CHAPTER RESOURCES • Chapter 11elementary.dmschools.org/uploads/1/3/6/0/13604257/c11.pdf · 2019....

CHAPTER RESOURCES • Chapter 11Angles

INCLUDES • School-Home Letter

• Vocabulary Game Directions

• Daily Enrichment Activities

• Reteach Intervention for every lesson

• Chapter 11 Test

• Chapter 11 Performance Task • Answer Keys and Individual Record Forms

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Copyright © by Houghton Mifflin Harcourt Publishing Company

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ContentsChapter 11 School-Home Letter (English) ....................................................11-1

Chapter 11 School-Home Letter (Spanish) ...................................................11-2

Vocabulary Game .........................................................................................11-3

11.1 Reteach ................................................................................................11-5

11.1 Enrich ....................................................................................................11-6

11.2 Reteach ................................................................................................11-7

11.2 Enrich ....................................................................................................11-8

11.3 Reteach ................................................................................................11-9

11.3 Enrich ..................................................................................................11-10

11.4 Reteach ..............................................................................................11-11

11.4 Enrich ..................................................................................................11-12

11.5 Reteach ..............................................................................................11-13

11.5 Enrich ..................................................................................................11-14

Chapter 11 Test ...........................................................................................11-15

Chapter 11 Performance Task .....................................................................11-21

Answer Keys ...............................................................................................11-26

Individual Record Forms .............................................................................11-33

Table of ContentsChapter Resources© Houghton Mifflin Harcourt Publishing Company

iii

School-HomeSchool-Home

LetterChapter

11

ActivityHelp your child measure angles in pictures of buildings and bridges and decide whether certain angle measures are more common. Then have your child draw his or her own building or bridge design and label each angle measure.

Dear Family,

Throughout the next few weeks, our math class will be learning about angles and angle measures. We will also learn to use a protractor to measure and draw angles.

You can expect to see homework in which students find and compute with angle measures.

Here is a sample of how your child will be taught how to relate degrees to fractional parts of a circle.

clockwise The direction the clock hands move

counterclockwise The direction opposite from the way clock hands move

degree (º) A unit for measuring angles

protractor A tool for measuring the size of an angle

Tips

STEP 1

A right angle turns 1 _ 4 through a circle. Write 1 _ 4 as an equivalent fraction with 360 in the denominator: 1 __

4 = 90 ____

360

STEP 2

A 1 ___ 360 turn measures 1º. So, a 90 ___ 360 turn measures 90º.

Find the measure of a right angle.

Find Angle Measures

Classifying Angles

An acute angle measures less than 90º. An obtuse angle measures more than 90º and less than 180º. A straight angle measures 180º.

11-1Chapter Resources© Houghton Mifflin Harcourt Publishing Company

para la casaCartaCartaCapítulo

11

ActividadAyude a su hijo o hija a medir ángulos en dibujos de edificios y puentes y decidan si ciertas medidas de ángulos son más comunes. Luego pídale que dibuje su propio diseño de edificio o puente y que le ponga nombre a cada medida de ángulo.

Querida familia,

Durante las próximas semanas, en la clase de matemáticas aprenderemos sobre ángulos y medidas de los ángulos. También aprenderemos a usar un transportador y a medir y trazar ángulos.

Llevaré a casa tareas en las que tenga que hallar y hacer cálculos con medidas de ángulos.

Este es un ejemplo de cómo vamos a relacionar los grados con las partes fraccionarias de un círculo.

PASO 1

Un ángulo recto gira 1 _ 4 de un círculo. Escribe 1 _ 4 como una fracción equivalente con 360 en el denominador: 1 _ 4 = 90 ___ 360

PASO 2

Un giro de 1 ___ 360 mide 1º. Por lo tanto, un giro de 90 ___ 360 mide 90º.

Halla la medida de un ángulo recto.

Hallar medidas de ángulos

en el sentido de las manecillas del reloj La dirección en que se mueven las manecillas del reloj

en sentido contrario a las manecillas del reloj La dirección opuesta a cómo se mueven las manecillas del reloj

grado (º) Una unidad para medir los ángulos

transportador Una herramienta para medir el tamaño de un ángulo

Pistas

Clasificar ángulos

Un ángulo agudo mide menos de 90º. Un ángulo obtuso mide más de 90º y menos de 180º. Un ángulo llano mide 180º.


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Going Places with words

Picture It For 3 to 4 players

Materials

• timer

• sketch pad

How to Play

1. Take turns to play.

2. To take a turn, choose a word from the Word Box, but do

not tell the word to the other players.

3. Set the timer for 1 minute.

4. Draw pictures and numbers on the sketch pad to give clues

about the word. Do not use words.

5. The first player to guess the word before time runs out gets

1 point. If that player can use the word in a sentence, he or

she gets 1 more point. Then that player gets a turn choosing

a word.

6. The first player to score 10 points wins.

Word Boxacute angleclockwisecounterclockwisedegree(°)protractor rayright anglevertex

Chapter 11 600A

Chapter 11Vocabulary Game

11-3 Game DirectionsChapter Resources© Houghton Mifflin Harcourt Publishing Company

16

16

1 61 6

1616

Name

six

2

six

Tell what fraction of the circle the shaded angle represents.

1. 2. 3.

Angles and Fractional Parts of a Circle

Find how many 1 _ 6 turns make a complete circle.

Materials: fraction circles

Step 1 Place a 1 _ 6 piece so the tip of the fraction

piece is on the center of the circle.Trace the fraction piece by drawing along the dashed lines in the circle.

Step 2 Shade and label the angle formed by

the 1 _ 6 piece.

Step 3 Place the 1 _ 6 piece on the shaded angle.

Turn it clockwise (in the direction that the

hands on a clock move). Turn the fraction piece

to line up directly beside the shaded section.

Step 4 Trace the fraction piece. Shade and

label it. You have traced sixths in all.

Step 5 Repeat until you have shaded the entire circle.

There are angles that come together in the center of the circle.

So, you need 1 _ 6 turns to make a circle.

Lesson 11.1Reteach

11-5 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

W

T

S

P

ON

I

H

E

D

AStart

Name

A Turning Riddle

What is the best way to eat soup?

Use the circle below. For each exercise, start at the top of the circle, make the indicated turn, and write the letter on the blank line. When you have finished, read the letters from top to bottom to answer the riddle.

1. 1 ___ 12

turn counterclockwise

2. 5 ___ 12

turn clockwise

3. 1 __ 6


4. 1 __ 3

turn clockwise

5. 1 ___ 12

turn clockwise

6. 1 __ 4


7. 8 ___ 12

turn clockwise

8. 7 ___ 12

turn clockwise

9. 5 ___ 12


10. 1 __ 2


11. Make up your own riddle and answer circle. Exchange it with a classmate and solve.

Lesson 11.1Enrich

11-6 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

5121

8

1539

360

16

50360

Name

60°

Tell the measure of the angle in degrees.

1. 2.

3. 4.

Degrees

Angles are measured in units called degrees. The symbol for degrees is °. If a circle is divided into 360 equal parts, then an angle that turns through 1 part of the 360 measures 1°.

An angle that turns through 50 ___ 360

of a circle measures 50°.

Find the measure of an angle that turns through 1 _ 6 of a circle.

Step 1 Find a fraction that is equivalent to 1 _ 6 with 360 in the

denominator. Think: 6 3 60 5 360.

1 _ 6 5 1 3 60 ______

6 3 60 5 60 ___

360

Step 2 Look at the numerator of 60 ___ 360

.

The numerator tells how many degrees are in 1 _ 6 of a circle.

So, an angle that turns through 1 _ 6

of a circle measures .

Lesson 11.2Reteach


Name

Time by Degrees

Use the hands of a clock to answer each question.

1. How many degrees does the minute hand turn to get from 12:00 to 12:05?

3. How many degrees does the hour hand turn in one hour?

5. What is the measure in degrees of the angle formed by the hands of a clock when the time is 3:00?

7. What is the degree measure of the angle formed by the hands of a clock when the time is 9:00?

2. How many degrees does the minute hand turn to get from 12:00 to 12:20?

4. How many degrees does the hour hand turn to get from 12:00 to 12:20?

6. What is the degree measure of the angle formed by the hands of a clock when the time is 12:00?

8. What is the measure in degrees of the angle formed by the hands of a clock when the time is 6:00?

9. Stretch Your Thinking What is the degree measure of the angle formed by the hands of a clock when the time is 3:30?

Lesson 11.2Enrich


A

C B

Step 4

9090

8010070

1106012050

130

40140

30150

2016

0

10 170

0 180

10080

11070 12060 13050 14040 15030

1602017010

1800

Step 3

A

C B

Step 2

9090

8010070

1106012050

130

40140

30150

2016

0

10 170

0 180

10080

11070 12060 13050 14040 15030

1602017010

1800

Step 1

M

K

NG

F

H

Name

Use a protractor to find the angle measure.

1.

m/FGH

2.

m/KMN

Use a protractor to draw the angle.

3. 110° 4. 55°

30°

Measure and Draw Angles

A protractor is a tool for measuring the size of an angle.

Follow the steps below to measure / ABC.

Step 1 Place the center point of the protractor on vertex B of the angle.

Step 2 Align the 0° mark on the protractor with ray BC. Note that the 0° mark ison the outer scale or top scale.

Step 3 Find where ray BA intersects the same scale.

Step 4 Read the angle measure on the scale.

The m/ ABC 5 .

Lesson 11.3Reteach


Name

5. Stretch Your Thinking Compare your triangles with those of several classmates. What do you notice?

Drawing Triangles

For Exercises 1–4, draw and label a triangle with the given angle measures.

1. 60°, 60°, 60°

3. 42°, 64°, 74°

2. 90°, 35°, 55°

4. 118°, 31°, 31°

Lesson 11.3Enrich


45° 20°

R P

S

T

70°60°

K L

NM

E70°

35°

G

J H

A

C

D

B

Name

Join and Separate Angles

The measure of an angle equals the sum of the measures of its parts.

Use your protractor and the angles at the right.

Step 1 Measure / ABC and /CBD. Record the measures.

m/ABC 5 ; m/CBD 5

Step 2 Find the sum of the measures.

1 5

Step 3 Measure /ABD. Record the measure.

m/ABD 5

So, m/ABC 1 m/CBD 5 m/ABD.

75°

40°

75°40°35°

35°

Add to find the measure of the angle. Write an equation to record your work.

1.

m/EGJ 5

2.

m/KLN 5

3.

m/PRT 5

Use a protractor and the art at the right.

4. Find the measure of each angle. Label each angle with its measure.

5. Write the sum of the angle measures as an equation.

Lesson 11.4Reteach

W

X

YT

Z


Name

5. Describe how you used a protractor to

complete the exercises.

Degrees of Separation

Use a protractor. For each exercise, measure and label the angle. Then separate the angle as instructed and label the measures of its parts.

1. Separate the angle into two equal

angles.

3. Separate the angle into two angles

such that one angle is 15° greater

than the other.

2. Separate the angle into three equal

angles.

4. Separate the angle into three angles

such that the greatest angle is 2 times

as large as the smallest angle. The

greatest angle also measures 20°

more than the third angle.

Lesson 11.4Enrich


x45°

60° x

110°

R

x 110°60°

PM

N

Name

m/MNR 5 110°

110°

50°

50°

50°60°

write an equation to solve the problem

draw a bar model to represent the problem

60° 110°

measure, or m/PNRm/MNP 5 60° and over, or m/PNR

find the unknown angle measures I know: measure of the part left

draw a bar model to the angle the angle

Problem Solving • Unknown Angle Measures

Use the strategy draw a diagram.

Mrs. Allen is cutting a piece of wood for a set for the school play. She needs a piece of wood with a 60° angle. After the cut, what is the angle measure of the part left over?

Read the Problem

What do I need to find? What information do I need to use?

How will I use the information?

I need to find

.

I can use

.

I can

.

Solve the Problem

I can .

Then I can .

m/MNP 1 m/PNR 5 m/MNR

1 x 5

x 5 2 , or

So, m/PNR 5

The angle measure of the part left over is .

1. Cal is cutting a rectangular board as shown. What is the angle measure of the part left over?

2. What equation did you use to solve?

Lesson 11.5Reteach


Name

5. Stretch Your Thinking Draw any two triangles and measure

the angles in each. Find the sum of the angle measures.

Look back at the angle measures you found in Exercises 1–4.

Can you draw a triangle for each set? Explain.

Unknown Measures

In Exercises 1–4, three angles join to form a straight angle. Use the information given to find the measure of each angle.

1. One angle is a right angle. Give

three pairs of possible measures

for the other two angles.

3. All three angles have the same

measure. What is the measure of

each angle?

2. One angle measures 40°. The other

two angles have the same measure.

What is the measure of each angle?

4. One angle measures 30°. The measure

of the second angle is 2 times as large

as the measure of the third angle.

What are the measures of the other

two angles?

Lesson 11.5Enrich


Chapter 11 TestPage 1

1. An angle represents 1 __ 10

of a circle. Use the numbers to show

how to find the measure of the angle in degrees.

1 ___ 10

= 1 × ___________

10 × = _______

The angle measure is .

2. Match the measure of each ∠R with the measure of ∠S that

forms a right angle.

∠R ∠S

25° 65°

75°

44°39°

51°58°

46°

38° 52°

3. Alejandro drew an acute angle. Which could be the measure

of the angle he drew? Mark all that apply.

A 60° C 97°

B 12° D 90°

4. Draw an angle that represents a 3 _ 4 turn clockwise

on the circle.

101

24

30

36

360

•

•

• •

•

•

•

•

•

•

Chapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

11-15 Chapter 11 Test


5. Nina drew the figure shown. For 5a–5c, select Yes or No

to tell whether the statement is true.

5a. The measure of a straight

angle is 360°. Yes No

5b. To find the measure of x, Nina

can subtract 105° from 360°. Yes No

5c. The measure of x is 75°. Yes No

6. Kayla drew this figure with a protractor.

Part A

Write an equation that can be used to find the m∠XST .

Part B

What is the measure of ∠XST ? Describe how you solved the

equation and how you can check your answer.

7. Use a protractor to find the measure of the angle.

The angle measures .

105° x

65° 90°

R S T

XW

?


Name

Chapter 11 Test


8. Paula drew this angle on the circle. Which describes the angle? Mark all that apply.

A 1 __ 2 turn C clockwise

B 1 __ 4 turn D counterclockwise

9. Marla has a piece of felt that is 1 _ 3 of a large circle. She cuts the piece of felt in half from the center point of the circle. What is the angle measure of each part?


10. Use a protractor to find the measure of each angle. Write each angle and its measure in a box ordered by the measure of the angles from least to greatest.

C

AB

Angle:

Measure:

Angle:

Measure:

Angle:

Measure:

11. Use the numbers and symbols to write an equation that can be used to find the measure of the unknown angle.

90° 52° x

What is the measure of the unknown angle?

52

x = + ×

90 180 360


Name



12. Choose the word or number to complete a true statement

about ∠MNO.

∠MNO is a(n)

acute

obtuse

right

angle that has a measure of

30°

120°

150°

.

13. Rachael began walking her dog at 3:00 P.M. She stopped

at 3:30 P.M. How many degrees did the minute hand turn

during Rachael’s walk? Explain how you found your answer.

8910

11 12

7 6 543

21

Start

8910

11 12

7 6 543

21

Stop

14. An angle measures 51°. Through what fraction of a circle

does the angle turn?

_____ of a circle

M NO


Name

Chapter 11 Test


15. Write the letter for each angle measure in the correct box.

A 20° B 77° C 111° D 180° E 175° F 90°

acute obtuse right straight

16. For numbers 16a–16b, select the fraction that

makes a true statement about the figure.

16a. The angle in Figure 1 represents a

1 __ 4

1 __ 2

3 __

4

turn.

16b. The angle in Figure 2 represents a

1 __ 4

1 __ 2

3 __

4

turn.

17. Jeffrey cuts a rectangle out of a piece of scrap paper

as shown. He wants to calculate the angle measure

of the piece that is left over.

Part A

Draw a bar model to represent the problem.

Part B

Write and solve an equation to find x.


Figure 1 Figure 2

220°

XA

C

BD


Name



18. Two angles, ∠M and ∠N, form a straight angle.

∠M measures 50°. For numbers 18a–18c, select

True or False for the statement.

18a. ∠N is an acute angle. True False

18b. The equation 180° − 50° = x ° can

be used to find the measure of ∠N. True False

18c. The measure of ∠N is 130°. True False

19. A circle is divided into parts. Which sum could represent the

angle measures that make up the circle? Mark all that apply.

A 120° + 120° + 120°

B 47° + 61° + 78° + 83° + 101°

C 15° + 40° + 53° + 62° + 90° + 100°

D 20° + 30° + 60° + 70°

20. Use a protractor to find the measures of the unknown angles.

Y

X

Chestnut St

Maple St

m∠X = m∠Y =

What do you notice about the measures of the unknown

angles? Is this what you would have expected? Explain

your reasoning.


Name

Chapter 11 Test

Name Chapter 11

Klee Kat

Paul Klee was an artist who painted using geometric shapes. A cat painted by Paul Klee might look something like this.

73°

11-21 Chapter 11 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company

1. Find these angles in the cat. Use the letters to mark each angle on the drawing as you find it. Then write the angle measures on the drawing. One angle measure is shown as an example.a. an angle of 34°b. the angle closest to 90°c. two angles whose sum is 196°d. the smallest anglee. the greatest angle

2. Make your own geometric drawing. Include the following angles and mark them on the drawing.

a. one angle of 58° b. one right angle c. two angles whose sum is 145°


Angles

Klee Kat COMMON CORE STANDARDS

4.MD.C.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.

4.MD.C.5b An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Also MP1, MP5

PURPOSETo assess the ability to measure angles and draw angles of a specific measure

TIME25–30 minutes

GROUPINGIndividuals

MATERIALS• Performance Task, paper, pencil

• Protractor, straightedge

PREPARATION HINTS• Review the proper way to measure an angle.

• Review how to draw a given angle.

• Review vocabulary, including sum, angle, right angle, degree, and the symbol for degree.

Chapter 11


IMPLEMENTATION NOTES • Read the task aloud to students and make sure that all students have a clear understanding

of the task.

• Students may use manipulatives to complete the task.

• Allow students as much paper as they need to complete the task.

• Allow as much time as students need to complete the task.

• Students must complete the task individually, without collaboration.

• Collect all student work when the task is complete.

TASK SUMMARYStudents measure angles. They add to find a specific angle. They make their own geometric drawing that includes four given angles.

REPRESENTATION In this task, teachers can…

• Customize the display of information by guiding some students to work on enlarged copies of the drawing.

• Increase comprehension by guiding students to use a straightedge to extend short lines to the outer scale of the protractor.

ACTION and EXPRESSION In this task, teachers can…

• Vary methods by encouraging students to estimate the degrees in angles before measuring them.

• Build fluency by suggesting that students refer to a set of benchmark angles (30°, 45°, 90°, 135°) drawn on the board.

ENGAGEMENT In this task, teachers can…

• Increase mastery by providing swift and detailed feedback.

EXPECTED STUDENT OUTCOMES• Complete the task within the time allowed

• Reflect engagement in a productive struggle

• Measure and draw angles

SCORING Use the associated Rubric to evaluate each student’s work.


Performance Task Rubric

KLEE KAT

A level 3 response • Demonstrates that the student has made sense of the task and persevered

• Shows evidence of using tools strategically

• Demonstrates an ability to measure an angle to the nearest whole degree with ease and understanding

• Demonstrates an ability to draw angles to a given degree smoothly and precisely

A level 2 response • Demonstrates that for the most part, the student has made sense of the task and persevered

• Shows evidence of using most tools strategically

• Demonstrates an ability to measure an angle to the nearest whole degree with understanding

• Demonstrates an ability to draw angles to a given degree competently

• May include a minor error in measurement precision

A level 1 response • Demonstrates that for the most part, the student has made some sense of the task and persevered

• Shows evidence of some struggle to use tools strategically

• Demonstrates some understanding of how to measure angles

• Demonstrates little ability to draw angles to a given degree

• May include more than one significant error in measurement precision

A level 0 response • Shows little evidence that the student has made sense of the task or persevered

• Reflects a lack of understanding of how to use the proper tools for the task

• Demonstrates little understanding of how to measure or draw angles

• Shows little evidence of addressing the components of the task


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x 65°

90°

RS

TXW

?

45°

11-16

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

Chap

ter 1

1 Te

st

Chap

ter 1

1 Te

stPa

ge 1

1

.A

n a

ngle

repre

sents

1

__

10 o

f a c

ircle

. U

se t

he n

um

bers

to s

how

how

to f

ind t

he m

easu

re o

f th

e a

ngle

in d

egre

es.

1

___

10 =

1

×

36

___________

1

0 ×

36

=

36

_______

The a

ngle

measu

re is

.

2

. M

atc

h t

he m

easu

re o

f each ∠

R w

ith t

he m

easu

re o

f ∠

S th

at

form

s a r

ight

angle

.

∠R

∠S

25°

65°

75°

44°

39°

51°

58°

46°

38°

52°

3

. A

leja

ndro

dre

w a

n a

cute

angle

. W

hic

h c

ould

be t

he m

easu

re

of

the a

ngle

he d

rew

? M

ark

all

that

apply

.

A

60°

C

97°

B

12°

D

90°

4

. D

raw

an a

ngle

that

repre

sents

a 3

_

4 t

urn

clo

ckw

ise

on t

he c

ircle

. P

oss

ible

an

swer

is s

ho

wn

.

101

24

30

36

36

0

• • ••• •• • •

•

36°

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

11-15

Chap

ter 1

1 Te

st

11-26 Answer KeyChapter Resources© Houghton Mifflin Harcourt Publishing Company

Chap

ter 1

1 Te

stPa

ge 4

12

. C

hoose

the w

ord

or

num

ber

to c

om

ple

te a

tru

e s

tate

ment

about ∠

MN

O.

∠M

NO

is a

(n)

acute

obtu

se

right

angle

that

has

a m

easu

re o

f

30°

12

0°

15

0°

.

13

. R

achael began w

alk

ing h

er

dog a

t 3

:00

P.M

. She s

topped

at

3:3

0 P.M

. H

ow

many

degre

es

did

the m

inute

hand t

urn

duri

ng R

achael’s

walk

? E

xpla

in h

ow

you f

ound y

our

answ

er.

891011

12

76

5432

1

Star

t

891011

12

76

5432

1

Stop

180°

; po

ssib

le e

xpla

nat

ion

: I s

had

ed t

he

par

t o

f th

e cl

ock

th

at t

he

min

ute

han

d tu

rned

fro

m 3

:00

to 3

:30

and

fou

nd

th

at it

was

a 1 _ 2 t

urn

. Th

en I

fou

nd

th

at 1 _ 2 =

180

___

360

to fi

nd

th

e n

um

ber

of

deg

rees

th

e m

inu

te h

and

turn

ed.

14

. A

n a

ngle

measu

res

51°.

Thro

ugh w

hat

fraction o

f a c

ircle

does

the a

ngle

turn

?

_____ o

f a c

ircle

51 360

MN

O 11-18

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

Chap

ter 1

1 Te

st

Chap

ter 1

1 Te

stPa

ge 3

8

.Paula

dre

w t

his

angle

on t

he c

ircle

. W

hic

h d

esc

ribes

the

angle

? M

ark

all

that

apply

.

A

1

__

2 t

urn

C

clo

ckw

ise

B

1

__

4 t

urn

D

counte

rclo

ckw

ise

9

. M

arl

a h

as

a p

iece o

f fe

lt t

hat

is 1

_

3 o

f a larg

e c

ircle

.

She c

uts

the p

iece o

f fe

lt in h

alf f

rom

the c

ente

r poin

t

of

the c

ircle

. W

hat

is t

he a

ngle

measu

re o

f each p

art

?

The

angle

measu

res

.

10

. U

se a

pro

tracto

r to

fin

d t

he m

easu

re o

f each a

ngle

.

Wri

te e

ach a

ngle

and its

measu

re in a

box

ord

ere

d b

y th

e

measu

re o

f th

e a

ngle

s fr

om

least

to g

reate

st.

C

AB

Angle

: B

Measu

re: 80

°

Angle

: A

Measu

re: 13

0°

Angle

: C

Measu

re: 15

0°

11

. U

se t

he n

um

bers

and s

ymbols

to w

rite

an e

quation t

hat

can

be u

sed t

o f

ind t

he m

easu

re o

f th

e u

nknow

n a

ngle

.

90°

52° x

90 +

52

+ x

= 1

80

What

is t

he m

easu

re o

f th

e u

nknow

n a

ngle

?

52 x

=+

×

90

18

03

60 38

°

60°

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

11-17

Chap

ter 1

1 Te

st


Chap

ter 1

1 Te

stPa

ge 6

18

. Tw

o a

ngle

s, ∠

M a

nd ∠

N, fo

rm a

str

aig

ht

angle

.

∠M

measu

res

50

°. F

or

num

bers

18

a–1

8c, se

lect

Tru

e o

r Fals

e f

or

the s

tate

ment.

18a

. ∠N

is a

n a

cute

angle

.

Tru

e

Fals

e

18b.

The e

quation 1

80

° − 5

0° =

x °

can

be u

sed t

o f

ind t

he m

easu

re o

f ∠

N.

Tru

e

Fals

e

18c

. The m

easu

re o

f ∠

N is

13

0°.

Tru

e

Fals

e

19

. A

cir

cle

is

div

ided into

part

s. W

hic

h s

um

could

repre

sent

the

angle

measu

res

that

make u

p t

he c

ircle

? M

ark

all

that

apply

.

A

12

0° +

12

0° +

12

0°

B

47

° + 6

1° +

78

° + 8

3° +

10

1°

C

15

° + 4

0° +

53

° + 6

2° +

90

° + 1

00

°

D

20

° + 3

0° +

60

° + 7

0°

20

. U

se a

pro

tracto

r to

fin

d t

he m

easu

res

of

the u

nknow

n a

ngle

s.

YX

Che

stnu

t St

Map

le S

t

m∠

X =

m∠

Y =

What

do y

ou n

otice a

bout

the m

easu

res

of

the u

nknow

n

angle

s? Is

this

what

you w

ould

have

exp

ecte

d?

Exp

lain

your

reaso

nin

g.

Po

ss

ible

an

sw

er:

Th

e m

ea

su

res

of

the

an

gle

s h

ave

a

su

m o

f 18

0°.

Eve

n t

ho

ug

h t

he

an

gle

s a

re d

ivid

ed

by

a l

arg

e b

ar

tha

t re

pre

se

nts

Ma

ple

Str

ee

t, t

his

ma

ke

s

se

ns

e b

ec

au

se

th

e a

ng

les

ma

ke

up

a s

tra

igh

t a

ng

le.

35

°14

5°

11-20

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

Chap

ter 1

1 Te

st

Chap

ter 1

1 Te

stPa

ge 5

15

. W

rite

the lett

er

for

each a

ngle

measu

re in t

he c

orr

ect

box.

A 2

0°

B 7

7°

C 1

11

° D

1

80

° E

17

5°

F9

0°

acute

A, B

obtu

se

C, E

right

F

stra

ight

D

16

. For

num

bers

16

a–1

6b, se

lect

the f

raction t

hat

makes

a t

rue s

tate

ment

about

the f

igure

.

16a

. The a

ngle

in F

igure

1 r

epre

sents

a

1

__

4

1

__

2

3

__

4

turn

.

16b

. The a

ngle

in F

igure

2 r

epre

sents

a

1

__

4

1

__

2

3

__

4

turn

.

17

. Je

ffre

y cuts

a r

ecta

ngle

out

of

a p

iece o

f sc

rap p

aper

as

show

n. H

e w

ants

to c

alc

ula

te t

he a

ngle

measu

re

of

the p

iece t

hat

is left

ove

r.

Par

t A

Dra

w a

bar

model to

repre

sent

the p

roble

m.

180°

220°

X

Par

t B

Wri

te a

nd s

olv

e a

n e

quation t

o f

ind x

.

m∠ABD

+ m

∠CBD

= m

∠ABC

;

18

0 +

x =

22

0; x

= 4

0

The a

ngle

measu

res

.

Figu

re 1

Figu

re 2

220°

XA

C

BD

Po

ss

ible

dra

win

g i

s s

ho

wn

.

40

°

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

11-19

Chap

ter 1

1 Te

st


Sample Level 3 Response


11-33© Houghton Mifflin Harcourt Publishing Company

Chapter Resources Individual Record Form

Student’s Name Date

Chapter 11 Test

Item Lesson Standard Content Focus Intervene with

Personal Math Trainer

1, 3, 13-15 11.2 4.MD.C.5a Relate degrees to angles and fractional

parts of a circle. R—11.2 4.MD.5a

2, 5, 19 11.4 4.MD.C.7 Determine the measure of an angle separated into parts. R—11.4 4.MD.7

4, 8, 16 11.1 4.MD.C.5a Relate angles to fractional parts of a circle. R—11.1 4.MD.5a

6, 9, 11, 17, 18 11.5 4.MD.C.7 Draw diagrams and use equations

to find unknown angle measures. R—11.5 4.MD.7

7, 10, 12, 20 11.3 4.MD.C.6 Use a protractor to measure

and draw angles. R—11.3 4.MD.6

Key: R—Reteach

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