Name
14.1
?
Angles and Fractional Parts
of a Circle
Essential Question
Geometry and
Measurement—4.7.A
MATHEMATICAL PROCESSES
4.1.C, 4.1.E, 4.1.F
How can you relate angles and fractional parts of a circle?
Investigate
Investigate
Materials ■ fraction circles
1 piece on the circle. Place the tip of the fraction
A. Place a __
12
piece on the center of the circle. Trace the fraction piece.
What figure is formed by the fraction piece? __
What parts of the fraction piece represent the rays of
the angle? ___
On what part of the circle is the vertex of the angle?
_____
1 piece. Label it __
1.
B. Shade the angle cut out by the __
12
12
1 piece back on the shaded
C. Place the __
12
angle. Turn it counterclockwise.
Counterclockwise is the direction
opposite from the way the hands
move on a clock.
Trace the fraction piece in its new
position. How many twelfths have
2
you traced in all? _ Label __
12 .
D. Turn the fraction piece
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counterclockwise again and trace it.
Label the total number of twelfths.
Continue until you reach the shaded
angle. What figure is formed by turning
and tracing the fraction piece? __
1 piece to make a circle? __
How many times did you need to turn the __
12
How many angles came together in the center of the circle? __
Module 14
487
Make
Make Connections
Connections
You can relate fractions and angles to the hands of a clock.
Let the hands of the clock represent the rays of an angle that cuts
out a fraction of the clock face. Each 5-minute mark represents
1
a __
12 turn clockwise.
11 12 1
2
10
9
3
4
8
7 6 5
11 12 1
2
10
9
3
4
8
7 6 5
15 minutes elapse.
30 minutes elapse.
The minute hand makes a
The minute hand makes a
__ turn clockwise.
__ turn clockwise.
11 12 1
2
10
9
3
4
8
7 6 5
Math Talk
11 12 1
2
10
9
3
4
8
7 6 5
11 12 1
2
10
9
3
4
8
7 6 5
45 minutes elapse.
60 minutes elapse.
The minute hand makes a
The minute hand makes a
__ turn clockwise.
__ turn clockwise.
Mathematical Processes
Explain how an angle
formed in a circle using a
1
_ -fraction piece is like
4
a 1_4 turn and 15 minutes
elapsing on a clock.
Share
Share and
and Show
Show
Look at the shaded part of the circle. Tell what fraction of the circle the angle cuts out.
2.
_
3.
_
_
Tell whether the angle on the circle shows a 1_4 , 1_2 , 3_4 , or 1 full turn
clockwise or counterclockwise.
4.
5.
__
488
6.
__
__
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1.
Name
Problem
Problem Solving
Solving
Sense or Nonsense?
7. Analyze Whose statement makes
sense? Whose statement is nonsense?
Explain your reasoning.
The shaded angle
cuts out 3_8 of
the circle.
The shaded angle
cuts out 1_4 of
the circle.
Carla’s Statement
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8.
9.
Adam’s Statement
Susan watched the game from 1 p.m. to 1:30 p.m.
Describe the turn the minute hand made.
11 12 1
2
10
9
3
4
8
7 6 5
11 12 1
2
10
9
3
4
8
7 6 5
Write Math
Compare the angles in the two circles.
Does the position of the angle affect the size of the angle? Explain.
Module 14 • Lesson 1
489
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
10. Multi-Step Carrie does her homework from 4 p.m. to 4:45 p.m.
Which describes the turn the minute hand makes?
A
1_
4
turn clockwise
B
3_
4
turn clockwise
C
1_
2
turn counterclockwise
D
1_
4
turn counterclockwise
11 12 1
2
10
9
3
4
8
7 6 5
11 12 1
2
10
9
3
4
8
7 6 5
11. Which angle shows 1_2 turn counterclockwise?
A
C
B
D
12. Look at the shaded part of the circle. What fraction
of the circle does the angle cut out?
A
_1
4
B
1
__
C
_3
4
D
_1
2
12
TEXAS Test Prep
What fraction of a turn did the minute hand make?
490
A
_1
4
turn clockwise
B
_1
2
turn clockwise
C
_3
4
turn clockwise
D
1 full turn clockwise
11 12 1
2
10
9
3
4
8
7 6 5
11 12 1
2
10
9
3
4
8
7 6 5
© Houghton Mifflin Harcourt Publishing Company
13. Phillip watched a beach volleyball game from 1:45 p.m. to 2:00 p.m.
Number and Operations—4.7.A
MATHEMATICAL PROCESSES 4.1.C, 4.1.E,
4.1.F
H o mewo rk
and Practice
14.1
Name
Angles and Fractional Parts of a Circle
Look at the shaded part of the circle. Tell what fraction of the circle the angle cuts out.
1.
2.
3.
Tell whether the angle on the circle shows a 1_4 , 1_2 , 3_4 , or 1 full turn
clockwise or counterclockwise.
4.
5.
6.
7.
8.
9.
Problem
Problem Solving
Solving
10. Evan practiced the piano from
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3 p.m. to 3:45 p.m. Describe
the turn the minute hand
made.
11 12 1
2
10
9
3
4
8
7 6 5
11 12 1
2
10
9
3
4
8
7 6 5
11. As soon as Evan finished
practicing, he ate a snack.
When he finished his snack,
it was 4:00. Describe the
turn the minute hand made.
11 12 1
2
10
9
3
4
8
7 6 5
11 12 1
2
10
9
3
4
8
7 6 5
Module 14 • Lesson 1
491
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
12. Which angle shows a 3_4 turn
13. Look at the shaded part of the circle. What
fraction of the circle does the angle cut out?
A
C
B
D
A
B
14. Multi-Step Hannah takes a break from
10 a.m. to 10:15 a.m. Which describes the
turn the minute hand makes?
11 12 1
2
10
9
3
4
8
7 6 5
A
B
C
D
1__ turn counterclockwise
4
1__ turn clockwise
4
3__ turn counterclockwise
4
3__ turn clockwise
4
for 15 minutes each day. Which fraction
describes the turn of the minute hand
on the clock face during the time Ben
babysits?
B
492
1
__
2
3__
4
C
D
12
___
12
1__
4
C
D
1
__
3
1__
4
15. Multi-Step Inez walks her dog each
morning from 7:45 a.m. to 8:15 a.m.
Which describes the turn the minute
hand makes?
11 12 1
2
10
9
3
4
8
7 6 5
16. Multi-Step Ben babysits his little sister
A
1
__
2
3__
4
11 12 1
2
10
9
3
4
8
7 6 5
11 12 1
2
10
9
3
4
8
7 6 5
A
1__ turn clockwise
2
B
1 full turn clockwise
C
1__ turn counterclockwise
2
1__ turn clockwise
4
D
17. Multi-Step Standard time begins in the
fall. On a certain day each year, many
people turn their clocks back one hour.
Which fraction describes the turn of the
minute hand on the clock face?
A
B
12
___
12
9
___
12
C
D
3
___
12
6
___
12
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counterclockwise?