using a full-circle protractor - everyday math a full-circle protractor ... the protractor is a tool...

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Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

Lesson 6�6 431

Advance PreparationFor 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

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 ActivitiesStudents use transparent protractors to

measure and draw angles.

Ongoing Assessment: Informing Instruction See page 434.

Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip (Math Masters,page 389). [Measurement and Reference Frames

Goal 1]

Key Vocabularyangle (∠) � sides (of an angle) � vertex (of an

angle) � clockwise rotation � counterclockwise

rotation � full-circle protractor

MaterialsMath Journal 1, p. 155

Student Reference Book, pp. 92 and 142

Study Link 6�5

Math Masters, p. 389 (optional)

transparency of Math Masters, p. 439 �

drinking straw for demonstration purposes �

straightedge

Playing Division DashStudent 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.

Math Boxes 6�6Math Journal 1, p. 156

Students practice and maintain skills

through Math Box problems.

Study Link 6�6Math Masters, p. 190

full-circle protractor

Students practice and maintain skills

through Study Link activities.

READINESS

Making and Using a Waxed-Paper ProtractorMath Masters, p. 191

waxed paper � scissors

Students make and use a waxed-paper

protractor.

ENRICHMENTPlaying Angle Add-Up 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.

EXTRA PRACTICE

Playing Angle TangleStudent Reference Book, p. 230


full-circle protractor � straightedge

Students practice estimating and

measuring angles.

ELL SUPPORT

Building Background for Mathematics Wordscolored pencils � dictionary

Students discuss the meanings of the terms

clockwise and counterclockwise.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

��

Using a Full-CircleProtractor

Objective To provide practice using a full-circle protractor

to measure and draw angles less than 360°.t

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

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.

angle formed by 2 segments

Geometry and Constructions

angle formed by 2 rays

Measure of �Ais 60º

Measure of �Bis 225º

Measure of �C is 300º

full-circle protractor

half-circle protractor

Student Reference Book, p. 92

Student Page

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.

� 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 measure angles of varying degrees.

� Demonstrating Angles WHOLE-CLASS ACTIVITY

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 one half of the straw counterclockwise about 1 _ 3 of a turn. Ask another student to draw a line along each side of the straw to form an angle.

ELL

Getting Started

Math Message Read the top half of page 92 in your Student Reference 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 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.

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°

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Measuring an Angle with a Full-Circle Protractor

Measurement

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 .̊

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.

Student Reference Book, p. 142

Student Page

Lesson 6�6 433

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 (thepart 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 60C

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 WHOLE-CLASS ACTIVITY

(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.

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

Angle C measures 270°.

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

ELL

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.

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[ART: EM2007TLG1_G4_U06_L06_T_0037: angle A]

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: 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.

126

11

5

10

4

1

7

2

83

9

degrees

12

6

11

5

10

4

1

728

3

9

degrees

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.

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 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.

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.

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6. = 96 ÷ 4 7. 66 ÷ 8 =

8. = 314 ÷ 2 9. 928 ÷ 5 =

STUDY LINK

6�6 Measuring Angles 141 142

Name Date Time

1. This angle measures (>, <) 90°.

measure of ∠G: °


measure of ∠I: °


measure of ∠H: °


measure of ∠J: °85

<

52

<

>

101

>

144

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

8 R2

157

24

Practice

GH

I

J

185 R3

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Study Link Master

Lesson 6�6 435

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?

Monday

b. About what fraction of the students

prefer Saturday?

1 _ 2

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 with unknown:

34 ∗ 52 = m

Answer: 1,768 minutes

Summary number model:

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

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Math Journal 1, p. 156

Student PageRemind students to draw an arc with an arrowhead to identify the direction 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.

Ongoing Assessment: Recognizing Student Achievement

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.

[Measurement and Reference Frames Goal 1]

2 Ongoing Learning & Practice

� Playing Division Dash 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 INDEPENDENTACTIVITY

(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 INDEPENDENTACTIVITY

(Math Masters, p. 190)

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

Exit Slip �



LESSON

6�6

Name Date Time

A Waxed-Paper Protractor

py

gg

p

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.

fold

fold fold

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

a. b.

Angle M measures about 3

1

_ 2

wedges. Angle R measures about 7 wedges.

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

Measure the angles and record the numbers of wedges.

M R

fold

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Teaching Master

Name Date Time

py

gg

p

132

4Angle Add-Up

Materials □ 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.

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.

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Game Master

3 Differentiation Options

READINESS SMALL-GROUP ACTIVITY

� Making and Using a 15–30 Min

Waxed-Paper Protractor(Math Masters, p. 191)

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.”

ENRICHMENT PARTNER ACTIVITY

� Playing Angle Add-Up 5–15 Min

(Math Masters, pp. 439 and 507–509)

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 PARTNER ACTIVITY

� Playing Angle Tangle 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 SMALL-GROUP ACTIVITY

� Building Background for 5–15 Min

Mathematics WordsTo 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.”


6. = 96 ÷ 4 7. 66 ÷ 8 =

8. = 314 ÷ 2 9. 928 ÷ 5 =

STUDY LINK

6�6 Measuring AnglesC

opyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

190

141 142

Name Date Time


measure of ∠G: °


measure of ∠I: °


measure of ∠H: °


measure of ∠J: °

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

Practice

GH

I

J

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Name Date Time

507

Copyright

© W

right

Gro

up/M

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raw

-Hill

132

4Angle Add-Up

Materials □ 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.

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.

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Name Date Time

508

Copyrig

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Wrig

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roup/M

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132

4Angle 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 2 °

=

°

m∠ABD 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 1 ° +

7 2 °

=

°


Suma uses her full-circle protractor to show that m∠ABD + m∠DBC = m∠ABC.

123

12

6

11

5

10

4

1

7

2

8

39

degrees

A

B

D

C


Name Date Time

509

Copyright

© W

right

Gro

up/M

cG

raw

-Hill

132

4Angle Add-Up Record Sheet

Game 1

Round 1:

Draw 4 cards. ° +

°

=

°


Round 2:

Draw 2 cards. ° +

°

=

90°


Round 3:

Draw 2 cards.

°

+

°

=

180°


Total Points =

Game 2

Round 1:

Draw 4 cards. ° +

°

=

°


Round 2:

Draw 2 cards. ° +

°

=

90°


Round 3:

Draw 2 cards.

°

+

°

=

180°


Total Points =


using a full-circle protractor - everyday math a full-circle protractor ... the protractor is a tool...

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