The Half-Circle Protractor - Everyday Math Half-Circle Protractor ... the two sides meet to form a...

www.everydaymathonline.com

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

Lesson 6�7 437

Advance PreparationFor the optional Enrichment activity in Part 3, obtain the book Sir Cumference and the Great Knight

of Angleland by Cindy Neuschwander (Charlesbridge Publishing, 2001).

Teacher’s Reference Manual, Grades 4–6 pp. 44–46, 178–180, 234–236

Key Concepts and Skills• Add and subtract to find unknown angle

measures.

[Operations and Computation Goal 2]

• Use reference points to estimate the

measures of angles; 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 ActivitiesStudents identify types of angles. They

measure and draw angles with a half-circle

protractor. They identify an angle as obtuse

or acute to help them determine which

protractor scale to use. They add and

subtract to find unknown angle measures.

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

Ongoing Assessment: Informing Instruction See page 440.

Key Vocabularyacute angle � obtuse angle � reflex angle �

straight angle � half-circle protractor �

base line

MaterialsMath Journal 1, pp. 157 and 158

Study Link 6�6 � half-circle protractor �

protractor for demonstration purposes �

straightedge � chart paper

World Tour Option: Visiting EuropeMath Journal 1, p. 171 (optional);

pp. 172, 173, 180, and 181

Student Reference Book, pp. 276,

277, 280, 284, 285, 297, and 302–305

Math Masters, pp. 419–421 (optional)

Students resume the World Tour

in Europe.

Math Boxes 6�7Math Journal 1, p. 159

Students practice and maintain skills

through Math Box problems.

Study Link 6�7Math Masters, p. 192

protractor

Students practice and maintain skills

through Study Link activities.

READINESS

Modeling AnglesStudent Reference Book, p. 93

rope or string

Students model angles with a rope.

ENRICHMENTMeasuring Angles in TrianglesMath Masters, p. 193

straightedge � protractor � glue or tape

Students determine that the sum of the

measures of the angles of any triangle

is 180°.

ENRICHMENTExploring Angles in LiteratureMath Masters, p. 388 or 389

Students read Sir Cumference and the Great

Knight of Angleland.

ELL SUPPORT

Building Background for Mathematics WordsStudents create a graphic organizer for the

word angle.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

��

The Half-CircleProtractor

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.

437_EMCS_T_TLG1_G4_U06_L07_576817.indd 437437_EMCS_T_TLG1_G4_U06_L07_576817.indd 437 2/16/11 8:46 AM2/16/11 8:46 AM

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

Links to the FutureIdentifying and describing acute, obtuse,

straight, and reflex angles is a Grade 5 Goal.

�

Ongoing Assessment: Mental Math

and Reflexes �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]

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASS ACTIVITY

(Math Journal 1, p. 157)

In discussing the answers, talk about the angles in terms of rotations: ∠ A is less than a 1 _ 4 turn, ∠ B is more than a 1 _ 4 turn but less than a 1 _ 2 turn, and ∠C is between a 1 _ 2 turn and 1 full turn. Call attention to the names for the various types of angles. To support English language learners, write the names on chart paper next to an example of each. Display the chart paper throughout the unit.

� An acute angle measures between 0° and 90°.

� An obtuse angle measures between 90° and 180°.

� A reflex angle measures between 180° and 360°.

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

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

ELL

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 read them 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?

EM3cuG4TLG1_438-442_U06L07.indd 438EM3cuG4TLG1_438-442_U06L07.indd 438 1/14/11 12:58 PM1/14/11 12:58 PM

Drawing and Measuring AnglesLESSON

6�7

Date Time

Math Message

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

∠A: any angle that ∠B: any angle that measures ∠C: any angle that

measures less more than 90° and less measures more

than 90° than 180° than 180°

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

Measuring Angles with a Protractor

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

∠SDE is acute . ∠COR is acute . ∠RTV is obtuse.

∠SDE measures 55 °. ∠COR measures 40 °

. ∠RTV measures 140 °.

Answers may vary by 3 degrees either way.

D

S E

OR

C

T

R

V

92 93141

Sample answers:

A

B

C

EM3MJ1_G4_U06_137-169.indd 157 1/13/11 3:28 PM

Math Journal 1, p. 157

Student Page

Lesson 6�7 439

The arc indicates which angle to consider.

908070

60

50

40

3020

10

100 110120

130

140150

160170

1800

100110

120

130

140

150

160

170

80 7060

50

4030

2010

0

180

centerbaseline

a 40° angle

908070

60

50

40

3020

10

100 110120

130

140150

160170

1800

100110

120

130

140

150

160

170

80 7060

50

4030

2010

0

180

a 115° angle

� Introducing the Half-Circle WHOLE-CLASS ACTIVITY

ProtractorHave students examine their half-circle protractors. Students can use either the protractor on the Geometry Template or any other protractor. If some students’ protractors do not have labels for the 0° and 180° marks, have them write the labels. The marks may 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 is different from the full-circle protractor they used in the previous lesson. 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 of the 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 English language 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 WHOLE-CLASS ACTIVITY

Half-Circle Protractor(Math Journal 1, p. 157)

Draw an angle on the board or overhead projector, but omit the arc that indicates the direction of the rotation. Mention that without the directional arc, this angle could represent a rotation less than 180° or a rotation greater than 180°. Draw directional arcs with arrowheads to show the two possible angles. Explain that 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 measures more or less than 90°. Ask: Is the angle acute or obtuse? They can also use 45° and 180° as reference angles to refine their estimate. If students develop this good habit, they will seldom 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 the protractor remains over the vertex.

ELL



Drawing AnglesLESSON

6�7

Date Time

1. Draw a 35° angle, using

line segment GH as one

of its sides.


ray CD as one of its sides.


ray EF as one of its sides.


ray AB as one of its sides.


ray IJ as one of its sides.

BA

CD

E F

H G

JI

143

Try This

EM3MJ1_G4_U06_137-169.indd 158 1/13/11 2:28 PM


Student Page

Step 4

908070

60

50

40

3020

10

100 110120

130

140150

160170

1800

100110

120

130

140

150

160

170

80 7060

50

4030

2010

0

180

Steps 2 and 3

Step 1

Ongoing Assessment: Informing Instruction

Watch that students are measuring carefully.

A difference of 3 degrees either way should

be enough leeway.

4. 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 determine the degree measure of the angle. If it is acute, use the smaller number; if it is obtuse, use the larger number.

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

� Drawing Angles with a INDEPENDENTACTIVITY

Half-Circle Protractor(Math Journal 1, p. 158)

Have students complete Problem 1 on journal page 158 with a partner or on their own. Ask students to describe a procedure for using a half-circle protractor to draw angles while you or a student demonstrates 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 of the protractor. Make a dot where the other ray should cross the edge of the protractor.

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

Have students complete journal page 158 on their own. Remind students that they can check whether they have chosen the appropriate scale by noting if the angle is acute or obtuse.

Share strategies for Problem 5, which requires students to draw a reflex angle. Sample strategy: Subtract 330° from 360° (= 30°). Draw a 30° angle; then draw an arc on the “outside” of the angle.

� Adding and Subtracting to WHOLE-CLASS ACTIVITY

Find Missing Angle MeasuresShow students that you can add and subtract angle measures to find unknown angle measures. Draw the diagram below on the board or overhead.

30°a

Point out that a straight angle measures 180° and the smaller angle measures 30°. Let a stand for the measure of the missing angle. Explain to students that the angle measure of the whole is the sum of the angle measures of the parts. Therefore, 30° + a = 180°, so a = 150°.

Pose additional problems on the board using either a straight angle or a 90° angle as the main angle. Have students use addition or subtraction to find the missing angle measures.

PROBLEMBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMBLEBLBLBLBLEBLELLLLLBLEBLEBLEBLEBLEEEMMMMMMMMMMMMMOOOOOOOOOOBBBLBLBLBLBLBLLLLLPROPROPROPROPROPROPROPROPROPROPROPPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROROROOPPPPPPP MMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEELEEEELELEEEEEEELLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBBB EEELEMMMMMMMOOOOOOOOOBBBLBLBLBLBLBLBBROOOOROROROROROROROROROO LELELELEEEEEELEEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGLLLLLLLLLLLLLVINVINVINVINVINNNVINVINVINNVINVINVINVINV GGGGGGGGGGGOLOOOLOOOLOLOO VINVINVVLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGGOOOLOLOLOLOLOLOOO VVVLLLLLLLLLLVVVVVVVVVOSOSOOSOSOSOSOSOSOSOOSOSOSOSOSOOOOOSOSOSOSOSSOOSOSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVVLLLLLLLVVVVVVVVLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIISOLVING

438-442_EMCS_T_TLG1_G4_U06_L07_576817.indd 440438-442_EMCS_T_TLG1_G4_U06_L07_576817.indd 440 2/16/11 8:47 AM2/16/11 8:47 AM

Math Boxes LESSON

6�7

Date Time

129 315 44

150 128

1141

1

2114

34

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:

1 _ 4 ,

3

_ 4 , 1, 1 1 _ 4 and 1 1

_ 2

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 with unknown:

582 � 6 = n

Answer: 97 newspapers

Summary number model:

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 1 _ 3 shaded.

A. B.

EM3MJ1_G4_U06_137-169.indd 159 1/13/11 3:28 PM


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: 32 °

6. ∠KLM: 300°105

Practice

7. 93 ∗ 6 = 8. = 547 ∗ 7

9. = 48 ∗ 39 10. 51 ∗ 64 = 3,2641,872

3,829558

Try This

143

EM3MM_G4_U06_177-202.indd 192 1/13/11 2:16 PM

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.

2 Ongoing Learning & Practice

� World Tour Option: SMALL-GROUP ACTIVITY

Visiting Europe(Math Journal 1, pp. 171–173, 180, and 181; Student Reference Book,

pp. 276, 277, 280, 284, 285, 297, and 302–305; Math Masters, pp. 419–421)

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

of 4 or 5. Each group visits one of the remaining countries in Europe and records their country data on journal pages 180 and 181, or on Math Masters, pages 419 and 420.

� Math Boxes 6�7 INDEPENDENTACTIVITY

(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 6 previews Unit 7 content.

Writing/Reasoning Have students write a response to thefollowing: Wei said that both squares in Problem 6 have 1 _ 3 shaded. Do you agree or disagree? Explain your answer.

Sample answer: I disagree. Both of the squares are divided into three parts and both of the squares have one part shaded. However, only A shows 1 _ 3 because A is divided into equal parts. The three parts in B are not equal.

� Study Link 6�7 INDEPENDENTACTIVITY

(Math Masters, p. 192)

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

3 Differentiation Options

READINESS SMALL-GROUP ACTIVITY

� Modeling Angles 5–15 Min

(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 Student Reference Book, page 93 as a guide.



LESSON

6

�7

Name Date Time

Exploring Triangle Measures

py

gg

p

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

EM3MM_G4_U06_177-202.indd 193 1/13/11 2:13 PM

Math Masters, p. 193

Teaching Master

ENRICHMENT PARTNER ACTIVITY

� Measuring Angles in Triangles 15–30 Min

(Math Masters, p. 193)

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

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

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

Cut

Cut

C A

BCut

CAB

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

ENRICHMENT SMALL-GROUP ACTIVITY

� Exploring Angles in Literature 15–30 Min

(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 what Radius learned on his quest.

ELL SUPPORT PARTNER ACTIVITY

� Building Background for 5–15 Min

Mathematics WordsTo provide language support for angles, have students create a graphic organizer for the word angle. They may list words and draw pictures that are connected to the word angle. See Differentiation Handbook, page 34 for more information.

438-442_EMCS_T_TLG1_G4_U06_L07_576817.indd 442438-442_EMCS_T_TLG1_G4_U06_L07_576817.indd 442 2/16/11 8:47 AM2/16/11 8:47 AM

The Half-Circle Protractor - Everyday Math Half-Circle Protractor ... the two sides meet to form a...

Documents

Transcript of The Half-Circle Protractor - Everyday Math Half-Circle Protractor ... the two sides meet to form a...