A Story of Units® Fractions Are Numbers
Module 1 ▸ Place Value Concepts for Multiplication and Division with Whole Numbers
Student
Fractions Are Numbers ▸ 5 APPLY
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®
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 27 26 25 24 23 ISBN 978-1-64497-660-9
Multiplication of Whole Numbers
Multiply two- and three-digit numbers by two-digit numbers by using the distributive property.
1 Copyright © Great Minds PBC 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
Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Multiply
familiar methods. Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Multiply two- and three-digit
by
Lesson 10 59 Multiply three- and four-digit numbers by three-digit numbers
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.
by using
numbers
two-digit numbers by using the standard algorithm.
by using the standard algorithm.
Copyright © Great Minds PBC 2 5 ▸ M1 EUREKA MATH2 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
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.
10 as a factor
Key Terms
10 × 10 × 10 = 1,000 Factors “10 to the third power”
Product
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.
103 Exponent Exponential Form
When multiplying by 10, digits shift to the left. When dividing by 10, digits shift to the right.
1
1 liter = 1,000 milliliters
1
= 1,000 grams
1 kiloliter = 1,000 liters
Students use powers of 10 to understand relationships between metric units and to solve problems.
Copyright © Great Minds PBC 3 Module 1 Topic A
ten thousands (10,000) thousands (1,000) hundreds (100) tens (10) ones (1) ÷ 10 ÷ 10 ÷ 10 100,000 1 10 100 1,000 10,000 × 10 × 10 × 10 × 10 × 10 × 10
kilometer, meter, centimeter, millimeter 1 meter
centimeters
meters longest shortest kilogram, gram, centigram, milligram heaviest lightest 1 gram =
centigrams
= 100
1 meter = 1,000 millimeters 1 kilometer = 1,000
100
1 gram = 1,000 milligrams
kiloliter, liter, centiliter, milliliter greatest capacity least capacity
kilogram
liter
= 100 centiliters
centigram centiliter exponent exponential form kiloliter milligram millimeter power
of 10
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.
• “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?”
Copyright © Great Minds PBC 4 FAMILY MATH ▸ Module 1 ▸ Topic A 5 ▸ M1 ▸ TA EUREKA MATH2
Name 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.
EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 1 Copyright © Great Minds PBC 5
1
Use the place value chart to complete problems 3–5. 6 5 5 7 8 4 7
millions hundred thousands ten thousands thousands hundreds tens ones
3. The 6 in 6,557,847 represents 6,000,000 .
4. 500,000 ÷ 10 = 50,000
5. 7 thousands is 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 the tape diagram for box A to show the total of 72 paper clips. I need to find the number of paper clips in box B, so I label it with a question mark.
72 A B ?
I divide to find the number of paper clips in box B.
5 ▸ M1 ▸ TA ▸ Lesson 1 EUREKA MATH2 Copyright © Great Minds PBC 6 PRACTICE PARTNER
7. Complete the table.
I draw a number line to help me.
I know 1 yd = 3 ft, so I multiply each number of yards by 3.
Copyright © Great Minds PBC 7 PRACTICE PARTNER EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 1
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 yd 1 ft
1 yd 2 yd 3 yd 4 yd 5 yd 6 yd 7 yd
2 × 3 = 6 3 × 3 = 9 5 × 3 = 15 7 × 3 = 21 1 yd 3 ft 6 ft 9 ft 1 2 ft 1 5 ft 1 8 ft 2 1 ft 2 yd 3 yd 4 yd 5 yd 6 yd 7 yd
1. Use the place value chart to complete the statement and equation. millions hundred thousands ten thousands thousands 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.
millions hundred thousands ten thousands thousands hundreds tens ones
÷ 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 9,000,000 .
4. 800,000 ÷ 10 = 80,000
5. 3 thousands is 1,000 times as much as 3 ones.
Copyright © Great Minds PBC 9
EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 1 1
Name Date
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.
Copyright © Great Minds PBC 10 PRACTICE 5 ▸ M1 ▸ TA ▸ Lesson 1 EUREKA MATH2
Yards Feet 4 12 8 24 9 27 12 36