Student
LEARN ▸ Module 1 ▸ Multiplication and Division with Units of 2, 3, 4, 5, and 10
3 A Story of Units® Units of Any Number
What does this painting have to do with math?
Swiss-born artist Paul Klee was interested in using color to express emotion. Here he created a grid, or array, of 35 colorful squares arranged in 5 rows and 7 columns. We will learn how an array helps us understand a larger shape by looking at the smaller shapes inside. Learning more about arrays will help us notice patterns and structure— an important skill for multiplication and division.
On the cover
Farbtafel “qu 1,” 1930
Paul Klee, Swiss, 1879–1940
Pastel on paste paint on paper, mounted on cardboard Kunstmuseum Basel, Basel, Switzerland
Paul Klee (1879–1940), Farbtafel “qu 1” (Colour Table “Qu 1” ), 1930, 71. Pastel on coloured paste on paper on cardboard, 37.3 x 46.8 cm. Kunstmuseum Basel, Kupferstichkabinett, Schenkung der Klee-Gesellschaft, Bern. © 2020 Artists Rights Society (ARS), New York.
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 978-1-64497-093-5
A Story of Units® Units of Any Number ▸ 3 LEARN Module 1 Multiplication and Division with Units of 2, 3, 4, 5, and 10 2 Place Value Concepts Through Metric Measurement 3 Multiplication and Division with Units of 0, 1, 6, 7, 8, and 9 4 Multiplication and Area
Fractions as Numbers
Geometry, Measurement, and Data
5
6
Topic C
Topic B
Topic D Two Interpretations of Division
Copyright © Great Minds PBC 2 3 ▸ M1 EUREKA MATH2 Contents Multiplication and Division with Units of 2 , 3 , 4 , 5 , and 10 Topic A Conceptual Understanding of Multiplication Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Organize, count, and represent a collection of objects. Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Interpret equal groups as multiplication. Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Relate multiplication to the array model. Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Interpret the meaning of factors as number of groups or number in each group. Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Represent and solve multiplication word problems by using drawings and equations.
Conceptual Understanding of Division Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Explore measurement and partitive division by modeling concretely and drawing. Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Model measurement and partitive division by drawing equal groups. Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Model measurement and partitive division by drawing arrays. Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Represent and solve division word problems using drawings and equations.
Properties of Multiplication Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Demonstrate the commutative property of multiplication using a unit of 2 and the array model. Lesson 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Demonstrate the commutative property of multiplication using a unit of 4 and the array model. Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Demonstrate the distributive property using a unit of 4 Lesson 13 107 Demonstrate the commutative property of multiplication using a unit of 3 and the array model. Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Demonstrate the distributive property using units of 2, 3, 4, 5, and 10.
Lesson 15 123 Model division as an unknown factor problem. Lesson 16 133 Model the quotient as the number of groups using units of 2, 3, 4, 5, and 10. Lesson 17 141 Model the quotient as the size of each group using units of 2, 3, 4, 5, and 10. Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Represent and solve measurement and partitive division word problems.
3 Copyright © Great Minds PBC EUREKA MATH2 3 ▸ M1 Topic E Application of Multiplication and Division Concepts Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 63 Use the distributive property to break apart multiplication problems into known facts. Lesson 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 73 Use the distributive property to break apart division problems into known facts. Lesson 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Compose and decompose arrays to create expressions with three factors. Lesson 22 1 87 Represent and solve two-step word problems using the properties of multiplication. Lesson 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 99 Represent and solve two-step word problems using drawings and equations. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . 207
For this counting collection, I am partners with .
We are counting .
We estimate there are about of them.
This is how we organized and counted the collection:
We counted altogether. An equation that describes how we found the total is
Copyright © Great Minds PBC 5 EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 1
Name 1
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?
3 ▸ M1 ▸ TA ▸ Lesson 1 EUREKA MATH2 Copyright © Great Minds PBC 6 LESSON
Name
1. What unit did you use to count your collection? Explain why you chose that unit.
2. If you counted your collection again, would you choose the same unit? Explain.
EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 1 Copyright © Great Minds PBC 7 1