Objective To provide practice using a full-circle protractor
to measure and draw angles less than 360°.
1
materials
Teaching the Lesson
Key Activities
Students use transparent protractors that resemble the full-circle protractor they labeled
with degrees in Lesson 6 5. They use these protractors to measure and draw angles.
Math Journal 1, p. 155
Student Reference Book, pp. 92 and 142
Study Link 6 5
Teaching Aid Master (Math Masters, p. 389)
Transparency (Math Masters, p. 439)
Key Concepts and Skills
• Draw and measure angles with a full-circle protractor.
drinking straw for demonstration purposes
straightedge
[Measurement and Reference Frames Goal 1]
• Use ray and line segment vocabulary. [Geometry Goal 1]
• Describe a circle as having 360°. [Geometry Goal 2]
• Rotate objects a given number of degrees. [Geometry Goal 3]
See Advance Preparation
Key Vocabulary
angle () • sides (of an angle) • vertex (of an angle) • clockwise rotation •
counterclockwise rotation • full-circle protractor
Ongoing Assessment: Informing Instruction See page 434.
Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip.
[Measurement and Reference Frames Goal 1]
2
materials
Ongoing Learning & Practice
Students play Division Dash to practice dividing 2- or 3-digit dividends by 1-digit divisors.
Students practice and maintain skills through Math Boxes and Study Link activities.
Math Journal 1, p. 156
Student Reference Book, p. 241
Study Link Master (Math Masters, p. 190)
Game Master (Math Masters, p. 471)
full-circle protractor
per partnership: 4 each of number cards 1–9
3
materials
Differentiation Options
READINESS
Students make and use a
waxed-paper protractor.
EXTRA PRACTICE
Students play Angle Tangle
to practice estimating and
measuring angles.
ELL SUPPORT
Students discuss the
meanings of clockwise
and counterclockwise.
Additional Information
Advance Preparation For Part 1, make enough transparencies of Math Masters,
page 439 so each student will have a full-circle protractor and there will be
a reserve supply for future activities.
Student Reference Book, p. 230
Teaching Master (Math Masters, p. 191)
Game Master (Math Masters, p. 457)
waxed paper; full-circle protractor; straightedge; colored pencils; scissors; dictionary
Technology
Assessment Management System
Exit slip
See the iTLG.
Lesson 6 6
431
Getting Started
Mental Math and Reflexes
Math Message
Students make different angle openings with their arms.
Have students begin each angle with arms in the
12 o’clock position and use clockwise movement.
Suggestions:
Read the top half of page 92 in your Student
Reference Book. Be prepared to tell some things
that all angles have in common.
90°
45°
180°
less than 90°
more than 90°
more than 180°
270°
120°
355°
Study Link 6 5 Follow-Up
Consider having a student go through the motions
as you go over the answer. Find an empty space
on the classroom floor. Mark a starting point. The
student should step heel-to-toe while following the directions.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
(Student Reference Book, p. 92)
Draw an angle on the board. As you review the parts of an angle,
label them. To support English language learners, leave this
drawing on the board throughout the lesson as a visual reference.
An angle is formed by 2 rays or 2 line segments that have the
same endpoint.
The rays or line segments are called the sides of the angle.
The endpoint is called the vertex of the angle.
is the symbol for angle.
Student Page
If the vertex of an angle is point T, the angle can be named T,
or angle T.
Geometry and Constructions
Angles
An angle is formed by 2 rays or 2 line segments that share
the same endpoint.
Tell students that in this lesson they will learn how to measure
angles of varying degrees.
angle formed by
2 segments
angle formed by 2 rays
A
The endpoint where the rays or segments meet is called
the vertex of the angle. The rays or segments are called the
sides of the angle.
T
sides
vertex
C
Naming Angles
The symbol for an angle is . An angle can be named in
two ways:
Measuring Angles
The protractor is a tool used to measure angles. Angles
are measured in degrees. A degree is the unit of measure
for the size of an angle.
The degree symbol ° is often used in place of the word degrees.
The measure of T above is 30 degrees, or 30°.
0
0
30
0
33
12
0
24
90
270
30
60
0
0
180
0
21
C
15
B
full-circle protractor
In Lesson 6-5, angles were used to represent clockwise
rotations. Angles can also be used to represent
counterclockwise rotations. To demonstrate, ask a student
to fold a straw in half and hold it against the board. Rotate one
1
half of the straw counterclockwise about 3 of a turn. Ask another
student to draw a line along each side of the straw to form
an angle.
A
Measure of C
is 300º
80 90 100
70 100 90 80 110 12
70
60 0 110
60 0 13
50 0 12
50 0
13
0 10
20
180 170 160
30
15
0 14 40
0
Measure of B
is 225º
170 180
0
0 160 10
15 20
0 30
14
40
Measure of A
is 60º
half-circle protractor
Student Reference Book, p. 92
432
WHOLE-CLASS
ACTIVITY
and Rotations
1. Name the vertex. The angle shown above is angle T. Write
this as T.
2. Name 3 points: the vertex and one point on each side of the
angle. The angle above can be named angle ATC ( ATC)
or angle CTA (CTA). The vertex must always be listed in
the middle, between the points on the sides.
Sometimes there is confusion about which angle should be
measured. The small curved arrow in each picture shows
which angle opening should be measured.
Demonstrating Angles
Unit 6 Division; Map Reference Frames; Measures of Angles
Student Page
Draw a directional arc to show that this angle represents a
counterclockwise rotation. Name the vertex. Then use the angle
symbol to name the angle. (See below.) Write counterclockwise
rotation next to the angle.
Measurement
Measuring an Angle with a Full-Circle Protractor
Example
Use the full-circle protractor to measure angle A.
Step 1: Place the hole in the center of the protractor over the
vertex of the angle, point A.
Step 2: Line up the 0˚ mark with the side of the angle so that
you can measure the angle clockwise. Make sure that
the hole stays over the vertex.
Step 3: Read the degree measure at the mark on the
protractor that lines up with the second side of
the angle. This is the measure of the angle. The
measure of A is 45 .
˚
300
33
24
0
270
0
210
0
30
A
180
A
60
90
120
15
0
M
Check Your Understanding
Use your full-circle protractor to measure angles B and C to the nearest degree.
∠M
1.
2.
Using a straw to demonstrate a counterclockwise rotation
C
B
B measures about _____ .
C measures about _____ .
˚
˚
Check your answers on page 344.
Using a Full-Circle Protractor
WHOLE-CLASS
ACTIVITY
Student Reference Book, p. 142
(Math Journal 1, p. 155; Student Reference Book,
p. 142; Math Masters, p. 439)
Distribute the squares from the transparencies of Math Masters,
page 439. Explain that full-circle protractors are tools used to
measure angles. Write full-circle protractor on the board.
Show students how to use the full-circle protractor to measure
angle B on page 142 of the Student Reference Book. Point out that
the marks on the edge are labeled from 0° to 360° in a clockwise
direction. Therefore, students must be careful to measure the
angle in a clockwise direction.
Ask them to measure reflex angle C. To support English language
learners, write reflex angle on the board and discuss its meaning.
Student Page
Date
LESSON
66
Time
Measuring Angles
Use your full-circle protractor to measure each angle.
92
250
0
270
0
24
30
D
0 310
21
200
190
180
170
10
1
5
30
1. C measures
60
°
.
2. D measures
120
°
.
310
°
.
14
40
0
C
20
3
2
4
0
15
0
360
350
12
6
degrees
11
7
C
340
0
33
10
9
8
160
290
0
32
0 220
23
280
260
Try This
50
60
70
80
90
0 130
12
100
110
F
Angle C measures 270°.
Students work in partnerships to measure the angles on
journal page 155.
E
3. F measures
150
°
.
4. E measures
5. Without using your full-circle protractor, give the measure of the reflex angle in Problem 3 (the
part not marked by the blue arrow). Explain your answer.
Sample answer: A full turn corresponds to
360°. Angle F measures 150° so the reflex
angle measures 360 150 210°.
155
Math Journal 1, p. 155
Lesson 6 6
433
Ongoing Assessment: Informing Instruction
Watch for students who
line up the 0° mark on the full-circle protractor with the right-hand side of
the angle and incorrectly read the protractor in a counterclockwise direction.
de
gre
es
10
9
8
10 11 12
6
5
degrees
11 12 1
7
9
1
2
8
7
3
3
2
4
6
Incorrect
5
4
Correct
do not place the center of the full-circle protractor at the vertex of the angle.
have difficulty measuring angles like angle A below that do not have one side
of the angle parallel to the bottom of the page.
[ART: EM2007TLG1_G4_U06_L06_T_0037: angle A]
A
Drawing an Angle
WHOLE-CLASS
ACTIVITY
Have students use a straightedge and their full-circle protractors
to draw a 60° angle. (See margin.) Ask someone to describe how
he or she drew the angle.
Step
Step 11
Step
Step 22
Step
Step 33
Step 2: Place the center of the full-circle protractor on the
endpoint of the ray, and align the 0° mark with the
ray. Make a dot on the paper at the 60° mark.
0
360
degrees
11
12
1
10
2
9
3
8
4
7
6
5
Step 1: Draw a ray.
R
Step 3: Draw a second ray from the endpoint of the first
ray through the dot.
Remind students to draw an arc with an arrowhead to identify the
direction of the rotation and use a letter to name the vertex point.
Using a full-circle protractor and a straightedge to
draw an angle
434
Have partners take turns: One partner names a degree measure;
the other draws an angle with that degree measure.
Unit 6 Division; Map Reference Frames; Measures of Angles
Student Page
Date
Time
LESSON
Ongoing Assessment:
Recognizing Student Achievement
Exit Slip
Math Boxes
6 6
1. Ms. Kawasaki’s fourth grade class made a circle graph to show students’ favorite
days of the week.
Favorite Day of the Week
a. Which day of the week is the least favorite in
Ms. Kawasaki’s classroom?
Use an Exit Slip (Math Masters, page 389) to assess students’ ability to draw
angles less than or greater than 90°. Ask students to draw one angle that
measures less than 90° and one angle that measures more than 90°. Students
should then use the full-circle protractor to measure the angles and record
their measures. Students are making adequate progress if they are able to draw
angles measuring less and more than 90°. Some students may be able to
correctly measure the angles to within a few degrees.
Monday
Sunday
Monday
b. About what fraction of the students
Saturday
1
2
Friday
2. Juan talked on the phone an average of
3. Divide with a paper-and-pencil algorithm.
34 minutes per week for 1 whole year.
About how many minutes did Juan spend
on the phone in 1 year?
Write the remainder as a fraction.
883 / 7 Number model: 34 52 1,768
Answer:
Wednesday
Thursday
prefer Saturday?
[Measurement and Reference Frames Goal 1]
y
da
es
Tu
1,768
126 17
minutes
22 23
179
18 19
4. Write , , or to make each number
5. For this spinner, what color would you be
most likely to land on?
sentence true.
a. 420,000,000
2 Ongoing Learning & Practice
b. 65,000,000
Playing Division Dash
PARTNER
ACTIVITY
2
red
92,000,000
c. four hundred thousand
d. 10
white
four hundred
twenty million
blue
104
white
1,000
5 6
80 84
156
Math Journal 1, p. 156
(Student Reference Book, p. 241; Math Masters, p. 471)
Students play Division Dash to practice dividing 2- or 3-digit
dividends by 1-digit divisors. See Lesson 6-4 for additional
information.
Math Boxes 6 6
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 156)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 6-9. The skill in Problem 5
previews Unit 7 content.
Writing/Reasoning Have students write a response to the
following: Winnona said there isn’t enough information provided in
Problem 2 to answer the question. Do you agree or disagree?
Explain your answer. Sample answer: I disagree. There are
52 weeks in 1 year, so I multiplied 34 by 52 to get the number
of minutes Juan spends on the phone in 1 year.
Study Link 6 6
Study Link Master
Name
Date
STUDY LINK
Time
Measuring Angles
66
141 142
First estimate and then use your full-circle protractor to measure each angle.
1.
This angle is
G:
101
(, ) 90
.
2.
°
This angle is
52
H:
(, ) 90
.
°
INDEPENDENT
ACTIVITY
(Math Masters, p. 190)
H
G
3.
This angle is
I:
144
(, ) 90
.
4.
°
This angle is
85
J:
(, ) 90
.
°
Home Connection Students use a full-circle protractor
to measure angles.
I
J
Try This
5.
On the back of this page, draw and label angles with the following degree measures:
ABC 78
DEF 145
GHI 213
JKL 331
Practice
6.
8.
24
157
96 4
7.
66 8 314 2
9.
928 5 8 R2
185 R3
Math Masters, p. 190
Lesson 6 6
435
Teaching Master
Name
Date
LESSON
66
Time
3 Differentiation Options
A Waxed-Paper Protractor
Follow the steps below to make a waxed-paper protractor.
1.
Step 1: Take a sheet of waxed paper.
Step 2: Fold the paper in half. Be sure to
crease it tightly.
READINESS
fold
Step 3: Fold it in half again.
Step 4: Bring the folded edges together and
fold it in half. Repeat this step again.
fold
fold
Step 5: Cut off the top.
2.
15–30 Min
Waxed-Paper Protractor
(Math Masters, p. 191)
Step 6: Unfold.
To explore the use of a protractor to measure angles, have
students make and then use a waxed-paper protractor to
approximate the measure of angles using standard angles as
reference. Have students record the measurements as “wedges”
and fractions of “wedges.”
Use your waxed-paper protractor to measure the angles below.
a.
b.
R
M
312
Angle M measures about
3.
fold
Making and Using a
SMALL-GROUP
ACTIVITY
Angle R measures about
wedges.
7
Use a straightedge to draw more angles on the back of this sheet.
Measure the angles and record the numbers of wedges.
wedges.
EXTRA PRACTICE
Playing Angle Tangle
Math Masters, p. 191
PARTNER
ACTIVITY
5–15 Min
(Student Reference Book, p. 230; Math Masters, p. 457)
To practice estimating and measuring angles, have students play
Angle Tangle. See Lesson 6-8 for additional information.
ELL SUPPORT
Building Background for
SMALL-GROUP
ACTIVITY
5–15 Min
Mathematics Words
To provide language support for angle rotations, discuss the
meanings of the words clockwise and counterclockwise. Explain
that counter can be a noun with many meanings. Ask students to
provide some examples. Kitchen counter, using counters to make
an array Explain that counter- can also be used as a prefix. Have
students look up words in the dictionary that have the prefix
counter-. Countermove, counterattack, counterbalance Clarify
the meaning of counter in this context. Consider labeling your
classroom clock with an arrow arcing to the right labeled
“clockwise” and an arrow arcing to the left labeled
“counterclockwise.”
Student Page
Games
Angle Tangle
Materials 1 protractor
1 straightedge
several blank sheets of paper
Players
2
Skill
Estimating and measuring angle size
Object of the game To estimate angle sizes accurately
and have the lower total score.
Directions
In each round:
1. Player 1 uses a straightedge to draw an angle on
a sheet of paper.
2. Player 2 estimates the degree measure of the angle.
3. Player 1 measures the angle with a protractor.
Players agree on the measure.
4. Player 2’s score is the difference between the estimate
and the actual measure of the angle. (The difference
will be 0 or a positive number.)
5. Players trade roles and repeat Steps 1–4.
Players add their scores at the end of five rounds.
The player with the lower total score wins the game.
Example
Player 1
Estimate Actual
Score
Player 2
Estimate Actual
Score
Round 1
120°
108°
12
50°
37°
Round 2
75°
86°
11
85°
87°
Round 3
40°
44°
4
15°
19°
4
Round 4
60°
69°
9
40°
56°
16
Round 5
135°
123°
12
150°
141°
Total Score
48
13
2
9
44
Player 2 has the lower total score. Player 2 wins the game.
Student Reference Book, p. 230
436
Unit 6 Division; Map Reference Frames; Measures of Angles