A Story of Units® Fractional Units
Module 1 ▸ Place Value Concepts for Addition and Subtraction
Student
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 APPLY
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 978-1-64497-654-8
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.
1 Copyright © Great Minds PBC EUREKA MATH2 4 ▸ M1 Contents Place Value Concepts for Addition and Subtraction Topic A 3 Multiplication as Multiplicative Comparison Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Interpret multiplication as multiplicative comparison. Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Solve multiplicative comparison problems with unknowns in various positions. Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Describe relationships between measurements by using multiplicative comparison. Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Represent the composition of larger units of money by using multiplicative comparison. Topic B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Place Value and Comparison within 1,000,000 Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Organize, count, and represent
Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
a collection of objects.
Lesson 7 41
Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Write numbers to 1,000,000 in standard form and word form. Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Compare numbers within 1,000,000 using >, =, and < Topic C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Rounding Multi-Digit Whole Numbers Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Name numbers by using place value understanding. Lesson 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Find 1, 10, and 100 thousand more than and less than a given number. Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Round to the nearest thousand. Lesson 13 77 Round to the nearest ten thousand and hundred thousand. Lesson 14 83 Round multi-digit numbers to any place. Lesson 15 89 Apply estimation to real-world situations by using rounding.
Subtract by using the standard algorithm, decomposing larger units up to 3 times.
Copyright © Great Minds PBC 2 4 ▸ M1 EUREKA MATH2 Topic D 95 Multi-Digit Whole Number Addition and Subtraction Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Add by using the standard algorithm. Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Solve multi-step addition word problems by using the standard algorithm. Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Subtract by
the standard
decomposing larger units once. Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Lesson 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
decomposing larger units
times. Lesson 21 125 Solve two-step word problems by using addition and subtraction. Lesson 22 131 Solve multi-step word problems by using addition and subtraction. Topic E 135 Metric Measurement Conversion Tables Lesson 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Express metric measurements of length in terms of smaller units. Lesson 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Express metric measurements of mass and liquid volume in terms of smaller units. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 151
using
algorithm,
Subtract by using the standard algorithm,
multiple
Multiplication as Multiplicative Comparison
Dear Family,
Key Term times as many
In previous grades, your student learned to compare numbers and use addition or subtraction to describe how many more or how many less. Now, your student uses their prior knowledge of multiplication and division to compare numbers and describe their relationship as times as many. Your student explores a variety of patterns and models such as blocks, tape diagrams, and money, to explain what it means to say times as many. They find an unknown quantity when two quantities are compared by writing multiplication and division equations.
dollars dimes pennies 10 ¢
There are 4 times as many hexagons in figure F as there are in figure E.
There are 10 times as many cents in a dime as there are in 1 penny.
Comparison
as heavy times as much times as much times as tall times as long times as wide times as far
Amy’s tower is 3 times as tall as Gabe’s tower. 15 = 3 × 5
The comparison phrase times as many can be adjusted to match different contexts.
Copyright © Great Minds PBC 3 Module 1 Topic A FAMILY MATH
Figure E
Figure F
6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 CM 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 CM
Measurement weight liquid volume capacity height length width distance times
Amy’s Tower Gabe’s Tower
At-Home Activity
Use Comparison Language
Help your student practice describing multiplication and division equations by using times as many language. You may find it useful to use the comparison language provided in the chart of measurements.
• Use two different-size containers that can hold water, such as a small measuring cup and a large water glass. Have your student fill the larger container by using water from the smaller container. Discuss the amount of liquid each container holds. Help your student by asking a question such as, “What can we say about how much more liquid the larger container holds?” Then say, “We can say that the larger container holds about ____ times as much liquid as the smaller container.” Repeat with other different-size containers like a pot and a bowl, or a pitcher and a cup.
• Get two dry spaghetti noodles. Break off a small piece, about 1 inch, of the first noodle. Leave the second noodle whole. Use the piece of noodle to measure the whole noodle from one end to the other by moving the piece along the whole noodle with no gaps or overlaps. Then compare the length of the piece to the whole noodle by using times as long language. Use a comparison statement such as, “The whole noodle is about ____ times as long as the piece of noodle.” Encourage your student to describe about how many times as long one noodle is than the other.
• Consider starting conversations with your student such as, “I noticed it took you 2 minutes to brush your teeth and 10 minutes to eat your breakfast. How many times as long did it take you to eat your breakfast than it did to brush your teeth?”
Copyright © Great Minds PBC 4 FAMILY MATH ▸ Module 1 ▸ Topic A 4 ▸ M1 ▸ TA EUREKA MATH2
I can add to see that the total of 6 units of 8 is 48.
The tape diagram shows that 48 is 6 times as many as 8.
EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1 Copyright © Great Minds PBC 5 Name Date 1 Complete the statement and equation to match the tape diagram. 1. 8 48 48 is 6 times as many as 8. 48 = 6 × 8
. 8 48 8 8 8 8 8 8 8
I see 1 unit of 8 and 6 units of 8
2. Pablo eats 7 grapes. Luke eats 3 times as many grapes as Pablo. How many grapes does Luke eat?
3 × 7 = 21
Luke eats 21 grapes.
I can draw a tape diagram to represent the problem.
I draw 1 unit of 7 for Pablo.
I draw 3 units of 7 for Luke because he eats
3 times as many grapes as Pablo. 7
I can multiply to find the total number of grapes Luke eats.
4 ▸ M1 ▸ TA ▸ Lesson 1 EUREKA MATH2 Copyright © Great Minds PBC 6 PRACTICE PARTNER
? Pablo Luke
REMEMBER
Add or subtract.
3. 714 − 235 = 479
I can write the problem vertically.
I start by making my units ready to subtract. I can rename 1 ten as 10 ones. I add the 10 ones to 4 ones.
I also have to rename the hundreds, 1 hundred as 10 tens.
Now I am ready to subtract.
4. 252 + 388 = 640
To find 252 + 388, I can decompose each number into hundreds, tens, and ones.
252 + 388 200 50 2 300 80 8 I add like units.
200 + 300 = 500
50 + 80 = 130
2 + 8 = 10
Then I add.
500 + 130 + 10 = 640
EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1 Copyright © Great Minds PBC 7 PRACTICE PARTNER
2 - 3 5 7 1 4 2 - 3 5 7 1 4 0 14 2 - 3 5 7 1 4 6 0 10 14 2 - 3 7 1 4 5 6 0 10 14 4 7 9
Draw a tape diagram to represent the statement. Then complete the equation.
3. 21 is 3 times as many as 7.
4. Adam reads 6 pages in his book. Gabe reads 4 times as many pages in his book as Adam. How many pages does Gabe read?
EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1 Copyright © Great Minds PBC 9 Name Date 1 Complete the statement and equation to match the tape diagram.
36 9 9 9 9 9 36 is times as many as 9. = × 9
6 42 42 is times as many as 6 = × 6
1.
2.
21 =
× 7
REMEMBER
5. Add or subtract.
a. 613 – 164 =
b. 497 + 213 =
4 ▸ M1 ▸ TA ▸ Lesson 1 EUREKA MATH2 Copyright © Great Minds PBC 10 PRACTICE