EM2 Tennessee Learn | Grade 5 Module 6 by Great Minds

A Story of Units®

Fractions Are Numbers LEARN ▸ Module 6 ▸ Foundations to Geometry in the Coordinate Plane

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because . . . .

My drawing shows . . . . Agree or Disagree

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Ask for Reasoning

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related to

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Content Terms

Place a sticky note here and add content terms.

? Why?

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. Musée des Beaux-Arts, Nantes, France. © 2020 Artists Rights Society (ARS), New York. Image credit: © RMN-Grand Palais/Art Resource, NY

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Great Minds® is the creator of Eureka Math®, Wit & Wisdom®, Alexandria Plan™, and PhD Science®. Published by Great Minds PBC. greatminds.org Copyright © 2022 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 1 2 3 4 5 6 7 8 9 10 XXX 25 24 23 22 21 ISBN 978-1-63898-519-8

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A Story of Units®

Fractions Are Numbers ▸ 5 LEARN

Module

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1 2 3 4 5 6

Place Value Concepts for Multiplication and Division with Whole Numbers

Addition and Subtraction with Fractions

Multiplication and Division with Fractions

Place Value Concepts for Decimal Operations

Addition and Multiplication with Area and Volume

Foundations to Geometry in the Coordinate Plane

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EUREKA MATH2 Tennessee Edition

5 ▸ M6

Contents Foundations to Geometry in the Coordinate Plane Topic A

Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Coordinate Systems

Identify mixed-operation relationships between corresponding terms in number patterns. (Optional)

Lesson 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Construct a coordinate system on a line.

Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Construct a coordinate system in a plane. Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Identify and plot points by using ordered pairs. Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Describe the distance and direction between points in the coordinate plane.

Topic B Patterns in the Coordinate Plane Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Identify properties of horizontal and vertical lines.

Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Use properties of horizontal and vertical lines to solve problems.

Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Generate number patterns to form ordered pairs.

Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Identify addition and subtraction relationships between corresponding terms in number patterns.

Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Identify multiplication and division relationships between corresponding terms in number patterns.

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Topic C Solve Mathematical Problems in the Coordinate Plane Lesson 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Draw lines in the coordinate plane and identify points on the lines.

Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Graph and classify quadrilaterals in the coordinate plane.

Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Draw symmetric figures in the coordinate plane. Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Solve mathematical problems with rectangles in the coordinate plane.

Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Use the coordinate plane to reason about perimeters and areas of rectangles.

Topic D Solve Real-World Problems with the Coordinate Plane Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Interpret graphs that represent real-world situations.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6

Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Plot data in the coordinate plane and analyze relationships.

Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Interpret line graphs. Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Reason about visual patterns by using tables and graphs. (Optional) Lesson 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 Reason about patterns in real-world situations.

Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 218

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EUREKA MATH2 Tennessee Edition

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5 ▸ M6 ▸ TA ▸ Lesson 1 ▸ Slanted Line

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M6 ▸ TA ▸ Lesson 1

Date

1. Use the line to create a coordinate system.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 1

Name

Date

Use the number line to complete problems 1–3. 1. The coordinate of point A is

8 C

7 6

2. Point

has a coordinate of 4.

4 3 2

3. The distance from point A to point C is

units.

1 0

For problems 4 and 5, plot the point on the number line. 4. Plot point A so its distance from 0 is 2 units.

5. Plot point R so its distance from 0 is _5 units. 2

6 0

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 1

6. Use the number line to complete parts (a)–(c).

a. Plot and label point P at 3. b. Plot and label point R at 0.

c. Plot and label point S so that it is _5 units farther from 0 than point P. What is the coordinate 2

of point S?

7. Plot and label point L so that its distance from 0 is 125 units.

100

8. Plot point T so that it is _2 units farther from 3

0 than point S.

150

1 S

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 1

9. Construct a coordinate system on the line. Choose an interval length that allows each of the points described to be plotted. Plot and label the points.

a. Point A is located 3 units from 0.

  b. Point B is located at _ c. Point C is located 1 _1 3

Point D is located _2 units closer to 0 than point A. 3

10. Blake asks Sasha to plot a point, P, that is 3 units from point M. Sasha says the coordinate of point P could be 1 or 7. How can Blake make the directions clear so that Sasha knows exactly where to plot point P? Explain.

M 0

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 1

Name

Date

Construct a coordinate system on the line. Choose an interval length that allows each of the points described to be plotted. Plot and label the points.

a. Point A is located 1 unit from 0.

b. Point B is located at 2 _1 . 4

c. d.

  Point C is located _ Point D is located _1 unit closer to 0 than point B.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 2 ▸ Number Line

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 2 ▸ Coordinate System in a Plane

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M6 ▸ TA ▸ Lesson 2

Date

1. Use the coordinate plane to complete the problem. a. Label the axes x and y. b. Label the origin as 0. c. From the origin, label every grid line on both axes with a whole number from 1 to 10. d. Plot and label point P with x-coordinate 4 and y-coordinate 3. e. Plot and label point Q at (3, 4). f.

Plot and label point R located 9 units to the right of the y-axis and 7 units above the x-axis.

g. Plot and label point S at (7, 9).

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 2

2. Complete the table for the points plotted in problem 1. Point

x-Coordinate

y-Coordinate

Ordered Pair

(x, y)

P Q R S

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 2

Name

Date

Use the graph to complete problems 1–3. 1. Label the origin and the x- and y-axes.

10 9 8 7 6 5 4 3 2

1 0

2. Consider point M. a. The x-coordinate of point M is

b. The y-coordinate of point M is

c. The ordered pair that identifies the location of point M is (

3. What is the ordered pair that identifies the location of the origin?

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 2

4. Use the graph to complete parts (a)–(d). y 7 6

5 4

1 0

a. Write the name of the point with the given coordinates. Point

Ordered Pair

x-Coordinate

y-Coordinate

(1, 2)

(2, 1)

(4, 3)

(6, 1)

b. Point D is

units to the right of the y-axis.

c. Point D is

units above the x-axis.

(x, y)

d. Write the ordered pair that represents point D.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 2

5. Use the graph to complete parts (a)–(c). y 7

6 5

4 3 2 1 0

a. Complete the table for points E and F. Point

x-Coordinate

y-Coordinate

Ordered Pair

(x, y)

E F b. Plot a point at (5, 1). Label the point G. c. Plot a point at (4, 2). Label the point H.

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 2

6. Consider the ordered pair (6, 2). a. Construct a coordinate plane and plot a point at (6, 2).

b. Explain how to locate the point from the origin.

7. Yuna makes a mistake and says the point plotted at (6, 2) is located 2 units to the right of the y-axis and 6 units above the x-axis. Write a statement to correct Yuna’s mistake.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 2

Name

Date

Use the graph to complete parts (a)–(c). y 10 9 8

7 6 5

4 3 2 1 0

a. Complete the table for points A and B. Point

x-Coordinate

y-Coordinate

Ordered Pair

(x, y)

A B b. Plot a point at (5, 3). Label the point C. c. Plot a point at the origin. Label the point D.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 3 ▸ Grid with Points

B D

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 3 ▸ Grid with Points

Coordinate Plane A y 8 7 6 5 4 3 2 1 0

Coordinate Plane B y

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M6 ▸ TA ▸ Lesson 3

Date

1. Write the coordinates and ordered pairs for points P, Q, R, S, and T in the table. Point

x-Coordinate y-Coordinate

Ordered Pair

y 3

Q R

S T

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 3

Name

Date

1. Use the graph to complete parts (a)–(e). y 100 90 80 70

60 50

40 30 20

10 0

a. The ordered pair (35, 15) describes the location of point b. The ordered pair that describes the location of point K is ( c. Point

100

. ,

is located at the origin.

d. Which two points have an x-coordinate of 0? e. Which two points are located on the x-axis?

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 3

2. Use the graph to complete parts (a) and (b). y 80 70 60 50

40 30

10 0

a. Write the x-coordinate, y-coordinate, and ordered pair for each point in the table. Point

x-Coordinate

y-Coordinate

Ordered Pair

L M N b. Lacy says the ordered pair for point J is (31, 11). Is Lacy correct? Explain.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 3

3. Use the coordinate plane to complete parts (a)–(e). y 10 9 8 7 6 5 4 3 2 1 0

a. Plot and label the following points. Point E (0, 4)

Point F (4, 0)

1 1 , 2   _ Point H (_ ) 2

b. Point H is

units above the x-axis.

c. Point H is

units to the right of the y-axis.

d. The interval length of the x-axis is

units.

e. The interval length of the y-axis is

units.

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Point I  

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 3

Use the grid to complete problems 4 and 5.

4. Draw a coordinate plane. Include a scale that will allow the following points to be plotted. Plot and label the points. Point J (18, 10) Point L (4, 11) Point M (18, 6) 5. Describe the similarities and differences between the locations of points M and J.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 3

Name

Date

Use the graph to complete parts (a)–(f). y 5

B 4

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 3

a. Write the coordinates and ordered pair for each point in the table.

x-Coordinate

Point

y-Coordinate

Ordered Pair

(x, y)

A B b. Plot point C at (_1 , 2  _1). 2

c. Point C is

units to the right of the y-axis.

d. Plot point D at (4  _1 , 2  _3). 4

e. Plot point E at (3  _1 , 0). 2

The interval length of the x-axis is is

units.

EXIT TICKET

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units. The interval length of the y-axis

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M6 ▸ TA ▸ Lesson 4

Date

1. Use the coordinate plane to answer each question. a. Kayla is at the ticket stand and wants to see the lions. How many units away from the ticket stand is the lion exhibit and in which direction?

y 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2

b. Lacy eats lunch at the snack bar. Which animal exhibit is 4 units away from Lacy?

1 0

10 11 12 13 14 15 16

c. Which exhibit is 4 units to the right and 1 unit down from the restrooms?

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 4

Name

Date

1. The graph shows the screen of a video game in which a rabbit must hop to various garden locations to find treats. Use this graph to complete parts (a)–(g).

y 18 16 14

Cabbage

Radish

Cucumber

Watermelon

8 6

Lettuce

Carrot

Squash

Apple 2

Rabbit

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 4

a. Complete the table with the ordered pair for each treat. Treat

Ordered Pair

Apple Carrot Cucumber Lettuce Radish Squash b. Estimate the coordinates of the cabbage and write the ordered pair for the location of the cabbage. c. If a rabbit starts at the origin, describe the movements he should make to get to the cabbage. units right and then

units up

d. If a rabbit starts at the origin, travels 8 units right, and then travels 2 units up, which treat will he find? e. Describe the movements a rabbit would need to make to get from the squash to the carrot. units right and then f.

units up

Which treat is exactly 12 units closer to the x-axis than the radish?

g. The farmer drops a banana on the ground. The banana is located closer to the x-axis than the lettuce and has the same x-coordinate as the apple. Write one possible ordered pair to represent the location of the banana.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 4

2. The coordinate plane shows the locations of landmarks in Atlanta, Georgia. Each unit represents

1 mile. Use this graph to complete parts (a)–(d).

a. Write the ordered pair for each location. y

Location Morehouse College

Ordered Pair

(0, 0)

E S

Waterworks Park

Waterworks Park Oakland Cemetery Martin Luther King Jr.’s Birthplace Georgia Institute of Technology

Georgia Institute of Technology

Martin Luther King Jr’s Birthplace

Morehouse College 1

Oakland Cemetery 2

b. Which landmark is directly north of Oakland Cemetery? c. How are the coordinates of the Oakland Cemetery and the coordinates of Martin Luther King Jr.’s birthplace the same and different? d. Describe how to get from Martin Luther King Jr.’s birthplace to the Georgia Institute of Technology by moving horizontally and then vertically.

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TA ▸ Lesson 4

Name

Date

The coordinate plane shows the locations of different places in Lisa’s town. a. Write the ordered pair for each location. Location Lisa’s House

Ordered Pair

Train Station

Baseball Field City Hall

Baseball Field

School

Post Office

E S

City Hall

Train Station

5 4 3 2

School

1 Lisa’s 0

House 1

b. Lisa travels 2 units east and 4 units north from her house. Where does Lisa go? c. Describe how to travel from the baseball field to the school.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 5 ▸ Coordinate Plane with Points

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 5 ▸ Ordered Pairs and Grid

Version 1 Part A Use the grid to construct a labeled coordinate plane. Then plot the points listed. Ordered Pairs: (4, 7), (4, 10), (4, 0), (4, 1), (4, 4)

Part B Write the ordered pairs for three points that lie on a horizontal line. Use different points from the ones listed above. Write the ordered pairs for three points that lie on a vertical line. Use different points from the ones listed above. © Great Minds PBC •

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 5 ▸ Ordered Pairs and Grid

Version 2 Part A Use the grid to construct a labeled coordinate plane and plot the points listed. Ordered Pairs: (2, 7), (4, 7), (0, 7), (10, 7), (9, 7)

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 5

Name

Date

1. Line � is shown in the coordinate plane. y 10 9 8 7

6 5 4 3 2 1 0

a. Draw a line in the coordinate plane that is parallel to the x-axis but a greater distance from the x-axis than line �. Label this line �. Write the ordered pairs for three points on line �. b. Draw a line in the coordinate plane that is parallel to the x-axis but a shorter distance from the x-axis than line �. Label this line �. Write the ordered pairs for three points on line �.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 5

2. The graph shows point F. y 22 20 18 16 14 12 10

8 6 4 2 0

8 10 12 14 16 18 20 22

a. Plot a point that would lie on the same vertical line as point F. Name the new point E and record its ordered pair on the coordinate plane.

⟷

b. Draw EF .

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 5

Name

Date

1. Use the graph to complete parts (a)–(e).

10 9 8 7 6 5 4 3 2 1 0

Points on Line �

( 2 , 5)

(7, 3 )

( 2 , 8)

(9, 3 )

( 2 , 3)

(6, 3 )

1 2 3 4 5 6 7 8 9 10

a. Highlight the coordinates that are the same for line �. b. Is line � horizontal or vertical?

c. Highlight the coordinates that are the same for line �.

d. Is line � horizontal or vertical?

e. Line � is parallel to the

-axis and perpendicular to the

-axis.

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 5

2. Use the graph to complete parts (a)–(f). y 50 45 40 35

30 25 20 15

10 5 0

a. Write the ordered pairs for points G and H in the table. Point

Ordered Pair

G H ⟷

b. Write the ordered pair for a different point that also lies on GH .

⟷

c. Is GH horizontal or vertical? d. Draw a line in the coordinate plane that is parallel to the y-axis but is a greater distance from ⟷ the y-axis than GH . Label this line 𝓅. Write the ordered pairs for three points on the line.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 5

e. Draw a line in the coordinate plane that is parallel to the y-axis but a shorter distance from ⟷ the y-axis than GH . Label this line 𝓁.

Write the ordered pairs for three points on line 𝓁.

3. The ordered pairs for four points are shown. Do the points lie on a horizontal line, a vertical line, or neither? How do you know?

(45, 2) (45, 60) (45, 15) (45, 34)

4. The ordered pairs for four points are shown. Do the points lie on a horizontal line, a vertical line, or neither? How do you know?

(4, 0) (0, 0) (0, 9)

1_ (39 2 , 0)

EM2_0506SE_B_L05_problem_set.indd 53

PROBLEM SET

12/3/2021 10:28:46 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 5

5. The points (2, 5) and (7, 5) lie on line 𝒶. a. Is line 𝒶 horizontal or vertical? b. Line 𝒶 is parallel to the

c. Line 𝒶 is perpendicular to the

-axis. -axis.

d. Write the ordered pair for another point that lies on line 𝒶.

e. Describe the distance between line 𝒶 and the x-axis. Explain how you know.

PROBLEM SET

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12/3/2021 10:28:46 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 5

Name

Date

Use the graph to complete parts (a)–(d). y 10 9 8 7 6 5

3 2 1 0

a. Plot a point that lies on the same vertical line as point B. Name the new point C. Record its ordered pair beside it on the coordinate plane. b. What do the coordinates for point B and point C have in common? c. Plot a point that lies on the same horizontal line as point A. Name the new point D. Record its ordered pair beside it on the coordinate plane. d. What do the coordinates for point A and point D have in common?

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12/3/2021 10:28:33 AM

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 6 ▸ Coordinate Plane with Points

J G 0

C 1

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 6

Name

Date

1. Use the coordinate plane to complete parts (a)–(h). a. Draw and label point A at (8, 1). b. Draw a line that is perpendicular to the x-axis through point A. Label the line 𝓂.

c. Plot a point on line 𝓂 that is 6 units farther from the x-axis than point A. Label this point B and write its ordered pair next to it. d. Plot a point on line 𝓂 that is halfway between points A and B. Label this point C and write its ordered pair next to it.

e. Draw line 𝓃 so that it is 2 units from the x-axis and 𝓃 ⊥ 𝓂.

Point E is on line 𝓃. It is 2 units from the y-axis. Plot point E and write its ordered pair next to it.

g. Draw line 𝓁 so that it passes through point E and 𝓁 ǁ 𝓂.

12 11 10 9 8 7 6 5 4 3 2 1 0

9 10 11 12

h. Point F is on line 𝓁 and is farther from the x-axis than point E. Plot point F and write its ordered pair next to it.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 6

2. The graph shows line �.

y 12 11 10 9 8 7 6 5 4 3 2 1 0

1 2 3 4 5 6 7 8 9 10 11 12

a. Use red to color the region of the plane in which all x-coordinates are less than 2. b. Line � is a vertical line that intersects the x-axis at the point (8, 0). Draw and label line � on the graph.

c. Use blue to shade the region of the plane where points are more than 8 units from the y-axis.

d. Use green to shade the region of the plane with points that have x-coordinates that are greater than 2 and less than 8.

LESSON

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 6

Name

Date

⟷ 1. Indicate whether each statement about DE  is true or false. y

Statement

⟷ Each point on DE has the same x-coordinate. ⟷ Each point on DE has the same y-coordinate. ⟷ All points on DE  are collinear.

11 10

9 8 7 6

⟷ Each point on    

5 4

⟷ Each point on DE  is the same distance from the y-axis.

2 1 0

True False

10 11 12

x ⟷

⟷

DE  is vertical.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 6

2. Use the graph to complete parts (a)–(d).

y 12 11 10

9 8 7 6 5 4 3

2 1 0

10 11 12

a. Draw a line that is parallel to line � through point M. Label the line �.

b. Plot a point that is 4 units farther from the x-axis than point M and has the same x-coordinate as point M. Label the point N.

c. Draw a line through points M and N. Label the line �.

d. Fill in each blank with ǁ or ⊥ to make the statement true.

� �

�

� �

�

PROBLEM SET

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 6

3. Use the coordinate plane to complete parts (a)–(d). y

6 5 4 3 2 1 0

a. Draw a line, 𝓃, that is parallel to the y-axis and 4 2 units from the y-axis.

b. Write the ordered pair for the point on line 𝓃 that is 4 units from the x-axis.

c. Lightly shade the region of the plane where points are greater than 4 2 units from the y-axis. d. Circle the ordered pairs for points that appear in the shaded region.

(5, 4 _2 )  1

EM2_0506SE_B_L06_problem_set.indd 63

(48 , 5)

(12, 3)

PROBLEM SET

12/3/2021 10:32:09 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 6

4. Use the coordinate plane to complete parts (a)–(e).

y 4 3.6 3.2 2.8 2.4 2 1.6 1.2 0.8 0.4 0

0.4 0.8 1.2 1.6

2.4 2.8 3.2 3.6

a. Draw a line, 𝒶, that is parallel to the x-axis and 0.8 units from the x-axis.

b. Draw a line, 𝒹, that passes through the point (1.2, 2.4) and 𝒹 ǁ 𝒶.

c. Lightly shade the region between line 𝒹 and line 𝒶. Complete the statement. All points in the shaded region have a y-coordinate greater than

but less than

d. Is point R(6, 1.8) in the shaded region? Explain. e. What is the distance between line 𝒶 and line 𝒹?

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 6

Name

Date

1. Use the graph to complete parts (a)–(d). y

a. Draw a vertical line through point A. b. Plot a point on the vertical line that is 2 units farther from the x-axis than point A. Label this point B and write the ordered pair next to it. ⟷ c. Is AB parallel or perpendicular to the y-axis?

10 9 8 7 6 5

⟷ d. Is AB parallel or perpendicular to line �?

3 2 1 0

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 6

2. Use the graph of line � to complete parts (a)–(b). y

7 6 5

4 3 2 1 0

a. Lightly shade the region of the plane where points are less than 3 2 units from the x-axis.

_1 _3

b. Noah says that the point (3 4 , 2 4 ) is located in the shaded region because the

y-coordinate is less than 3 _2 . Is Noah correct? Explain. 1

EXIT TICKET

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 7

Name

Date

1. The table shows the first three terms in pattern A and in pattern B. Pattern A

Pattern B

2 _12

a. Complete each pattern in the table. b. What will be the number in pattern B when the number in pattern A is 18? c. What will be the number in pattern A when the number in pattern B is 17  _2 ? 1

2. Leo and Sasha create number patterns. Leo’s pattern: Start at 6 and multiply by 4. Sasha’s pattern: Start at 85 and subtract 6. Record the first five terms of Leo’s pattern and of Sasha’s pattern in the table. Leo’s Pattern Sasha’s Pattern

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 7

3. Use the table to complete parts (a)–(c). a. Use the rules to complete the patterns. b. Write the ordered pair for each pair of corresponding terms by writing the number from pattern A as the x-coordinate and the number from pattern B as the y-coordinate. Pattern A Add 2

Pattern B Add 3

Ordered Pair

c. Plot the points in the coordinate plane. y 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

LESSON

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 7

Name

Date

1. Use pattern N to complete parts (a) and (b).

Pattern N

  _2 1

a. Write the rule for pattern N.

b. Complete the table.

2. Use the table to complete parts (a)–(c). a. The rule for pattern Y is add 4. The rule for pattern Z

Pattern Y

Pattern Z

3  _2

is subtract 2 . Complete the table.

b. What is the number in pattern Z when the number in pattern Y is 24?

c. What is the number in pattern Y when the number in pattern Z is 0?

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12/3/2021 10:36:30 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 7

3. Use the table of ordered pairs to complete parts (a)–(e). a. Write the rule for pattern A.

Pattern A

Pattern B

c. Use the numbers from pattern A and pattern B to create ordered pairs and complete the table.

d. Plot the ordered pairs from the table in the coordinate plane.

b. Write the rule for pattern B.

Ordered Pair

(x, y)

y 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

9 10 11 12 13 14 15

e. Describe the movement needed to get from point (6, 6) to (9, 7).

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 7

4. Use the table to complete parts (a)–(c). Pattern P

Pattern Q

Ordered Pair

(2, 0)

3_2 1

(3 _2  , 3)

(5, 6)

6_2

(6 _2 , 9)

(x, y)

a. Every time a number in pattern P increases by 1 2 , what happens to the numbers in pattern Q?

b. If patterns P and Q continue, what will be the next ordered pair on the table?

c. If patterns P and Q continue, would the ordered pair (11, 18) be part of the pattern? How do you know?

EM2_0506SE_B_L07_problem_set.indd 71

PROBLEM SET

12/3/2021 10:36:31 AM

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 7

Name

Date

Consider the table shown. Pattern A

Pattern B

The rule for pattern A is add 1 2 . The rule for pattern B is add 3 . a. Complete the table by using the rules for pattern A and pattern B. b. What is the number in pattern B when the number in pattern A is 15 ?

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12/3/2021 10:36:02 AM

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12/3/2021 10:36:02 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 8

Name

Date

1. The rule for the x-coordinate is add 1.5. The rule for the y-coordinate is add 1.5. a. Complete the table.

x-Coordinate

y-Coordinate

Ordered Pair

(1, 5)

b. Plot the four ordered pairs in the coordinate plane. y 10 9 8 7 6 5 4 3 2 1 0

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12/3/2021 10:39:30 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 8

2. Each y-coordinate is 1.5 more than its corresponding x-coordinate. a. Complete the table.

x-Coordinate

Calculation

y-Coordinate

Ordered Pair

0 + 1.5 = 1.5

1.5

(0, 1.5)

3 6 9 b. Plot the four ordered pairs in the coordinate plane. y 10 9 8 7 6 5 4 3 2 1 0

LESSON

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12/3/2021 10:39:30 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 8

3. Use the graph to complete parts (a)–(f). y 5 4 3 2 1

a. Describe the movement from one point to the next.

b. What is the rule for the x-coordinate?

c. What is the rule for the y-coordinate?

d. Use the rules for the coordinates to plot the next three points in the coordinate plane. What are the ordered pairs for the points?

EM2_0506SE_B_L08_classwork.indd 77

LESSON

12/3/2021 10:39:30 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 8

e. Fill in the blanks to describe the relationship between the x- and y-coordinates. The f.

-coordinates are

the corresponding

-coordinates.

When the x-coordinate is 10, what is the corresponding y-coordinate? Show how you know.

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 8

Name

Date

1. Use the table and graph to complete parts (a)–(c). •

Rule for the x-coordinate: Add 4

•

Rule for the y-coordinate: Add 4 y

x-Coordinate y-Coordinate

Ordered Pair

(2, 3)

(6, 7)

(10, 11)

(14, 15)

16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

a. To get from point (2, 3) to point (6, 7), move right up

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

units and then move

units.

b. When the x-coordinate is 18, the corresponding y-coordinate is

c. When the y-coordinate is 22, the corresponding x-coordinate is

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12/3/2021 10:40:53 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 8

2. Use the table to complete parts (a)–(e).

x-Coordinate

y-Coordinate

Ordered Pair

(0, 2)

1 1_

3 _1

(12 , 3 2 )

(3, 5)

4 1_

6 1_

(4 2 , 6 2 )

_1 1_

a. Plot points that represent the four ordered pairs in the coordinate plane. y 9 8 7 6 5 4 3 2 1 0

b. What is the rule for the x-coordinate?

PROBLEM SET

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 8

c. What is the rule for the y-coordinate?

d. Describe the movement from point (3, 5) to point (4 _1 , 6 _1 ). 2

e. Fill in the blanks to describe the relationship between the x- and y-coordinates. The

-coordinates are 2 more than the corresponding

-coordinates.

3. Use the graph to complete parts (a)–(g). y 4

EM2_0506SE_B_L08_problem_set.indd 81

PROBLEM SET

12/3/2021 10:40:54 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 8

a. Describe the movement from one point to the next.

b. What is the rule for the x-coordinate?

c. What is the rule for the y-coordinate?

d. Use the rules for the coordinates to plot the next three points in the coordinate plane. What are the ordered pairs for the points?

e. Fill in the blank to describe the relationship between the x- and y-coordinates. The y-coordinates are

the corresponding x-coordinates.

When the x-coordinate is 16 _1 , what is the corresponding y-coordinate? 2

g. When the y-coordinate is 16 _1 , what is the corresponding x-coordinate? 2

PROBLEM SET

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12/3/2021 10:40:54 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 8

Name

Date

Each y-coordinate is 5 more than its corresponding x-coordinate. a. Complete the table.

x-Coordinate

Calculation

y-Coordinate

Ordered Pair

1+5=6

(1, 6)

3 5 7 b. Plot the four ordered pairs in the coordinate plane. y 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

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9 10 11 12 13 14 15

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 8

c. What is the rule for the x-coordinate?

d. What is the rule for the y-coordinate?

e. When the x-coordinate is 15, what is the corresponding y-coordinate?

EXIT TICKET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 9

Name

Date

1. Consider the coordinates and ordered pairs in the table. a. Complete the table.

x-Coordinate

y-Coordinate

Ordered Pair

(1, 2)

(3, 6)

(5, 10)

b. Plot the six ordered pairs in the coordinate plane. y 22 20 18 16 14 12 10 8 6 4 2 0

EM2_0506SE_B_L09_classwork.indd 85

10 12 14 16 18 20 22

12/3/2021 10:41:14 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 9

c. Describe the movement from one point to the next.

2. Multiply each x-coordinate by 4 to get its corresponding y-coordinate. a. Complete the table.

x-Coordinate

Calculation

y-Coordinate

Ordered Pair

0×4=0

(0, 0)

 _4  1

 _2  1

_3  4

1 b. Plot the five ordered pairs in the coordinate plane. y

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 9

c. Describe the movement from one point to the next.

d. What is the rule for the x-coordinate?

e. What is the rule for the y-coordinate?

Fill in the blanks to describe the relationship between the x- and y-coordinates. The

-coordinates are

the corresponding

-coordinates.

g. When the x-coordinate is _7 , what is the corresponding y-coordinate? Show how you know. 2

h. When the y-coordinate is 20, what is the corresponding x-coordinate? Show how you know.

EM2_0506SE_B_L09_classwork.indd 87

LESSON

12/3/2021 10:41:15 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 9

3. Use the graph to complete parts (a)–(d). y 14 12 10 8 6 4 2 0

100

200

300

400

500

600

700

a. Use the rules for the coordinates to plot the next three points in the coordinate plane. What are the ordered pairs for the points?

b. Fill in the blanks to describe the relationship between the x- and y-coordinates. The

-coordinates are

the corresponding

LESSON

EM2_0506SE_B_L09_classwork.indd 88

-coordinates.

12/3/2021 10:41:15 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 9

c. What is the corresponding y-coordinate when the x-coordinate is 1,000? Show how you know.

d. What is the corresponding x-coordinate when the y-coordinate is 1,000? Show how you know.

EM2_0506SE_B_L09_classwork.indd 89

LESSON

12/3/2021 10:41:15 AM

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 9

Name

Date

1. Use the table and graph to complete parts (a)–(c). Rule: Add 1

Rule: Add 3

x-Coordinate y-Coordinate

Ordered Pair

10 8

(0, 0)

(1, 3)

(2, 6)

(3, 9)

7 6 4 2 1 0

a. To get from point (0, 0) to point (1, 3), move right move up

units.

c. When the y-coordinate is 15, the corresponding x-coordinate is

EM2_0506SE_B_L09_problem_set.indd 91

units and then

b. When the x-coordinate is 4, the corresponding y-coordinate is

. .

12/3/2021 10:41:51 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 9

2. Use the table and coordinate plane to complete parts (a)–(e).

x-Coordinate

y-Coordinate

Ordered Pair

(4, 2)

(8, 4)

(12, 6)

(16, 8)

a. Plot points that represent the four ordered pairs in the coordinate plane. y 16 14 12 10 8 6 4 2 0

b. What is the rule for the x-coordinate?

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 9

c. What is the rule for the y-coordinate?

d. Describe the movement to get from point (4, 2) to point (8, 4).

e. Fill in the blanks to describe the relationship between the x- and y-coordinates. The

-coordinates are _1 as much as the corresponding 2

-coordinates.

3. Use the graph to complete parts (a)–(f). y

A 0

EM2_0506SE_B_L09_problem_set.indd 93

1 2

PROBLEM SET

12/3/2021 10:41:51 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 9

a. Write the x- and y-coordinates and ordered pairs for points A, B, C, and D. Point

x-Coordinate

b. Every time _1 is added to an x-coordinate, 2

y-Coordinate

Ordered Pair

is added to the corresponding y-coordinate.

c. Describe the movement to get from point C to point D.

d. Describe the relationship between the x- and y-coordinates.

e. When the x-coordinate is 6, what is the corresponding y-coordinate?

When the y-coordinate is 16, what is the corresponding x-coordinate?

PROBLEM SET

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12/3/2021 10:41:52 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 9

Name

Date

Use the table to complete parts (a)–(e).

x-Coordinate

y-Coordinate

Ordered Pair

(4, 1)

(8, 2)

(12, 3)

(16, 4)

a. Plot the four ordered pairs in the coordinate plane. y 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 9

b. What is the rule for the x-coordinate?

c. What is the rule for the y-coordinate?

d. Describe the relationship between the x- and y-coordinates.

e. When the x-coordinate is 40, what is the corresponding y-coordinate?

EXIT TICKET

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12/3/2021 10:41:31 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ Sprint ▸ Two- and Three-Factor Expressions

Sprint Write the product. 1.

8×5

3×5×2

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12/4/2021 12:06:59 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ Sprint ▸ Two- and Three-Factor Expressions

Number Correct:

Write the product. 1.

6×1

23.

4×6

3×2×1

24.

6×8

3×3

25.

2×6×2

3×1×3

26.

3×8×2

4×4

27.

8×7

2×2×4

28.

9×6

6×5

29.

4×7×2

2×3×5

30.

3×6×3

9×5

31.

9×9

10.

3×3×5

32.

2×4

11.

5×4

33.

3×9×3

12.

5×2×2

34.

1×2×4

13.

6×6

35.

8 × 10

14.

6×2×3

36.

9 × 11

15.

7×6

37.

6 × 12

16.

7×3×2

38.

4 × 10 × 2

17.

8×8

39.

3 × 11 × 3

18.

8×2×4

40.

3 × 12 × 2

19.

9×8

41.

9 × 12

20.

9×4×2

42.

12 × 12

21.

10 × 9

43.

3 × 12 × 3

22.

10 × 3 × 3

44.

6 × 12 × 2

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12/3/2021 10:44:23 AM

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ Sprint ▸ Two- and Three-Factor Expressions

Number Correct: Improvement:

Write the product. 1.

4×1

23.

4×5

2×2×1

24.

6×7

3×3

25.

2×5×2

3×1×3

26.

3×7×2

4×3

27.

8×6

2×2×3

28.

9×5

6×4

29.

4×6×2

2×3×4

30.

3×5×3

9×4

31.

9×8

10.

3×3×4

32.

2×3

11.

4×4

33.

3×8×3

12.

4×2×2

34.

1×2×3

13.

5×6

35.

6 × 10

14.

5×2×3

36.

4 × 11

15.

6×6

37.

4 × 12

16.

6×3×2

38.

3 × 10 × 2

17.

7×8

39.

2 × 11 × 2

18.

7×2×4

40.

2 × 12 × 2

19.

8×8

41.

8 × 12

20.

8×4×2

42.

10 × 12

21.

9×9

43.

4 × 12 × 2

22.

9×3×3

44.

5 × 12 × 2

100

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 10

Name

Date

1. Use one color to plot points with the coordinates shown in table A. Use another color to plot points with the coordinates shown in table B. Table A

Table B

x-Coordinate

y-Coordinate

x-Coordinate

y-Coordinate

y 15 14 13 12 11 10 9

Color for Table A coordinates

Color for Table B coordinates

7 6 5 4 3 2 1 0

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 10

2. Complete the table.

x-Coordinate

Multiply by 3

Subtract 1

y-Coordinate

Ordered Pair

3×3=9

9−1=8

(3, 8)

5 7 9

102

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 10

Name

Date

1. Use the table to complete parts (a)–(c).

x-Coordinate

y-Coordinate

a. What is the rule for the x-coordinate?

b. What is the rule for the y-coordinate?

c. Fill in the blank to describe the relationship between the x- and y-coordinates. The y-coordinate is

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times as much as the corresponding x-coordinate.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 10

2. Use the table to complete parts (a) and (b). a. Complete the table.

x-Coordinate

Multiply by 3

Subtract 2

y-Coordinate

Ordered Pair

2×3=6

6−2=4

(2, 4)

4 6 8 b. When the x-coordinate is 9, what is the corresponding y-coordinate?

104

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 10

3. Use the graph to complete parts (a)–(c). y 15 14 13 12 11 10 9 8 7 6 5 4 3 2 E 1 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

a. Complete the table.

x-Coordinate

Multiply by 2

y-Coordinate

0×2=0

2×2=4

4×2=8

= 10

6 × 2 = 12

12 +

= 14

b. Describe the relationship between the x- and y-coordinates.

c. When the x-coordinate is 8, what is the corresponding y-coordinate?

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 10

4. Label each graph or table with the letter of the statement that correctly describes the relationship between the x- and y-coordinates. A. Multiply the x-coordinates by _1 to get the 2 corresponding y-coordinates.

B. Multiply the x-coordinates by _1 and then 2 add 2 to get the corresponding y-coordinates.

C. Multiply the x-coordinates by 2 and then subtract 1 to get the corresponding y-coordinates.

D. Add 2 to the x-coordinates to get the corresponding y-coordinates.

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

106

Coordinate

Ordered Pair

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Coordinate

Ordered Pair

(2, 1)

(2, 3)

(6, 3)

(6, 5)

(10, 5)

(10, 7)

(14, 7)

(14, 9)

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TB ▸ Lesson 10

Name

Date

Use the graph shown to complete parts (a)–(e). y 15 E 14 13 12 D 11 10 9 C 8 7 6 B 5 4 3 A 2 1 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

a. Complete the table. Point

x-Coordinate

y-Coordinate

Ordered Pair

A B C D E

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5 ▸ M6 ▸ TB ▸ Lesson 10

b. What is the rule for the x-coordinate?

c. What is the rule for the y-coordinate?

d. Describe the relationship between the x- and y-coordinates.

e. When the x-coordinate is 5, what is the corresponding y-coordinate?

108

EXIT TICKET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 11 ▸ Coordinate Planes A–D

9 10

1 1

9 10

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9 10

109

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 11

Name

Date

1. Use the graphs to complete parts (a)–(d). Use a straightedge to draw a line through the points in each coordinate plane in parts (a) and (b). a.

y 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10

b. 10 9 8 7 6 5 4 3 2 1 0

1 2 3 4 5 6 7 8 9 10

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 11

c. In both graphs, point C is located at (

d. Draw a line through point C that is different from the lines shown in parts (a) and (b).

y 10 9 8 7 6 5 4 3 2 1 0

112

1 2 3 4 5 6 7 8 9 10

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 11

2. Use the graph of point M to complete parts (a)–(d).

y 15 14 13 12 11 10 9 8 7 6 5 4 M 3 2 1 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

a. Point M is located at (1, 3). One possible relationship between the x- and y-coordinates of this point is that the y-coordinate is 2 more than the corresponding x-coordinate. Write three more ordered pairs with this relationship between the x- and y-coordinates.

b. Plot the points from part (a). Use a straightedge to draw a line through the points. c. Consider another line that passes through point M. Write a relationship between the x- and y-coordinates of points that are on the new line.

d. Write three more ordered pairs with the relationship you wrote in part (c). Plot these points. Use a straightedge to draw a line through the points.

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PROBLEM SET

113

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 11

3. Use the coordinate plane to complete parts (a)–(d). y 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

a. Plot points (1, 3) and (5, 15). Use a straightedge to draw a line through the points.

b. Each y-coordinate is 3 times as much as the corresponding x-coordinate for all points that lie on the line. Name two other points on the line.

c. Does the point (_2 , 2) lie on the line? How do you know? 3

114

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 11

d. Sort the following ordered pairs by writing them in the correct column of the table.

(3, 12)

(5, 15)

(9, 27)

(3, 0)

Points on the Line

EM2_0506SE_C_L11_problem_set.indd 115

(9, 3)

(1 3  , 4) 1

(1, 3)

(0, 3)

(7, 21)

Points Not on the Line

PROBLEM SET

115

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 11

Name

Date

Use the coordinate plane to complete parts (a)–(c). y 10 9 8 7 6 5 4 3 2 1 0

a. Plot the points (3, 1) and (8, 6) in the coordinate plane. b. Use a straightedge to draw a line through the points. c. Write ordered pairs for three other points that lie on the line.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 12

Name

Date

1. Use the graph to complete parts (a) and (b).

y 4

¯  is vertical and has a length of 1  _3  units. Use a straightedge a. Plot point Q so that PQ 4 to draw PQ̄  . What is the ordered pair for point Q?

¯  is horizontal and has a length of _1  unit. Use a straightedge to draw RS ¯  . b. Plot point S so that RS 2 What is the ordered pair for point S?

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119

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 12

2. Use the graph to complete parts (a)–(d).

y 10 9

8 7

5 4 3 2

1 1

a. What is the measure of ∠HIJ ?

⟶ b. Plot point N so that ∠MLN is a right angle. Draw LN  . What is the measure of ∠MLN ? ⟶ c. Plot point O so that ∠MLO is an obtuse angle. Draw LO  . What is the measure of ∠MLO ? ⟶ d. Plot point P so that ∠MLP is an acute angle. Draw LP  . What is the measure of ∠MLP ?

120

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 12

Name

Date

1. Use the coordinate plane to complete parts (a)–(c). y 7 6 5 4 3 2 1 0

a. Draw a horizontal line segment with a length of 4 units and one endpoint at (2, 4).

b. Write the ordered pair for the other endpoint.

c. All points on the line segment have the same

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-coordinate but different

-coordinates.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 12

⟶ 2. Use the graph of RC to complete parts (a)–(d). y 8 7 6 5

4 3

2 1 0

a. Plot point G so that ∠CRG is a right angle.

b. Plot point F so that ∠CRF is an obtuse angle. c. Plot point M so that ∠CRM is an acute angle. d. Explain how you know ∠CRM is an acute angle.

122

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 12

3. Use the coordinate plane to complete parts (a)–(e). y 10 9 8 7 6 5 4 3 2 1 0

a. Plot and label the following vertices: D(1  _1 , 2), E(1  _1 , 8), F(4, 8), G(4, 2). Connect the vertices to create polygon DEFG.

¯  ? Explain. b. Which side has the same length as DE

¯  ? c. Which sides are perpendicular to DG

d. Describe the angles of this polygon.

e. What is the most specific name for polygon DEFG?

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PROBLEM SET

123

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 12

4. Use the graph of polygon FGHI to complete parts (a)–(e). y 11 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

a. The length of FḠ  is

units.

b. The length of IH̄  is

units.

¯  is parallel to c. FG

d. Describe the angles of this polygon.

e. What is the most specific name for polygon FGHI?

124

PROBLEM SET

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12/3/2021 10:47:42 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 12

5. Use the coordinate plane to complete parts (a)–(e). y 100 90 80 70 60 50 40 30 20 10 0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

a. Plot and label the following vertices: L(110, 30), M(130, 90), N(50, 90), O(30, 30). Connect the vertices to create polygon LMNO.

¯  ? b. What is the length of NM

¯  equal to the length of NM ¯  ? Explain. c. Is the length of OL

d. Describe the angles of this polygon.

e. What is the most specific name for polygon LMNO?

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PROBLEM SET

125

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 12

Name

Date

Use the coordinate plane for parts (a)–(g). y 10 9 8 7 6 5 4 3 2 1 0

a. Plot the given points in the coordinate plane.

A(2, 2) B(2, 9) C(8, 9) D(5, 2) b. Connect the points to make a quadrilateral. c. Write one acute angle in the quadrilateral.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 12

d. Write one right angle in the quadrilateral.

e. Write one obtuse angle in the quadrilateral.

‾ ? What is the length of BC

g. Circle the most specific name for the quadrilateral.

128

kite

parallelogram

rectangle

rhombus

square

trapezoid

EXIT TICKET

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 13 ▸ Coordinate Plane

y 10

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129

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 13

Name

Date

Consider the figure shown in the coordinate plane. y 10 9 8 7 6 5 4 3

1 0

C 1

a. Create a figure that is symmetric across line 𝓂 by using the given points.

b. Describe how the x- and y-coordinates for points B, C, and D relate to the x- and y-coordinates for the points that are symmetric to points B, C, and D.

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131

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12/3/2021 10:48:47 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 14 ▸ Rectangle Vertices

Part A: Plot any two points in the coordinate plane that do not lie on the same horizontal or vertical line. y 10 9 8 7 6 5 4 3 2 1 0

9 10

Part B: Plot any two points in the coordinate plane that lie on the same vertical line. y 10 9 8 7 6 5 4 3 2 1 0

EM2_0506SE_C_L14_removable_rectangle_vertices.indd 133

9 10

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 14 ▸ Rectangle Vertices

Part C: Plot any two points in the coordinate plane that lie on the same horizontal line. Write a number between 1 and 5:

y 10 9 8 7 6 5 4 3 2 1 0

9 10

Part D: The segment shown is one side of a rectangle. Circle the ordered pair for any point that could be a vertex of the rectangle. y

(8, 2)

(8, 7)

(2, 8)

(15, 2)

(1, 2)

(0, 7)

(1, 7)

(2, 0)

(3 1_ , 2)

(12.1, 7)

10 9 8 7 6

3 2 1 0

134

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 14 ▸ Rectangle Vertices

Part E: A rectangle with a length of 5 units and a width of 3 units has one vertex at (4, 4) as shown. y 10 9 8 7 6 5 4 3 2 1 0

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135

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 14

Name

Date

1. Three of the vertices of a rectangle are A(2, 3), B(2, 8), and C(6, 8). y 10 9 8 7 6 5 4 3 2 1 0

9 10

a. Plot and label the three vertices in the coordinate plane. b. Determine the ordered pair for point D, the fourth vertex. c. Draw rectangle ABCD. d. Identify the ordered pair for a point on CD other than point C or point D.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 14

Name

Date

1. Rectangle MNOP is shown in the coordinate plane. y 10 9 8 7 6

5 4 3 2 1 0

a. Circle the ordered pairs for vertices of rectangle MNOP.

(5, 6)

(8, 5)

(8, 2)

(8, 6)

(3, 2)

(4, 2)

(3, 4)

(3, 6)

b. Points M and N have the same horizontal line.

-coordinate because they are on the same

c. Points N and O have the same

-coordinate because they are on the same vertical line.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 14

2. Points R, S, and T are three of the vertices of a rectangle. Plot the fourth vertex of the rectangle. Label the point U and write its ordered pair next to the point. y 10

9 8 7 6 5 4 3 2 1 0

140

PROBLEM SET

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S 1

T 3

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 14

3. Points A and C are opposite vertices of a rectangle. a. Plot the other two vertices of the rectangle. Label the points B and D. b. Draw rectangle ABCD. c. What are the coordinates of points B and D? y 10 9 8

7 6 5 4 3

2 1 0

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PROBLEM SET

141

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 14

4. WX of rectangle WXYZ is shown in the coordinate plane. The width of rectangle WXYZ is 2 units. Determine whether each ordered pair could be the location of a vertex of rectangle WXYZ. Write each ordered pair in the correct column of the table.

y 10 9 8 7

(9, 5)

(9, 6)

(2, 8)

(9, 9)

(2, 5)

(9, 8)

(2, 6)

(2, 9)

5 3

Possible Vertex of Rectangle WXYZ

Not a Possible Vertex of Rectangle WXYZ

2 1 0

142

PROBLEM SET

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9 10

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 14

5. Point H is plotted at (4, 5). a. Draw a rectangle with a length of 5 units and a width of 4 units. Use point H as one of the rectangle’s vertices. b. What are the coordinates of the three other vertices of your rectangle? y 10 9 8 7 6 5

4 3 2 1 0

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PROBLEM SET

143

12/3/2021 10:51:37 AM

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 14

Name

Date

The points A(2, 4) and C(6, 7) are two opposite vertices of a rectangle. a. Plot the four vertices of rectangle ABCD in the coordinate plane and draw the rectangle. y 10 9 8 7 6 5 4 3 2 1 0

b. Write the coordinates of point B and point D.

c. What are the length and width of rectangle ABCD ?

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145

12/3/2021 10:51:18 AM

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 15

Name

Date

1. Determine the perimeter of rectangle ABCD. y 9

7 6 5 4 3 2 1 0

2. Determine the perimeter of rectangle EFGH. y 45 40

35 30 25 20 15 10 5 0

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5 10 15 20 25 30 35 40 45

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 15

3. The graph shows one side of rectangle MNPQ.

y 8 7 6 5

4 3 2 1 0

a. Rectangle MNPQ has a perimeter of 16 units. Plot points P and Q. b. What are the ordered pairs for points P and Q?

148

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 15

4. Circle every rectangle that has an area of 36 square units. A.

y 10 9 8 7 6 5 4 3 2 1 0

1 2 3 4 5 6 7 8 9 10

20 18 16 14 12 10 8 6 4 2

1 0

20 18 16 14 12 10 8 6 4 2

33 30 27 24 21 18 15 12 9 6 3 3 6 9 12 15 18 21 24 27 30 33

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2 4 6 8 10 12 14 16 18 20

LESSON

149

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 15

5. Use the coordinate plane to answer parts (a)–(e). y 9 8 7 6 5 4 3 2 1 0

a. Plot and label the points S(2  , 3) and U(7, 8  2 ). b. Points S and U are two vertices of a rectangle. Locate, plot, and label the other two vertices of the rectangle, points T and V. What are the coordinates of points T and V?

c. What are the length and width of rectangle STUV?

d. What is the perimeter of rectangle STUV?

150

LESSON

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5 ▸ M6 ▸ TC ▸ Lesson 15

e. What is the area of rectangle STUV?

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LESSON

151

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 15

Name

Date

1. The graph shows rectangle MNOP.

¯ is a. The length of   MP

units.

¯ is b. The length of   PO

units.

¯ is c. The length of   ON

units.

¯ is d. The length of   NM

units.

e. The perimeter of rectangle MNOP is

units.

14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

O x

1 2 3 4 5 6 7 8 9 10 11 12 13 14

2. Rectangle EFGH and rectangle HIJK are each graphed in one of the coordinate planes shown. y

3.5

3 2.5

2 1.5

10 5

0.5 0

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

5 10 15 20 25 30 35 40 45 50 55 60

a. The interval length of the axes of the coordinate plane with rectangle HIJK is times as much as the interval length of the axes of the coordinate plane with rectangle EFGH. b. Which rectangle has a greater perimeter?

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EUREKA MATH2 Tennessee Edition

5 ▸ M6 ▸ TC ▸ Lesson 15

3. Use the coordinate plane to complete parts (a)–(c).

a. Plot points E(2   2 , 2), F(8, 2),

G(8, 6  _2 ), and H(2  _2 , 6  _2 ). 1

Use a straightedge to connect the points and create rectangle EFGH. b. What is the perimeter of rectangle EFGH?

10 9 8 7 6 5 4 3

c. What is the area of rectangle EFGH?

2 1 0

b. Draw rectangle QRST. c. What is the perimeter of rectangle QRST?

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

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4. The graph shows one side of rectangle QRST. a. Rectangle QRST has an area of 45 square units. Plot and label points S and T.

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5. Tara says the perimeter of rectangle WXYZ is 38 units. Adesh says the perimeter of rectangle WXYZ is 19 units. Who is correct? Explain.

5 ▸ M6 ▸ TC ▸ Lesson 15

y 8 7 6

5 4 3 2 1 0

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PROBLEM SET

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5 ▸ M6 ▸ TC ▸ Lesson 15

Name

Date

1. Rectangle ABCD is graphed in the coordinate plane. y 10 9 8 7

6 5 4 3 2 1 0

a. What is the perimeter of rectangle ABCD ?

b. What is the area of rectangle ABCD ?

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5 ▸ M6 ▸ TC ▸ Lesson 15

2. Rectangle RSTU is graphed in the coordinate plane. y 9 8 7

6 5 4 3 2 1 0

a. What is the perimeter of rectangle RSTU?

b. What is the area of rectangle RSTU?

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5 ▸ M6 ▸ TD ▸ Lesson 16 ▸ Equivalent Expressions Cards Set A

2÷3

2_ 4

3÷2

3÷3

1_ 13

2_ 3

3_ 2

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5 ▸ M6 ▸ TD ▸ Lesson 16 ▸ Equivalent Expressions Cards Set A

_4 3

_4 2

2÷4

4÷3

1_ 12

3_ 3

4÷2

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5 ▸ M6 ▸ TD ▸ Lesson 16

Name

Date

1. The graph shows the number of minutes Tara practiced piano each day in one week. a. How many minutes did Tara practice on day 1?

c. On which day did Tara practice for the most minutes?

Number of Minutes Spent Practicing Piano

b. On which day did Tara practice for 10 minutes?

d. How many more minutes did Tara practice on day 6 than on day 7?

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Tara’s Piano Practice

40 35 30 25 20 15 10 5 0

Day

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5 ▸ M6 ▸ TD ▸ Lesson 16

2. The graph shows the total number of miles Kelly drove after a given number of hours on a road trip. a. How many miles did Kelly drive in the first hour of her trip?

Kelly’s Road Trip

y 195 180

c. How many miles did Kelly drive between hours 3 and 4?

165 Total Distance (miles)

b. How many hours did it take Kelly to drive a total distance of 150 miles?

150 135 120 105 90 75 60 45 30

d. Kelly drove 180 miles in 5 hours. Plot a point to represent this information on the graph.

164

LESSON

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Hours

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5 ▸ M6 ▸ TD ▸ Lesson 16

Name

Date

1. Use the graph to complete parts (a)–(f). a. What story does this graph tell us about how many miles Leo runs each day?

Leo’s Daily Run

10 9

c. Which point on the graph represents the day that Leo runs the most miles? d. How many fewer miles does Leo run on day 2 than on day 1?

Number of Miles Run

b. On day 1, Leo runs 4 miles. Which point on the graph shows this information?

7 6 5 4 3 2

e. Which pairs of points represent days that Leo runs the same number of miles?

and

Day

and f.

Riley says that Leo runs a total of 2 miles during the week because the point (7, 2) represents him running a total of 2 miles in 7 days. Is Riley correct? Explain.

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5 ▸ M6 ▸ TD ▸ Lesson 16

2. Use the graph to complete parts (a)–(f). a. How much money did Blake earn for mowing the first lawn?

c. What are the coordinates of the point that represents how much money Blake earned after mowing 2 lawns? d. After mowing 7 lawns, Blake earned a total of $170. How much money did Blake earn for mowing the seventh lawn?

Total Amount Earned (dollars)

b. How many lawns did Blake mow to earn $150?

Blake’s Lawn Mowing Money

180 160 140 120 100 80 60 40 20 0

Number of Lawns Mowed

e. Plot the point on the graph that represents the total amount of money Blake earned after mowing 7 lawns. f.

166

What are the coordinates of the point you plotted in part (e)?

PROBLEM SET

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5 ▸ M6 ▸ TD ▸ Lesson 16

Name

Date

Use the graph to complete parts (a)–(e). Tyler’s Bike Rides

y 80

Total Number of Miles

70 60 50 40 30 20 10 0

Number of Hours

a. How long does it take Tyler to ride the first 20 miles? b. How many miles does Tyler ride in 6 hours? c. What does the point located at (4, 40) mean? d. How many miles does Tyler ride between hours 2 and 3? e. Look at the points representing the total distance Tyler rode. Why don’t these points appear to lie on the same line?

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5 ▸ M6 ▸ TD ▸ Lesson 17 ▸ Equivalent Expressions Cards Set B

5÷6

6÷6

5÷7

1_ 16

5_ 6

7_ 5

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5 ▸ M6 ▸ TD ▸ Lesson 17 ▸ Equivalent Expressions Cards Set B

6_ 6

7_ 6

7÷5

6÷5

1_ 15

5_ 7

7÷6

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5 ▸ M6 ▸ TD ▸ Lesson 17 ▸ Grid Paper

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5 ▸ M6 ▸ TD ▸ Lesson 17

Name

Date

1. Complete the table. Word

Number of Consonants

Number of Vowels

imagine idea students enter letter right left data coordinates education

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5 ▸ M6 ▸ TD ▸ Lesson 17

2. Consider the coordinate plane. a. Label the x-axis Number of Consonants and the y-axis Number of Vowels. Label the title Word Data. Use the data collected in problem 1 to form ordered pairs. Plot points that represent the ordered pairs in the coordinate plane. y 8 7 6 5 4 3 2 1 0

b. Draw a dotted line from (0, 0) to (8, 8). How many plotted points lie on the dotted line? What does this tell you? c. How many plotted points lie below the dotted line? What do the words these points represent have in common? d. How many plotted points lie above the dotted line? What do the words these points represent have in common?

176

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5 ▸ M6 ▸ TD ▸ Lesson 17

e. Why is the point that represents the word idea closer to the y-axis than to the x-axis?

Why is the point that represents the word left closer to the x-axis than to the y-axis?

g. What is an ordered pair for a point that lies on the same vertical line as the point that represents the word letter? What do the words these points represent have in common?

h. What is an ordered pair for a point that lies on the same horizontal line as the point that represents the word letter? What do the words these points represent have in common?

Why is the point that represents the word education left 2 units from the point that represents the word coordinates?

Why is the point that represents the word students down 3 units from the point that represents the word coordinates?

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LESSON

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5 ▸ M6 ▸ TD ▸ Lesson 17

3. Consider the table. a. Write a word of each type, the number of consonants in the word, and the number of vowels in the word. Do not write the same words as the words in problem 1.

Type of Word

Word

Number of Consonants

Number of Vowels

1-letter word 2-letter word 3-letter word 4-letter word 5-letter word 6-letter word 7-letter word 8-letter word 9-letter word 10-letter word

178

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5 ▸ M6 ▸ TD ▸ Lesson 17

b. Label the x-axis Number of Consonants and the y-axis Number of Vowels. Label the title Word Data. Use the data collected in part (a) to form ordered pairs. Plot points that represent the ordered pairs in the coordinate plane.

y 8 7 6 5 4 3 2 1 0

c. Based on the data, do you think it is true that the more consonants a word has, the more vowels it has? Why?

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LESSON

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5 ▸ M6 ▸ TD ▸ Lesson 17

Name

Date

Use the graph to answer parts (a)–(c). Measurements of Leaves

y 12 11 10 9

Width (cm)

8 7 6 5 4 3 2 1 0

Length (cm)

a. What does the point (11, 4) represent? b. Are there any leaves with the same width? How can you tell from the graph?

c. Are there any leaves with the same length? How can you tell from the graph?

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5 ▸ M6 ▸ TD ▸ Lesson 18 ▸ Area Match Cards Set A

23 1 4 1

1 4

3 4

1 3 2 3

1 4

3 4

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2 4

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5 ▸ M6 ▸ TD ▸ Lesson 18 ▸ Area Match Cards Set A

2 3

4 3

1 3

1 4

1 2 1 2

3 4

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1 3

185

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x-Coordinate

5 ▸ M6 ▸ TD ▸ Lesson 18 ▸ Number Patterns Table

y-Coordinate

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Ordered Pair

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5 ▸ M6 ▸ TD ▸ Lesson 18 ▸ Distance Walked

Leo’s Walk

3.5 Distance Walked (miles)

Distance Walked (miles)

3.5 3 2.5 2 1.5 1

3 2.5 2 1.5 1 0.5

0.5 0

Yuna’s Walk

5 10 15 20 25 30 35 40 45 50 55 60 65

Time (minutes)

Discussion questions: •

What does the point (0, 0) represent on Yuna’s graph? Does it represent the same thing on Leo’s graph?

•

Why do you think the line is horizontal on Leo’s graph between 25 and 35 minutes?

•

Did Yuna walk faster between minutes 30 and 40 or between minutes 40 and 50? How do you know?

•

Did Yuna return to where she started? How do you know?

•

Why don’t any line segments go down from left to right?

•

A line segment on Leo’s graph goes through the point (20, 0.75). Do we know for certain that Leo walked 0.75 miles after 20 minutes?

•

Can you use this line graph to predict how far Yuna walked after 70 minutes? Why?

189

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5 ▸ M6 ▸ TD ▸ Lesson 18

Name

Date

1. The line graph shows the number of dogs in an animal shelter at the start of each month over a year. Use the graph to complete parts (a)–(d). a. At the start of which month does the animal shelter have the greatest number of dogs?

Number of Dogs at Animal Shelter

y 18

b. At the start of which month does the animal shelter have 2 dogs?

Number of Dogs

16 14 12 10 8 6 4 2 0

10 11 12

Month

c. Between the starts of which 2 months does the number of dogs not change?

d. How many more dogs are at the shelter at the start of month 5 than at the start of month 4?

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5 ▸ M6 ▸ TD ▸ Lesson 18

2. The line graph shows the number of health points a video game character has at the start of each segment of a quest. Use the graph to complete parts (a)–(d). a. During which segment does the number of the character’s health points decrease most rapidly?

Video Game Character’s Health

y 100 90

b. During which segment does the number of the character’s health points stay the same?

Health Points

80 70 60 50 40 30 20 10 0

Segments

c. During which segment does the character add health points? Explain.

d. How many health points does the character use from the start of segment 1 to the start of segment 3?

192

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5 ▸ M6 ▸ TD ▸ Lesson 18

3. Sasha measures the amount of rainfall during a rainstorm every half hour for 5 hours. Use the graph that shows her results to complete parts (a)–(d). Hourly Rainfall

Total Rainfall (inches)

Hours

a. How many inches of rain fell during this 5-hour period?

b. During which half-hour period did 0.5 inches of rain fall?

c. During which half-hour period did rain fall the fastest?

d. Why is the line segment horizontal between 1.5 hours and 2.5 hours?

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PROBLEM SET

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5 ▸ M6 ▸ TD ▸ Lesson 18

Name

Date

Use the graph to complete parts (a)–(e). Plant Growth

y 80

Plant Height (cm)

70 60 50 40 30 20 10 0

Month

a. What story does this line graph tell?

b. Why does the graph not have any flat line segments?

c. How long did it take the plant to grow to a height of 60 centimeters?

d. Approximately how tall is the plant at month 10?

e. During which month did the plant grow the most? How do you know?

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5 ▸ M6 ▸ TD ▸ Lesson 19 ▸ Area Match Cards Set B

4 5 1 5

3 4

1 5

14 1 3 1 3

4 5

3 4

2 1 4

1 4

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1 5

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4 5

5 ▸ M6 ▸ TD ▸ Lesson 19 ▸ Area Match Cards Set B

2 3 5

24 1 5

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1 4

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x-Coordinate

5 ▸ M6 ▸ TD ▸ Lesson 19 ▸ Number Patterns Table

y-Coordinate

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Ordered Pair

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5 ▸ M6 ▸ TD ▸ Lesson 19

Name

Date

1. The first three iterations in a pattern of stars and hearts is shown.

a. The table represents the number of stars and hearts in each iteration. Complete the table where x represents the number of stars and y represents the number of hearts in each step.

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Number of Stars

Number of Hearts

Ordered Pair

(1, 1)

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b. Use the coordinate plane to plot the ordered pairs from part (a). Label the axes. y

Growing Patterns of Stars and Hearts

40 36 32 28 24 20 16 12 8 4 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

c. What is the relationship between the number of stars and the number of hearts in corresponding figures?

d. If the number of stars is 34, what is the number of hearts?

204

LESSON

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5 ▸ M6 ▸ TD ▸ Lesson 19

2. Square 1 is made of 1 unit square. Square 2 is made of 4 unit squares. Square 3 is made of 9 unit squares.

Square 1

Square 2

Square 3

a. Draw square 4 and square 5. b. Complete the table that shows the relationship between the area and perimeter of each square. The first row is completed for you.

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Area (square units)

Perimeter (units)

Ordered Pair

(1, 4)

LESSON

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c. Plot the ordered pairs from part (b) in the coordinate plane. Area and Perimeter of Squares

Perimeter (units)

y 22 20 18 16 14 12 10 8 6 4 2 0

8 10 12 14 16 18 20 22 24

Area (square units)

206

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5 ▸ M6 ▸ TD ▸ Lesson 19

Name

Date

The first three steps in a pattern of stars and squares are shown.

a. The table represents the number of stars and squares in each step. Complete the table where x represents the number of stars and y represents the number of squares in each step.

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Number of Stars

Number of Squares

Ordered Pair

(1, 3)

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b. Use the coordinate plane to plot the ordered pairs from part (a). Label the axes. Stars and Squares Pattern

y 10 9 8 7 6 5 4 3 2 1 0

c. Describe the pattern for the number of stars.

d. Describe the pattern for the number of squares.

e. How many stars and squares would be in the fifth step of the pattern?

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5 ▸ M6 ▸ TD ▸ Lesson 20 ▸ Coordinate Plane

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5 ▸ M6 ▸ TD ▸ Lesson 20 ▸ Grid Paper

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5 ▸ M6 ▸ TD ▸ Lesson 20

Name

Date

1. Write the focus question.

2. An estimate that is too low is estimate is

. An estimate that is too high is

. My best

3. What information do you need to answer the focus question?

4. Answer the focus question. Show or explain your strategy.

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Name

5 ▸ M6 ▸ TD ▸ Lesson 20

Date

Use this space to reflect on today’s lesson.

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5 ▸ M6

Credits Great Minds® has made every effort to obtain permission for the reprinting of all copyrighted material. If any owner of copyrighted material is not acknowledged herein, please contact Great Minds for proper acknowledgment in all future editions and reprints of this module. Cover, Wassily Kandinsky (1866–1944), Thirteen Rectangles, 1930. Oil on cardboard, 70 x 60 cm. Musee des Beaux-Arts, Nantes, France. © 2020 Artists Rights Society (ARS), New York. Image credit: © RMN-Grand Palais/Art Resource, NY.; All other images are the property of Great Minds. For a complete list of credits, visit http://eurmath.link/media-credits.

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EUREKA MATH2 Tennessee Edition

5 ▸ M6

Acknowledgments Kelly Alsup, Adam Baker, Agnes P. Bannigan, Christine Bell, Reshma P Bell, Joseph T. Brennan, Dawn Burns, Amanda H. Carter, David Choukalas, Mary Christensen-Cooper, Nicole Conforti, Cheri DeBusk, Lauren DelFavero, Jill Diniz, Mary Drayer, Christina Ducoing, Karen Eckberg, Melissa Elias, Danielle A Esposito, Janice Fan, Scott Farrar, Gail Fiddyment, Ryan Galloway, Krysta Gibbs, January Gordon, Torrie K. Guzzetta, Kimberly Hager, Jodi Hale, Karen Hall, Eddie Hampton, Andrea Hart, Stefanie Hassan, Tiffany Hill, Christine Hopkinson, Rachel Hylton, Travis Jones, Laura Khalil, Raena King, Jennifer Koepp Neeley, Emily Koesters, Liz Krisher, Leticia Lemus, Marie Libassi-Behr, Courtney Lowe, Sonia Mabry, Bobbe Maier, Ben McCarty, Maureen McNamara Jones, Ashley Meyer, Pat Mohr, Bruce Myers, Marya Myers, Kati O’Neill, Darion Pack, Geoff Patterson, Victoria Peacock, Maximilian Peiler-Burrows, Brian Petras, April Picard, Marlene Pineda, DesLey V. Plaisance, Lora Podgorny, Janae Pritchett, Elizabeth Re, Meri Robie-Craven, Deborah Schluben, Colleen Sheeron-Laurie, Michael Short, Erika Silva, Jessica Sims, Tara Stewart, Heidi Strate, Theresa Streeter, Mary Swanson, James Tanton, Cathy Terwilliger, Saffron VanGalder, Rafael Vélez, Jessica Vialva, Allison Witcraft, Jim Wright, Jackie Wolford, Caroline Yang, Jill Zintsmaster Trevor Barnes, Brianna Bemel, Lisa Buckley, Adam Cardais, Christina Cooper, Natasha Curtis, Jessica Dahl, Brandon Dawley, Delsena Draper, Sandy Engelman, Tamara Estrada, Soudea Forbes, Jen Forbus, Reba Frederics, Liz Gabbard, Diana Ghazzawi, Lisa Giddens-White, Laurie Gonsoulin, Nathan Hall, Cassie Hart, Marcela Hernandez, Rachel Hirsh, Abbi Hoerst, Libby Howard, Amy Kanjuka, Ashley Kelley, Lisa King, Sarah Kopec, Drew Krepp, Crystal Love, Maya Márquez, Siena Mazero, Cindy Medici, Ivonne Mercado, Sandra Mercado, Brian Methe, Patricia Mickelberry, Mary-Lise Nazaire, Corinne Newbegin, Max Oosterbaan, Tamara Otto, Christine Palmtag, Andy Peterson, Lizette Porras, Karen Rollhauser, Neela Roy, Gina Schenck, Amy Schoon, Aaron Shields, Leigh Sterten, Mary Sudul, Lisa Sweeney, Samuel Weyand, Dave White, Charmaine Whitman, Nicole Williams, Glenda Wisenburn-Burke, Howard Yaffe

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Talking Tool Share Your Thinking

I know . . . . I did it this way because . . . . The answer is

because . . . .

My drawing shows . . . . I agree because . . . .

Agree or Disagree

That is true because . . . . I disagree because . . . . That is not true because . . . . Do you agree or disagree with

Ask for Reasoning

Why did you . . . ? Can you explain . . . ? What can we do first? How is

Say It Again

related to

I heard you say . . . . said . . . . Another way to say that is . . . . What does that mean?

? Why?

Thinking Tool When I solve a problem or work on a task, I ask myself Before

Have I done something like this before? What strategy will I use? Do I need any tools?

During

Is my strategy working? Should I try something else? Does this make sense?

After

What worked well? What will I do differently next time?

At the end of each class, I ask myself

What did I learn? What do I have a question about?

MATH IS EVERYWHERE Do you want to compare how fast you and your friends can run? Or estimate how many bees are in a hive? Or calculate your batting average? Math lies behind so many of life’s wonders, puzzles, and plans. From ancient times to today, we have used math to construct pyramids, sail the seas, build skyscrapers—and even send spacecraft to Mars. Fueled by your curiosity to understand the world, math will propel you down any path you choose. Ready to get started?

Module 1 Place Value Concepts for Multiplication and Division with Whole Numbers Module 2 Addition and Subtraction with Fractions Module 3 Multiplication and Division with Fractions Module 4 Place Value Concepts for Decimal Operations Module 5 Addition and Multiplication with Area and Volume Module 6 Foundations to Geometry in the Coordinate Plane

ISBN 9781638985198

781638 985198