as much as the underlined digit.

c. Complete the equations to show the relationships between the boxed and underlined digits. = 10 × ÷ 10 =

d. Explain how the digit in the hundred thousands place is related to the digit in the tens place.

14. Kayla and Blake both write a number.

Kayla’s Number 2,30 8,467 Bl ake’s Nu mb er 71 3, 54 8

a. Kayla says, “The 3 in my number is 10 times as much as the 3 in Blake’s number.” Do you agree with Kayla? Explain.

b. Write a division equation to relate the 8 in Kayla’s number to the 8 in Blake’s number.

Name

52 ,285

Date

a. Write a division equation that relates the 2 on the left to the 2 on the right.

b. Use the words times as much to compare the 5 on the left to the 5 on the right.

1. 5 × 10 =

2. 5 × 100 =

3. 5 × 1,000 =

4. 50 × 10 =

5. 50 × 100 =

6. 50 × 1,000 =

7. 48 × 30 =

8. 48 × 300 =

9. 48 × 3,000 =

Name

Date

1. Complete the statement. The 8 in 58,701 represents times as much as the 8 in 5,870.

2. Write a multiplication equation to relate the 7 in 58,701 to the 7 in 587,019.

3. Write a division equation to show the relationship between the value of the 5 in 587,019 and the value of the 5 in 5,870.

Multiply.

4. 62 × 1 ten = 62 × 10 =

5. 62 × 1 hundred = 62 × 100 =

6. 62 × 1 thousand = 62 × 1,000 =

Complete the equations and expressions.

Multiply or divide.

28. Toby finds the product of 3,240 and 1,000. 3,24 0 x 1, 000 = 32 4, 000

Use the number of zeros in the product to explain why Toby’s answer is not correct.

Use the Read–Draw–Write process to solve the problem.

29. A banker has a total of $54,200, all in one hundred-dollar bills. How many one hundred-dollar bills does the banker have?

Name Date

Find each product.

1. 80 × 10 =

2. 80 × 100 =

3. 80 × 1,000 =

Find each quotient.

4. 340,000 ÷ 10 =

5. 340,000 ÷ 100 =

6. 340,000 ÷ 1,000 =

7. How does the value the 6 represents in 3,604 compare to the value the 6 represents in the product of 3,604 and 1,000? Explain how you know without multiplying.

Name

Multiply.

1. 10,000 × 100 =

Date

2. 1,000 × 103 =

Multiply.

3. 7 × 102 =

4. 300 × 103 =

Divide.

5. 10,000 ÷ 102 =

6. 1,000,000 ÷ 103 =

Divide.

7. 9,000 ÷ 103 =

8. 360,000 ÷ 104 =

Complete the table to represent each number in three different forms. The first one is done for you.

Write each product or quotient in exponential form.

100 × 100 =

100 × 104 =

10. Consider the expression shown. 1,000 × 103

How does the exponent help you think about shifting the digits in the first factor to find the product?

11. Use words and equations to explain how 105 is different from 10 × 5.

Rewrite each expression by using an exponent. Then find the product or quotient and write it in standard form.

Find each product or quotient and write it in standard form.

14. 8 × 104 =

15. 500,000 ÷ 105 =

16. 39,000 ÷ 102 =

17. 400 × 103 =

18. 620 × 104 =

19. 9,180,000 ÷ 103 =

20. Explain how you found the quotient in problem 16.

21. Yuna finds 300 × 103. Explain Yuna’s strategy.

Name Date

Multiply or divide. Then write each product or quotient in exponential form.

1. 10 × 10 × 10 × 10 =

2. 10 × 1,000 =

3. 100 × 10 4 =

4. 100,000 ÷ 10 2 =

Multiply or divide. Then write each product or quotient in standard form.

5. 4 × 10 5 =

6. 200 × 10 4 =

7. 70,000 ÷ 10 4 =

8. 340,000 ÷ 10 3 =

Estimate each product. Show your thinking.

1. 7,114 × 20

2. 1,009 × 51

3. 92 × 396,285

4. Which number is the best estimate of 976 × 52?

A. 4,500

B. 45,000

C. 50,000

D. 500,000

Estimate each quotient. Show your thinking. 5.

8. Miss Baker buys 327 hats for students at her school. Each hat costs $18. About how much do the hats cost in total? Show your thinking.

9. A runner climbs 1,276 stairs in 11 minutes. Estimate the number of stairs the runner climbs in 1 minute. Show your thinking.

Estimate each product. Show your thinking.

1. 48 × 6

2. 247 × 9

3. 4 × 7,081

4. 32 × 18

5. 673 × 54

6. 1,235 × 43

7. Scott started to make an estimate for 718 × 41 but did not finish.

a. Complete the equations to finish Scott’s estimate.

700 × 40 = 7 × × 4 × = × 10 =

b. Is Scott’s estimate greater or less than the actual product of 718 and 41? Explain how you know without calculating the actual product.

8. Kelly and Adesh each write an expression to show how to estimate 1,846 × 7.

Kelly’s Way 2, 000 × 7 Adesh’s Way 2, 000 × 10

Whose estimate is closer to the actual product? Explain your answer. Estimate each quotient. Show your thinking.

15. Tim makes a mistake when he estimates 3,714 ÷ 94. What mistake does Tim make? 3,71 4 ÷ 94 ≈ 3, 60 0 ÷ 90

16. The table shows the cost of tickets for a concert.

a. There are 8,309 adults at the concert. About how much was spent on adult tickets?

b. The total amount spent on children’s tickets was $6,288. About how many children are at the concert?

Name Date

A large helicopter can carry 25,000 pounds. The average weight of a car is 4,110 pounds. If there is enough space, about how many cars can the helicopter carry at one time? Explain how you know.

Convert.

1. 456 kL = L

2. 6,985 g = mg

3. cm = 308 m

4. The label on a water bottle shows the capacity of the bottle is 50 centiliters. What is the capacity of the bottle in milliliters?

5. The label on a bag of rice reads 2 kg 300 g. The label on a bag of beans reads 2,300 mg. Which bag is heavier?

Grade 5 Mathematics Reference Sheet

Conversions

1 yard = 3 feet

1 mile = 5,280 feet

1 mile = 1,760 yards

1 centimeter = 10 millimeters

1 meter = 1,000 millimeters

Volume Formula

Right rectangular prism

1 cup = 8 fluid ounces

1 pint = 2 cups

1 quart = 2 pints

1 gallon = 4 quarts

1 liter = 1,000 milliliters

1 pound = 16 ounces

1 ton = 2,000 pounds

1 kilogram = 1,000 grams

V = B × h or V = l × w × h

Convert each measurement. Write an expression to help you convert. The first one is started for you.

Consider the expressions.

a. Circle the expression that does not represent how to convert 600 liters to milliliters.

b. Explain your choice.

Convert.

8. 6 L 34 cL = cL

9. mg = 60 g 52 mg

10. mm = 87 m 61 mm

11. 8 kg 1,245 mg = mg

12. Riley runs 11 kilometers. What is the distance Riley runs in meters?

13. Mr. Sharma’s dog weighs 21 kg 96 g. What is the weight of Mr. Sharma’s dog in grams?

Name Date

Convert each measurement. Use the reference sheet if needed.

1. 4 km = m

2. 9,430 cL = mL

3. 108 kg = g

Name Date

Use the Read–Draw–Write process to solve the problem.

1. Sasha has 6 meters 40 centimeters of ribbon. She plans to divide the ribbon equally to wrap 8 gifts that are the same size. How many centimeters of ribbon should Sasha cut for each gift?

Use the Read–Draw–Write process to solve the problem.

2. A family takes a road trip from New York City to Seattle, and they stop in Chicago on the way. The distance from New York City to Chicago is 1,963 kilometers less than the distance from Chicago to Seattle. The distance from Chicago to Seattle is 3,288 kilometers. If the family travels the same route to Seattle and back, how many total meters do they travel?

Name

Use the Read–Draw–Write process to solve each problem.

Date

1. Mr. Perez pours water into 8 beakers. He pours 750 milliliters of water into each beaker.

a. About how many milliliters of water are in the beakers altogether?

b. Exactly how many milliliters of water are in the beakers altogether?

c. How do you know your answer in part (b) is reasonable?

2. A newborn lion cub weighs 1 kg 736 g. The lion cub weighs 8 times as much as a newborn puppy.

a. Convert the weight of the lion cub to grams.

b. About how many grams does the puppy weigh?

c. Exactly how many grams does the puppy weigh?

d. How do you know your answer in part (c) is reasonable?

3. Leo uses oil and vinegar to make a bottle of salad dressing. He uses 12 centiliters of vinegar. He uses 3 times as much oil as vinegar. How many milliliters of salad dressing does Leo make?

4. Eddie has a blue ribbon that is 4 m 23 cm long and a green ribbon that is 756 cm long. He cuts each ribbon into pieces that are 9 cm long. How many more pieces of green ribbon than blue ribbon does Eddie have?

5. A farmer puts apples into 36 crates. Each crate has 25 kilograms of apples in it. She sells 486,235 grams of apples. How many grams of apples does she have left?

Name

Date

Use the Read–Draw–Write process to solve the problem. Lacy needs 650 centimeters of ribbon for a project. She already has 2 m 596 mm of ribbon. How many more millimeters of ribbon does Lacy need?

Name Date

1. Write the following number in as many ways as you can.

28,741

Use the Read–Draw–Write process to solve the problem.

2. On a typical day, a grade 5 student takes 24,165 breaths in one day. How many breaths will you and 5 friends take in one day?

Multiply. Show or explain your work.

3. 4 times as much as 32,157

Name

Multiply. Show or explain your strategy.

1. 4 times as much as 362

2. 7 times as long as 3,098 kilometers

Date

3. 6 × 12,345

4. 9 × 21,876

Use the Read–Draw–Write process to solve each problem.

5. Mrs. Chan takes 13,564 steps each day for 4 days. How many total steps does she take in those 4 days?

6. An airplane weighs 40,823 kilograms. What is the total weight of 7 of these airplanes?

Name Date

Multiply. Show or explain your strategy.

73,613 × 5

Name Date

Use the Read–Draw–Write process to solve the problem.

1. There are 122 cities competing in a math relay race. Each city sends 41 grade 5 students to compete. How many students compete?

2. 24 × 40 =

3. 22 × 41 =

4. 21 × 343 =

5. 32 × 201 =

Complete the area model. Then multiply by showing two partial products.

Draw an area model to find two partial products. Then multiply by showing two partial products.

4. 34 × 121

Estimate the product. Then multiply.

Use the Read–Draw–Write process to solve the problem.

9. A toy giraffe is 403 millimeters tall. A real giraffe is 12 times as tall as the toy giraffe. How tall is the real giraffe?

Name Date

Consider the expression shown.

31 × 213

a. Complete the area model.

b. Multiply by showing two partial products. × +

c. Complete the equation.

31 × 213 =

Sprint

Write the product.

1. 1 × 20 =

2. 2 × 600 =

3. 3 × 9,000 =

Number Correct:

Write the product.

1. 1 × 10 =

2. 1 × 30 =

3. 2 × 30 =

4. 3 × 30 =

5. 30 × 3 =

6. 40 × 4 = 7. 50 × 5 = 8. 1 × 100 = 9. 2 × 200 = 10. 3 × 400 =

Sprint ▸ Multiply by Multiples of 10, 100, 1,000, and 10,000

Write the product.

1. 1 × 10 =

2. 1 × 20 =

3. 2 × 20 =

4. 3 × 20 =

5. 20 × 3 = 6. 30 × 4 = 7. 40 × 5 = 8. 1 × 100 = 9. 2 × 200 = 10. 3 × 400 =

EUREKA MATH2 New York Next Gen

Number Correct:

Improvement:

×

Name Date

1. Mr. Perez paints the gymnasium wall. The wall is 24 feet wide and 33 feet long. How many square feet does Mr. Perez paint?

2. 28 × 63 =

3. Flatback turtles lay 52 eggs in a nest. How many turtle eggs would there be in 427 nests?

Draw an area model to find the partial products. Then multiply by using the standard algorithm.

3. 47 × 32 ×

4. 25 × 638

Estimate the product. Then multiply.

5. 38 × 529 ≈ × =

63 × 804 ≈ ×

7. Julie makes a mistake when she uses the distributive property to find 83 × 624. Look at her work.

a. What mistake did Julie make?

b. Find the product. 83 × 624 =

Use

8. A school bus travels 508 kilometers each week. How many kilometers does the school bus travel in 36 weeks?

Name

Consider the expression shown.

446 × 81

a. Draw an area model to find the partial products.

Date

b. Multiply by using the standard algorithm.

Name Date

1. Lisa tiles a rectangular floor that is 204 inches long and 123 inches wide. How many square inches of tile does Lisa use?

2. The population of Waverly, Pennsylvania, is 604 people. The population of Scranton, Pennsylvania, is 127 times as much as the population of Waverly. What is the population of Scranton?

3. 1,429 × 312

Complete the area model and find the sum of the partial products. Then multiply by using the standard algorithm. Compare your answers in each part to check that the product is correct.

Draw an area model to find the partial products and find their sum. Then multiply by using the standard algorithm. Compare your answers in each part to check that the product is correct.

1.

Estimate the product. Then multiply.

Use the Read–Draw–Write process to solve the problem.

7. Sana drinks from a bottle that holds 946 milliliters of water. She fills the bottle and drinks all the water in it twice each day.

a. How many milliliters of water does Sana drink each day?

b. How many milliliters of water does Sana drink in 365 days?

Estimate the product. Then multiply by using the standard algorithm.

5. Blake wants to find 312 × 675. Look at Blake’s work.

a. Is Blake’s answer reasonable? How do you know?

b. What mistakes did Blake make?

Multiply.

651 × 823

508 × 977

6.

7.

8. 467 times as much as 2,083

9. 6,254 × 379

Use the Read–Draw–Write process to solve the problem.

10. A cow weighs 712 kilograms. A blue whale is 255 times as heavy as the cow. How many kilograms does the blue whale weigh?

Name Date

Use

1. Tyler wants to donate boxes of crayons to kindergarten classes. He has 347 boxes. He donates sets of 40 boxes to as many classes as he can. How many boxes remain?

Name

Complete the tape diagram. Then complete the vertical form and check your work.

Check: 80 = ×

30 240

Check: 240 = ×

Estimate the quotient. Complete the tape diagram. Then complete the vertical form and check your work.

40 81

Quotient:

Remainder:

Check: 81 = × +

50 324

Quotient:

Remainder:

Check: 324 = × +

3. 81 ÷ 40 ≈ ÷

4. 324 ÷ 50 ≈ ÷

Divide. Then check your work.

5. 120 ÷ 30 30 120

6. 72 ÷ 60

4

Quotient:

Remainder:

Check:

7. 731 ÷ 80

Quotient:

Remainder:

Check:

8. 560 ÷ 70

Quotient:

Remainder:

Check:

Quotient:

Remainder:

Check:

9. A number divided by 40 has a quotient of 6 and a remainder of 15. What is the number?

Use the Read–Draw–Write process to solve the problem.

10. A student has 174 centimeters of ribbon for making bows. Each bow is made with 20 centimeters of ribbon. The student wants to make as many bows as possible. How many bows can the student make? How many centimeters of ribbon will be left over?

Name Date

Consider the expression shown.

655 ÷ 80

a. Draw and label a tape diagram to represent the expression.

b. Determine the quotient and remainder.

Quotient:

Remainder:

c. Write an equation to check your work.

Name Date

Use the Read–Draw–Write process to solve each problem.

1. Sasha is training for a competition and plans to do 96 push-ups in one day. She plans to do these push-ups in sets of 16. How many sets of push-ups will she need to do to reach her goal of 96 push-ups? Show your thinking, including an estimate and a check.

Estimate:

Divide:

Check:

2. A camp plans to take its 92 students on a field trip. Each bus holds 21 students. How many buses does the camp need for the field trip? Show your thinking.

3. There are 92 coins split into 21 piles. Each pile has the same number of coins and as many coins as possible. How many coins are in each pile?

Estimate the quotient. Complete the tape diagram. Then complete the vertical form and check your work.

Check: 72 = ×

Estimate the quotient. Complete the tape diagram. Then complete the vertical form and check your work.

5 1 39

Quotient:

Remainder:

Check: 95 = × + 4.

4 9 18

Quotient:

Remainder:

Check: 84 = × +

Divide. Then check your work.

5. 96 ÷ 32 32 96

Quotient:

Remainder:

Check:

6. 54 ÷ 27

Quotient:

Remainder: Check:

7. 83 ÷ 21

Quotient:

Remainder:

Check:

8. 95 ÷ 19

Quotient:

Remainder:

Check:

9. Scott wants to find 78 ÷ 42. First, he estimates the quotient. Then he uses his estimate to divide.

a. What should Scott do next?

b. Find 78 ÷ 42.

Use the Read–Draw–Write process to solve the problem.

10. An auditorium has 25 seats in each row. How many rows are needed to seat 92 students?

Sprint

Write each power of 10 in exponential form.

1. 100

2. 10 × 10 × 10 × 10

3. Ten to the third power

4. One million

Number Correct:

Write each power of 10 in exponential form.

1. 100 2. 1,000 3. 100,000 4. 10,000 5. 1,000,000 6. 10 7. 10 × 10

8. 10 × 10 × 10

9. 10 × 10 × 10 × 10 × 10 × 10

10. 10 × 10 × 10 × 10

11. 10 × 10 × 10 × 10 × 10 12. 10

13. Ten to the second power 14. Ten to the third power 15. Ten to the fifth power 16. Ten to the sixth power 17. Ten to the fourth power 18. One hundred

One thousand

One million

One hundred thousand

Ten thousand

Number Correct:

Improvement:

Write each power of 10 in exponential form. 1. 100 2. 1,000 3. 10,000 4. 100,000 5. 1,000,000 6. 10 7. 10 × 10

8. 10 × 10 × 10

9. 10 × 10 × 10 × 10 × 10

10. 10 × 10 × 10 × 10

11. 10 × 10 × 10 × 10 × 10 × 10 12. 10 13. Ten to the second power 14. Ten to the third power 15. Ten to the sixth power 16. Ten to the fifth power 17. Ten to the fourth power 18. One hundred

One thousand 20. One million

Ten thousand 22. One hundred thousand

Name Date

Use the Read–Draw–Write process to solve each problem.

1. A school activity has 301 students split into 43 equal-size groups. How many students are in each group?

2. Eddie has 34 days to read a 170-page book. If he reads the same number of pages each day, how many pages does he need to read each day to finish the book in 34 days?

3. Miss Baker needs to order 546 pencils. If each pack has 72 pencils, what is the fewest number of packs Miss Baker should order?

4. Riley has 457 centimeters of ribbon. Each costume he makes needs 55 centimeters of ribbon. How many costumes can Riley make?

Name

Estimate the quotient. Then complete the vertical form and check your work. Draw a tape diagram if it helps you divide.

Quotient:

Remainder:

Check: 156 = ×

Quotient:

Remainder:

Check: 136 = ×

1. 156 ÷ 52 ≈ ÷ =

2. 136 ÷ 34 ≈ ÷

Divide. Then check your work.

5. 287 ÷ 41 41 287

Quotient:

Remainder:

Check:

7. 555 ÷ 91

Quotient:

Remainder:

Check:

6. 415 ÷ 83

Quotient:

Remainder:

Check:

8. 702 ÷ 78

Quotient:

Remainder:

Check:

9. Consider the division work.

39 284 – 273 11

a. Show another division problem with the same quotient and remainder as 284 ÷ 39.

b. Explain how you found another division problem with the same quotient and remainder as 284 ÷ 39.

Use the Read–Draw–Write process to solve the problem.

10. Kayla’s book has 307 pages. She plans to read 45 pages each day. How many days will it take Kayla to finish reading the book?

Name Date

There are 418 people going on a field trip. Each bus can hold 72 people. What is the least number of buses the school must use? Explain your answer.

1. Determine the unknown values in the area model. Then write a multiplication equation and a division equation that the area model represents.

1. Julie started the division for 464 ÷ 29 by using the area model shown.

a. Complete Julie’s model.

b. Use the partial quotients from part (a) to show the division for 464 ÷ 29 in vertical form.

c. What is 464 ÷ 29? How do you know?

Divide by using an area model. Then check your work.

2. 234 ÷ 18

Check: 234 = × 18

Estimate the partial quotients as you divide. Then check your work.

3. 436 ÷ 17

Quotient:

Remainder:

Check: 436 = × 17 +

Divide. Then check your work.

4.

5.

Quotient:

6.

Quotient:

Quotient:

Use the Read–Draw–Write process to solve the problem.

7. Tara uses 25 blocks to build a tower. She has 362 blocks. How many towers of 25 blocks can she build?

Name Date

A parking lot has 567 parking spots in 27 rows. If each row has the same number of parking spots, how many parking spots are in each row?

Name Date

Use the Read–Draw–Write process to solve the problem.

1. A tree farm has 15 rows of trees. Each row has the same number of trees. If there is a total of 1,635 trees, how many trees are in each row?

Use the Read–Draw–Write process to solve the problem.

2. Lacy plans to ride her bike 2,900 miles, which is about the distance from San Francisco to New York. If she rides 68 miles each week, how many weeks will it take Lacy to ride 2,900 miles?

Estimate the partial quotients as you divide. The first estimate is started for you. Make as many estimates as you need to. Then check your work.

Quotient: Remainder:

Quotient:

Remainder:

5. 3,164 ÷ 45

Check:

Quotient:

Remainder:

6. 5,123 ÷ 47

Check:

Quotient:

Remainder:

Use the Read–Draw–Write process to solve the problem.

7. A warehouse has 1,250 video games to distribute evenly to 12 stores. If the warehouse distributes as many as possible, how many games does each store get? How many games are left over?

7,139 ÷ 31

Quotient:

Remainder:

Name Date

Write an expression to represent the statement. Use the tape diagram to help you.

1. 3 times the sum of 15 and 25

15 + 25 15 + 25 15 + 25 ?

Draw a tape diagram and write an expression to represent the statement.

2. The difference between 72 and 48, then divide by 2

Write a statement and equation to represent the tape diagram.

Use >, =, or < to compare the expressions.

4. 22 × (18 + 31) (18 + 31) × 34

5. (2 × 8) + (10 × 8) (7 × 8) − (4 × 8)

6. 145 × 71 (100 + 45) × (70 + 1)

Name Date

Draw a tape diagram and write an expression to represent the statement.

1. Double the sum of 9 and 6

2. The difference between 67 and 43, then divide by 2

3. 3 times as much as the sum of 11 and 29

4. The sum of two 18s and three 12s

Write a statement and an expression to represent the tape diagram. Then evaluate your expression.

5. 37 18 37 18 37 18 37 18

Statement:

Expression:

Value of expression:

6. 9999 7 7

Statement:

Expression:

Value of expression:

7. Evaluate.

a. 40 + (3 × 9) − 6

b. (40 + 3) × (9 − 6)

c. Why do expressions (a) and (b) have different values?

Use >, =, or < to compare the expressions. Explain how you can compare the expressions without evaluating them.

8. 35 × (12 + 28) (12 + 28) × 70

Explain:

9. 225 × 81 (200 + 25) × (80 + 1)

Explain:

10. (48 × 7) − (37 × 7) (5 × 7) + (5 × 7)

Explain:

11. Consider the statement.

5 times as much as the sum of 319 and 758

a. Adesh makes a mistake when he writes an expression to represent the statement. What mistake does Adesh make?

(5 × 31 9) + 75 8

b. Write an expression to represent the statement.

c. Evaluate the expression you wrote in part (b).

Name Date

1. Write an expression to represent the statement. Draw a tape diagram if it helps you. 4 times as much as the sum of 3 and 12

2. Use >, =, or < to compare the expressions.

4. (24 − 6)

5. (9 + 4) × 3 − 6

Name Date

1. Draw lines to match the expressions to the word problems.

a. (3 + 9 − 5) × 12

Yuna buys 3 bags of oranges. There are 9 oranges in each bag. She eats 5 oranges. Then she gives 12 oranges to her friends. How many oranges does Yuna have now?

b. 3 × 9 − 5 − 12

Tyler has 3 pencils. He finds 9 more pencils. Sasha has 5 times as many pencils as Tyler. Eddie has 12 fewer pencils than Sasha. How many pencils does Eddie have?

c. (3 + 9) × 5 − 12

Riley gets 3 books from the library on Monday and 9 more books on Tuesday. She reads and returns 5 books on Wednesday. Riley has 12 times as many books on her bookshelf as she still has from the library. How many books are on Riley’s bookshelf?

2. Write an expression that represents the tape diagram. Then write a word problem that can be represented by the tape diagram and expression. 12

? 12 12 17

3. Consider the expression.

4 × (15 + 8)

Write a word problem that can be represented by the given expression.

4. Consider the expression.

(26 − 8) ÷ 2

a. Write a word problem that can be represented by the given expression.

b. Solve your problem.

Name Date

Write a word problem that can be solved by using the expression shown.

(6 + 7) × 11 − 34

Name Date

Use the Read–Draw–Write process to solve each problem.

1. A florist uses 2,448 flowers to make bouquets. They put 24 flowers in each bouquet and sell the bouquets for $25 each. If the florist sells all the bouquets of flowers, how much money do they earn?

2. Miss Song buys 15 boxes of fruit snacks for the school field day. Each box holds 24 packs of fruit snacks. She gives as many packs of fruit snacks as possible to 22 classrooms so that they each get the same number. How many extra packs of fruit snacks does Miss Song have?

3. A carton of eggs has 12 eggs. A box of eggs holds 12 cartons. A baker uses 5 eggs for each cake he makes. If the baker buys 3 boxes of eggs, what is the greatest number of cakes he can make?

Name

Use the Read–Draw–Write process to solve each problem.

Date

1. Miss Baker orders 13 cases of soup for her grocery store. Each case has 48 cans of soup. She puts all the cans on the shelves so that each shelf has an equal number. If there are 16 shelves, how many cans of soup are on each shelf?

2. Mr. Sharma bakes 732 cupcakes each week for his bakery. He puts 12 cupcakes in each box and earns $14 for each box he sells. If he sells all the boxes of cupcakes, how much money does he earn?

3. There are 9,675 people at a concert. An equal number of people sit in each of the 15 sections. A ticket for a seat in section B costs $47. What is the total cost of the tickets for the seats in section B?

4. 24 students are in each classroom at Oak Street School. There are 37 classrooms. Each row in the auditorium has 45 seats. What is the fewest number of rows needed for all the students to have a seat?

5. A box of name tags holds 18 name tags. A case of name tags has 25 boxes. Principal Song buys 17 cases of name tags. She gives an equal number of name tags to each of 42 classrooms. If she gives out as many name tags as possible, how many extra name tags does Principal Song have?

6. A farmer’s cows produce 9,548 liters of milk in 31 days. Each cow produces 28 liters of milk a day. The farmer feeds each cow 17 kilograms of hay each day. What is the total number of kilograms of hay the cows eat each day?

Name Date

Use the Read–Draw–Write process to solve the problem.

Blake buys 6 cases of water for a picnic. Each case has 32 water bottles. Blake plans to give everyone the same number of water bottles. If there are 48 people at the picnic, how many water bottles does each person get?

Name Date

1. Match each mathematical expression with the real-world situation it represents.

Mathematical Expression

Real-World Situation

A. (18 × 4) + 5 Leo buys 4 pens. Blake buys 5 pens. The total cost of the pens is $18. If all the pens cost the same amount, what is the cost for 1 pen?

B. 18 ÷ (4 + 5) At a camp, 1 group has 18 kids, and 4 groups have 5 kids each. How many kids are at the camp?

C. (18 × 4) − 5

Sana buys 4 cases of water. Each case has 18 bottles. If she also has 5 cans of juice, how many total drinks does she have?

D. 18 + (4 × 5)

Yuna mows 4 lawns and gets paid $18 per lawn. If Yuna spends $5, how much money does she have left over?

Use the Read–Draw–Write process to solve the problem. Show your thinking.

2. Jada is saving money for a computer that costs $1,149. That is three times as much money as she has already saved. Her parents also gave her $150 for the computer. Jada earns $14 each hour at her job. How many hours does Jada need to work to earn the remaining money she needs to buy the computer?

Name Date

Use the Read–Draw–Write process to solve each problem.

1. Noah delivers packages 4 days per week. He is expected to deliver 115 packages each day that he works. This week, he delivers 48 extra packages. How many packages does Noah deliver this week?

2. A motorcycle is 24 times as heavy as a bike. The motorcycle weighs 1,329 kilograms less than a car. The car weighs 1,521 kilograms. How many kilograms does the bike weigh?

3. The school librarian has $9,050 to spend on new carpet and chairs for the library. The library is 42 feet long and 37 feet wide. He buys carpet that costs $4 for each square foot. How much money does the librarian have to spend on chairs?

4. A load of bricks is twice as heavy as a load of wood. The total weight of 4 loads of bricks and 4 loads of wood is 768 kilograms. What is the total weight of 17 loads of wood?

5. A driver earns $17 each hour. He earns a total of $1,224 in 4 weeks. A gardener works twice as many hours as the driver and earns $21 each hour. How much more money does the gardener earn than the driver in 4 weeks?

6. Each fish tank at the pet store holds 662 liters of water. There are 9 tanks of goldfish and 4 tanks of angelfish. The aquarium at the zoo holds 78 times as many liters of water as all the tanks at the pet store. How many more liters of water does the aquarium hold than the fish tanks?

Name

Use the Read–Draw–Write process to solve the problem.

Date

Sasha builds a fence around part of her yard. The three sides of the fence measure 88 feet, 32 feet, and 48 feet. The fence comes in pieces that are 8 feet long. Each piece costs $48. How much does the fence cost?

Credits

Great Minds® has made every effort to obtain permission for the reprinting of all copyrighted material. If any owner of copyrighted material is not acknowledged herein, please contact Great Minds for proper acknowledgment in all future editions and reprints of this module.

All United States currency images Courtesy the United States Mint and the National Numismatic Collection, National Museum of American History.

Cover, Wassily Kandinsky (1866–1944), Thirteen Rectangles, 1930. Oil on cardboard, 70 x 60 cm. Musee des Beaux-Arts, Nantes, France. © 2020 Artists Rights Society (ARS), New York. Image credit: © RMN-Grand Palais/Art Resource, NY.; page 47, Brovko Serhii/Shutterstock.com; All other images are the property of Great Minds.

For a complete list of credits, visit http://eurmath.link/media-credits.

Acknowledgments

Kelly Alsup, Adam Baker, Agnes P. Bannigan, Reshma P Bell, Joseph T. Brennan, Dawn Burns, Amanda H. Carter, David Choukalas, Mary Christensen-Cooper, Cheri DeBusk, Lauren DelFavero, Jill Diniz, Mary Drayer, Karen Eckberg, Melissa Elias, Danielle A Esposito, Janice Fan, Scott Farrar, Kelli Ferko, Ryan Galloway, Krysta Gibbs, January Gordon, Torrie K. Guzzetta, Kimberly Hager, Karen Hall, Eddie Hampton, Andrea Hart, Stefanie Hassan, Tiffany Hill, Christine Hopkinson, Rachel Hylton, Travis Jones, Laura Khalil, Raena King, Jennifer Koepp Neeley, Emily Koesters, Liz Krisher, Leticia Lemus, Marie Libassi-Behr, Courtney Lowe, Sonia Mabry, Bobbe Maier, Ben McCarty, Maureen McNamara Jones, Pat Mohr, Bruce Myers, Marya Myers, Kati O’Neill, Darion Pack, Geoff Patterson, Lillian Patterson, Victoria Peacock, Maximilian Peiler-Burrows, Brian Petras, April Picard, Marlene Pineda, DesLey V. Plaisance, Lora Podgorny, Janae Pritchett, Elizabeth Re, Meri Robie-Craven, Deborah Schluben, Michael Short, Erika Silva, Jessica Sims, Heidi Strate, Theresa Streeter, James Tanton, Cathy Terwilliger, Rafael Vélez, Allison Witcraft, Jackie Wolford, Caroline Yang, Jill Zintsmaster Trevor Barnes, Brianna Bemel, Lisa Buckley, Adam Cardais, Christina Cooper, Natasha Curtis, Jessica Dahl, Brandon Dawley, Delsena Draper, Sandy Engelman, Tamara Estrada, Soudea Forbes, Jen Forbus, Reba Frederics, Liz Gabbard, Diana Ghazzawi, Lisa Giddens-White, Laurie Gonsoulin, Nathan Hall, Cassie Hart, Marcela Hernandez, Rachel Hirsh, Abbi Hoerst, Libby Howard, Amy Kanjuka, Ashley Kelley, Lisa King, Sarah Kopec, Drew Krepp, Crystal Love, Maya Márquez, Siena Mazero, Cindy Medici, Ivonne Mercado, Sandra Mercado, Brian Methe, Patricia Mickelberry, Mary-Lise Nazaire, Corinne Newbegin, Max Oosterbaan, Tamara Otto, Christine Palmtag, Andy Peterson, Lizette Porras, Karen Rollhauser, Neela Roy, Gina Schenck, Amy Schoon, Aaron Shields, Leigh Sterten, Mary Sudul, Lisa Sweeney, Samuel Weyand, Dave White, Charmaine Whitman, Nicole Williams, Glenda Wisenburn-Burke, Howard Yaffe

Share Your Thinking

Talking Tool

I know . . . .

I did it this way because . . . .

The answer is because . . . .

My drawing shows . . . .

Agree or Disagree

I agree because . . . .

That is true because . . . .

I disagree because . . . .

That is not true because . . . .

Do you agree or disagree with ? Why?

Ask for Reasoning

Why did you . . . ?

Can you explain . . . ?

What can we do first?

How is related to ?

Say It Again

I heard you say . . . . said . . . .

Another way to say that is . . . .

What does that mean?

Thinking Tool

When I solve a problem or work on a task, I ask myself

Before

Have I done something like this before?

What strategy will I use?

Do I need any tools?

During

Is my strategy working?

Should I try something else?

Does this make sense?

After

At the end of each class, I ask myself

What worked well?

What will I do differently next time?

What did I learn?

What do I have a question about?

MATH IS EVERYWHERE

Do you want to compare how fast you and your friends can run?

Or estimate how many bees are in a hive?

Or calculate your batting average?

Math lies behind so many of life’s wonders, puzzles, and plans. From ancient times to today, we have used math to construct pyramids, sail the seas, build skyscrapers—and even send spacecraft to Mars.

Fueled by your curiosity to understand the world, math will propel you down any path you choose.

Ready to get started?

ISBN 979-8-89012-142-4

Module 1

Place Value Concepts for Multiplication and Division with Whole Numbers

Module 2

Addition and Subtraction with Fractions

Module 3

Multiplication and Division with Fractions

Module 4

Place Value Concepts for Decimal Operations

Module 5

Addition and Multiplication with Area and Volume

Module 6

Foundations to Geometry in the Coordinate Plane

What does this painting have to do with math?

Color and music fascinated Wassily Kandinsky, an abstract painter and trained musician in piano and cello. Some of his paintings appear to be “composed” in a way that helps us see the art as a musical composition. In math, we compose and decompose numbers to help us become more familiar with the number system. When you look at a number, can you see the parts that make up the total?

On the cover

Thirteen Rectangles, 1930

Wassily Kandinsky, Russian, 1866–1944

Oil on cardboard

Musée des Beaux-Arts, Nantes, France

Wassily Kandinsky (1866–1944), Thirteen Rectangles, 1930. Oil on cardboard, 70 x 60 cm. Musée des Beaux-Arts, Nantes, France. © 2020 Artists Rights Society (ARS), New York. Image credit: © RMN-Grand Palais/Art Resource, NY

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