11

   

  clockwise The direction the clock
hands move

counterclockwise The direction

opposite from the way clock hands
Dear Family, move

degree (º) A unit for measuring

Throughout the next few weeks, our math class will angles
be learning about angles and angle measures. We will protractor A tool for measuring the
also learn to use a protractor to measure and draw size of an angle
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.

Find Angle Measures

Find the measure of a right angle.

STEP 1 Classifying Angles

A right angle turns 1_4 through a circle. An acute angle measures

less than 90º. An obtuse
Write 1_4 as an equivalent fraction with
90 angle measures more than
360 in the denominator: 1 __ 5 ____
4 360 90º and less than 180º.
STEP 2
A straight angle
measures 180º.
A ___
1 turn measures 1º. So, a ___
360
90
360
turn
measures 90º.

Activity
© Houghton Mifflin Harcourt Publishing Company

Help 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.

Chapter 11 P205
 11
 



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
Querida familia, se mueven las manecillas del reloj

Durante las próximas semanas, en la clase de grado (º) Una unidad para medir los
ángulos
matemáticas aprenderemos sobre ángulos y medidas
transportador Una herramienta para
de los ángulos. También aprenderemos a usar un medir el tamaño de un ángulo
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.

Hallar medidas de ángulos

Halla la medida de un ángulo recto.


PASO 1 Clasificar ángulos

Un ángulo recto gira 1_4 de un círculo.

Un ángulo agudo mide menos
de 90º. Un ángulo obtuso
Escribe 1_4 como una fracción equivalente
mide más de 90º y menos de
con 360 en el denominador: 1_4 5 __90
360 180º. Un ángulo llano
mide 180º.
PASO 2

Un giro de __1
360
mide 1º. Por lo tanto, un
__
90
giro de 360 mide 90º.

Actividad © Houghton Mifflin Harcourt Publishing Company

Ayude 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.

P206
 Lesson 11.1
Name
COMMON CORE STANDARD MACC.4.MD.3.5a
Angles and Fractional Parts of a Circle
Geometric measurement: understand concepts of
angle and measure angles.

Tell what fraction of the circle the shaded angle represents.

1. 2. 3.

1
_
4
Tell whether the angle on the circle shows a 1 3, or
1, __
__, __
4 2 4
1 full turn clockwise or counterclockwise.
4. 5. 6.

7. Shelley exercised for 15 minutes. Describe 8. Mark took 30 minutes to finish lunch.
the turn the minute hand made. Describe the turn the minute hand made.

11 12 1 11 12 1 11 12 1 11 12 1
10 2 10 2 10 2 10 2
© Houghton Mifflin Harcourt Publishing Company

9 3 9 3 9 3 9 3
8 4 8 4 8 4 8 4
7 6 5 7 6 5 7 6 5 7 6 5

Start End Start End

Chapter 11 P207
Lesson Check (MACC.4.MD.3.5a)
1. What fraction of the circle does the 2. Which describes the turn shown below?
shaded angle represent?

A 1
__ turn clockwise
4
A 1
__ or 1 C 1
__
1 2 B 1
__ turn clockwise
2
3 1
B __
4
D __
4 C 1
__ turn counterclockwise
4
D 1
__ turn counterclockwise
2

Spiral Review (MACC.4.OA.2.4, MACC.4.NF.1.1, MACC.4.NF.2.4c, MACC.4.NF.3.7)

2 3
3. Which shows __ and __ written as a pair of
3
4. Raymond bought __ of a dozen rolls. How
3 4 4
fractions with a common denominator? many rolls did he buy? (Lesson 8.4)
(Lesson 6.4)
A 3
A 2 and 4
__ __
3 3 B 6
B 6 and __
__ 6
9 8 C 7
C 2 3
___ and ___ D 9
12 12
D 8 and ___
___ 9
12 12

5. Which of the following lists all the factors 6. Jonathan rode 1.05 miles on Friday,
of 18? (Lesson 5.1) 1.5 miles on Saturday, 1.25 miles on
© Houghton Mifflin Harcourt Publishing Company

A 1, 2, 4, 9, 18 Monday, and 1.1 miles on Tuesday.

On which day did he ride the shortest
B 1, 2, 3, 6, 9, 18 distance? (Lesson 9.7)
C 2, 3, 6, 9 A Monday C Friday
D 1, 3, 5, 9, 18 B Tuesday D Saturday

P208
 Lesson 11.2
Name
COMMON CORE STANDARDS MACC.4.MD.3.5a,
Degrees MACC.4.MD.3.5b

Geometric measurement: understand concepts of

angle and measure angles.

Tell the measure of the angle in degrees.

1. 2. 3.
(
-' ) (
*-' +

60°

Classify the angle. Write acute, obtuse, right, or straight.

4. 5. 6.
(('—
),—
-'—

Classify the triangle. Write acute, obtuse, or right.

7. 8. 9. -'— .'—
+'—
),— -,—
*'— (('— ,'—
© Houghton Mifflin Harcourt Publishing Company

Ann started reading at 4:00 P.M. and finished at 4:20 P.M.

10. Through what fraction of a circle did the
minute hand turn?
11 12 1 11 12 1
10 2 10 2
_______ 9 3 9 3
8 4 8 4
11. How many degrees did the minute 7 6 5 7 6 5
hand turn?

_______
Start End

Chapter 11 P209
Lesson Check (MACC.4.MD.3.5a, MACC.4.MD.3.5b)
1. What kind of angle is shown? 2. How many degrees are in an angle that
¡
turns through 1
__ of a circle?
4
A 45°
A acute B 90°
B obtuse C 180°
C right D 270°
D straight

Spiral Review (MACC.4.OA.1.3, MACC.4.NF.2.3b, MACC.4.NF.2.4a, MACC.4.NF.3.5)

3. Mae bought 15 football cards and
1
4. Each part of a race is ___ mile long.
10
18 baseball cards. She separated them Marsha finished 5 parts of the race. How
into 3 equal groups. How many sports far did Marsha race? (Lesson 8.1)
cards are in each group? (Lesson 4.12)
A ___1 mile
10
A 5 5 mile
B ___
B 6 12
C 1
__ mile
C 11 2
D 5___1 miles
D 12 10

11
5. Jeff said his city got ___ inches of snow.
3
6. Amy ran __ mile. Which decimal shows
3 4
Which shows this fraction written as a how many miles she ran? (Lesson 9.3)
mixed number? (Lesson 7.6) A 0.25 mile
A 32
© Houghton Mifflin Harcourt Publishing Company
__
3 B 0.34 mile
B 31__
C 0.5 mile
3
C 22__ D 0.75 mile
3
D 12__
3

P210
 Lesson 11.3
Name
COMMON CORE STANDARD MACC.4.MD.3.6
Measure and Draw Angles
Geometric measurement: understand concepts of
angle and measure angles.

Use a protractor to find the angle measure.

1. 2. 3.
3
" .

# $ 4 5
/ 1

m/ABC 5 __ 120° m/MNP 5 __ m/RST 5 __

Use a protractor to draw the angle.

4. 40° 5. 170°

Draw an example of each. Label the angle with its measure.

6. a right angle 7. an acute angle
© Houghton Mifflin Harcourt Publishing Company

8
The drawing shows the angles a stair tread 9
makes with a support board along a wall. Use
your protractor to measure the angles.

8. What is the measure of /A? __

9. What is the measure of /B? __

Chapter 11 P211
Lesson Check (MACC.4.MD.3.6)
1. What is the measure of /ABC? 2. What is the measure of /XYZ?

"
;
# $
9 :
A 15° C 155°
A 20° C 150°
B 25° D 165° B 30° D 160°

Spiral Review (MACC.4.NBT.2.6, MACC.4.NF.2.3c, MACC.4.MD.3.5a, MACC.4.G.1.1)

3. Derrick earned $1,472 during the 7 dozen muffins. Nina
4. Arthur baked 1___
12
1 dozen
4 weeks he had his summer job. If he baked 1___ muffins. How many
12
earned the same amount each week, dozen muffins did they bake in all?
how much did he earn each week? (Lesson 7.7)
(Lesson 4.10)
2
A 3__
A $360 3
B 22
__
B $368 3
C 21
__
C $3,680 2
6
D ___
D $5,888 12

5. Trisha drew the figure below. What figure 6. Which describes the turn shown by the
did she draw? (Lesson 10.1) angle? (Lesson 11.1)

4 5

A line segment ST
B ray ST
© Houghton Mifflin Harcourt Publishing Company

C ray TS A 1 full turn clockwise

D line TS
B 3
__ turn clockwise
4
C 1
__ turn clockwise
2
D 1
__ turn clockwise
4

P212
 Lesson 11.4
Name
COMMON CORE STANDARD MACC.4.MD.3.7
Join and Separate Angles
Geometric measurement: understand concepts of
angle and measure angles.
Add to find the measure of the angle. Write an
equation to record your work.
1. 2. ? 3.
D
: = (+'— G
8 )'—
> A *'— 0'—
,'— B +,—
.,— C E
9 ;

50° 1 75° 5 125°

125°
m/ABD 5 __ m/FGJ 5 __ m/KLN 5 __

Use a protractor to find the measure of each

angle in the circle. $

4. m/ABC 5 __ 5. m/DBE 5 __

6. m/CBD 5 __ 7. m/EBA 5 __ "

# %

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

________ &
© Houghton Mifflin Harcourt Publishing Company

9. Ned made the design at the right. Use a protractor.

Find and write the measure of each of the 3 angles.

________
_
10. Write an equation to find the measure of the _ _
total angle.

________

Chapter 11 P213
Lesson Check (MACC.4.MD.3.7)
1. What is the measure of /WXZ? 2. Which equation can you use to find the
m/MNQ?

P Q G
),—
(+/— )+—
H
,/— D E
N O

A 32° A 148° 2 24° 5 n

B 83° B 148° 3 24° 5 n
C 88° C 148° 4 24° 5 n
D 97° D 148° 1 24° 5 n

Spiral Review (MACC.4.NBT.2.5, MACC.4.NF.2.3d, MACC.4.MD.3.5a, MACC.4.MD.3.5b, MACC.4.G.1.2)

3. Joe bought 6 packages of envelopes.
3
4. The Lake Trail is ___ mile long and the
10
5 long.
Each package contains 125 envelopes. Rock Trail is ___ Bill hiked each trail
10
How many envelopes did he buy? once. How many miles did he hike in all?
(Lesson 2.11) (Lesson 7.5)

A 750 A 1__ mile

5
B 723 4 mile
B ___
10
C 720
C 1__ mile
2
D 650 8
D ___ mile
10

5. Ron drew a quadrilateral with 4 right 6. How many degrees are in an angle that © Houghton Mifflin Harcourt Publishing Company

angles and 4 sides with the same length. turns through 3

__ of a circle? (Lesson 11.2)
4
Which best describes the figure he drew?
A 45°
(Lesson 10.4)
B 90°
A square
C 180°
B rhombus
D 270°
C trapezoid
D parallelogram

P214
 PROBLEM SOLVING
Name
Lesson 11.5
HE8B;CÃEBL?D=ÃÄÃDADEMDÃ
COMMON CORE STANDARD MACC.4.MD.3.7
Angle Measures Geometric measurement: understand concepts of
angle and measure angles.

Solve each problem. Draw a diagram to help.

1. Wayne is building a birdhouse. He is cutting a

board as shown. What is the angle measure of
the piece left over? o
()'—
Draw a bar model to represent the problem.
x 1 120° 5 180°
o ()'—
x 5 180° 2 120°

(/'— x 5 60°

____ 60°
2. An artist is cutting a piece of metal as shown.


What is the angle measure of the piece left over?


____

3. Joan has a piece of material for making a

costume. She needs to cut it as shown. What is
© Houghton Mifflin Harcourt Publishing Company

the angle measure of the piece left over?



____

Chapter 11 P215
Lesson Check (MACC.4.MD.3.7)
1. Angelo cuts a triangle from a sheet of 2. Cindy cuts a piece of wood as shown.
paper as shown. What is the measure What is the angle measure of the piece
of /x in the triangle? left over?

)('—




o
A 15°
B 25°
C 75°
A 30° C 120°
D 105°
B 90° D 150°

Spiral Review (MACC.4.OA.1.3, MACC.4.NF.1.2, MACC.4.NF.3.6, MACC.4.MD.3.7)

7
3. Tyronne worked 21 days last month. He 4. Meg inline skated for __
10 mile. Which
earned $79 each day. How much did shows this distance written as a decimal?
Tyronne earn last month? (Lesson 3.7) (Lesson 9.1)

A $869 A 0.07 mile

B $948 B 0.1 mile
C $1,659 C 0.7 mile
D $2,169 D 7.1 miles

5. Kerry ran 3_4 mile. Sherrie ran 1_2 mile. 6. What is the measure of /ABC? (Lesson 11.4)
2
_
Marcie ran mile. Which list orders the
3
friends from least to greatest distance 8
run? (Lesson 6.8)
© Houghton Mifflin Harcourt Publishing Company

;
A Kerry, Sherrie, Marcie
,/—
B Kerry, Marcie, Sherrie )-—
9 :
C Sherrie, Kerry, Marcie
D Sherrie, Marcie, Kerry A 32° C 88°
B 84° D 94°

P216
 COMMON CORE STANDARDS MACC.4.MD.3.5a,
Name MACC.4.MD.3.5b, MACC.4.MD.3.6, MACC.4.MD.3.7

Chapter 11 Extra Practice

Lesson 11.1
Tell whether the angle on the circle shows 1
__, 1
__, 3
__, or
4 2 4
1 full turn clockwise or counterclockwise.
1. 2. 3.

Lesson 11.2
Tell the measure of the angle in degrees.

1. 2. 3.

(
+ (*'
*-'
*
+

Classify the triangle. Write acute, obtuse, or right.

© Houghton Mifflin Harcourt Publishing Company

4. 8 5. 8 6. 8

+'— -'— -,—

),—
9 :
-'— -'—
(('— *'— 9 :
9 :

Chapter 11 P217
Lesson 11.3
1. Use a protractor to find the angle measure. 2. Use a protractor to draw an angle with the
measure 72º.
3

2
1

m/PQR 5 __

Lesson 11.4
Add to find the measure of the angle. Write an equation
to record your work.
1. 2. 3.
J

C ),— ,'—
,'— .'— +,—
*'— ?
K L = >
D E

m/LMN 5 __ m/STU 5 __ m/FGH 5 __

Lesson 11.5
Use the diagram for 1–2.
© Houghton Mifflin Harcourt Publishing Company

1. Luke is cutting a board to make a

trapezoid for a project. What is the :lk9
angle measure of the piece left over :lk8
after Cut A? (*'—
o p
,,— .'—

2. What is the angle measure of the piece

left over after Cut B?

P218