Teaching the Lesson materials

Key ActivitiesStudents 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.

Key Concepts and Skills• Draw and measure angles with a full-circle protractor.

[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]

Key Vocabularyangle (�) • 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]

Ongoing Learning & Practice materialsStudents 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.

Differentiation Options materials

Students make and use awaxed-paper protractor.

Students play Angle Tangleto practice estimating andmeasuring angles.

Students discuss themeanings of clockwiseand counterclockwise.

� Student Reference Book, p. 230

� Teaching Master (Math Masters, p. 191)

� Game Master (Math Masters, p. 457)

� waxed paper; full-circle protractor; straight-edge; colored pencils; scissors; dictionary

ELL SUPPORTEXTRA PRACTICEREADINESS

3

� 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

2

� 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)

� drinking straw for demonstration purposes

� straightedge

See Advance Preparation

1

Objective To provide practice using a full-circle protractor

to measure and draw angles less than 360°.

Technology Assessment Management SystemExit slip

See the iTLG.

Additional InformationAdvance 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.

Lesson 6�6 431

432 Unit 6 Division; Map Reference Frames; Measures of Angles

� Math Message Follow-Up(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 thisdrawing on the board throughout the lesson as a visual reference.

� An angle is formed by 2 rays or 2 line segments that have thesame 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.

� If the vertex of an angle is point T, the angle can be named �T,or angle T.

Tell students that in this lesson they will learn how to measureangles of varying degrees.

� Demonstrating Angles and RotationsIn 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 onehalf 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.

WHOLE-CLASS ACTIVITY

WHOLE-CLASS ACTIVITY

1 Teaching the Lesson

Getting Started

Math Message Read the top half of page 92 in your StudentReference Book. Be prepared to tell some things that all angles have in common.

Study Link 6�5 Follow-Up Consider having a student go through the motionsas 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.

Mental Math and Reflexes 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:

90° less than 90° 270°

45° more than 90° 120°

180° more than 180° 355°

Angles

An angle is formed by 2 rays or 2 line segments that share the same endpoint.

The endpoint where the rays or segments meet is called the vertex of the angle. The rays or segments are called thesides of the angle.

Naming AnglesThe symbol for an angle is �. An angle can be named in two ways:

1. Name the vertex. The angle shown above is angle T. Writethis as �T.

2. Name 3 points: the vertex and one point on each side of theangle. The angle above can be named angle ATC (� ATC) or angle CTA (�CTA). The vertex must always be listed inthe middle, between the points on the sides.

Measuring AnglesThe 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 bemeasured. The small curved arrow in each picture shows which angle opening should be measured.

sidesT

A

Cvertex

angle formed by 2 segments

Geometry and Constructions

angle formed by 2 rays

0330

300

270

240

210180

150

12090

60

30

90100110

120

130

140

150

160

170

18

0

80 7060

50

4030

20

10

0

90 100 110 120130140

150

160

170

18

0

8070

60

50

40

30

20

10

0

A

BC

Measure of �Ais 60º

Measure of �Bis 225º

Measure of �Cis 300º

full-circle protractor

half-circle protractor

Student Reference Book, p. 92

Student Page

Draw a directional arc to show that this angle represents a counterclockwise rotation. Name the vertex. Then use the anglesymbol to name the angle. (See below.) Write counterclockwiserotation next to the angle.

Measuring an Angle with a Full-Circle Protractor

Measurement

ExampleExample Use the full-circle protractor to measure angle A.

Step 1: Place the hole in the center of the protractor over thevertex of the angle, point A.

Step 2: Line up the 0˚ mark with the side of the angle so thatyou can measure the angle clockwise. Make sure thatthe 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. Themeasure of �A is 45 .̊

A

0

330300

270

240

210

180

150120

90

6030

A

Check Your UnderstandingCheck Your Understanding

Use your full-circle protractor to measure angles B and C to the nearest degree.1. 2.

�B measures about _____ ˚. �C measures about _____ ˚.Check your answers on page 344.

B

C

Student Reference Book, p. 142

Student Page

Lesson 6�6 433

155

Measuring AnglesLESSON

6�6

Date Time

92

Use your full-circle protractor to measure each angle.

1. �C measures °. 2. �D measures

°.

3. �F measures °. 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.

360°. Angle F measures 150° so the reflex

Sample answer: A full turn corresponds to

310150

120 60

C

D

F

E

Try This

angle measures 360 � 150 � 210°.

Math Journal 1, p. 155

Student Page

M

∠M

Using a straw to demonstrate a counterclockwise rotation

� Using a Full-Circle Protractor(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 tomeasure angles. Write full-circle protractor on the board.

Show students how to use the full-circle protractor to measureangle B on page 142 of the Student Reference Book. Point out thatthe marks on the edge are labeled from 0° to 360° in a clockwisedirection. Therefore, students must be careful to measure theangle in a clockwise direction.

Ask them to measure reflex angle C. To support English languagelearners, write reflex angle on the board and discuss its meaning.

Angle C measures 270°.

Students work in partnerships to measure the angles on journal page 155.

C

126

1234

5

1110

987

0

180

30

210

60

240

90

270

120

300

150

33010

190

20

200

40

220

50

230

70

250

80

260

100

280

110

290

130

310

140

320

160

340

170

350degrees360

WHOLE-CLASS ACTIVITY

434 Unit 6 Division; Map Reference Frames; Measures of Angles

[ART: EM2007TLG1_G4_U06_L06_T_0037: angle A]

Ongoing Assessment: Informing InstructionWatch 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.

Incorrect 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.

� Drawing an AngleHave students use a straightedge and their full-circle protractorsto draw a 60° angle. (See margin.) Ask someone to describe howhe or she drew the angle.

Step 1: Draw a ray.

Step 2: Place the center of the full-circle protractor on theendpoint 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.

Remind students to draw an arc with an arrowhead to identify thedirection of the rotation and use a letter to name the vertex point.

Have partners take turns: One partner names a degree measure;the other draws an angle with that degree measure.

WHOLE-CLASS ACTIVITY

A

12

6

11

5

10

4

1

7

28

3

9

degrees

126

11

5

10

4

1

7

2

8

39

de

gre

es

Step 1 Step 2 Step 3

R

12

6

12

3

45

1110

9

87

0

degrees360

Using a full-circle protractor and a straightedge to

draw an angle

Step 1 Step 2 Step 3

R

Ongoing Assessment:Recognizing Student Achievement

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.

[Measurement and Reference Frames Goal 1]

� Playing Division Dash(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(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 5previews Unit 7 content.

Writing/Reasoning Have students write a response to the following: Winnona said there isn’t enough information provided inProblem 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(Math Masters, p. 190)

Home Connection Students use a full-circle protractor to measure angles.

INDEPENDENTACTIVITY

INDEPENDENTACTIVITY

PARTNER ACTIVITY

2 Ongoing Learning & Practice

Exit Slip

STUDY LINK

6�6 Measuring Angles 141 142

Name Date Time

1. This angle is (�, ) 90.

�G: °

3. This angle is (�, ) 90.

�I:°

2. This angle is (�, ) 90.

�H:°

4. This angle is (�, ) 90.

�J:°85

52

144�

101�

First estimate and then use your full-circle protractor to measure each angle.

5. On the back of this page, draw and label angles with the following degree measures:

�ABC 78 �DEF 145 �GHI 213 �JKL 331

Try This

6. � 96 � 4 7. 66 � 8 �

8. � 314 � 2 9. 928 � 5 � 185 R3157

8 R224

Practice

GH

I

J

Math Masters, p. 190

Study Link Master

Lesson 6�6 435

156

Math Boxes LESSON

6�6

Date Time

3. Divide with a paper-and-pencil algorithm.

Write the remainder as a fraction.

883 / 7 �126 �1

7�

1. Ms. Kawasaki’s fourth grade class made a circle graph to show students’ favorite

days of the week.

a. Which day of the week is the least favorite in

Ms. Kawasaki’s classroom?

b. About what fraction of the students

prefer Saturday?

Monday

4. Write , �, or � to make each number

sentence true.

a. 420,000,000 four hundred

twenty million

b. 65,000,000 92,000,000

c. four hundred thousand 104

d. 102 1,000

�

�

2. 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?

Number model:

Answer: minutes 1,768

34 � 52 � 1,768

5 6

18 19

80 84

22 23179

5. For this spinner, what color would you be

most likely to land on?

white

white

red

blue

Favorite Day of the Week

Saturday

Sunday

Friday

Thursday

Tuesday

Monday

Wednesday

�12

�

Math Journal 1, p. 156

Student Page

436 Unit 6 Division; Map Reference Frames; Measures of Angles

LESSON

6�6

Name Date Time

A Waxed-Paper Protractor

1. Follow the steps below to make a waxed-paper protractor.

Step 1: Take a sheet of waxed paper.

Step 3: Fold it in half again.

Step 5: Cut off the top.

Step 2: Fold the paper in half. Be sure to

crease it tightly.

Step 4: Bring the folded edges together and

fold it in half. Repeat this step again.

Step 6: Unfold.

foldfold

fold

2. Use your waxed-paper protractor to measure the angles below.

a. b.

Angle M measures about wedges. Angle R measures about wedges.

3. Use a straightedge to draw more angles on the back of this sheet.

Measure the angles and record the numbers of wedges.

73�12

�

M R

fold

Math Masters, p. 191

Teaching Master

� Making and Using a Waxed-Paper Protractor(Math Masters, p. 191)

To explore the use of a protractor to measure angles, havestudents 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.”

� Playing Angle Tangle(Student Reference Book, p. 230; Math Masters, p. 457)

To practice estimating and measuring angles, have students playAngle Tangle. See Lesson 6-8 for additional information.

� Building Background for Mathematics WordsTo provide language support for angle rotations, discuss themeanings of the words clockwise and counterclockwise. Explainthat counter can be a noun with many meanings. Ask students toprovide some examples. Kitchen counter, using counters to makean array Explain that counter- can also be used as a prefix. Havestudents look up words in the dictionary that have the prefixcounter-. 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.”

5–15 Min

SMALL-GROUP ACTIVITYELL SUPPORT

5–15 Min

PARTNER ACTIVITYEXTRA PRACTICE

15–30 Min

SMALL-GROUP ACTIVITY

READINESS

3 Differentiation Options

Angle Tangle

Materials 1 protractor 1 straightedge several blank sheets of paper

Players 2Skill Estimating and measuring angle size Object of the game To estimate angle sizes accuratelyand have the lower total score. Directions

In each round:

1. Player 1 uses a straightedge to draw an angle ona 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 differencewill 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.

ExampleExample

Player 2 has the lower total score. Player 2 wins the game.

Games

Player 1 Player 2

Estimate Actual Score Estimate Actual Score

Round 1 120° 108° 12 50° 37° 13

Round 2 75° 86° 11 85° 87° 2

Round 3 40° 44° 4 15° 19° 4

Round 4 60° 69° 9 40° 56° 16

Round 5 135° 123° 12 150° 141° 9

Total Score 48 44

Student Reference Book, p. 230

Student Page