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52 Unit 1 Naming and Constructing Geometric Figures

Teaching the Lesson materials

Key ActivitiesStudents explore constructions that involve more than one circle.

Key Concepts and Skills• Measure line segments to the nearest centimeter. [Measurement and Reference Frames Goal 1]• Demonstrate and explain the meaning of intersect. [Geometry Goal 1]• Use a compass to draw circles. [Geometry Goal 2]• Demonstrate and explain the meanings of concentric, radius, and congruent.

[Geometry Goal 2]

Key Vocabularycircle • radius • congruent • concentric circles • intersect

Ongoing Assessment: Recognizing Student Achievement Use journal page 17. [Geometry Goal 2]

Ongoing Learning & Practice materials

Students play Polygon Pair-Up to practice identifying properties of polygons.

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

Differentiation Options materials

Students use a compass toconstruct tangent circles.

Students use diameters,chords, and radii to inscribepolygons in circles.

Students add intersect totheir Math Word Banks.

� Teaching Masters (Math Masters,pp. 27–29)

� Differentiation Handbook� compass; straightedge; red pencil

ELL SUPPORTENRICHMENTENRICHMENT

3

� Math Journal 1, p. 20� Student Reference Book, p. 258� Study Link Master (Math Masters,

p. 26)� Polygon Pair-Up Property Cards

and Polygon Cards (Math Masters,pp. 496 and 497)

2

� Math Journal 1, pp. 17–19� Study Link 1�6� Teaching Master (Math Masters,

p. 25)� slate; Geometry Template;

compass; tape; scissors� board compass for demonstration

purposes

See Advance Preparation

1

Objectives To guide students in defining a circle; and to provide opportunities to explore designs with circles.

Technology Assessment Management SystemJournal page 17, Problem 1See the iTLG.

Additional InformationAdvance Preparation For Part 1, be sure students have plenty of paper for constructions.Copy and cut apart Math Masters, page 25 so that each student has one answer sheet. Placethe sheets near the Math Message.

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� Math Message Follow-Up(Math Masters, p. 25)

Have partners compare results. A circle is the set of all pointsthat are a given distance from a given point called the center ofthe circle. All of the 20 points on the paper that are 2 centimetersfrom point A form a circle with center A.

A circular pattern of points

The radius of a circle is a line segment from the center of a circleto any point on the circle. (It is also the length of such a linesegment.) Ask students to connect one of the 20 points to thecenter point and label the line segment radius. To support Englishlanguage learners, draw a picture of a circle on the board. Drawand label the radius of the circle.

Ask students to draw another circle with their compasses. Havethem mark the center point and a point on the circle and connectthem with a line segment. Ask students to measure the radius tothe nearest centimeter. Suggest that they measure another radiusto emphasize that all points on the same circle are the samedistance from the center.

A

WHOLE-CLASS ACTIVITY

1 Teaching the Lesson

Lesson 1�7 53

Getting Started

Mental Math and Reflexes Pose addition facts and extended facts. Suggestions:

5 � 5 � 106 � 2 � 81 � 8 � 99 � 3 � 128 � 6 � 145 � 8 � 1350 � 40 � 9060 � 70 � 13070 � 80 � 150

Math MessageTake an answer sheet (Math Masters, page 25)and complete it.

Study Link 1�6 Follow-Up Have partners compare answers. Ask volunteersto share solutions to the Try This problem.Students should be able to construct circles withtwo different radii.

Hold this pencil at the center. This pencil

traces the circles.

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Adjusting the Activity


18

Circle Constructions continuedLESSON

1�7

Date Time

2. a. Make a dot near the center ofyour paper. Use your compassto draw a circle with that dot asits center.

b. Without changing the opening of your compass, draw acongruent circle that intersectsthe center of the first circle. Markthe center of the second circle.

c. Without changing the opening of your compass, draw a thirdcongruent circle that intersectsthe center of each of the first2 circles.

Try and try again until you are satisfiedwith your work. Then cut out your circledesign and tape it in the space below.

Math Journal 1, p. 18

Student Page

17

Circle ConstructionsLESSON

1�7

Date Time

Do each of the following 3 constructions on a separate sheet of paper. Try and tryagain until you are satisfied with your work. Then cut out your 3 best constructions and tape them in your journal.

20

3

5

17

12

2

9

15

14

10

11 9

8

13

16

4

7

18

19

1

1. Use your compass to draw a pictureof a circular dartboard. It is notnecessary to include the details ofthe board. Tape your best work inthe space below. The circles in thedartboard and in your picture arecalled concentric circles.

�


Student Page

� Practicing Circle Constructions(Math Journal 1, pp. 17–19)

Tell students that this lesson consists of activities designed to givethem practice using a compass to draw circles. Students shouldpractice the constructions on sheets of paper until they are satisfied with the results and then tape their final work ontopages 17–19 in their journals.

Write the word constructions on the board. To support Englishlanguage learners, discuss the distinction between the everydayand mathematical meanings of constructions.

Drawing a DartboardTo introduce students to the idea of concentric circles, ask them touse a compass to draw a picture of a circular dartboard. Studentsdo not need to include details on the dartboard.

Ongoing Assessment:Recognizing Student Achievement

Use journal page 17, Problem 1 to assess students’ ability to construct circleswith a compass. Students are making adequate progress if the concentric circles they draw have the same center point. Some students may be able to comparethe area of the smallest circle with the area of the entire dartboard.

[Geometry Goal 2]

Drawing Three Circles That Pass through One Another’s CentersOn journal page 18, students construct two congruent circles(circles of the same size) so that each circle passes through thecenter of the other circle. Then they add a third congruent circlethat passes through the center of each of the first two circles.

Making Circle DesignsHave students construct and color a circle design that extends thethree-circle construction from journal page 18.

� Drawing Conclusions about CirclesBring the class together to discuss students’ work. Studentsshould recognize that each circle on the dartboard has the samecenter, but the radius—the distance from the center to the pointson the circle—is different for each circle.

Have students use a straightedge to draw the radius of each of the circles they drew on journal page 17. Have them measure each radius to thenearest centimeter and record it on the journal page.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

WHOLE-CLASSDISCUSSION

Journal page 17Problem 1

�

INDEPENDENTACTIVITY


Tell students that circles with the same center are called concentric circles. Concentric circles do not intersect(touch or cross).

Concentric circlesdo not intersect

Not concentric circles Not concentric circles intersect at 1 point intersect at 2 points

Ask students to give other examples of things that suggest concentric circles. Sample answers: archery target, saucer,doughnut, CD, ripples in a pond, merry-go-round, car wheel, sewer cover

NOTE The word concentric is derived from the Greek words con, which means“same,” and centrom, which means “center.”

� Playing Polygon Pair-Up(Student Reference Book, p. 258; Math Masters,pp. 496 and 497)

Students play Polygon Pair-Up to practice identifying properties of polygons. See Lesson 1-6 for additional information.

� Math Boxes 1�7(Math Journal 1, p. 20)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 1-5. The skill in Problem 6previews Unit 2 content.

Writing/Reasoning Have students write a response to the following: How can you use a basic subtraction fact like 9 � 7 in Problem 1 to solve an extended subtraction fact

like 900 � 700? Sample answer: 900 � 700 is the same as 9hundreds � 7 hundreds. 9 hundreds � 7 hundreds � 2 hundreds. 2 hundreds � 200, so 900 � 700 � 200.

INDEPENDENTACTIVITY

PARTNER ACTIVITY

2 Ongoing Learning & Practice

19

Circle Constructions continuedLESSON

1�7

Date Time

3. Draw this design with your compass.Work on separate sheets of paperuntil you are satisfied with yourwork. Color your best design. Thencut it out and tape it in the spacebelow.

Hint: Start by making the 3-circledesign on page 18. Then add morecircles to it.

Try This


Student Page

20

Math Boxes LESSON

1�7

Date Time

3. Draw and label line segment GP.

What is another name for GP?

PG�

P G

Sample answer:4. Name as many rays as you can in the

figure below.

Write their names.

L M N

1. Subtract mentally.

a. 9 � 7 �

b. 10 � 6 �

c. � 16 � 8

d. � 17 � 7

e. 13 � 7 �

f. � 15 � 966

108

42

2. Draw �TIF. What is the vertex of �TIF?

Point

F

T

I

I

5. Draw a quadrangle with 1 pair ofparallel sides.

What kind of quadrangle is this?

trapezoid

Sample answer:

6. Put these numbers in order from least to greatest.

32,000 3,200

23,000 2,300

32,00023,000

3,2002,300

92

91

499 100

90

LM�� (or LN��), ML��, MN��,NM�� (or NL��)

Sample answers:


Student Page

Lesson 1�7 55



� Study Link 1�7(Math Masters, p. 26)

Home Connection Students draw circles and measureeach radius to the nearest centimeter.

� Drawing Tangent Circles(Math Masters, pp. 27 and 28)

To apply students’ understanding of circle constructions,have them explore tangent circles. Two circles that barelytouch (touch at just one point) are said to be tangent to

each other. Students first construct two tangent circles of the samesize (radius). Then they construct a third circle of the same size sothat each circle is tangent to the other two circles.

� Using Diameters, Chords,and Radii(Math Masters, p. 29)

To apply students’ understanding of attributes of polygons, have them inscribe polygons in circles using line segments thatrepresent chords and radii of the circles. When they have finishedthe page, have students share their strategies and describe howthey know they have correctly constructed the specified polygons.

� Building a Math Word Bank(Differentiation Handbook)

To provide language support for geometry, have students use theWord Bank Template found in the Differentiation Handbook. Askstudents to write the term intersect, draw pictures relating to theterm, and write other related words. See the DifferentiationHandbook for more information.

5–15 Min

SMALL-GROUP ACTIVITYELL SUPPORT

5–15 Min

INDEPENDENTACTIVITYENRICHMENT

15–30 Min

INDEPENDENTACTIVITYENRICHMENT

3 Differentiation Options

INDEPENDENTACTIVITY

LESSON

1�7

Name Date Time

Radius, Chord, and Diameter

A radius is a line segment that connects thecenter of a circle with any point on the circle.

A chord is a line segment that connects2 points on a circle.

A diameter is a special chord. It is specialbecause it is the chord with the largestpossible length for that circle.

Use your straightedge to inscribe the polygons described in Problems 1–4.

1. Draw 4 chords to make a rectangle.

3. Draw 3 chords to make an isoscelestriangle.

2. Draw a diameter and 3 chordsto make a trapezoid.

4. Draw 4 chords to make a kite.

radius

center

chord

diameter

104

Sample answers:

Math Masters, p. 29

Teaching Master

STUDY LINK

1�7 The Radius of a Circle

104

Name Date Time

1. Find 3 circular objects. Trace around them to make 3 circlesin the space below or on the back of this page. For each circle, do the following:

a. Draw a point to mark the approximate centerof the circle. Then draw a point on the circle.

b. Use a straightedge to connect these points.This line segment is a radius of the circle.

c. Use a ruler to measure the radius to thenearest centimeter. If you do not have a rulerat home, cut out the one at the bottom of this page.

d. Record the measure of the radius next to the circle.

2. � 80 � 20 3. � 30 � 90 4. 580 � 370 �

5. 120 � 30 � 6. 160 � 70 � 7. 650 � 280 �

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150cm

3709090950120100

Practice

1 cm

Example:

Math Masters, p. 26

Study Link Master

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1 teaching the lesson materials - ellis family - home

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