EM2 LEARN Level 5 Module 1 Lesson 1 Thin Slice by General

5 A Story of Units® Fractions Are Numbers

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

Student

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.

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

Great Minds® is the creator of Eureka Math® , Wit & Wisdom® , Alexandria Plan™, and PhD Science® Published by Great Minds PBC. greatminds.org © 2021 Great Minds PBC. All rights reserved. No part of this work may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying or information storage and retrieval systems—without written permission from the copyright holder. Printed in the USA B-Print 1 2 3 4 5 6 7 8 9 10 XXX 25 24 23 22 21 ISBN 978-1-64497-113-0

Fractions Are Numbers ▸ 5 LEARN

Module 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 Addition and Multiplication with Area and Volume

6 Foundations to Geometry in the Coordinate Plane

A Story of Units®

Place Value Concepts for Multiplication and Division with Whole Numbers

Topic A

Topic B Multiplication of Whole Numbers

Topic C

Contents

Value Understanding for Whole Numbers Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Multiply and divide

and

the products and quotients. Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Use exponents to multiply and divide by powers of 10. Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Estimate products and quotients by using powers of 10 and their multiples. Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Convert measurements and describe relationships between metric units. Lesson 6 53 Solve multi-step word problems by using metric measurement conversion.

Place

Relate adjacent place value units by using place value understanding.

by 10, 100, and 1,000

identify patterns in

Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Multiply by using familiar methods. Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Multiply two- and three-digit numbers by two-digit numbers by using the distributive property. Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Multiply two- and three-digit numbers by two-digit numbers by using the standard algorithm. Lesson 10 87 Multiply three- and four-digit numbers by three-digit numbers by using the standard algorithm. Lesson 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Multiply two multi-digit numbers by using the standard algorithm.

Division of Whole Numbers Lesson 12 99 Divide two- and three-digit numbers by multiples of 10. Lesson 13 107 Divide two-digit numbers by two-digit numbers in problems that result in one-digit quotients. Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Divide three-digit numbers by two-digit numbers in problems that result in one-digit quotients. Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Divide three-digit numbers by two-digit numbers in problems that result in two-digit quotients. Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Divide four-digit numbers by two-digit numbers.

Topic D

Multi-Step Problems

Numbers Lesson 17 145 Write, interpret, and compare numerical expressions. Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Create and solve real-world problems for given numerical expressions. Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Solve multi-step word problems involving multiplication and division. Lesson 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Solve multi-step word problems involving the four operations. Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 7 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 178

with Whole

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 1 ▸ Place Value Chart to Millions Copyright © Great Minds PBC 5 Standard Form: Expanded Form: millions (1,000,000) hundred thousands (100,000) ten thousands (10,000) thousands (1,000) hundreds (100) tens (10) ones (1)

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?

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

millions hundred thousands ten thousands thousandshundreds tensones

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

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 thousandshundreds tensones ×10 millions hundred thousands ten thousands thousandshundreds tensones ÷10

×10

Name Date

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

9,000

9,000 ÷ 10 =

9 millions ÷ 10 = 9 millions

900

The 9 in 3,429,015 represents . 9 hundred thousands is 10 times as much as

hundred thousands. 9 ten thousands 9 hundred thousands is 10 times as much as .

millions hundred thousands ten thousands thousandshundreds tensones ÷10

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 1 Copyright © Great Minds PBC 11 PROBLEM SET Use the place value chart to complete problems 6–12. millions hundred thousands ten thousands thousandshundredstensones 7 4 4 5 3 8 5

7,445,385 = (7,000,000) + (400,000) + ( ) + ( ) + ( ) + ( ) + ( )

The 7 in 7,445,385 represents .

4 hundred thousands is 10 times as much as

400,000 = 10 × 10. ÷ 10 = 40,000 11. 5 thousands is times as much as 5 ones. 12. 5,000 = × 5

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 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.

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 2 ▸ Place Value Chart to Millions Copyright © Great Minds PBC 15 millions (1,000,000) hundred thousands (100,000) ten thousands (10,000) thousands (1,000) hundreds (100) tens (10) ones (1)