Technology Assessment Management System

Exit SlipSee the iTLG.

810 Unit 10 Reflections and Symmetry

Teaching the Lesson materials

Key ActivitiesStudents use a transparent mirror to complete symmetric pictures and to find lines of symmetry in symmetric objects. They fold paper to sort polygons by the number of lines of symmetry.

Key Concepts and Skills• Identify polygons and describe properties of regular polygons.

[Geometry Goal 2]• Identify and draw lines of symmetry. [Geometry Goal 3]• Explore the connection between reflections and line symmetry.

[Geometry Goal 3]• Solve problems involving spatial visualization. [Geometry Goal 3]• Describe rules for patterns and use them to solve problems.

[Patterns, Functions, and Algebra Goal 1]

Key Vocabularyline of symmetry • symmetric • rotation (turn) symmetry

Ongoing Assessment: Informing Instruction See page 812.

Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip.[Patterns, Functions, and Algebra Goal 1]

Ongoing Learning & Practice materialsStudents practice and maintain skills through Math Boxes and Study Link activities.

Differentiation Options materials

Students interpret acartoon involvingline symmetry.

Students exploreturn or rotation symmetry.

Students use patternblocks to createshapes with linesymmetry.

Students create aLine SymmetryMuseum.

� Teaching Masters (Math Masters,pp. 316 and 317)

� magazines and newspapers� scissors � Geometry Template; pattern blocks;

tape

ELL SUPPORTEXTRA PRACTICEENRICHMENTENRICHMENT

3

� Math Journal 2, p. 280� Study Link Master (Math Masters,

p. 315)

2

� Math Journal 2, p. 279� Student Reference Book, p. 109

(optional)� Study Link 10�3 � Teaching Masters (Math Masters,

pp. 311–314)� Teaching Aid Master (Math Masters,

p. 389)� 1 transparent mirror per partnership� scissors� slate

1

Objective To guide exploration of the connection between

reflections and line symmetry.

� Math Message Follow-UpAsk students to share what they know about symmetry. Tell themto indicate “thumbs-up” if they have a similar answer. Then askstudents to explain how they know the classroom object that theychose has line symmetry.

Tell students that in this lesson they will investigate howsymmetry and reflections are related.

� Completing Symmetric Pictures(Math Journal 2, p. 279; Math Masters, p. 311)

Ask students to turn to journal page 279. Partners share a transparent mirror while working on the activities.

Tell the class that each drawing on Math Masters, page 311 isonly half of a picture. Students are to figure out what each picturewould look like if it were complete and then use their transparentmirrors to complete each picture. Remind them to use the recessededge to draw the line of reflection. Bring the class together todiscuss results. Ask the following questions:● How are these drawings like the dog picture in Lesson 10-3?

How are they different? As in the dog picture, there are twosides that look exactly alike (congruent) but are facing inopposite directions. Here, however, the end results are singledrawings instead of pairs of drawings.

Point out that here the lines of reflection are in the middle of thepictures or objects—not outside, as in the dog picture. When a lineof reflection is in the middle of a picture or object, it is called aline of symmetry. In this case, the pictures or objects are said tobe symmetric.

PARTNER

ACTIVITY

WHOLE-CLASS

DISCUSSION

1 Teaching the Lesson

279

Line SymmetryLESSON

10 � 4

Date Time

You will need Math Masters, pages 311–314.

1. The drawings on Math Masters, page 311 are only half-pictures. Figure out whateach whole picture would show. Then use a transparent mirror to complete eachpicture. Use the recessed side of the mirror to draw the line of reflection.

2. The pictures on Math Masters, page 312 are symmetric.

a. Use the transparent mirror to draw the line of symmetry for the bat and the turtle.

b. Cut out the other three pictures and find their lines of symmetry by folding.

c. Which picture has two lines of symmetry?

3. Cut out each polygon on Math Masters, pages 313 and 314. Find all the lines ofsymmetry for each polygon. Record the results below.

4. Study the results in the tables above.

a. How many lines of symmetry are in a regular pentagon(Polygon I)? lines

b. How many lines of symmetry are in a regular hexagon(Polygon J)? lines

c. How many lines of symmetry are in a regular octagon?(An octagon has 8 sides.) lines8

65

Bow

�

�

Polygon Number of Linesof Symmetry

A 3B 1C 4D 2E 2

Polygon Number of Linesof Symmetry

F 0G 1H 0I 5J 6

109

Math Journal 2, p. 279

Student Page

Lesson 10�4 811

Getting Started

Math Message What is symmetry? Be ready toname an object in the classroom that has line symmetry.

Study Link 10�3Follow-UpHave partners compare answers and describe how they know each image is a reflection of the preimage.

Mental Math and Reflexes Pose mental addition problems. Suggestions:

13 � 6 � 19 225 � 7 � 232 438 � 253 � 69118 � 5 � 23 146 � 7 � 153 316 � 496 � 81216 � 9 � 25 334 � 8 � 342 529 � 144 � 673

Adjustingthe Activity

English language learners may find it helpfulif you use page 109 in the Student ReferenceBook to summarize the discussion of linesymmetry.

AUDITORY � KINESTHETIC � TACTILE � VISUAL

ELL

Adjusting the Activity

812 Unit 10 Reflections and Symmetry

LESSON

10�4

Name Date Time

Symmetric Pictures 109

Math Masters, p. 312

Teaching Master

LESSON

10�4

Name Date Time

Half-Pictures 109

Math Masters, p. 311

Teaching MasterNOTE Students may be familiar with line symmetry from previous work but maynot have made a connection between line symmetry and reflections. Thinking about line symmetry in terms of reflections is a more powerful approach because it can be generalized to other kinds of symmetry. Rotation (turn) symmetry, forexample, can be thought of in terms of turns.

� Finding Lines of Symmetry(Math Journal 2, p. 279; Math Masters, p. 312)

Students use their transparent mirrors to draw lines of symmetryin the pictures of a bat and a turtle on Math Masters, page 312.Then they cut out the other three pictures on the page and findtheir lines of symmetry by folding. Point out that a picture mayhave more than one line of symmetry. Have students answer thequestion in Problem 2c on journal page 279.

Bring the class together to discuss results. Ask: Which picture hasmore than one line of symmetry? The bow

This activity works best if the pictures are carefully cut out. If there are students in your class who have difficulty with scissors, consider having avolunteer cut out their shapes for them ahead of time. The same is true forPolygons A–J on Math Masters, pages 313 and 314 in the activity that follows.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

� Exploring Lines of Symmetry of Polygons(Math Journal 2, p. 279; Math Masters, pp. 313 and 314)

Students cut out the polygons on Math Masters, pages 313 and314. They find all lines of symmetry for each polygon by folding,and then they record the results in the tables and answer therelated questions on journal page 279.

Ongoing Assessment: Informing InstructionWatch for students who think that Polygon F, the parallelogram, has linesymmetry. Many people think this is true because Polygon F does have symmetry; however, it is turn or rotation symmetry, rather than line symmetry.Polygon F cannot be folded (or reflected) so that the two halves match, but it can be turned to match its original shape.

Bring the class together to share results. Students should havefound that a regular polygon has the same number of lines ofsymmetry as it has sides. For example, a regular octagon has 8 sides and 8 lines of symmetry.

PARTNER

ACTIVITY

PARTNER

ACTIVITY

Ongoing Assessment:Recognizing Student Achievement

Use an Exit Slip (Math Masters, page 389) to assess students’ ability to describea pattern and use it to solve problems. Have students describe patterns they seein Problems 3 and 4 on journal page 279. Students are making adequateprogress if they state that a regular polygon has the same number of lines ofsymmetry as it has sides. Some students may extend the pattern by stating thenumber of lines of symmetry in additional regular polygons.

[Patterns, Functions, and Algebra Goal 1]

� Math Boxes 10�4(Math Journal 2, p. 280)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 10-1. The skill in Problem 6previews Unit 11 content.

� Study Link 10�4(Math Masters, p. 315)

Home Connection Students complete a Venn diagram to identify capital letters of the alphabet that havehorizontal and/or vertical line symmetry. They list words with horizontal or vertical line symmetry.

INDEPENDENT

ACTIVITY

INDEPENDENT

ACTIVITY

2 Ongoing Learning & Practice

LESSON

10�4

Name Date Time

Polygons A–E

E

C

AD

B

109

Math Masters, p. 313

Teaching Master

LESSON

10�4

Name Date Time

Polygons F–J

J

F

I

G H

109

Math Masters, p. 314

Teaching Master

Lesson 10�4 813

Exit Slip�

280

Math Boxes LESSON

10 � 4

Date Time

4. Insert the decimal point in each product.

a. 4 � 6.7 � 2 6 8b. 1 4 5 6 � 28 � 5.2

c. 7.3 � 46 � 3 3 5 8d. 2 2 2 5 � 0.25 � 89•

•

•

•

1. Use your Geometry Template to draw theimage of the figure that is shown abovethe line of reflection.

2. Use the following list of numbers to answerthe questions.

7, 8, 24, 8, 9, 17, 17, 8, 12, 13, 19

a. What is the median?

b. Mode?

c. Maximum?

d. Minimum?

e. Range? 17724

812

3. Order the fractions from least to greatest.

a. �89�, �

49�, �

19�, �

99�, �

39�

b. �44�, �

49�, �1

42�, �

43�, �

42�

c. �37�, �

12�, �

78�, �

15�, �

44�

5. Jaleel missed 20% of the 30 problems on his science test. How many problemsdid he miss? Fill in the circle next to thebest answer.

A. 5

B. 20

C. 3

D. 6

6. What are the perimeter and area of therectangle? Include the correct units.

Perimeter �

Area �

15 m

22 m

330 m274 m

preimage

image

�142�, �

49�, �

44�, �

43�, �

42�

�15�, �

37�, �

12�, �

78�, �

44�

�19�, �

39�, �

49�, �

89�, �

99�

73106

131 1343839 62

18 1953 54

Math Journal 2, p. 280

Student Page

814 Unit 10 Reflections and Symmetry

LESSON

10�4

Name Date Time

Interpreting a Cartoon

LESSON

10�4

Name Date Time

Interpreting a Cartoon

1. What answer does Ruthie’s brother expect?

2. Explain and draw pictures to show why both of Ruthie’s answers are correct.

4

1. What answer does Ruthie’s brother expect?

2. Explain and draw pictures to show why both of Ruthie’s answers are correct.

“Up and down,it’s three.”

“Across, it’s zero.”

Math Masters, p. 316

Teaching Master

STUDY LINK

10�4 Line Symmetry in the Alphabet

315

109

Name Date Time

1. Print the 26 capital letters of the alphabet below.

2. The capital letter A has a vertical line of symmetry.

The capital letter B has a horizontal line of symmetry.

Use the letters of the alphabet to complete the Venn diagram.

3. The word BED has a horizontal line of symmetry.

The word HIT has a vertical line of symmetry.

Use capital letters to list words that havehorizontal or vertical line symmetry.

horizontal vertical

Capital Letters of the Alphabet

Vertical Line of Symmetry

Horizontal Line of Symmetry

Sample answers:

4. 86 � 9 � 5. � 68 / 4

6. 6�7�4�2� � 7. � 855 / 7

17123�46�

Practice

122�17�

9 R5

Math Masters, p. 315

Study Link Master

� Interpreting a Cartoon (Math Masters, p. 316)

To apply students’ understanding of line symmetry, havethem interpret a cartoon.

� Exploring Rotation or Turn SymmetryTo further explore symmetry, have students use combinations of pattern blocks to perform and analyze transformations. Askstudents to tape together a trapezoid and an equilateral trianglepattern block to form a parallelogram.

Ask the following questions:● Will the parallelogram look exactly the same if it is flipped

over? No. If it slanted to the right before the flip, then it willslant to the left after the flip.

● Does the parallelogram have line symmetry? No. Students havealready tried folding a parallelogram to find a line of symmetry,and they know that it does not have one.

● Will the parallelogram look exactly the same if it is turned through a �

12�-turn? yes Have students trace the parallelogram

and show that after a �12�-turn, the tracing matches the original

figure.

Shapes that look the same after they have been turned less than a full turn have rotation or turn symmetry. Have students usepattern blocks and tape to make their own turn-symmetric shapes.Have them use their Geometry Templates to record the shapesthey make.

Sample answers:

14 -turn symmetry1

3 -turn symmetry12 -turn symmetry

15–30 Min

SMALL-GROUP

ACTIVITYENRICHMENT

5–15 Min

INDEPENDENT

ACTIVITYENRICHMENT

3 Differentiation Options

� Exploring Line Symmetry(Math Masters, p. 317)

To practice identifying lines of symmetry using a concrete model,have students use combinations of pattern blocks to create figureswith a specified number of lines of symmetry.

� Creating a LineSymmetry MuseumTo provide language support for symmetry, have students bring inpictures of objects with line symmetry to create a Line SymmetryMuseum. Have students describe the objects in the pictures andthe lines of symmetry they see. They may even draw the lines ofsymmetry on the pictures. If some of the pictured objects are notperfectly symmetric, consider setting up a section of the museumcalled Almost Symmetric.

15–30 Min

SMALL-GROUP

ACTIVITYELL SUPPORT

15–30 Min

PARTNER

ACTIVITYEXTRA PRACTICE

Lesson 10�4 815

LESSON

10�4

Name Date Time

Line Symmetry

Use pattern blocks to create shapes with the given number of lines of symmetry.Use your Geometry Template to record the shapes and draw the lines of symmetry.

1. 1 yellow hexagon, 2 orange squares 2. 1 orange square, 4 green triangles2 lines of symmetry 0 lines of symmetry

3. 2 red trapezoids 4. 5 orange squares 6 lines of symmetry 1 line of symmetry

Sampleanswer:

Sample answer:

Sample answer

5. 5 red trapezoids1 line of symmetryShow two different ways.

6. On the back of this page, make up a problem of your own. Give it to a partner to solve.

Try This

109

Math Masters, p. 317

Teaching Master