EM2 APPLY Level 5 Module 1 Lesson 1 Thin Slice

A Story of Units®

5 Fractions Are Numbers

APPLY

Module 1 ▸ Place Value Concepts for Multiplication and Division with Whole Numbers

Student

A Story of Units®

Fractions Are Numbers ▸ 5 APPLY

Module

1 2 3 4 5 6

Place Value Concepts for Multiplication and Division with Whole Numbers

Addition and Subtraction with Fractions

Multiplication and Division with Fractions

Place Value Concepts for Decimal Operations

Addition and Multiplication with Area and Volume

Foundations to Geometry in the Coordinate Plane

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Printed in the USA B-Print 1 2 3 4 5 6 7 8 9 10 XXX 27 26 25 24 23 ISBN 978-1-64497-660-9

EUREKA MATH2 5 ▸ M1

Contents Place Value Concepts for Multiplication and Division with Whole Numbers Topic A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Place Value Understanding for Whole Numbers Lesson 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Relate adjacent place value units by using place value understanding.

Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Multiply and divide by 10, 100, and 1,000 and

identify patterns in the products and quotients.

Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Use exponents to multiply and divide by powers of 10.

Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Estimate products and quotients by using powers of 10 and their multiples.

Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Convert measurements and describe relationships between metric units.

Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Solve multi-step word problems by using metric measurement conversion.

Topic B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Multiplication of Whole Numbers Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Multiply by using familiar methods.

Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Multiply two- and three-digit numbers by two-digit numbers by using the distributive property.

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Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Multiply two- and three-digit numbers by two-digit numbers by using the standard algorithm.

Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Multiply three- and four-digit numbers by three-digit numbers by using the standard algorithm.

Lesson 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Multiply two multi-digit numbers by using the standard algorithm.

Topic C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Division of Whole Numbers Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Divide two- and three-digit numbers by multiples of 10.

Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Divide two-digit numbers by two-digit numbers in problems that result in one-digit quotients.

Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Divide three-digit numbers by two-digit numbers in problems that result in one-digit quotients.

Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Divide three-digit numbers by two-digit numbers in problems that result in two-digit quotients.

Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Divide four-digit numbers by two-digit numbers.

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Topic D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Multi-Step Problems with Whole Numbers Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Write, interpret, and compare numerical expressions.

Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Create and solve real-world problems for given numerical expressions.

Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Solve multi-step word problems involving multiplication and division.

Lesson 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Solve multi-step word problems involving the four operations.

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 129

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Module 1 Topic A

FAMILY MATH Place Value Understanding for Whole Numbers Dear Family, Your student is learning to multiply and divide by 10, 100, and 1,000. They begin by representing multiplication and division on the place value chart. Students recognize patterns in products and quotients, which prepares them to calculate mentally. They write repeated multiplication by using exponents and explore how powers of 10 relate to place value and metric units. Your student solves problems by converting between metric measurements and describing the relationships between the units.

ten thousands hundreds thousands (1,000) (100) (10,000)

tens (10)

Key Terms centigram

kiloliter

centiliter

milligram

exponent

millimeter

exponential form

power of 10

10 as a factor

ones (1)

10 × 10 × 10 = 1,000

÷ 10 ÷ 10

Factors

÷ 10

100,000

10,000

1,000

100

× 10 × 10

× 10

10

1

× 10

× 10

“10 to the third power”

103

Exponential Form

× 10

The place value chart shows each place value unit is 10 times as much as the unit to its right. This understanding can be applied to multiplying and dividing by powers of 10.

Exponent

When multiplying by 10, digits shift to the left.

When dividing by 10, digits shift to the right.

kilometer, meter, centimeter, millimeter

kilogram, gram, centigram, milligram

longest

heaviest

shortest

Product

lightest

kiloliter, liter, centiliter, milliliter greatest capacity

least capacity

1 meter = 100 centimeters

1 gram = 100 centigrams

1 liter = 100 centiliters

1 meter = 1,000 millimeters

1 gram = 1,000 milligrams

1 liter = 1,000 milliliters

1 kilometer = 1,000 meters

1 kilogram = 1,000 grams

1 kiloliter = 1,000 liters

Students use powers of 10 to understand relationships between metric units and to solve problems.

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At-Home Activity Would You Rather?

Help your student practice converting metric units by asking “Would you rather” questions.

For example, you could ask some of the following questions, replacing the pizza, chocolate milk, or scooter with your student’s favorite items. As they answer each question, have them explain why.

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“Would you rather eat 100 grams of pizza or 10,000 centigrams of pizza?”

•

“Would you rather drink 1 liter of chocolate milk or 1,000 milliliters of chocolate milk?”

•

“Would you rather ride on a scooter for 5 kilometers or ride on a scooter for 500,000 centimeters?”

FA M I LY M AT H ▸ Module 1 ▸ Topic A

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 1

Name

1

Date

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

hundred thousands

ten thousands

thousands

hundreds

tens

ones

× 10

4 ten thousands is 10 times as much as 4 thousands .

40,000 = 10 ×

4,000 Units on the place value chart follow a pattern. Beginning with the ones and moving left, each adjacent unit to the left is 10 times as much as the unit to the right.

The value of 4 in the ten thousands place is 10 times as much as the value of 4 in the thousands place.

2. Use the place value chart to complete the equation. millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones

÷ 10

90,000 ÷ 10 =

9,000

Each adjacent unit to the right is 10 times as small as the unit to the left.

The value of 9 in the thousands place is 10 times as small as the value of 9 in the ten thousands place.

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Use the place value chart to complete problems 3–5. millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones

6

5

5

7

8

4

7

3. The 6 in 6,557,847 represents 4.

500,000

5. 7 thousands is

6,000,000 .

÷ 10 = 50,000 1,000

times as much as 7 ones.

The 6 is in the millions place. The value of the 6 is 6,000,000.

The value of 5 in the ten thousands place is 10 times as small as the value of 5 in the hundred thousands place.

Thousands is 3 place value units to the left of ones. Each place value unit to the left is 10 times as much as the unit to the right. So 7 thousands is 10 × 10 × 10, or 1,000, times as much as 7 ones.

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

6. Box A has 72 paper clips in it. Box A has 4 times as many paper clips as box B. How many paper clips does box B have?

72 ÷ 4 = 18 Box B has 18 paper clips.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw two tape diagrams: one to represent box A and one to represent box B. I draw the tape diagram for box A to show box A has 4 times as many paper clips as box B. I label A the tape diagram for box A to show the total of 72 paper clips.

B I need to find the number of paper clips in box B, so I label it with a question mark.

72

?

I divide to find the number of paper clips in box B. 6

P R ACT I C E PA R T N E R

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 1

7. Complete the table.

Yards

Feet

2

6

3

9

5

15

7

21

1 yard = 3 feet 1 yard is 3 times as long as 1 foot.

1 yd = 3 × 1 ft

1 ft

1 yd I draw a number line to help me.

1 yd

2 yd 3 yd 4 yd 5 yd 6 yd 7 yd

I know 1 yd = 3 ft, so I multiply each number of yards by 3.

2× 3=6 3× 3=9 5 × 3 = 15

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7 × 3 = 21

1 yd

2 yd 3 yd 4 yd 5 yd 6 yd 7 yd

3 ft

6 ft

9 ft 12 ft 15 ft 18 ft 21 ft

P R ACT I C E PA R T N E R

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 1

Name

1

Date

1. Use the place value chart to complete the statement and equation. hundred thousands

millions

ten thousands

thousands

hundreds

tens

ones

hundreds

tens

ones

× 10

6 ten thousands is 10 times as much as 6 thousands .

60,000 = 10 ×

6,000

2. Use the place value chart to complete the equation. hundred thousands

millions

ten thousands

thousands

÷ 10

50,000 ÷ 10 =

5,000

Use the place value chart to complete problems 3–5. millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones

9

8

8

3

4

7

3

3. The 9 in 9,883,473 represents 4.

800,000

5. 3 thousands is Copyright © Great Minds PBC

9,000,000 .

÷ 10 = 80,000 1,000

times as much as 3 ones.

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

6. Mrs. Chan has 96 bottles of paint. She has 8 times as many bottles of paint as paintbrushes. How many paintbrushes does Mrs. Chan have?

96 ÷ 8 = 12 Mrs. Chan has 12 paintbrushes.

7. Complete the table.

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P R ACT I C E

Yards

Feet

4

12

8

24

9

27

12

36

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