Teaching the Lesson materials

Key ActivitiesStudents identify types of angles and measure angles with a half-circle protractor.They identify an angle as obtuse or acute to help them determine which protractor scale they should use. They draw angles with a half-circle protractor.

Key Concepts and Skills• Use reference points to estimate the measures of angles.

[Measurement and Reference Frames Goal 1]

• Use a half-circle protractor to measure and draw angles. [Measurement and Reference Frames Goal 1]

• Classify angles according to their measure. [Geometry Goal 1]

Key Vocabulary acute angle • obtuse angle • reflex angle • straight angle • half-circle protractor • base line

Ongoing Assessment: Recognizing Student AchievementUse Mental Math and Reflexes. [Number and Numeration Goal 1]

Ongoing Assessment: Informing Instruction See page 440.

Ongoing Learning & Practice materials

Students resume the World Tour in Europe.

Students practice and maintain skills through Math Boxes and Study Link activities.

Differentiation Options materials

Students modelangles with arope.

Students determine thatthe sum of themeasures of theangles of any triangle is 180°.

Students readSir Cumferenceand the GreatKnight ofAngleland.

Students createa graphic organizer for the word angle.

� Student Reference Book, p. 93

� Teaching Masters (Math Masters, p. 193)

� Teaching Aid Master (Math Masters, pp. 388 or 389)

� Differentiation Handbook

� rope/string; protractor; straightedge; glue/tape

See Advance Preparation

ELL SUPPORTENRICHMENTENRICHMENTREADINESS

3

� Math Journal 1,pp. 159, 171 (optional), 172–173,180, and 181

� Student ReferenceBook

� Study Link Master(Math Masters, p. 192)

� Teaching Aid Masters(Math Masters,pp. 419–421; optional)

2

� Math Journal 1, pp. 157 and 158

� Study Link 6�6

� half-circle protractor (Geometry Template; optional)

� protractor for demonstration purposes

� straightedge

� slate

1

Objectives To guide students as they classify angles as acute,

right, obtuse, straight, and reflex; and to provide practice using a

half-circle protractor to measure and draw angles.

Technology Assessment Management SystemMental Math and Reflexes

See the iTLG.

Additional InformationAdvance Preparation For the optional Enrichment activity in Part 3, obtain the book Sir Cumference and the Great Knight of Angleland by Cindy Neuschwander (CharlesbridgePublishing, 2001).

Lesson 6�7 437

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

Ongoing Assessment:Recognizing Student Achievement

Use Mental Math and Reflexes to assess students’ ability to identify places in

decimals and the values of the digits in those places. Students are making

adequate progress if they can correctly identify and express the values of digits

through thousandths. Some students may correctly identify and express the

values of digits through ten thousandths.

[Number and Numeration Goal 1]

� Math Message Follow-Up(Math Journal 1, p. 157)

In discussing the answers, talk about the angles in terms of rotations: �A is less than a �

14� turn, �B is more than a �

14� turn but

less than a �12� turn, and �C is between a �

12� turn and 1 full turn.

Call attention to the names for the various types of angles. Tosupport English language learners, write the names on chartpaper next to an example of each. Display the chart paperthroughout the unit.

� An acute angle is greater than 0° and less than 90°.

� An obtuse angle is greater than 90° and less than 180°.

� A reflex angle is greater than 180°.

Remind students that a 90° angle is called a right angle.

Complete the list of angle names by mentioning that a 180° angleis called a straight angle. Ask: Why is this a good name for thisangle? In a 180° angle, the two sides meet to form a straight line.

WHOLE-CLASS ACTIVITY

1 Teaching the Lesson

Mental Math

and Reflexes �

Getting Started

Math MessageComplete the Math Message problems on journal page 157.

Study Link 6�6 Follow-Up Students compare answers. Make sure they understand that the directional arc shows the path and direction of the rotation.

Mental Math and Reflexes Write decimals on the board and have volunteers readthem aloud. Suggestions:

3.45 12.358 10.005

0.27 60.893 2.6074

6.89 83.591 26.0801

Ask questions such as:

• What digit is in the hundredths place?

• What is the value of the digit x?

Links to the FutureIdentifying and describing acute, obtuse,

straight, and reflex angles and proficient use

of a half-circle protractor are Grade 5 Goals.

�

� Introducing the Half-Circle ProtractorHave students examine their half-circle protractors. Students canuse either the protractor on the Geometry Template or any otherprotractor. If some students’ protractors do not have labels for the 0° and 180° marks, have them write the labels. The marksmay smear and disappear later, but they are helpful for this introduction to the half-circle protractor.

Ask partnerships to decide how the half-circle protractor isdifferent from the full-circle protractor they used in the previouslesson. Review observations. Have students indicate “thumbs-up”if they had a similar answer.

� The curved edge of the protractor is a half circle. The edge ofthe full-circle protractor is a full circle.

� There are two scales on the half-circle protractor: one scale goes from 0° to 180° in a clockwise direction and the other from 0° to 180° in a counterclockwise direction. To support Englishlanguage learners, discuss the meaning of scale in this context.

� The 0° mark on one side of the half-circle protractor is connected with the 180° mark on the other side by a line segment. This segment is the base line of the protractor.

� The midpoint of the base line is the center of the half-circleprotractor. There is often a hole at the center.

� Measuring Angles with a Half-Circle Protractor(Math Journal 1, p. 157)

Draw an angle on the board or overhead projector, but omit thearc that indicates the direction of the rotation. Mention thatwithout the directional arc, this angle could represent a rotationless than 180° or a rotation greater than 180°. Draw directionalarcs with arrowheads to show the two possible angles. Explainthat if no arc is shown, the smaller of the two angles is intended.(See margin.)

Draw another angle on the board or overhead. Use your demonstration protractor to show how to measure the angle.

1. Students should first estimate whether the angle measuresmore or less than 90°. Ask: Is the angle acute or obtuse?They can also use 45° and 180° as reference angles to refinetheir estimate. If students develop this good habit, they willseldom read the wrong scale.

2. Put the center of the protractor over the vertex of the angle.

3. Move the protractor so that one side of the angle is on the base line, as shown in the margin. Make sure the center of theprotractor remains over the vertex.

WHOLE-CLASSACTIVITY

WHOLE-CLASSACTIVITY

157

Drawing and Measuring AnglesLESSON

6�7

Date Time

92 93141

Math Message

Use a straightedge to draw the following angles. Do not use a protractor.

�A: any angle �B: any angle more than �C: any angle

less than 90° 90° and less than 180° more than 180°

Sample answers:

A�A is called an acute angle. �B is called an obtuse angle. �C is called a reflex angle.

B

C

Measuring Angles with a Protractor

Write whether the angle is acute or obtuse. Then measure it as accurately as you can.

�SDE is . �COR is . �RTV is .

�SDE is about °. �COR is about

°. �RTV is about

°.

Answers may vary by 3 degrees either way.

1404055

obtuseacuteacute

D

S E

OR

C

T

R

V

Math Journal 1, p. 157

Student Page

Lesson 6�7 439

The arc indicates which angle to consider.

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center

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

Drawing AnglesLESSON

6�7

Date Time

1. Draw a 35° angle, using

line segment GH as one

of its sides.

2. Draw a 150° angle, using

ray CD as one of its sides.

3. Draw a 60° angle, using

ray EF as one of its sides.

4. Draw a 15° angle, using

ray AB as one of its sides.

5. Draw a 330° angle, using

ray IJ as one of its sides.

BA

CD

E F

H G

JI

143

Try This

Math Journal 1, p. 158

Student Page4. Find the place where the other side of the angle crosses a

mark on the edge of the protractor.

5. Decide which of the two 0°-to-180° scales to use to determinethe degree measure of the angle. If it is acute, use the smallernumber; if it is obtuse, use the larger number.

Ask students to measure angles SDE, COR, and RTV at thebottom of journal page 157 and compare their measurements.

Ongoing Assessment: Informing InstructionWatch that students are measuring carefully. A difference of 3 degrees either

way should be enough leeway.

� Drawing Angles with a Half-Circle Protractor(Math Journal 1, p. 158)

Have students complete Problem 1 on journal page 158 with apartner or on their own. Ask students to describe a procedure forusing a half-circle protractor to draw angles while you or a studentdemonstrates at the board or overhead.

One method:

1. Draw a ray.

2. Place the center of the protractor at the endpoint of the ray so that the base line is along the ray.

3. Use the scale that shows 0° where the ray crosses the edge ofthe protractor. Make a dot where the other ray should crossthe edge of the protractor.

4. Draw a ray from the vertex through the dot.

Have students complete journal page 158 on their own. Remindstudents that they can check whether they have chosen the appro-priate scale for drawing an angle by noting if the angle is acute orobtuse.

Share strategies for solving Problem 5, which requires students todraw a reflex angle. One possible strategy: Subtract 330° from360° (� 30°). Draw a 30° angle; then draw an arc on the “outside”of the 30° angle.

INDEPENDENTACTIVITY

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Step 4

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EM07TLG1_G4_U06_L07.qxd 7/26/07 2:19 PM Page 440

� World Tour Option:Visiting Europe(Math Journal 1, pp. 171–173, 180, and 181; Student Reference Book;Math Masters, pp. 419–421)

Social Studies Link If you have chosen to extend the scopeof the World Tour for your class, divide students into groups

of 4 or 5. Each group visits one of the remaining countries inEurope and records their country data on journal pages 180 and181, or on Math Masters, pages 419 and 420.

� Math Boxes 6�7(Math Journal 1, p. 159)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 6-5. The skill in Problem 6previews Unit 7 content.

Writing/Reasoning Have students write a response to thefollowing: Wei said that both squares in Problem 6 have �

13�

shaded. Do you agree or disagree? Explain your answer.Sample answer: I disagree. Both of the squares are divided intothree parts and both of the squares have one part shaded. However, only A shows �

13� because A is divided into equal parts. The three

parts in B are not equal.

� Study Link 6�7(Math Masters, p. 192)

Home Connection Students measure angles using a half-circle protractor. Some students may prefer to use afull-circle protractor from Lesson 6-6.

� Modeling Angles(Student Reference Book, p. 93)

To explore estimating angle measures using a concrete model,have students use rope to model angles. (See margin.) Ask the“vertex” to tell the two “points” the type of angle or the measure of the angle that they should form. Have students use StudentReference Book, page 93 as a guide.

5–15 Min

SMALL-GROUPACTIVITY

READINESS

3 Differentiation Options

INDEPENDENTACTIVITY

INDEPENDENTACTIVITY

SMALL-GROUPACTIVITY

2 Ongoing Learning & Practice

159

Math Boxes LESSON

6�7

Date Time

129 315 44

150 128

11

41

1

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22 23 18 19

( )

( )

( ) ( )

1. Insert parentheses to make each number

sentence true.

a. 12 � 15 � 2 � 1

b. 66 � 16 � 4 � 200

c. 49 � 4 � 3 � 42 / 6

2. Draw a line segment that is 2 inches

long. Mark and label the following inch

measurements on the line segment:

�14

�, �34

�, 1, 1�14

� and 1�12

�

3. Six classrooms collected newspapers

for one week. If they collected a total of

582 newspapers by the end of the week,

on average about how many newspapers

did each class collect?

Number model:

Answer: newspapers97

582 / 6 � 97

4. Multiply with a paper-and-pencil algorithm.

67 � 34 � 2,278

5. How many centimeters are in 9.7 meters?

Circle the best answer.

A. 907

B. 900.7

C. 970

D. 9,700

6. Circle the square that has �13

� shaded.

A. B.

Math Journal 1, p. 159

Student Page

STUDY LINK

6�7 Measuring Angles with a Protractor

Name Date Time

First estimate whether the angles measure more or less than 90°. Then use a

half-circle protractor to measure them.

B

C

S

R

Q

P

N

O

M

L

K

A

1. �A: °

2. �B: °

3. �C: °8415060

4. �QRS: °

5. �NOP: °

6. �KLM: °30032105

Practice

7. 93 � 6 � 8. � 547 � 7

9. � 48 � 39 10. 51 � 64 � 3,2641,872

3,829558

Try This

143

Math Masters, p. 192

Study Link Master

Lesson 6�7 441

Three students, acting as points,

use rope to represent line segments

and form an acute angle.

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

LESSON

6�7

Name Date Time

Exploring Triangle Measures

You need 2 sheets of paper, a straightedge, and a protractor.

1. Draw a large triangle on each sheet of paper. The 2 triangles should

not look the same.

2. Label the vertices of one triangle A, B, and C. Label the vertices of the

other triangle D, E, and F. Be sure to write the labels inside the triangles.

3. Using your protractor, measure each angle as accurately as you can.

Record the degree measures in the tables below.

4. Find the sum of the degree measures in triangle ABC and in triangle DEF.

5. Write a true statement about the sum of the measures of the 3 angles of a triangle.

The sum of the angle measures of a triangleis 180.

Angle Degree Measure

�A About °

�B About °

�C About °

Sum About °180

90

45

45

143

Sample answers:Angle Degree Measure

�D About °

�E About °

�F About °

Sum About °180

60

60

60

Math Masters, p. 193

Teaching Master

� Measuring Angles in Triangles(Math Masters, p. 193)

To apply students’ understanding of measuring angles,have them draw two triangles, measure the angles, andfind the sum of the angle measures for each triangle. The

sum of the students’ measures of the angles of a triangle shouldrange from 170° to 190°, with most sums close to 180°.

Guide students as they “prove” that the sum of the measures ofthe angles of any triangle is 180°. Have them cut off the threecorners of one of their triangles and arrange them so that thethree angles touch each other but do not overlap. From this, itshould be clear that the angles form a straight angle, and so thesum of their measures is 180°.

Encourage students to extend this exploration to “prove” that thesum of the measures of the angles of any quadrilateral is 360°.Students may reason that since any quadrilateral can be dividedinto two triangles, the sum of the angles is twice 180°, or 360°.

� Exploring Angles in Literature(Math Masters, p. 388 or 389)

Literature Link To further explore the half-circle protractor and angles, have students read and discuss

Sir Cumference and the Great Knight of Angleland by Cindy Neuschwander (Charlesbridge Publishing, 2001). In a Math Log or on an Exit Slip, ask students to summarize whatRadius learned on his quest.

� Building Background for Mathematics Words(Differentiation Handbook)

To provide language support for angles, have students create agraphic organizer for the word angle. They may list words anddraw pictures that are connected to the word angle. See theDifferentiation Handbook for more information.

5–15 Min

PARTNER ACTIVITY

ELL SUPPORT

15–30 Min

SMALL-GROUP ACTIVITY

ENRICHMENT

CAB

Cut

Cut

C A

BCut

15–30 Min

PARTNER ACTIVITY

ENRICHMENT