Objectives
To review rotations; and to guide students as they
make and use a full-circle protractor.
1
materials
Teaching the Lesson
Students review clockwise rotations. They make a full-circle protractor by measuring rotations
in degrees; then they use the protractor to form angles of given measures.
Math Journal 1, pp. 152 and 153
Study Link 6 4
drinking straws
Students solve problems that involve measuring elapsed time in degrees.
demonstration clock
Key Activities
Key Concepts and Skills
•
•
•
•
•
Use multiples of 30. [Number and Numeration Goal 3]
Form angles of a given measure. [Measurement and Reference Frames Goal 1]
Describe right angles. [Geometry Goal 1]
Rotate objects a given number of degrees. [Geometry Goal 3]
Investigate the relationship between rotations and degrees. [Geometry Goal 3]
Key Vocabulary
rotation • turn • clockwise • degree • right angle
Ongoing Assessment: Informing Instruction See page 427.
2
materials
Ongoing Learning & Practice
Students make a bar graph showing percent of population (ages 0–14) for Region 2 countries.
Students practice and maintain skills through Math Boxes and Study Link activities.
Ongoing Assessment: Recognizing Student Achievement Use journal page 154.
[Data and Chance Goal 1]
3
materials
Differentiation Options
READINESS
Students match
alternate ways of
naming time.
Math Journal 1, pp. 151 and 154
Student Reference Book, p. 301
Study Link Master (Math Masters,
p. 185)
ENRICHMENT
EXTRA PRACTICE
ELL SUPPORT
Students determine
elapsed time for 1°
increments on a
clock face.
Students play Robot
to practice making
rotations of a given
size.
Students add degree
to their Math Word
Banks.
Math Journal 1, pp. 152 and 153
Teaching Masters (Math Masters,
pp. 186–189)
Differentiation Handbook
scissors
Technology
Assessment Management System
Journal page 154
See the iTLG.
Lesson 6 5
425
Getting Started
Mental Math and Reflexes
Have students imagine standing in the center of a clock with their right hand extended as the minute hand. Ask them to rotate
their bodies to make turns such as the following:
1
2
1
4
turn clockwise
turn clockwise
full turn clockwise
3
4
3
4
1
2
90° turn clockwise
180° turn clockwise
360° turn clockwise
turn counterclockwise
turn clockwise
turn counterclockwise
Math Message
Study Link 6 4 Follow-Up
How many minutes does it take the minute hand to
move through a full turn on the face of a clock?
1
1
60 min A 2 turn? 30 min A 4 turn? 15 min
Have students discuss how they handled the
remainders in Problems 1 and 2.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
The Math Message reminds students who used Third Grade
Everyday Mathematics of previous experiences with rotations.
Review answers using a clock with an hour and minute hand or a
demonstration clock to model movements of the minute hand.
3
1
Pose additional problems: A 4 turn? 45 min A 6 turn? 10 min
1
2
A 3 turn? 20 min A 3 turn? 40 min
3
Student Page
Date
LESSON
6 5
Time
Making a Full-Circle Protractor
There are 360 marks around the circle. They divide the edge of the circle into
360 small spaces. Twelve of the marks are longer than the rest. They are in the same
positions as the 12 numbers around a clock face. Your teacher will tell you how to label
the 12 large marks on the circle.
330°
360°/0°
30°
300°
60°
10
2
9
4
7
6
5
240°
210°
120°
180°
152
Math Journal 1, p. 152
426
90°
3
8
150°
1
92
For a 6 turn—Since there are 12 five-minute intervals in 1 full
turn of the minute hand, there are 2 five-minute intervals in
1
of a turn. Therefore, it takes the minute hand 10 minutes to
6
1
move through a 6 turn.
2
11 12 1
270°
1
For a 4 turn—Since there are 3 five-minute intervals in 4 of
1
3
a turn (3 4 of 12), there are three times as many in 4 of a
turn, or 9 five-minute intervals. Therefore, it takes the minute
3
hand 45 minutes to move through 4 of a turn.
1
For a 3 turn—Since there are 4 five-minute intervals in 3 of a
1
2
turn (4 3 of 12), there are twice as many in 3 of a turn, or
8 five-minute intervals. Therefore, it takes the minute hand
2
40 minutes to move through 3 of a turn.
Investigating Rotations
WHOLE-CLASS
ACTIVITY
and Degree Measures
(Math Journal 1, p. 152)
Tell the class that in this lesson they will investigate the markings
on a full-circle protractor and compare them to familiar markings
on an analog clock.
Unit 6 Division; Map Reference Frames; Measures of Angles
Discuss the marked circle on journal page 152.
There are three different lengths of marks.
The shortest marks divide the circle into 360 small spaces.
360 1° 360°
The longest marks are in the same positions as the 12 numbers
around a clock face. These 12 long marks divide the circle into
12 spaces. 12 30° 360°
The middle-size marks divide the circle into 72 spaces.
72 5° 360°
Ask students to write 0° beneath the large mark at the 12 o’clock
position on the circle.
Ask students to fold a straw in half. Show them how to place it on
the circle on journal page 152. The bend of the straw should touch
the center of the circle, and both halves of the straw should point
to the 0-degree mark.
NOTE Think of an angle as “in motion”
opening from 0° to the desired angle. For
example, to measure a 15° angle, start with a
0° angle and open the angle to 1°, 2°, and so
on until 15° is reached. Thinking this way can
help students realize that counting the spaces
in between the marks of the protractor is
more accurate than counting the marks.
Keeping one part of the straw pointing to the 0-degree mark, move
the other half of the straw clockwise to the first large mark, or
1
of a turn.
12
Links to the Future
Students will discuss counterclockwise rotations in Lesson 6-6.
The straw-halves form an angle. Remind students that angles are
measured in degrees and that the degree symbol (°) is often used
in place of the word degree. To support English language learners,
write degree on the board and explain that this word has different
meanings when it is used to measure angles and temperature.
30°
Now show students how to measure the straw angle they just
made: To measure the angle, count the number of small spaces
created by the shortest marks. (See note in margin.) 30 spaces, so
the angle measures 30 degrees, or 30° Ask students to write 30°
at the first large mark on the circle.
Tell students to move the straw-half back to its original position
1
and then repeat the routine for a 4 turn. (See margin.)
●
What is the measure of the angle? 90° Ask students to write
1
90° at the 4-turn mark on the circle. (See margin.)
0°
30°
Ongoing Assessment: Informing Instruction
Watch for the different strategies that students use to determine that the result of
a
1
4
90°
turn of the straw is an angle that measures 90°.
Count the 90 spaces along the circle between the sides of the straw.
Recognize that the angle is 3 times as large as the first angle, and multiply
by 3 to get 90°.
Recognize that the angle is a right angle, and right angles measure 90°.
Lesson 6 5
427
Student Page
Date
Time
LESSON
●
Clock Angles
6 5
Use the clock below and the full-circle protractor on journal page 152 to help you
answer the questions.
92 141
1. How many minutes and how many degrees does the minute hand move
60
45
30
20
15
10
5
1
a. from 3:00 to 4:00?
b. from 7:00 to 7:45?
c. from 8:15 to 8:45?
d. from 6:30 to 6:50?
e. from 5:15 to 5:30?
f.
from 1:00 to 1:10?
g. from 12:00 to 12:05?
h. from 5:00 to 5:01?
360
270
180
120
90
60
30
6
minutes
minutes
minutes
minutes
minutes
minutes
minutes
minutes
°
°
12
11
10
°
1
2
°
9
°
3
8
°
7
6
5
°
Try This
30
15
1
b. in 2 hour?
What is the measure of the angle? 360°
Ask students to write 360° at the full-turn mark on the circle,
right next to the 0° mark. Have students label the rest of the large
tick marks on the circle until all 12 marks have been labeled.
°
2. How many degrees does the hour hand move
a. in 1 hour?
Now tell students to move the straw-half back to its original
position, and then repeat the procedure for a full turn.
●
4
What is another name for a 90-degree angle? A right angle
To support English language learners, review the different
meanings of right discussed in Unit 1—right answer, right
hand, right angle.
°
°
5
c. in 10 minutes?
°
Adjusting the Activity
3. Explain how you solved Problem 2c.
Have students describe a strategy for labeling the remaining large tick
marks without using the folded straw. Sample answer: Count by 30s; each large
tick mark corresponds to a multiple of 30.
Sample answer: I know that the hour hand
moves 30° in 1 hour. There are 6 groups of
10 minutes in 1 hour (60 minutes). So there
are 6 groups of 5° in 30°, or 30°/ 6 5°.
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
153
Math Journal 1, p. 153
Forming Angles of
WHOLE-CLASS
ACTIVITY
Given Measures
(Math Journal 1, p. 152)
Direct students to use their bent straws to form angles of various
degree measures. For example, Show me a 120° angle; a 45° angle;
a 77° angle.
Measuring Elapsed Time
in Degrees
Student Page
Date
LESSON
6 5
PARTNER
ACTIVITY
(Math Journal 1, pp. 152 and 153)
Time
Population Bar Graph
The table below shows the percent of
the population (number of people out
of 100) who are 14 years old or
younger in the Region 2 countries.
Percent of Population
Ages 0 –14
Country
France
19
Greece
15
Hungary
16
Iceland
23
Italy
14
Netherlands
18
Norway
20
Poland
18
Spain
15
United Kingdom
19
76 301
Students solve problems and share solution strategies about the
number of degrees the minute and hour hands of a clock move in
a given amount of time.
2 Ongoing Learning & Practice
1. Make a bar graph to display the information given in the table above.
Percent of Population Ages 0–14
25
Making a Bar Graph
Percent
20
15
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 154; Student Reference Book, p. 301)
10
5
ain
nd
om
Kin
gd
Sp
Po
la
ay
w
s
he
U
nit
N
ed
et
N
or
ly
nd
rla
nd
Ic
ela
Ita
e
ry
H
un
ga
ec
re
G
Fr
an
ce
0
Country in Region 2
2. Why might it be important to know what percent of the population of a country
is 0 through 14 years of age?
Social Studies Link Students make a bar graph to show
percent of population (ages 0–14 years) for Region 2
countries. Direct students to page 301 of the Student Reference
Book for additional data.
Sample answer: A government will know how much money
to give schools for grades 8 and below.
154
Math Journal 1, p. 154
428
Unit 6 Division; Map Reference Frames; Measures of Angles
Student Page
Date
Ongoing Assessment:
Recognizing Student Achievement
Journal
page 154
Use journal page 154 to assess students’ ability to create a bar graph. Students
are making adequate progress if they can draw the bars at the appropriate
height on the graph. Some students may be able to provide a title and label
each axis.
[Data and Chance Goal 1]
Time
LESSON
Math Boxes
6 5
1. Insert parentheses to make each number
sentence true.
(
2. Draw a line segment that is 2 inches long.
Mark and label the following inch
measurements on the line segment:
)
a. 15 5 6 120
1 3
, ,
2 4
( )
77 (1 6)(6 5)
b. 7 9 2 25
c.
1 3
2 4
150
3. The Sports Boosters raised $908 at their
annual chili supper. Four athletic teams
will share the money equally.
1, 112, and 2
1 1 12 2
128
4. Multiply with a paper-and-pencil algorithm.
66 62 4,092
How much money will each team receive?
Number model:
Answer:
Math Boxes 6 5
908 / 4 227
$227
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 151)
22
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 6-7. The skill in Problem 6
previews Unit 7 content.
b.
c.
e.
INDEPENDENT
ACTIVITY
(Math Masters, p. 185)
900 cm
1,500 cm 15 m
350 cm 3.5 m
4 m 58
458 cm 3.2 m 320 cm
18 19
1
6. a. Shade 2 of
the square.
a. 9 m d.
Study Link 6 5
23
5. Complete.
Sample
answers:
2
b. Shade 3 of
the square.
cm
129
44
151
Math Journal 1, p. 151
Home Connection Students follow directions, given as
fractions of turns and distances, to trace a path on a
coordinate grid. When reviewing answers, point out that
the length of each horizontal line segment equals the difference of
the x-coordinates and that the length of each vertical line segment
equals the difference of the y-coordinates.
Study Link Master
Name
Date
STUDY LINK
Time
Treasure Hunt
65
Marge and her friends are playing Treasure Hunt. Help them find the treasure.
Follow the directions. Draw the path from the oak tree to the treasure. Mark the
spot where the treasure is buried.
1.
Start at the dot under the oak tree; face north. Walk 4 steps.
2.
Make a quarter turn, clockwise. Walk 5 steps.
3.
Face south. Walk 2 steps.
4.
Face east. Walk 2 steps.
5.
Make a turn, clockwise. Walk 5 steps.
6.
Make a
7.
Make an X to mark the spot where you end.
107
1
2
3
4
3
4
1
2
turn, clockwise. Walk 6 steps.
10
9
8
7
N
W
6
E
S
5
1 step
4
3
2
Oak Tree
1
0
0
1
2
3
4
5
6
7
8
9
10
Practice
8.
10.
29 R1
86 R1 603 / 7
88 3 9.
11.
11 R5 71 6
186 R4
934 / 5 Math Masters, p. 185
Lesson 6 5
429
3 Differentiation Options
PARTNER
ACTIVITY
READINESS
Matching Alternate Time Displays
11
10
12
1
Quarterpast
5 o’clock
2
9
3
8
4
7
6
5–15 Min
(Math Masters, pp. 186–188)
5
Alternate ways of naming time from Math Masters,
pages 186–188
To explore alternate ways of naming time, have students
match cards that indicate the same time in analog, digital,
and word form.
ENRICHMENT
Measuring Elapsed Time
INDEPENDENT
ACTIVITY
5–15 Min
in Degrees
(Math Journal 1, pp. 152 and 153; Math Masters, p. 189)
To further investigate the relationship between elapsed time
and angle measures, have students use a full-circle protractor to
determine how long it takes the minute and the hour hands to
move 1 degree.
EXTRA PRACTICE
Playing Robot
PARTNER
ACTIVITY
5–15 Min
To practice rotations expressed as both fractions of turns and
degree measures, have students play Robot. One partner is the
“Controller” and the other is the “Robot.” The Controller picks a
destination. The Controller gives the Robot directions for the
amount of each turn and the number of steps to take until the
Robot reaches the destination. The amount of each turn may be
given as a fraction of a full turn or as a degree measure.
Example: “Make a half-turn clockwise and go forward 5 steps.
Now turn clockwise a quarter-turn (90 degrees), and go back
3 steps.”
ELL SUPPORT
Building a Math Word Bank
Name
Date
LESSON
Clock Angle Challenge
65
Sample explanations:
1.
How long does it take the hour hand to move 1°?
Explain.
141 142
2 minutes
The hour hand takes 60 minutes to move 30ⴗ, so it
takes 10 minutes to move 5ⴗ and 2 minutes to move 1ⴗ.
2.
How long does it take the minute hand to move 1°?
Explain.
10 seconds
To provide language support for angle rotations, have students use
the Word Bank template found in the Differentiation Handbook.
Ask students to write the term degree, draw a picture or give an
example to represent the term, and write other related words. See
the Differentiation Handbook for more information.
It takes the minute hand 60 minutes to move 360ⴗ,
so it moves 6ⴗ every minute (or 60 seconds). Dividing
60 by 6, I get that it moves 1ⴗ every 10 seconds.
Math Masters, page 189
430
5–15 Min
(Differentiation Handbook)
Time
Use the full-circle protractor and the clock from journal pages 152
and 153 to help you solve the problems below.
PARTNER
ACTIVITY
Unit 6 Division; Map Reference Frames; Measures of Angles