Using a Full-Circle
Protractor
Objective To provide practice using a full-circle protractor
tto measure and draw angles less than 360°.
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ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Draw and measure angles with a
full-circle protractor. Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Division Dash
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Student Reference Book, p. 241
Math Masters, p. 471
per partnership: 4 each of number
cards 1–9 (from the Everything Math
Deck, if available)
Students practice dividing 2- or 3-digit
dividends by 1-digit divisors.
Making and Using a Waxed-Paper
Protractor
Math Boxes 6 6
Playing Angle Add-Up
Key Activities
Math Journal 1, p. 156
Students practice and maintain skills
through Math Box problems.
Students use transparent protractors to
measure and draw angles.
Study Link 6 6
Math Masters, pp. 507–509
per partnership: 4 of each of number cards
1–8 and 1 of each of number cards 0 and 9
(from the Everything Math Deck, if available)
full-circle protractor (transparency of Math
Masters, p. 439) dry-erase markers straightedge
Students draw angles and then use addition
and subtraction to find the measures of
unknown angles.
[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]
Ongoing Assessment:
Informing Instruction See page 434.
Ongoing Assessment:
Recognizing Student Achievement
Math Masters, p. 190
full-circle protractor
Students practice and maintain skills
through Study Link activities.
Use an Exit Slip (Math Masters,
page 389). [Measurement and Reference Frames
Goal 1]
Key Vocabulary
angle (∠) sides (of an angle) vertex (of an
angle) clockwise rotation counterclockwise
rotation full-circle protractor
Math Masters, p. 191
waxed paper scissors
Students make and use a waxed-paper
protractor.
ENRICHMENT
EXTRA PRACTICE
Playing Angle Tangle
Student Reference Book, p. 230
Math Masters, p. 457
full-circle protractor straightedge
Students practice estimating and
measuring angles.
Materials
Math Journal 1, p. 155
Student Reference Book, pp. 92 and 142
Study Link 65
Math Masters, p. 389 (optional)
transparency of Math Masters, p. 439 drinking straw for demonstration purposes straightedge
ELL SUPPORT
Building Background for
Mathematics Words
colored pencils dictionary
Students discuss the meanings of the terms
clockwise and counterclockwise.
Advance Preparation
For Part 1 and the optional Enrichment activity in Part 3, 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.
Teacher’s Reference Manual, Grades 4–6 pp. 178–180, 225
Lesson 6 6
431
Mathematical Practices
SMP2, SMP3, SMP5, SMP6, SMP7, SMP8
Content Standards
Getting Started
4.NBT.6, 4.MD.2, 4.MD.5a, 4.MD.5b, 4.MD.6, 4.MD.7
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
(Student Reference Book, p. 92)
WHOLE-CLASS
ACTIVITY
ELL
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
Tell students that in this lesson they will learn how to measure
angles of varying degrees.
An angle is formed by 2 rays or 2 line segments that share
the same endpoint.
angle formed by
2 segments
angle formed by 2 rays
Demonstrating Angles
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.
Naming Angles
The symbol for an angle is ∠ . An angle can be named in
two ways:
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.
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
half of the straw counterclockwise about _13 of a turn. Ask another
student to draw a line along each side of the straw to form
an angle.
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°.
Sometimes there is confusion about which angle should be
measured. The small curved arrow in each picture shows
which angle opening should be measured.
full-circle protractor
Measure of
is 60º
∠A
Measure of
is 225º
∠B
Measure of
is 300º
∠C
half-circle protractor
Student Reference Book, p. 92
087_118_EMCS_S_G4_SRB_GEO_576507.indd 92
432
WHOLE-CLASS
ACTIVITY
3/1/11 8:49 AM
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
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 .
˚
M
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
⬔B measures about _____ .
⬔C measures about _____ .
˚
˚
Check your answers on page 344.
Using a Full-Circle Protractor
(Math Journal 1, p. 155; Student Reference Book,
p. 142; Math Masters, p. 439)
WHOLE-CLASS
ACTIVITY
Student Reference Book, p. 142
ELL
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
Time
LESSON
Measuring Angles
66
䉬
Use your full-circle protractor to measure each angle.
92
250
0
270
0
24
290
30
0
D
31
0
0
22
32
0
23
280
260
30
20
200
190
180
170
3
2
4
1.
⬔C measures
60
°
.
2.
14
40
0
C
10
1
5
160
350
0
360
12
6
degrees
11
7
0
15
340
0
21
0
33
10
9
8
C
⬔D measures
120
°
.
310
°
.
Try This
50
60
70
80
90
0
12
100
0
13
110
F
Angle C measures 270°.
E
Students work in partnerships to measure the angles on
journal page 155.
3.
5.
⬔F measures
150
°
.
4.
⬔E measures
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°.
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
Discuss Problem 5 with students. Explain that angle measures
can be added and subtracted to find unknown angle measures.
For example, suppose you want to know the measure of the
reflex angle in Problem 1. Angle C measures 60° and a full turn
measures 360°. If a stands for the measure of the reflex angle,
then 60° + a = 360°, or 360° - 60° = a. So, a = 300°.
Drawing an Angle
Step
Step 11
Step
Step 22
Step
Step 33
0
360
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 1: Draw a ray.
degrees
11
12
1
10
2
9
3
8
4
7
6
5
R
Using a full-circle protractor and a straightedge
to draw an angle
434
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.
Step 3: Draw a second ray from the endpoint of the first
ray through the dot.
Unit 6 Division; Map Reference Frames; Measures of Angles
Student Page
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.
Date
Time
LESSON
Math Boxes
66
1.
Have partners take turns: One partner names a degree measure;
the other draws an angle with that degree measure.
Ms. Kawasaki’s fourth grade class made a circle graph to show students’ favorite
days of the week.
a.
Favorite Day of the Week
Which day of the week is the least favorite in
Ms. Kawasaki’s classroom?
Monday
Monday
Sunday
ay
sd
e
Tu
b.
Ongoing Assessment:
Recognizing Student Achievement
Exit Slip
[Measurement and Reference Frames Goal 1]
Saturday
2
Friday
Juan talked on the phone an average of
34 minutes per week for 1 whole year.
About how many minutes did Juan spend
on the phone in 1 year?
3.
Divide with a paper-and-pencil algorithm.
Write the remainder as a fraction.
883 / 7 =
126 _17
Number model with unknown:
34 ∗ 52 = m
Answer:
1,768
minutes
Summary number model:
34 ∗ 52 = 1,768
4.
22 23
179
18 19
Write <, >, or = to make each number
sentence true.
=
a.
420,000,000
b.
65,000,000
c.
four hundred thousand
d.
102
<
5.
For this spinner, what color would you be
most likely to land on?
white
four hundred
twenty million
<
92,000,000
>
red
104
blue
white
1,000
5 6
2 Ongoing Learning & Practice
Playing Division Dash
Wednesday
Thursday
_1
2.
Use an Exit Slip (Math Masters, page 389) to assess students’ ability to draw
angles with measures 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.
About what fraction of the students
prefer Saturday?
80 84
Math Journal 1, p. 156
137-169_EMCS_S_MJ1_G4_U06_576361.indd 156
2/15/11 5:52 PM
PARTNER
ACTIVITY
(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)
Study Link Master
Name
Date
STUDY LINK
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
66
Measuring Angles
141 142
First estimate and then use your full-circle protractor to measure each angle.
1.
G
3.
> (>, <) 90°.
101 °
2.
This angle measures
measure of ∠G:
measure of ∠I:
< (>, <) 90°.
52 °
This angle measures
measure of ∠H:
H
> (>, <) 90°.
144 °
4.
This angle measures
< (>, <) 90°.
85 °
This angle measures
measure of ∠J:
I
INDEPENDENT
ACTIVITY
J
Try This
(Math Masters, p. 190)
5.
On the back of this page, draw and label angles with the following degree measures:
∠ABC 78°
Home Connection Students use a full-circle protractor
to measure angles.
Time
∠DEF
∠GHI
145°
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
177-202_EMCS_B_MM_G4_U06_576965.indd 190
2/12/11 10:32 AM
Lesson 6 6
435
Teaching Master
Name
Date
LESSON
66
1.
Time
3 Differentiation Options
A Waxed-Paper Protractor
Follow the steps below to make a waxed-paper protractor.
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
fold
(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.
b.
py g
g
p
a.
Making and Using a
SMALL-GROUP
ACTIVITY
R
M
3_2
1
Angle M measures about
3.
wedges.
Angle R measures about
7
wedges.
ENRICHMENT
Playing Angle Add-Up
Use a straightedge to draw more angles on the back of this sheet.
Measure the angles and record the numbers of wedges.
Math Masters, p. 191
PARTNER
ACTIVITY
5–15 Min
(Math Masters, pp. 439 and 507–509)
EM3MM_G4_U06_177-202.indd 191
1/13/11 2:13 PM
To further explore the idea that angle measures are additive,
have students draw angles and then use addition and subtraction
to find the measures of unknown angles. Note that Round 1
requires students to use addition to find the unknown angle
measure. Rounds 2 and 3 require subtraction. The given
measures of 90° and 180° degrees provide practice with
complementary and supplementary angles.
Before they play the game, tell students that the notation m∠ ABC
shown on the record sheet means “the measure of angle ABC.”
EXTRA PRACTICE
Game Master
Name
Date
Time
Angle Add-Up
Materials
1 2
4 3
Playing Angle Tangle
PARTNER
ACTIVITY
5–15 Min
(Student Reference Book, p. 230; Math Masters, p. 457)
□ number cards 1–8 (4 of each)
To practice estimating and measuring angles, have students play
Angle Tangle. See Lesson 6-8 for additional information.
□ number cards 0 and 9 (1 of each)
□ dry-erase marker
□ straightedge
□ full-circle protractor (transparency of Math Masters, p. 439)
□ Angle Add-Up Record Sheet (Math Masters, p. 509)
Players
2
Skills
Drawing angles of a given measure
ELL SUPPORT
Building Background for
Recognizing angle measures as additive
Solving addition and subtraction problems to find the measures
of unknown angles
Objective
SMALL-GROUP
ACTIVITY
5–15 Min
Mathematics Words
To score the most points in 3 rounds.
Directions
Shuffle the cards and place the deck number-side down on the table.
2.
In each round, each player draws the number of cards indicated
on the Record Sheet.
3.
Each player uses the number cards to fill in the blanks and form
angle measures so the unknown angle measure is as large
as possible.
4.
Players add or subtract to find the measure of the unknown angle
and record it in the circle on the Record Sheet. The measure of the
unknown angle is the player’s score for the round.
5.
Each player uses a full-circle protractor, straightedge, and marker
to show that the angle measure of the whole is the sum of the angle
measures of the parts.
6.
Players play 3 rounds for a game. The player with the largest total
number of points at the end of the 3 rounds wins the game.
py g
g
p
1.
Math Masters, p. 507
177-202_EMCS_B_MM_G4_U06_576965.indd 507
436
2/12/11 10:32 AM
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 a clock
with an arrow arcing to the right labeled “clockwise” and an
arrow arcing to the left labeled “counterclockwise.”
Unit 6 Division; Map Reference Frames; Measures of Angles
Name
Date
STUDY LINK
Time
Measuring Angles
66
141 142
First estimate and then use your full-circle protractor to measure each angle.
1.
(>, <) 90°.
°
This angle measures
measure of ∠G:
2.
°
measure of ∠H:
H
G
3.
(>, <) 90°.
This angle measures
(>, <) 90°.
This angle measures
4.
°
measure of ∠I:
(>, <) 90°.
This angle measures
°
measure of ∠J:
I
Try This
5.
On the back of this page, draw and label angles with the following degree measures:
∠ABC
78°
∠DEF
∠GHI
145°
213°
Practice
6.
= 96 ÷ 4
7.
66 ÷ 8 =
8.
= 314 ÷ 2
9.
928 ÷ 5 =
190
∠JKL
331°
Copyright © Wright Group/McGraw-Hill
J
Name
Date
Time
Angle Add-Up
Materials
1 2
4 3
□ number cards 1–8 (4 of each)
□ number cards 0 and 9 (1 of each)
□ dry-erase marker
□ straightedge
□ full-circle protractor (transparency of Math Masters, p. 439)
□ Angle Add-Up Record Sheet (Math Masters, p. 509)
Players
2
Skills
Drawing angles of a given measure
Recognizing angle measures as additive
Solving addition and subtraction problems to find the measures
of unknown angles
Objective
To score the most points in 3 rounds.
Copyright © Wright Group/McGraw-Hill
Directions
1.
Shuffle the cards and place the deck number-side down on the table.
2.
In each round, each player draws the number of cards indicated
on the Record Sheet.
3.
Each player uses the number cards to fill in the blanks and form
angle measures so the unknown angle measure is as large
as possible.
4.
Players add or subtract to find the measure of the unknown angle
and record it in the circle on the Record Sheet. The measure of the
unknown angle is the player’s score for the round.
5.
Each player uses a full-circle protractor, straightedge, and marker
to show that the angle measure of the whole is the sum of the angle
measures of the parts.
6.
Players play 3 rounds for a game. The player with the largest total
number of points at the end of the 3 rounds wins the game.
507
Name
Date
Time
1 2
4 3
Angle Add-Up Example
Example:
In Round 1, Suma draws a 2, 7, 1, and 5. She creates the angle
measures 51° and 72° and records them on her record sheet.
Round 1:
Draw 4 cards.
5
1 °+ 7
m∠ABD
°
2 °=
m∠DBC
m∠ABC
Using addition, Suma finds the sum of the measures of angles ABD and DBC.
She records the measure of angle ABC on her record sheet and scores
123 points for the round.
Round 1:
Draw 4 cards.
5
123
2 °=
1 °+ 7
m∠ABD
m∠DBC
°
m∠ABC
Suma uses her full-circle protractor to show that m∠ABD + m∠DBC = m∠ABC.
A
degrees
11 12 1
10
2
9
3
B
8
7
4
6
5
C
508
Copyright © Wright Group/McGraw-Hill
D
Name
Date
Time
1 2
4 3
Angle Add-Up Record Sheet
Game 1
°+
Round 1:
Draw 4 cards.
m∠ABD
°=
m∠DBC
m∠ABD
= 90°
m∠DBC
°
Round 3:
Draw 2 cards.
m∠ABC
° = 180°
+
m∠ABD
m∠ABC
°
°+
Round 2:
Draw 2 cards.
°
m∠DBC
m∠ABC
Total Points =
Game 2
°+
Round 1:
Draw 4 cards.
Copyright © Wright Group/McGraw-Hill
m∠ABD
°=
m∠DBC
m∠ABD
= 90°
m∠DBC
°
Round 3:
Draw 2 cards.
m∠ABC
° = 180°
+
m∠ABD
m∠ABC
°
°+
Round 2:
Draw 2 cards.
°
m∠DBC
m∠ABC
Total Points =
509