4 A Story of Units® Fractional Units
LEARN ▸ Module 1 ▸ Place Value Concepts for Addition and Subtraction
Student
What does this painting have to do with math?
American abstract painter Frank Stella used a compass to make brightly colored curved shapes in this painting. Each square in this grid includes an arc that is part of a design of semicircles that look like rainbows. When Stella placed these rainbow patterns together, they formed circles. What fraction of a circle is shown in each square?
On the cover
Tahkt-I-Sulayman Variation II, 1969
Frank Stella, American, born 1936 Acrylic on canvas Minneapolis Institute of Art, Minneapolis, MN, USA
Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Art, MN. Gift of Bruce B. Dayton/Bridgeman Images. © 2020 Frank Stella/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 978-1-64497-099-7
Module 1 Place Value Concepts for Addition and Subtraction
2 Place Value Concepts for Multiplication and Division
3 Multiplication and Division of Multi-Digit Numbers
4 Foundations for Fraction Operations
5 Place Value Concepts for Decimal Fractions
6 Angle Measurements and Plane Figures
A Story of Units® Fractional
4
Units ▸
LEARN
Contents
Place Value Concepts for Addition and Subtraction
Write numbers to 1,000,000 in standard form and word form.
Topic C
Rounding Multi-Digit Whole
Describe relationships between measurements by using multiplicative comparison.
Represent the composition of larger units of money by using multiplicative comparison.
Topic B
Place Value and Comparison Within 1,000,000
Organize, count, and represent a collection of objects.
Demonstrate that a digit represents 10 times the value of what it represents in the place to its right.
Write numbers to 1,000,000 in unit form and expanded form by using place value structure.
Copyright © Great Minds PBC 2 4 ▸ M1 EUREKA MATH2
Multiplicative Comparison Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Interpret multiplication as multiplicative comparison. Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Topic A Multiplication as
Solve multiplicative comparison problems with unknowns in various positions.
Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Lesson
7 61
Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Compare numbers within 1,000,000 by using >, =, and <
Numbers Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Name numbers by using place value understanding. Lesson 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Find 1, 10, and 100 thousand more than and less than a given number. Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Round to the nearest thousand. Lesson 13 111 Round to the nearest ten thousand and hundred thousand. Lesson 14 117 Round multi-digit numbers to any place. Lesson 15 129 Apply estimation to real-world situations by using rounding.
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Multi-Digit Whole Number Addition and Subtraction Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Add by using the standard algorithm. Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Solve multi-step addition word problems by using the standard algorithm. Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Subtract by using the standard algorithm, decomposing larger units once. Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Subtract by using the standard algorithm, decomposing larger units up to 3 times. Lesson 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Subtract by using the standard algorithm, decomposing larger units multiple times. Lesson 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Solve two-step word problems by using addition and subtraction. Lesson 22 181 Solve multi-step word problems by using addition and subtraction. Topic
Metric Measurement Conversion Tables Lesson 23 189 Express metric measurements of length in terms of smaller units. Lesson 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Express metric measurements of mass and liquid volume in terms of smaller units. Credits 203 Acknowledgments 204
Topic D
E
Write a rule for each pattern.
EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1 Copyright © Great Minds PBC 5 1
1.
Figure A
Figure B
Figure C
Date
Figure
D Rule: Name
Rule:
Draw sticky notes to represent 4 times as many. Then fill in the blanks.
Partner B
Partner B has times as many sticky notes as partner A. is times as many as .
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2.
Figure M
Figure L
Figure N
Figure O
3. Partner A
=×
EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1 Copyright © Great Minds PBC 7 LESSON Use the pictures to fill in the blanks. 4. Partner A Partner B 4 4444 =× is times as many as 5. Partner A Partner B 7 7777 =× is times as many as . 6. Partner A Partner B 9 9999 =× is times as many as
7. Draw a tape diagram to represent 36 is 4 times as many as 9. Then complete the equation.
Use the tape diagram to fill in the blanks. Then complete the equation and statement. 8.
=× is times as many as .
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=×
30 6
=× is times as many as .
=× is times as many as .
EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1 Copyright © Great Minds PBC 9 LESSON 9. 32 8
10. 42 7
1. Liz draws circles by using this rule: Multiply the number of circles by 2
a. How many circles should Liz draw for figure D? How do you know?
b. Complete the statements and equation to match the figures.
There are times as many circles in figure B than in figure A.
is times as many as 5 =×5
There are times as many circles in figure C than in figure B.
is times as many as 10 =×10
EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1 Copyright © Great Minds PBC 11 1
Figure A
Figure B
Figure C
Figure D
Date
Name
Complete the statement and equation to match the tape diagram.
20 is times as many as 5.
is times as many as 2.
is times as many as .
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© Great Minds PBC 12 PROBLEM SET
Copyright
2. 20 5 5555
=×5 3. 6 2 2
=× 4. 60 10
=×
Draw tape diagrams to represent each statement. Then complete the equation.
5. 12 is 3 times as many as 4
12=×4
6. 28 is 4 times as many as 7
28=×
EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1 Copyright © Great Minds PBC 13 PROBLEM SET
7. 5 times as many as 3 is 15.
8. 6 times as many as 8 is 48
9. There are 9 tables in the cafeteria. There are 8 times as many chairs as tables. How many chairs are in the cafeteria?
4 ▸ M1 ▸ TA ▸ Lesson 1 EUREKA MATH2 Copyright © Great Minds PBC 14 PROBLEM SET
×=
×=
Draw a model to represent the statement. Then complete the equation.
15 is 3 times as many as 5.
15=×
EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1 Copyright
Great Minds PBC 15 1
©
Name
Date
