EM2 Tennessee Learn | Grade 4 Module 6 by Great Minds

A Story of Units®

Fractional Units LEARN ▸ Module 6 ▸ Angle Measurements and Plane Figures

Student

Talking Tool Share Your Thinking

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

because . . . .

My drawing shows . . . . Agree or Disagree

I agree because . . . . 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?

Content Terms

Place a sticky note here and add content terms.

? Why?

What does this painting have to do with math? American abstract painter Frank Stella used a compass to make brightly colored curved shapes in this painting. Each square in this grid includes an arc that is part of a design of semicircles that look like rainbows. When Stella placed these rainbow patterns together, they formed circles. What fraction of a circle is shown in each square? On the cover Tahkt-I-Sulayman Variation II, 1969 Frank Stella, American, born 1936 Acrylic on canvas Minneapolis Institute of Art, Minneapolis, MN, USA Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Art, MN. Gift of Bruce B. Dayton/Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York

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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 978-1-63898-513-6

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A Story of Units®

Fractional Units ▸ 4 LEARN

Module

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1 2 3 4 5 6

Place Value Concepts for Addition and Subtraction

Place Value Concepts for Multiplication and Division

Multiplication and Division of Multi-Digit Numbers

Foundations for Fraction Operations

Place Value Concepts for Decimal Fractions

Angle Measurements and Plane Figures

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EUREKA MATH2 Tennessee Edition

4 ▸ M6

Contents Angle Measurements and Plane Figures Topic A

Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Use a protractor to draw angles up to 180°.

Lines and Angles Lesson 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Identify and draw points, lines, line segments, rays, and angles.

Topic C Determine Unknown Angle Measures

Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Identify right, acute, obtuse, and straight angles.

Decompose angles by using pattern blocks.

Draw right, acute, obtuse, and straight angles.

Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Find unknown angle measures within right and straight angles.

Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Identify, define, and draw perpendicular lines.

Find unknown angle measures within a decomposed angle of up to 180°.

Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Identify, define, and draw parallel lines. Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Relate geometric figures to a real-world context.

Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Find unknown angle measures around a point.

Topic D Two-Dimensional Figures and Symmetry

Topic B

Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

Angle Measurement Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Explore angles as fractional turns through a circle. Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Use a circular protractor to recognize

1 a 1° angle as a turn through ___ of a circle. 360

Recognize, identify, and draw lines of symmetry.

Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Analyze and classify triangles based on side length, angle measures, or both.

Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Construct and classify triangles based on given attributes.

Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Identify and measure angles as turns and recognize them in various contexts.

Lesson 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Sort polygons based on a given rule.

Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Use 180° protractors to measure angles.

Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Lesson 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Estimate and measure angles with a 180°

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 210

protractor. 2

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 1

Name

Date

Term

Example

Notation

point

line segment

line

ray

angle

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 1

Name

Date

Connect each figure to the words and notation that describe it. The first one has been done for you.

Point M

Line segment MN

Ray MN

Line MN

Draw and label the figure.

5. Point A

6. Line segment EF

7. Ray ZB

8. Line TJ

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 1

9. Follow the directions for parts (a)–(e). Use a straightedge. Points A and B are given. a. Draw line segment AB. b. Draw a point that is not on line segment AB. Label it C. c. Draw ray AC. d. Draw a point that is not on line segment AB or ray AC. Label it D. e. Draw line BD.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 1

10. Follow the directions for parts (a)–(f). Use a straightedge. a. Draw points P and Q.

⟷

b. Draw PQ .

⟷

c. Draw a point that is not on PQ. Label it R. ¯. d. Draw PR

⟷

e. Draw a point that is not on PQ or PR̄ . Label it S. f.

⟶

Draw SQ .

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 1

11. Find and label some points, rays, lines, and line segments on the picture. Then record them in the table. Point A has been done for you.

7629

Points

Point A

Rays Lines Line Segments

12. How are a line, a line segment, and a ray different from each other?

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TA ▸ Lesson 1

Date

Draw and label an example of each figure. Figure

Drawing of Figure

Ray AB

Line EF

Line segment CD

Point G

Angle

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 2

Name

Date

Use your right-angle tool to classify the angle as a right angle, an acute angle, or an obtuse angle. 1.

Identify the type of angle. 2.

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 2

LESSON

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 2

T L

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LESSON

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 2

Name

Date

Complete the table. Use your right-angle tool. The first one has been done for you.

Figure 1.

(same size, smaller than, larger than)

Type of Angle

(right, acute, obtuse)

Size Compared to a Right Angle

Smaller than

Acute

B 3.

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 2

Size Compared to a Right Angle

Figure 4.

(same size, smaller than, larger than)

Type of Angle

(right, acute, obtuse)

A B

C B A

B A

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 2

7. Use your right-angle tool to help identify right, acute, and obtuse angles within Charles Demuth’s painting My Egypt. Trace at least two of each kind of angle. Label them with points and an arc, and then name them in the table.

Charles Demuth (1883–1935). My Egypt. 1927. Oil, fabricated chalk, and graphite pencil on composition board. Overall: 35 15/16 x 30 in. (91.3 x 76.2 cm). Purchase, with funds from Gertrude Vanderbilt Whitney. Inv. N.: 31.172 Digital image © Whitney Museum of American Art/ Licensed by Scala/Art Resource, NY

Right Angle Acute Angle Obtuse Angle

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 2

8. Amy draws two angles that are the same size. David says they can’t be the same size because the rays in ∠QRX are drawn longer than the rays in ∠PWL. Explain how the angles can be the same size.

Q P R

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 2

Name

Date

Identify each angle as right, acute, or obtuse. Use your right-angle tool. Type of Angle (right, acute, obtuse)

Figure

Z Y

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 2

Type of Angle (right, acute, obtuse)

Figure

Y Z

EXIT TICKET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 3

Name

Date

Draw an angle with the given ray. Label the angle. ⟶ 1. Use LM to draw ∠KLM.

2. Draw and label an obtuse angle PRS.

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 3

Name

Date

Follow the directions to draw and name the angle. Then circle the type of angle. ⟶ 1. a. Draw a point not on CD . Label it X.

⟶

b. Draw CX .

c. Draw an arc to show the angle.

Acute

d. Name the angle three different ways.

∠

,∠

Obtuse Straight

⟶ ⟶ b. Draw KE .

2. a. Draw KZ .

Right

c. Draw a square to show the angle.

Acute

d. Name the angle three different ways.

∠

,∠

Right

,∠

Obtuse

Straight

⟶

3. a. Draw LQ .

⟶

b. Draw LP .

Right

c. Draw an arc to show the angle. d. Name the angle three different ways. ,

4. a. Draw ∠HBT.

b. Draw an arc to show the angle. c. Name the angle three different ways. ,

Acute Obtuse Straight

Right Acute Obtuse Straight

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 3

5. Complete the table. Angle Description

Drawing of Angle

Type of Angle

Right

Smaller than a right angle

Larger than a right angle

2 rays, with common endpoints, that together make a line

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 3

6. Use the figure to complete parts (a)–(d). Use your right-angle tool to help you. a. Name an acute angle.

b. Name an obtuse angle.

c. Name a right angle. d. Name a straight angle.

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TA ▸ Lesson 3

Date

1. Draw an acute angle KLM. Explain how you know the angle is acute.

2. Draw an obtuse angle XZY. Explain how you know the angle is obtuse.

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 4 ▸ Identify Sides in Polygons

Polygon 1

Polygon 2

M Polygon 3

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 4 ▸ Rectangular and Triangular Grid Paper

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 4

Name

Date

Trace at least one pair of line segments that appear to be perpendicular on each object. Mark their shared right angle with a small square. 1.

5. How do you know if two lines or lines segments are perpendicular?

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 4

Draw a line segment perpendicular to each given line segment. Use a straightedge and a right-angle tool. Mark the right angle with a small square. 6.

8. Use your straightedge and right-angle tool to draw a pair of perpendicular rays.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 4

Use your right-angle tool to find and name the perpendicular sides. If there are no perpendicular sides, write the word None. Mark each right angle with a small square. Problem 9 has been started for you. 9. C

12.

C D

V S

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10. P

11. K

13.

¯ ⊥ EF ¯ CE

14.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 4

River Way

Moun tai

Hom eS t r ee t

y Wa

Broadway Street

South Road

eet

Central Avenue River Avenue

Benchley Avenue

West Drive

Central Avenue

n Str

South Road

East Drive

Oak

North Road

East Drive

Broadway Street

North Road

River Avenue

West Drive

15. Use the map to complete parts (a)–(d).

a. Name a street perpendicular to Central Avenue.

b. Name a street perpendicular to West Drive.

c. Name two streets perpendicular to each other.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 4

d. Is Home Street perpendicular to River Avenue? Explain your thinking.

16. Mark each right angle on the figure with a small square. (Note: A right angle does not have to be inside the figure.) How many pairs of perpendicular sides does this figure have?

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 4

Name

Date

¯ and YZ ¯. Mark one of the right angles 1. Draw and label a pair of perpendicular line segments, WX with a small square.

2. Use a right-angle tool to find each right angle in the figure. Mark each right angle with a small square. Then name a pair of perpendicular sides.

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Rectangular and Triangular Grid Paper

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Identify Sides in Polygons

Polygon 1

Polygon 2

M Polygon 3

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 5

Name

Date

Trace at least one pair of line segments that appear to be parallel on each object. Mark the line segments as parallel by drawing arrow marks. 1.

5. How do you know whether two lines or line segments are parallel?

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 5

Draw a line segment parallel to each given line segment. Use a straightedge and a right-angle tool. Mark each line segment with an arrow mark. 6.

8. Use your straightedge and right-angle tool to draw a pair of parallel lines. Mark each line with an arrow mark.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 5

Use a straightedge and a right-angle tool to find and name the parallel sides. If there are no parallel sides, write the word None. Mark the parallel sides with arrow marks. Problem 9 has been started for you. 9. L

¯ ¯ ‖ OX LP

10. A

U V

X F

11.

12.

13.

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M X

14.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 5

River Way

Moun tai

Hom eS t r ee t

y Wa

Broadway Street

South Road

eet

Central Avenue River Avenue

Benchley Avenue

West Drive

Central Avenue

n Str

South Road

East Drive

Oak

North Road

East Drive

Broadway Street

North Road

River Avenue

West Drive

15. Use the map to complete parts (a)–(d).

a. Name a street parallel to North Road.

b. Name a street perpendicular to Broadway Street.

c. Name two streets parallel to each other.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 5

d. Is Mountain Street parallel to River Way? Explain your thinking.

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 5

Name

Date

1. Draw a pair of parallel line segments. Label their endpoints. Mark each segment with an arrow mark.

2. Mark the pair of parallel sides with arrow marks. Then name the pair of parallel sides.

E C

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EUREKA MATH2 Tennessee Edition

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4 ▸ M6 ▸ TA ▸ Lesson 6 ▸ Dot Paper

11/25/2021 9:45:59 AM

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 6 ▸ Geometric Figures Game

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 6

Name

Date

1. Use dot paper to create a floor plan of a home. Follow these guidelines: Include only one level. Do not include stairs. Use straight line segments. Include hallways. Include at least one example of each figure listed in the table. Label each room.

2. Use your floor plan to complete the table.

✓

Figure

Example of the Figure in the Floor Plan

Line segment

Parallel line segments

Perpendicular line segments

Right angle

Acute angle

Obtuse angle

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TA ▸ Lesson 6

Name

Date

1. Find an example of each figure in the floor plan. Use the numbers to complete the table.

Figure

1 Patio Living Room

Parallel line segments

Kitchen

Perpendicular line segments Right angle

Entry Closet

Line segment

Bedroom

Example in Floor plan

Bathroom

Acute angle Obtuse angle

Describe the figure. Use precise language. Figure

Description

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TB ▸ Lesson 7

Date

1. The blue figure turns _1 of 1 whole turn each time. Count by fourths to label the fraction 4 of 1 whole turn.

_1 4

2. The blue figure turns _1 of 1 whole turn each time. Count by eighths to label the fraction 8 of 1 whole turn.

5_ 8

3. What fractional turn makes a straight angle? Use problems 1 and 2 to help you. fourths:

eighths:

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 7

4. Can you make an obtuse angle when you turn by fourths? How do you know?

5. Draw and shade to show each fraction of 1 whole turn. Then write the type of angle. The first one is done for you.

Fraction of 1 Whole Turn

_4 8

Figure

Right

Angle Type

6. Carla says that _3 and _6 of 1 whole turn are the same angle. Do you agree? Use the circles to help 4

explain your answer.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 7

7. Are there more quarter turns or eighth turns in 1 whole turn? How do you know?

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 7

Name

Date

Complete the table. Figure

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Fraction of 1 Whole Turn

Angle Type

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EUREKA MATH2 Tennessee Edition

110

10 0

60 50

170

160

150

14 0

0 13

4 ▸ M6 ▸ TB ▸ Lesson 8 ▸ Circular Protractor

18 0

350

190

34 0

20 0

33 0

210 0

32 0

23 0

250

260

27 0

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280

29 0

30 0

0 31

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 8

Name

Date

1. Use your angle-maker tool and protractor to make and measure each benchmark angle. Then complete the table. Turn

1 _ 8

Sketch of Angle

Angle Measure

45°

2 _ 8

_____ 360

4 _ 8

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Angle Type

_____ 360

3 _ 8

Fraction of

1 Whole Turn

_____ 360

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 8

Turn

Sketch of Angle

Angle Measure

Fraction of

1 Whole Turn

5 _ 8

_____ 360

6 _ 8

_____ 360

7 _ 8

_____ 360

8 _ 8

LESSON

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Angle Type

_____ 360

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 8

Name

Date

Use the protractor to fill in the blanks. 1.

110

10 0

170

16 0

15 0

14 0

18 0

35 0

19 0

200

340

Fraction of 1 turn: ______ 4

Angle measure:

2 10

Type of angle:

22 23

25 0

260

270

280

10 0

29 0

0 31

2. 110

170

16 0

15 0

14 0

0 13

18 0 200

340

35 0

19 0

Angle measure:

Type of angle:

33 0

EM2_0406SE_B_L08_problem_set.indd 71

2 10

Fraction of 1 turn: ______

25 0

260

270

280

29 0

0 31

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 8

3. 0

110

10 0

Fraction of 1 turn: ______

170

16 0

15 0

14 0

0 12

18 0

35 0

19 0

200

340

Angle measure:

2 10

Type of angle:

22 23

25 0

260

270

280

10 0

29 0

0 31

4. 110

15 0

Fraction of 1 circle: ______

170

16 0

360

18 0

35 0

19 0

Angle measure:

340

200

Type of angle:

2 10 0

22 23

Fraction of 1 turn: ______

14 0

0 13

25 0

PROBLEM SET

EM2_0406SE_B_L08_problem_set.indd 72

260

270

280

29 0

0 31

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 8

5. 0

110

10 0

Fraction of 1 turn: ______ 8

170

16 0

15 0

14 0

18 0

360

200

340

35 0

19 0

Fraction of 1 circle: ______

2 10

Angle measure: Type of angle:

25 0

260

270

280

10 0

29 0

0 31

6. 0

110

Fraction of 1 turn: ______ 8

170

16 0

15 0

14 0

0 12

18 0

______

200

340

35 0

19 0

Angle measure:

2 10 0

EM2_0406SE_B_L08_problem_set.indd 73

Fraction of 1 circle:

25 0

260

270

280

29 0

0 30

Type of angle:

0 31

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 8

7. 1

170

16 0

15 0

14 0

0 13

10 0

110

18 0

Angle measure:

200

340

35 0

19 0

Type of angle:

2 10 0

22 23

25 0

260

270

280

29 0

0 31

8. 0

110

10 0

60 50

170

16 0

15 0

14 0

0 12

18 0

0 33

2 10

200

22 0

PROBLEM SET

EM2_0406SE_B_L08_problem_set.indd 74

Type of angle:

340

35 0

19 0

Angle measure:

250

260

27 0

280

29 0

0 31

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 8

9. 0

110

10 0

170

16 0

15 0

14 0

0 12

18 0

35 0

19 0

200

340

Angle measure:

2 10

Type of angle:

22 23

25 0

260

270

280

29 0

0 30

0 31

10. How many 1° angles make 1 turn?

EM2_0406SE_B_L08_problem_set.indd 75

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 8

11. An angle turns through _ of a circle. What is the measure of the angle in degrees? 3 4

55 ___

12. Zara draws an angle that turns through 360 of a circle. What type of angle does Zara draw? How do you know?

13. How many 30° angles make 1 turn?

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 8

Name

Date

1. What fraction of a turn is 1 degree?

______

2. Use the angle shown on the protractor to complete parts (a) and (b).

110

10 0

60 50

170

160

15 0

14 0

0 12

18 0

35 0

19 0

340

20 0

33 0

210

25 0

260

2 70

280

290

0 31

a. What is the measure of the angle?

b. What fraction of a whole turn is shown? Explain how you know.

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TB ▸ Lesson 9

Date

1. How many degrees does the minute hand turn from 2:15 to 3:00?

2. A plane takes off flying west. The plane turns and is now flying east. How many degrees does the plane turn?

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 9

3. Adam is in the seat at the top of the Ferris wheel. The Ferris wheel turns 270° clockwise. a. Circle where Adam’s seat is after the turn.

b. What turn brings Adam back to the top of the Ferris wheel?

4. Liz plays a game. She wants the green piece to fit into the white space. Which button should she press to make the piece fit? How do you know?

Buttons Turn 90°

PROBLEM SET

EM2_0406SE_B_L09_problem_set.indd 80

Turn 180°

11/22/2021 3:49:30 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 9

5. Luke, Mia, and James are at the park. They are standing on the star. They are facing the basketball court. basketball court

garden

pool

parking lot

a. Luke turns 90° counterclockwise. What part of the park is he facing?

b. Mia turns 180°. What part of the park is she facing?

c. James now faces the pool. Use degrees and the words clockwise or counterclockwise to describe how he turned.

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PROBLEM SET

11/22/2021 3:49:30 PM

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 9

Name

Date

1. David is doing a handstand. Describe how many degrees his body will turn to stand straight up again.

2. Gabe starts riding his bike at the point represented by the star. He rides north for 3 blocks, then turns 90° clockwise and rides for 2 blocks. What direction is he facing after the turn? a. Sketch Gabe’s route on the grid. Each square represents 1 block.

N W

E S

b. Gabe is facing

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after the turn.

11/22/2021 3:49:05 PM

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TB ▸ Lesson 10

Date

Identify the type of angle. Then use a protractor to measure the angle. 1. Type of Angle:

2. Type of Angle:

Measure:

3. Type of Angle: Measure:

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 10

4. Type of Angle: Measure:

5. Type of Angle: Measure:

LESSON

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 10

6. Type of Angle: Measure:

EM2_0406SE_B_L10_classwork.indd 87

LESSON

11/22/2021 3:51:53 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 10

7. Type of Angle: Measure:

LESSON

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TB ▸ Lesson 10

Date

Classify the angle as right, acute, obtuse, or straight. Then write the angle measure. 1. Type of Angle:

2. Type of Angle:

Measure:

3. Type of Angle: Measure:

EM2_0406SE_B_L10_problem_set.indd 89

Measure:

4. Type of Angle:

Measure:

11/22/2021 3:54:18 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 10

Use a protractor to measure the angle. Record the measurement in degrees. 5. Measure:

6. Measure:

7. Measure:

8. Measure:

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

9. Measure:

11. Measure:

4 ▸ M6 ▸ TB ▸ Lesson 10

10. Measure:

EM2_0406SE_B_L10_problem_set.indd 91

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 10

12. Measure:

° C

13. Gabe says the measure of the angle shown is 75°. Use a protractor to measure the angle. Then explain Gabe’s mistake.

PROBLEM SET

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11/22/2021 3:54:20 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TB ▸ Lesson 10

Date

Use a protractor to measure the angles. 1.

degrees

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 10

degrees

EXIT TICKET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 11 ▸ Angle Measure Sort

36°

87°

112°

172°

138°

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 11

Name

Date

1. Find the measure of each angle.

a. Measure of ∠A:

b. Measure of ∠B:

c. Measure of ∠C:

d. Measure of ∠D:

e. Measure of ∠E:

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11/22/2021 3:55:29 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 11

2. Identify the angle type and estimate the measure. Then use a protractor to find the actual angle measure. Angle Type and Angle Measure Estimate

Angle

Actual Angle Measure

a. Angle type:

Angle measure estimate:

b. Angle type:

Angle measure estimate:

LESSON

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 11

Angle Type and Angle Measure Estimate

Angle

Actual Angle Measure

c. Angle type:

Angle measure estimate:

d. Angle type:

Angle measure estimate:

EM2_0406SE_B_L11_Classwork.indd 99

LESSON

11/22/2021 3:55:30 PM

EM2_0406SE_B_L11_Classwork.indd 100

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 11

Name

Date

Complete the table. Angle Type and Angle Measure Estimate

Angle

Actual Angle Measure

1. Angle type:

Angle measure estimate:

2. Angle type:

Angle measure estimate:

3. Angle type:

Angle measure estimate:

EM2_0406SE_B_L11_problem_set.indd 101

101

11/22/2021 3:56:33 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 11

Angle Type and Angle Measure Estimate

Angle

Actual Angle Measure

4. Angle type:

Angle measure estimate:

5. Angle type:

Angle measure estimate:

6. Angle type:

Angle measure estimate:

102

PROBLEM SET

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11/22/2021 3:56:34 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 11

Angle Type and Angle Measure Estimate

Angle

Actual Angle Measure

7. Angle type:

Angle measure estimate:

8. Angle type:

Angle measure estimate:

EM2_0406SE_B_L11_problem_set.indd 103

PROBLEM SET

103

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 11

9. Deepa says the angle shown is an acute angle. Ivan says it is an obtuse angle. Use a protractor to measure the angle. Then explain who is correct.

104

PROBLEM SET

EM2_0406SE_B_L11_problem_set.indd 104

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 11

Name

Date

Complete the table. Angle

Angle Measure Estimate

Actual Angle Measure

About

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105

11/22/2021 3:56:00 PM

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ Sprint ▸ Compose 90

Sprint Complete the equations. 1.

60 +

= 90 + 45 = 90

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107

11/25/2021 9:48:16 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ Sprint ▸ Compose 90

Number Correct:

Complete the equations. 1.

80 +

= 90

23.

86 +

= 90

70 +

= 90

24.

76 +

= 90

60 +

= 90

25.

+ 66 = 90

50 +

= 90

26.

+ 56 = 90

90 +

= 90

27.

56 +

= 90

+ 20 = 90

28.

57 +

= 90

+ 40 = 90

29.

+ 67 = 90

+ 10 = 90

30.

+ 77 = 90

+ 30 = 90

31.

87 +

= 90

10.

+ 0 = 90

32.

88 +

= 90

11.

85 +

= 90

33.

+ 70 = 90

12.

75 +

= 90

34.

+ 60 = 90

13.

65 +

= 90

35.

10 + 70 +

= 90

14.

+ 55 = 90

36.

30 + 10 +

= 90

15.

+ 45 = 90

37.

10 +

+ 50 = 90

16.

+ 15 = 90

38.

10 +

+ 55 = 90

17.

25 +

= 90

39.

+ 55 + 20 = 90

18.

45 +

= 90

40.

+ 20 + 45 = 90

19.

35 +

= 90

41.

32 + 45 +

20.

+ 5 = 90

42.

25 +

21.

+ 65 = 90

43.

22.

+ 55 = 90

44.

108

EM2_0406SE_B_L12_removable_fluency_sprint.indd 108

= 90 + 32 = 90

+ 41 + 25 = 90 33 +

11/22/2021 4:02:11 PM

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11/22/2021 4:02:11 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ Sprint ▸ Compose 90

Number Correct: Improvement:

Complete the equations. 1.

80 +

= 90

23.

87 +

= 90

70 +

= 90

24.

77 +

= 90

60 +

= 90

25.

+ 67 = 90

50 +

= 90

26.

+ 57 = 90

90 +

= 90

27.

57 +

= 90

+ 10 = 90

28.

58 +

= 90

+ 30 = 90

29.

+ 68 = 90

+ 40 = 90

30.

+ 78 = 90

+ 20 = 90

31.

88 +

= 90

10.

+ 0 = 90

32.

89 +

= 90

11.

85 +

= 90

33.

+ 80 = 90

12.

75 +

= 90

34.

+ 70 = 90

13.

65 +

= 90

35.

70 + 10 +

= 90

14.

+ 55 = 90

36.

10 + 30 +

= 90

15.

+ 45 = 90

37.

50 +

+ 10 = 90

16.

+ 5 = 90

38.

55 +

+ 10 = 90

17.

15 +

= 90

39.

+ 20 + 55 = 90

18.

45 +

= 90

40.

+ 45 + 20 = 90

19.

55 +

= 90

41.

45 + 32 +

20.

+ 35 = 90

42.

32 +

21.

+ 65 = 90

43.

22.

+ 25 = 90

44.

110

EM2_0406SE_B_L12_removable_fluency_sprint.indd 110

= 90 + 25 = 90

+ 25 + 41 = 90 41 +

11/22/2021 4:02:12 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TB ▸ Lesson 12

Date

1. Use a protractor and a straightedge to draw a 40° angle.

Create a sketch of each angle. Then use a protractor and a straightedge to draw the angle. Draw an arc to show the angle. Angle

Sketch

Accurate Drawing

2. 97°

EM2_0406SE_B_L12_Classwork.indd 111

111

11/22/2021 3:59:11 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 12

Angle

Sketch

Accurate Drawing

3. 174°

4. 151°

5. 29°

112

LESSON

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11/22/2021 3:59:12 PM

EUREKA MATH2 Tennessee Edition

Angle

Sketch

4 ▸ M6 ▸ TB ▸ Lesson 12

Accurate Drawing

6. 83°

EM2_0406SE_B_L12_Classwork.indd 113

LESSON

113

11/22/2021 3:59:12 PM

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11/22/2021 3:59:12 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TB ▸ Lesson 12

Date

Use the ray, a protractor, and a straightedge to construct the angle. Draw an arc to show the angle. 1. 40°

2. 75°

3. 125°

4. 165°

EM2_0406SE_B_L12_problem_set.indd 115

115

11/22/2021 4:00:03 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TB ▸ Lesson 12

5. 63°

6. 148°

Construct the angle. Draw an arc to show the angle. 7. 10°

8. 115°

9. 37°

10. 128°

116

PROBLEM SET

EM2_0406SE_B_L12_problem_set.indd 116

11/22/2021 4:00:04 PM

EUREKA MATH2 Tennessee Edition

11. 82°

4 ▸ M6 ▸ TB ▸ Lesson 12

12. 173°

13. Jayla places a protractor over a ray. Show and explain how she can make a 40° angle.

EM2_0406SE_B_L12_problem_set.indd 117

PROBLEM SET

117

11/22/2021 4:00:04 PM

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11/22/2021 4:00:04 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TB ▸ Lesson 12

Date

Construct a 130° angle. Draw an arc to show the angle.

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119

11/22/2021 3:59:39 PM

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11/22/2021 3:59:39 PM

EUREKA MATH2 Tennessee Edition

EM2_0406SE_C_L13_removable_pattern_block_cutouts.indd 121

4 ▸ M6 ▸ TC ▸ Lesson 13 ▸ Pattern Block Cutouts

121

11/25/2021 9:50:39 AM

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 13

Name

Date

1. Decompose each angle to find its measure.

B D

EM2_0406SE_C_L13_classwork.indd 123

123

11/22/2021 4:30:58 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 13

Find the measure of the angle represented by the arc. 2.

I +

The measure of ∠I is

J +

The measure of ∠J is

124

LESSON

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11/22/2021 4:30:59 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 13

The measure of ∠K is

EM2_0406SE_C_L13_classwork.indd 125

LESSON

125

11/22/2021 4:30:59 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 13

5. Use pattern blocks to decompose ∠L.

a. Write an equation to find the measure of ∠L.

b. The measure of ∠L is

126

LESSON

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11/22/2021 4:30:59 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 13

Name

Date

Use the pattern blocks to complete problems 1–4. 30°

120°

150° 120°

150°

120°

60°

30° 60°

60°

120° 120°

60°

120°

60°

1. Find the measures of ∠A and ∠B. Then add to find the measure of ∠C.

A The measure of ∠A is .

The measure of ∠B is .

Addition equation:

The measure of ∠C is

90 .

2. Find the measures of ∠D and ∠E. Then add to find the measure of ∠F.

The measure of . ∠D is =

EM2_0406SE_C_L13_problem_set.indd 127

The measure of ∠E is .

Addition equation:

The measure of ∠F is

. 127

11/23/2021 10:58:23 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 13

3. Write an equation and find the measure of the angle represented by the arc. Angle

128

PROBLEM SET

EM2_0406SE_C_L13_problem_set.indd 128

Equation

Measure

11/23/2021 10:58:23 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 13

4. The measure of ∠Z is 120°. Describe two ways you could use pattern blocks to decompose ∠Z.

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PROBLEM SET

129

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 13

Name

Date

Use the pattern blocks to answer the question.

30°

120°

150° 120°

150°

120°

60°

30° 60°

60°

120° 60°

120°

60°

120°

What is the measure of the angle shown by the arc?

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131

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 14 ▸ Geometric Figures Game

133

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 14

Name

Date

Complete the equations and find the unknown angle measure. Check the measurement by using a protractor. 1. ∠ABC is a right angle.

2. ∠FQH is a right angle.

F D S 40°

B 40 +

65°

x° C

= 90

The measure of ∠DBC is

EM2_0406SE_C_L14_problem_set.indd 135

x°

= x=

The measure of ∠SQH is

135

11/22/2021 4:41:22 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 14

3. ∠OTM is a right angle.

4. ∠LGJ is a right angle.

12°

x°

O M 46°

x°

T +

= x=

The measure of ∠YTM is

The measure of ∠LGN is

5. ∠EFG is a straight angle.

6. ∠UCR is a straight angle.

B D x°

100° E 100 +

PROBLEM SET

EM2_0406SE_C_L14_problem_set.indd 136

= x=

136

R +

= 180

The measure of ∠BFG is

135°

x°

The measure of ∠DCR is

11/22/2021 4:41:22 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 14

7. ∠KVR is a straight angle.

8. ∠YJH is a straight angle.

H 27°

x°

P + V

The measure of ∠YJP is

x°

52°

E = x=

The measure of ∠KVE is

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PROBLEM SET

137

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 14

9. Robin builds a cat by using the shape pieces. Find the value of x. Explain your thinking.

x° 45°

10. A fan is open as shown below. How many more degrees does the fan need to open to make a straight angle? Write an equation to find the unknown angle measure. Explain your thinking.

147°

138

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 14

Name

Date

∠ABC is a straight angle. The measure of ∠DBC is 53°.

Write and solve an equation to find the measure of ∠ABD.

x° A

53° B

Equation:

Measure of ∠ABD:

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139

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 15

Name

Date

Write and solve an equation to find the unknown angle measure. 1. ∠LMN is a straight angle.

2. ∠QLP is a straight angle.

A J

B 70° L

x°

The measure of ∠BMN is

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x° 40°

80°

The measure of ∠JLT is

141

11/22/2021 4:42:05 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 15

3. ∠TNH is a straight angle.

4. ∠SVM is a straight angle.

F H

x°

55° x°

23°

The measure of ∠WNT is

142

PROBLEM SET

EM2_0406SE_C_L15_problem_set.indd 142

The measure of ∠SVY is

11/22/2021 4:42:06 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 15

5. ∠CZD is a straight angle.

6. ∠EFG is a straight angle.

125°

Z F

37° x° U

D W

The measure of ∠UZW is

EM2_0406SE_C_L15_problem_set.indd 143

x° 28°

96°

The measure of ∠OFP is

PROBLEM SET

143

11/22/2021 4:42:07 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 15

7. The measure of ∠YJH is 75°.

8. The measure of ∠ENB is 150°.

x° 40°

x°

55°

The measure of ∠YJT is

144

PROBLEM SET

EM2_0406SE_C_L15_problem_set.indd 144

The measure of ∠VNB is

11/22/2021 4:42:07 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 15

9. The measure of ∠HCE is 82°.

10. The measure of ∠RZU is 137°.

F S

T 17°

13°

x° C

x°

54° Z

30°

The measure of ∠FCG is

The measure of ∠RZS is

11. Pablo draws a design. The bottom of his design is a straight angle. Find the measure of the unknown angle.

20° The measure of the unknown angle is

EM2_0406SE_C_L15_problem_set.indd 145

35°

x°

35°

20°

PROBLEM SET

145

11/22/2021 4:42:08 PM

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11/22/2021 4:42:08 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 15

Name

Date

∠TUV is a straight angle.

Write and solve an equation to find the measure of ∠WUX.

X W

53° T

x° U

67° V

Equation:

Measure of ∠WUX:

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147

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ Sprint ▸ Compose 180

Sprint Complete the equations. 1.

140 +

+ 175 = 180

2. 3.

= 180

100 + 50 +

= 180

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149

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ Sprint ▸ Compose 180

Number Correct:

Complete the equations. 1.

80 +

= 180

23.

50 + 50 +

= 180

100 +

= 180

24.

40 + 40 +

= 180

110 +

= 180

25.

70 +

+ 100 = 180

170 +

= 180

26.

10 +

+ 100 = 180

160 +

= 180

27.

+ 60 + 100 = 180

60 +

= 180

28.

+ 100 + 20 = 180

+ 50 = 180

29.

50 + 100 +

= 180

+ 150 = 180

30.

100 + 30 +

= 180

+ 40 = 180

31.

40 +

+ 100 = 180

10.

+ 140 = 180

32.

100 +

+ 40 = 180

11.

+ 90 = 180

33.

+ 60 + 60 = 180 + 0 + 90 = 180

12.

105 +

= 180

34.

13.

175 +

= 180

35.

178 +

= 180

14.

+ 115 = 180

36.

177 +

= 180

15.

+ 165 = 180

37.

5 + 100 +

= 180 = 180

16.

125 +

= 180

38.

100 + 65 +

17.

155 +

= 180

39.

25 +

+ 100 = 180

18.

+ 135 = 180

40.

100 +

+ 45 = 180

19.

+ 145 = 180

41.

+ 25 + 90 = 180 + 75 + 80 = 180

20.

85 +

= 180

42.

21.

95 +

= 180

43.

65 +

22.

94 +

= 180

44.

60 + 85 +

150

EM2_0406SE_C_L16_removeable_fluency_sprint.indd 150

+ 70 = 180 = 180

11/22/2021 4:44:59 PM

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ Sprint ▸ Compose 180

Number Correct: Improvement:

Complete the equations. 1.

100 +

= 180

23.

50 + 50 +

= 180

80 +

= 180

24.

40 + 40 +

= 180

170 +

= 180

25.

100 +

+ 70 = 180

110 +

= 180

26.

100 +

+ 10 = 180

160 +

= 180

27.

+ 100 + 60 = 180

60 +

= 180

28.

+ 20 + 100 = 180

+ 150 = 180

29.

100 + 50 +

= 180

+ 30 = 180

30.

30 + 100 +

= 180

+ 140 = 180

31.

100 +

+ 40 = 180

10.

+ 40 = 180

32.

40 +

+ 100 = 180

11.

+ 90 = 180

33.

+ 60 + 60 = 180 + 90 + 0 = 180

12.

175 +

= 180

34.

13.

105 +

= 180

35.

179 +

= 180

14.

+ 165 = 180

36.

178 +

= 180

15.

+ 115 = 180

37.

100 + 5 +

= 180 = 180

16.

155 +

= 180

38.

65 + 100 +

17.

125 +

= 180

39.

100 +

+ 25 = 180

18.

+ 145 = 180

40.

45 +

+ 100 = 180

19.

+ 135 = 180

41.

+ 90 + 25 = 180 + 80 + 75 = 180

20.

95 +

= 180

42.

21.

85 +

= 180

43.

70 +

22.

84 +

= 180

44.

85 + 60 +

152

EM2_0406SE_C_L16_removeable_fluency_sprint.indd 152

+ 65 = 180 = 180

11/22/2021 4:45:00 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TC ▸ Lesson 16

Date

1. Follow the directions in parts (a)–(c) to draw the figure and find the measure of the angles. a. Draw 2 intersecting lines by using your straightedge.

b. Put a point where your lines intersect. c. Use your protractor to measure all 4 angles. Label the measures on the drawing.

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153

11/22/2021 4:42:35 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 16

¯ and YZ ¯ are line segments. WX ¯ and YZ ¯ intersect at O. WX U

m° W

k°

36°

n°

2. m° =

The measure of ∠UOZ is

3. n° =

The measure of ∠YOX is

4. k° =

The measure of ∠WOY is

154

LESSON

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 16

Name

Date

Write and solve an equation to find the unknown angle measure. 2.

40°

a°

b°

The unknown angle measure is

d°

53°

145°

c°

The unknown angle measure is

EM2_0406SE_C_L16_problem_set.indd 155

The unknown angle measure is

155

11/22/2021 4:43:25 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 16

Write and solve equations to find the unknown angle measures.

a. The measure of ∠ENG is

¯ intersect at N. ¯ and GH 5. EF

b. The measure of ∠GNF is

x°

150° N

30°

y°

a. The measure of ∠JNL is

¯ and LM̄ intersect at N. 6. JK J

M f° e°

c. The measure of ∠MNK is

g°

115° L

156

PROBLEM SET

EM2_0406SE_C_L16_problem_set.indd 156

b. The measure of ∠JNM is

. . .

11/22/2021 4:43:26 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 16

a. The measure of ∠UNX is

¯ intersect at N. ¯, XY ¯, and AN 7. UV

b. The measure of ∠ANY is

p° m°

s°

c. The measure of ∠XNV is

27° V

8. Eva turns a jar lid 70°. She then turns it 195° more. How much farther does Eva need to turn the lid to make 1 whole turn?

second turn 195°

first turn 70°

x°

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PROBLEM SET

157

11/22/2021 4:43:26 PM

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TC ▸ Lesson 16

Name

Date

∠AEB and ∠CED are straight angles.

Write and solve equations to find the measures of ∠AEC, ∠CEB, and ∠DEB.

D 66° A

x° C

The measure of ∠AEC is

The measure of ∠CEB is

The measure of ∠DEB is

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E y°

z° B

. . .

159

11/22/2021 4:42:56 PM

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 17

Name

Date

Draw all the lines of symmetry on each figure. 1.

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161

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 17

10.

11.

12.

13.

14.

15.

162

LESSON

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11/23/2021 10:15:17 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 17

The blue line represents a line of symmetry. Draw the other part of the figure. 16.

EM2_0406SE_D_L17_classwork.indd 163

17.

LESSON

163

11/23/2021 10:15:17 AM

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11/23/2021 10:15:17 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 17

Name

Date

Circle the figures that show a line of symmetry. 1.

Draw all lines of symmetry on each figure. Write the number of lines of symmetry for each figure. 5. Lines of symmetry:

EM2_0406SE_D_L17_problem_set.indd 165

6. Lines of symmetry:

7. Lines of symmetry:

165

11/23/2021 10:13:26 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 17

8. Lines of symmetry:

9. Lines of symmetry:

10. Lines of symmetry:

11. Lines of symmetry:

12. Lines of symmetry:

13. Lines of symmetry:

The line represents a line of symmetry. Draw the other part of the figure. 14.

166

15.

PROBLEM SET

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11/23/2021 10:13:28 AM

EUREKA MATH2 Tennessee Edition

16.

4 ▸ M6 ▸ TD ▸ Lesson 17

17.

18. Does the circle show all possible lines of symmetry? How do you know?

EM2_0406SE_D_L17_problem_set.indd 167

PROBLEM SET

167

11/23/2021 10:13:28 AM

EM2_0406SE_D_L17_problem_set.indd 168

11/23/2021 10:13:28 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 17

Name

Date

Does each shape show a line of symmetry? 1. Yes

Yes

4. Draw all lines of symmetry for the shape shown.

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169

11/23/2021 10:14:29 AM

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EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 18 ▸ Assorted Triangles

EM2_0406SE_D_L18_removable_assorted_triangles.indd 171

171

11/23/2021 10:09:54 AM

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11/23/2021 10:09:54 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 18 ▸ Assorted Triangles

J P

L O

EM2_0406SE_D_L18_removable_assorted_triangles.indd 173

173

11/23/2021 10:09:54 AM

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11/23/2021 10:09:54 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 18

Name

Date

1. Complete the table for each triangle.

Triangle

Attributes

△GHI G

△PQR R P Q

Classification Angle

Side Length

acute triangle

scalene triangle

obtuse triangle

isosceles triangle

right triangle

equilateral triangle

acute triangle

scalene triangle

obtuse triangle

isosceles triangle

right triangle

equilateral triangle

acute triangle

scalene triangle

obtuse triangle

isosceles triangle

right triangle

equilateral triangle

△ JKL K

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175

11/23/2021 10:14:04 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 18

Triangle

Attributes

△MNO O

△ABC

Classification Angle

Side Length

acute triangle

scalene triangle

obtuse triangle

isosceles triangle

right triangle

equilateral triangle

∠A is a right angle.

Sides AB and AC have the same length. A

△DEF F

176

LESSON

EM2_0406SE_D_L18_classwork.indd 176

∠E is obtuse.

Sides ED and EF have the same length.

11/23/2021 10:14:05 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 18

Name

Date

Use the triangles to complete problems 1–4.

1. Classify each triangle by its side lengths. Then classify each triangle by its angle measures. Equilateral

Isosceles

Scalene

Acute

Right

Obtuse

2. Which, if any, triangles are acute isosceles?

3. Which, if any, triangles are obtuse scalene?

4. Casey says that triangle C is a right equilateral triangle. Do you agree with Casey? Why?

EM2_0406SE_D_L18_problem_set.indd 177

177

11/23/2021 10:12:40 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 18

5. △STU has 1 line of symmetry. What does this tell you about the measures of ∠S and ∠T ?

6. △VWX has 3 lines of symmetry.

a. Fill in the blanks to name 3 pairs of angles that have equal measures.

∠

and ∠

∠

and ∠

b. The perimeter of △VWX is 42 centimeters. What is the length of each side?

178

PROBLEM SET

EM2_0406SE_D_L18_problem_set.indd 178

c. Classify △VWX based on the measure of its angles and sides.

11/23/2021 10:12:40 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 18

7. Use a ruler to connect 3 points to make a triangle.

A D

b. Classify your triangle based on its angles and sides.

a. Use the points you connected to name your triangle.

c. Oka connects points A, B, and C. She says, “I made △ABC.” Do you agree with Oka? Why or why not?

8. Can a triangle have 2 right angles? How do you know?

EM2_0406SE_D_L18_problem_set.indd 179

PROBLEM SET

179

11/23/2021 10:12:40 AM

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11/23/2021 10:12:41 AM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TD ▸ Lesson 18

Date

Complete the table for each triangle.

Triangle

Classification Angle Type

Side Length

Acute

Isosceles

Obtuse

Equilateral

Right

Scalene

Acute

Isosceles

Obtuse

Equilateral

Right

Scalene

Acute

Isosceles

Obtuse

Equilateral

Right

Scalene

181

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TD ▸ Lesson 19

Date

1. Draw a right isosceles triangle.

Label each vertex to name the triangle as △BDU.

Then measure and label each angle and side length.

183

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 19

2. Draw a scalene triangle.

Label each vertex to name the triangle as △TOP.

Then measure and label each angle and side length.

184

LESSON

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TD ▸ Lesson 19

Date

Use a protractor and a ruler to draw each triangle. Label the side lengths and angle measures. 1. Right isosceles triangle

2. Right scalene triangle

3. Obtuse scalene triangle

4. Acute isosceles triangle

185

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 19

5. Draw all lines of symmetry in the triangles in problems 1–4. Did you draw at least 1 line of symmetry in each triangle? Explain.

Check true or false for each statement about equilateral △QRS.

4 cm

True

False

RS is 4 cm. 6. The length of ¯ 7. △QRS is an isosceles triangle. 8. △QRS has an obtuse angle.

9. The measure of ∠Q is equal to the measure of ∠S.

10. △QRS has 3 acute angles.

11. △QRS has exactly 2 lines of symmetry.

186

PROBLEM SET

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 19

12. Circle one statement from problems 6–11 that is false. Explain why the statement is false.

AB and ¯ BC . 13. Mr. Endo draws ¯ C

6 cm

Shen says Mr. Endo can use the line segments to draw right isosceles △ ABC.

Zara says Mr. Endo can use the line segments to draw obtuse isosceles △ ABC.

Do you agree with Shen or Zara? Why?

PROBLEM SET

187

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TD ▸ Lesson 19

Date

1. Use a protractor and a ruler to draw an obtuse isosceles triangle. Label the side lengths and angle measures. Draw any lines of symmetry, if they exist.

2. Use a protractor and a ruler to draw a right scalene triangle. Label the side lengths and angle measures. Draw any lines of symmetry, if they exist.

189

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ Sprint ▸ Decompose Fractions

Sprint Complete the equations. 1.

_3 = 1_ + ___

_9 = 6_ + ___ + 1_

4 6

191

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ Sprint ▸ Decompose Fractions

Number Correct:

Complete the equations. 1.

2 1 = + 3 3 3

_ _ ___

19.

5 1 2 = + + 3 3 3 3

3 = +1 3 3 3

_ ___ _

20.

8 2 = + +2 4 4 4 4

3 1 = + 4 4 4

_ _ ___

21.

5 9 = +2+ 5 5 5 5

4 = +2 4 4 4

_ ___ _

22.

12 2 3 = + + 6 6 6 6

3 1 = + 5 5 5

_ _ ___

23.

8 15 1 = + + 8 8 8 8

4 = +2 5 5 5

_ ___ _

24.

5 7 16 = + + 10 10 10 10

5 4 = + 5 5 5

_ _ ___

25.

19 = 1 + + 4 12 12 12 12

4 1 = + 6 6 6

_ _ ___

26.

45 55 102 = + + 100 100 100 100

3 5 = + 6 6 6

_ ___ _

27.

2 1 = + 2 2 2

10.

6 5 = + 6 6 6

_ _ ___

28.

4 = +2 4 4 4

11.

7 2 = + 8 8 8

_ _ ___

29.

3 _1 = 1 + 1 + 1___

12.

8 = +4 8 8 8

_ ___ _

30.

6_ = 1 +

13.

__9 = __3 + ___

31.

9 _4 = 5 ___ + 1 1_ + 3

14.

5 10 = + 10 10 10

__ ___ __

32.

12 4_ = 2 1_ + 3 1_ +

15.

11 = 4 + 12 12 12

__ __ ___

33.

15 _ = 3 1_ +

16.

6 12 = + 12 12 12

__ ___ __

34.

4 17 __ = 5 ___ + 2 __ + 9 __

17.

8 78 = + 100 100 100

___ ___ ___

35.

19 __ = 1__ + 13 ___ + 4 __

18.

50 100 = + 100 100 100

___ ___ ___

36.

12 20 ___ = 2 ___ + 5 ___ + 12 ___

192

_ _ _ ___ _ _ ___ _ _ ___ _ _

__ _ _ ___

__ _ ___ _

__ ___ __ __ __ __ ___ __

___ ___ ___ ___ _ _ ___ _ ___ _

3 4

6 8

7 10

10 12

26 100

3 +2 4

6 12

100

2 6

3 2 +4 8 8 3 10

8 100

3 12

100

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ Sprint ▸ Decompose Fractions

Number Correct: Improvement:

Complete the equations. 1.

2 1 = + 3 3 3

_ _ ___

19.

4 2 1 = + + 3 3 3 3

3 = +2 3 3 3

_ ___ _

20.

7 2 = + +1 4 4 4 4

2 1 = + 4 4 4

_ _ ___

21.

5 8 = + +2 5 5 5 5

4 = +2 4 4 4

_ ___ _

21.

11 3 1 = + + 6 6 6 6

2 1 = + 5 5 5

_ _ ___

23.

14 8 = + +1 8 8 8 8

3 = +2 5 5 5

_ ___ _

24.

5 7 15 = + + 10 10 10 10

5 4 = + 5 5 5

_ _ ___

25.

3 18 = + + 1 12 12 12 12

3 1 = + 6 6 6

_ _ ___

26.

55 45 101 = + + 100 100 100 100

4 = +2 6 6 6

_ ___ _

27.

2 1 = + 2 2 2

10.

6 5 = + 6 6 6

_ _ ___

28.

3 = +2 3 3 3

11.

6 3 = + 8 8 8

_ _ ___

29.

3 1_ = 1 + 1 + 1___

12.

8 = +4 8 8 8

_ ___ _

30.

6_ = 2 +

13.

__8 = __3 + ___

31.

9 4_ = 5 ___ + 3 + 1 1_

14.

5 10 = + 10 10 10

__ ___ __

32.

12 4_ = 3 1_ + 2 1_ +

15.

10 = 4 + 12 12 12

__ __ ___

33.

15 _ = 4 _ +

16.

6 12 = + 12 12 12

__ ___ __

34.

4 17 __ = 5 ___ + 9 __ + 2 __

17.

8 68 ___ = ___ + ___

35.

19 __ = 4 __ + 13 ___ + 1 __

18.

50 100 = + 100 100 100

___ ___ ___

36.

12 20 ___ = 2 ___ + 12 ___ + 5 ___

194

100

_ _ _ ___

_ _ ___ _ _ ___ _ _ __ _ _ ___

__ _ ___ _

__ ___ __ __ __ __ ___ __

___ ___ ___ ___ _ _ ___

_ ___ _

_3 + 1

3 4

6 8

7 10

10 12

26 100

3 8

3 12

100

2 6

2 + 31 8 8 10

100

3 10

6 12

8 100

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 20 ▸ Centimeter Grid Paper

195

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 20 ▸ Polygons for Game

197

4 ▸ M6 ▸ TD ▸ Lesson 20 ▸ Guess My Rule Game Board

Follows Rule

Does Not Follow Rule

EUREKA MATH2 Tennessee Edition

199

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 20 ▸ Rules Page

Polygons with at least 1 right angle

Polygons with more than 1 right angle

Polygons with no right angles

Polygons with all angles having the same measure

Polygons with exactly 1 pair of angles having the same measure

Polygons with no angles having the same measure

Polygons with at least 1 acute angle

Polygons with at least 1 obtuse angle

Polygons with 2 pairs of perpendicular sides

Polygons with at least 1 pair of parallel sides

Polygons with more than 1 pair of parallel sides

Polygons with no parallel sides

201

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 20

Name

Date

1. Ivan sorts polygons A–J based on their sides. Exactly 1 Pair of Parallel Sides

At Least 2 Pairs of Parallel Sides

G J

a. Mark the pairs of parallel sides on each polygon. Polygon B is done for you.

b. Which polygons are trapezoids?

c. Which polygons are parallelograms?

d. Ivan notices that none of the polygons are triangles. Explain why triangles do not belong in either category.

203

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 20

e. Ivan wants to sort the polygons based on the types of their angles. Write the letters of the polygons that appear to belong in each category. At Least 1 Right Angle

No Right Angles

2. Amy draws polygons that have at least 2 obtuse angles. Pablo draws polygons that have at least 2 acute angles. ’s Polygons

’s Polygons

a. Write the names Amy or Pablo in the blanks to indicate which polygons Amy and Pablo draw.

204

PROBLEM SET

EUREKA MATH2 Tennessee Edition

4 ▸ M6 ▸ TD ▸ Lesson 20

b. Does the trapezoid belong in one group or both groups? Explain how you know.

c. Does the rectangle belong in one of the groups? Explain how you know.

3. Luke and David classify polygons K–N. Luke says that all the polygons appear to have at least 1 right angle. David says that all the polygons appear to have at least 1 pair of perpendicular sides. Who is correct? Explain how you know.

PROBLEM SET

205

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M6 ▸ TD ▸ Lesson 20

Date

Jayla sorts polygons A–F based on their angles. Exactly 2 Right Angles

At Least 3 Right Angles

a. Mark the right angles on each polygon. Polygon A is done for you. b. Which polygons are quadrilaterals? c. Which polygons are rectangles?

207

EUREKA MATH2 Tennessee Edition

4 ▸ 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, Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Arts, MN. Gift of Bruce B. Dayton/Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York; page 17, Charles Demuth (1883–1935). My Egypt. 1927. Oil, fabricated chalk, and graphite pencil on composition board. Overall: 35 15/16 x 30 in. (91.3 x 76.2 cm). Purchase, with funds from Gertrude Vanderbilt Whitney. Inv. N.: 31.172 Digital image © Whitney Museum of American Art/Licensed by Scala/Art Resource, NY; page 162, (top row) Serafima Dashkevich/Shutterstock. com, Engineer studio/Shutterstock.com, (middle row), Nicole Kwiatkowski/Shutterstock.com, Andrew Mayovskyy/Shutterstock.com, (bottom row) Shanvood/Shutterstock.com, Sakchai.K/Shutterstock.com; All other images are the property of Great Minds. For a complete list of credits, visit http://eurmath.link/media-credits.

209

EUREKA MATH2 Tennessee Edition

4 ▸ M6

Acknowledgments Kelly Alsup, Leslie S. Arceneaux, Lisa Babcock, Adam Baker, Christine Bell, Reshma P. Bell, Joseph T. Brennan, Dawn Burns, Leah Childers, Mary Christensen-Cooper, Nicole Conforti, Jill Diniz, Christina Ducoing, Janice Fan, Scott Farrar, Gail Fiddyment, Ryan Galloway, Krysta Gibbs, Torrie K. Guzzetta, Kimberly Hager, Jodi Hale, Karen Hall, Eddie Hampton, Andrea Hart, Rachel Hylton, Travis Jones, Jennifer Koepp Neeley, Liz Krisher, Courtney Lowe, Bobbe Maier, Ben McCarty, Maureen McNamara Jones, Ashley Meyer, Bruce Myers, Marya Myers, Geoff Patterson, Victoria Peacock, Maximilian Peiler-Burrows, Marlene Pineda, Elizabeth Re, Jade Sanders, Deborah Schluben, Colleen Sheeron-Laurie, Jessica Sims, Tara Stewart, Mary Swanson, James Tanton, Julia Tessler, Jillian Utley, Saffron VanGalder, Rafael Velez, Jackie Wolford, Jim Wright, Jill Zintsmaster Trevor Barnes, Brianna Bemel, 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

210

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 Addition and Subtraction Module 2 Place Value Concepts for Multiplication and Division Module 3 Multiplication and Division of Multi-Digit Numbers Module 4 Foundations for Fraction Operations Module 5 Place Value Concepts for Decimal Fractions Module 6 Angle Measurements and Plane Figures

What does this painting have to do with math? American abstract painter Frank Stella used a compass to make brightly colored curved shapes in this painting. Each square in this grid includes an arc that is part of a design of semicircles that look like rainbows. When Stella placed these rainbow patterns together, they formed circles. What fraction of a circle is shown in each square? On the cover Tahkt-I-Sulayman Variation II, 1969 Frank Stella, American, born 1936 Acrylic on canvas Minneapolis Institute of Art, Minneapolis, MN, USA Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Art, MN. Gift of Bruce B. Dayton/ Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York

ISBN 978-1-63898-513-6

781638 985136