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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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.
11-2Chapter Resources© Houghton Mifflin Harcourt Publishing Company
GGGGaaGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGaaaaaaaaaaaaa eeeeemmeeeeeeeeeeeeemmmmmeeeeeeeeeeeeemmmmmmeeemmmmmmeeeeeeeeeeeeGameGame©
Hou
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©Co
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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
turn counterclockwise
4. 1 __ 3
turn clockwise
5. 1 ___ 12
turn clockwise
6. 1 __ 4
turn counterclockwise
7. 8 ___ 12
turn clockwise
8. 7 ___ 12
turn clockwise
9. 5 ___ 12
turn counterclockwise
10. 1 __ 2
turn counterclockwise
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
11-7 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
11-8 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
11-9 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
11-10 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
11-11 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
11-12 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
11-13 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
11-14 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
Chapter 11 TestPage 2
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
?
11-16Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Chapter 11 Test
Chapter 11 TestPage 3
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?
The angle measures .
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
Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
11-17 Chapter 11 Test
Chapter 11 TestPage 4
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
11-18Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Chapter 11 Test
Chapter 11 TestPage 5
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.
The angle measures .
Figure 1 Figure 2
220°
XA
C
BD
Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
11-19 Chapter 11 Test
Chapter 11 TestPage 6
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.
11-20Chapter Resources© Houghton Mifflin Harcourt Publishing Company
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°
11-22 Chapter 11 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
11-23 Chapter 11 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
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.
11-24 Chapter 11 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
11-25 Chapter 11 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Chap
ter 1
1 Te
stPa
ge 2
5
. N
ina d
rew
the f
igure
show
n. For
5a–5
c, se
lect
Yes
or
No
to t
ell
wheth
er
the s
tate
ment
is t
rue.
5a.
The m
easu
re o
f a s
traig
ht
angle
is
36
0°.
Y
es
N
o
5b.
To f
ind t
he m
easu
re o
f x,
Nin
a
can s
ubtr
act
10
5° f
rom
36
0°.
Y
es
N
o
5c.
The m
easu
re o
f x
is 7
5°.
Y
es
N
o
6
. K
ayl
a d
rew
this
fig
ure
with a
pro
tracto
r.
Par
t A
Wri
te a
n e
quation t
hat
can b
e u
sed t
o f
ind t
he m∠
XST
.
90° +
65°
+ x
= 1
80°
Par
t B
What
is t
he m
easu
re o
f ∠
XST
? D
esc
ribe h
ow
you s
olv
ed t
he
equation a
nd h
ow
you c
an c
heck y
our
answ
er.
25°;
po
ssib
le a
nsw
er: I
fou
nd
th
e su
m o
f 90
° an
d 6
5°.
Th
en I
sub
trac
ted
th
is s
um
fro
m 1
80° t
o fi
nd
th
e va
lue
of x.
I ca
n c
hec
k th
e an
swer
by
rep
laci
ng
x w
ith
25
and
ch
ecki
ng
th
at it
mak
es a
tru
e eq
uat
ion
; 90
+ 6
5 +
25
= 1
80.
7
. U
se a
pro
tracto
r to
fin
d t
he m
easu
re o
f th
e a
ngle
.
The a
ngle
measu
res
.
105°
x 65°
90°
RS
TXW
?
45°
11-16
Chap
ter R
esou
rces
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ough
ton
Miff
lin H
arco
urt P
ublis
hing
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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
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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
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ough
ton
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lin H
arco
urt P
ublis
hing
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pany
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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
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ough
ton
Miff
lin H
arco
urt P
ublis
hing
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pany
Nam
e
11-17
Chap
ter 1
1 Te
st
11-27 Answer KeyChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
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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
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pany
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e
11-19
Chap
ter 1
1 Te
st
11-28 Answer KeyChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 3 Response
11-29 Chapter 11 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 2 Response
11-30 Chapter 11 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 1 Response
11-31 Chapter 11 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 0 Response
11-32 Chapter 11 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
11-33© Houghton Mifflin Harcourt Publishing Company
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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