810 emcs t tlg1 g4 u10 l04 576906 - everyday math · line symmetry objective to guide exploration...

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Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

810 Unit 10 Reflections and Symmetry

Advance Preparation

Teacher’s Reference Manual, Grades 4–6 pp. 180 –185, 200

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 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.

Ongoing Assessment: Informing Instruction See page 812.

Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip (Math Masters, p. 389). [Patterns, Functions, and Algebra Goal 1]

Key Vocabularyline of symmetry � symmetric � rotation (turn)

symmetry

MaterialsMath Journal 2, p. 279

Student Reference Book, p. 109 (optional)

Study Link 10�3

Math Masters, pp. 311–314; p. 389 (optional)

per partnership: 1 transparent mirror �

scissors � slate

Multiplying a Fraction by a Whole NumberMath Journal 2, pp. 280A and 280B

Students practice multiplying fractions

by whole numbers.

Math Boxes 10�4Math Journal 2, p. 280

Students practice and maintain skills

through Math Box problems.

Study Link 10�4Math Masters, p. 315

Students practice and maintain skills

through Study Link activities.

ENRICHMENTInterpreting a CartoonMath Masters, p. 316

Students interpret a cartoon involving

line symmetry.

ENRICHMENTExploring Rotation or Turn SymmetryGeometry Template � pattern blocks � tape

Students explore turn or rotation symmetry.

EXTRA PRACTICE

Exploring Line SymmetryMath Masters, p. 317

Geometry Template � pattern blocks

Students use pattern blocks to create

shapes with line symmetry.

ELL SUPPORT

Creating a Line Symmetry Museummagazines and newspapers � scissors � tape

Students create a Line Symmetry Museum.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

Line SymmetryObjective To guide exploration of the connection

between reflections and line symmetry.

�

810_EMCS_T_TLG1_G4_U10_L04_576906.indd 810810_EMCS_T_TLG1_G4_U10_L04_576906.indd 810 2/16/11 2:23 PM2/16/11 2:23 PM

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Ask students to share what they know about symmetry. Tell them to indicate “thumbs-up” if they have a similar answer. Then ask students to explain how they know the classroom object that they chose has line symmetry.

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

� Completing Symmetric Pictures PARTNER ACTIVITY

(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 is only half of a picture. Students are to figure out what each picture would look like if it were complete and then use their transparent mirrors to complete each picture. Remind them to use the recessed edge to draw the line of reflection. Bring the class together to discuss 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 two sides that look exactly alike (congruent) but are facing in opposite directions. Here, however, the end results are single drawings instead of pairs of drawings.

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

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 what

each whole picture would show. Then use a transparent mirror to complete each

picture. 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? Bow

3. Cut out each polygon on Math Masters, pages 313 and 314. Find all the lines of

symmetry 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)? 5 lines

b. How many lines of symmetry are in a regular hexagon

(Polygon J)? 6 lines

c. How many lines of symmetry are in a regular octagon?

(An octagon has 8 sides.) 8 lines

�

�

Polygon Number of Lines of Symmetry

A 3 B 1 C 4 D 2 E 2

Polygon Number of Lines of Symmetry

F 0 G 1 H 0 I 5 J 6

109

274-285_EMCS_S_MJ2_G4_U10_576426.indd 279 2/15/11 6:15 PM

Math Journal 2, p. 279

Student Page

Lesson 10�4 811

Getting Started

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

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

Mental Math and ReflexesWrite fraction addition problems on the board where tenths are added to tenths, hundredths to hundredths, and tenths to hundredths. Suggestions:

4 _ 10 + 1

_ 10 = 5

_ 10 , or 1 _ 2

25

_ 100 + 50

_ 100 = 75

_ 100 , or 3

_ 4 10

_ 100 + 5

_ 10 = 60

_ 100 , or 6

_ 10 , or 3

_ 5

6

_ 10 + 3

_ 10 = 9

_ 10 40

_ 100 + 20

_ 100 = 60

_ 100 , or 3

_ 5 4 _ 10 +

40

_ 100 = 80

_ 100 , or 8

_ 10 , or 4 _ 5

5

_ 10 + 2 _ 10 = 7

_ 10 75

_ 100 + 5

_ 100 = 80

_ 100 , or 4 _ 5

90

_ 100 + 1 _ 10 =

100

_ 100 , or 10

_ 10 , or 1

3

_ 10 + 1 _ 10 = 4

_ 10 , or 2 _ 5

65

_ 100 + 35

_ 100 = 100

_ 100 , or 1

25

_ 100 + 5

_ 10 = 75

_ 100 , or 3

_ 4

Adjusting the Activity

English language learners may find it helpful if you use page 109 in the Student Reference Book to summarize the discussion of line

symmetry.

AUDITORY � KINESTHETIC � TACTILE � VISUAL

ELL

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Exit Slip �


LESSON

10�4

Name Date Time

Symmetric Pictures

py

gg

p

109

304-326_EMCS_B_MM_G4_U10_576965.indd 312 2/14/11 4:56 PM

Math Masters, p. 312

Teaching Master

LESSON

10�4

Name Date Time

Half-Pictures 109



Teaching MasterNOTE Students may be familiar with line symmetry from previous work but may

not 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, for

example, can be thought of in terms of turns.

� Finding Lines of Symmetry PARTNER ACTIVITY

(Math Journal 2, p. 279; Math Masters, p. 312)

Students use their transparent mirrors to draw lines of symmetry in 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 find their lines of symmetry by folding. Point out that a picture may have more than one line of symmetry. Have students answer the question in Problem 2c on journal page 279.

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

� Exploring Lines of Symmetry PARTNER ACTIVITY

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

Students cut out the polygons on Math Masters, pages 313 and 314. They find all lines of symmetry for each polygon by folding, and then they record the results in the tables and answer the related questions on journal page 279.

Ongoing Assessment: Informing Instruction

Watch for students who think that Polygon F, the parallelogram, has line

symmetry. 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 have found that a regular polygon has the same number of lines of symmetry as it has sides. For example, a regular octagon has 8 sides and 8 lines of symmetry.

Ongoing Assessment:Recognizing Student Achievement

Use an Exit Slip (Math Masters, page 389) to assess students’ ability to describe

a pattern and use it to solve problems. Have students describe patterns they see

in Problems 3 and 4 on journal page 279. Students are making adequate

progress if they state that a regular polygon has the same number of lines of

symmetry as it has sides. Some students may extend the pattern by stating the

number of lines of symmetry in additional regular polygons.

[Patterns, Functions, and Algebra Goal 1]

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BBBBBBBBBBBBBBBBBBBBB EEELELEMMMMMMMMMMOOOOOOOOOOBBBLBLBBLBLBLBBBROOORORORORORORORORORORORO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGGGLLLLLLLLLLLLLVINVINVINVINVINVINNNNVINVINNVINVINVINVINV GGGGGGGGGGGGGOLOOOOOOLOLOLOO VVINVINLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINVINVINGGGGGGGGGGGOOOLOLOLOLOLLOOO VVVVVVLLLLLLLLLLLVVVVVVVVVOSOSOSOOSOSOSOSOSOSOOSOSOSOOOSOOSOOSOSOSOSOSOSOSOSOOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLLLLLVVVVVVVVVLLLLVVVVVVVVLLLLLLLVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIISOLVING

Adjusting the Activity The symmetry activities work best if

the pictures and polygons on Math Masters, pages 312–314 are carefully cut out. If there

are students in your class who have difficulty with scissors, consider having a volunteer cut out their shapes for them ahead of time.

AUDITORY � KINESTHETIC � TACTILE � VISUAL


2 Ongoing Learning & Practice

� Multiplying a Fraction by INDEPENDENTACTIVITY

a Whole Number(Math Journal 2, pp. 280A and 280B)

Students practice multiplying fractions by whole numbers.

� Math Boxes 10�4 INDEPENDENTACTIVITY

(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 6 previews Unit 11 content.

� Study Link 10�4 INDEPENDENTACTIVITY

(Math Masters, p. 315)

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

B

LESSON

10�4

Name Date Time

Polygons A–E

E

C

AD

109



Teaching Master

LESSON

10�4

Name Date Time

Polygons F–J

pyg

gp

F

JI

G H

109



Teaching Master

Lesson 10�4 813

280A

10�4Date Time

Write an equation to describe each number line.

1. 15

0 1

15

15

Equation: 3 ∗ 1 _ 5 =

3 _ 5

2.

66

1260

46

46

Equation: 2 ∗ 4 _ 6 =

Use the number lines to help you solve the problems.

3. = 4 ∗ 2 _ 5

105

55

25

25

25

25

0

4. 3 ∗ 2 _ 8 =

880

28

28

28

Solve. You may draw a visual fraction model such as a number line if you wish.

5. 6 ∗ 1 _ 7 =

6 _ 7 6. = 8 ∗ 2 _ 10

7. = 5 ∗ 3

_ 12 8. 4 ∗ 2 _ 9 =

8 _ 9

Multiplying Fractions by Whole NumbersLESSON

10�4

8 _ 6 , or 1 2 _ 6 , or 1 1 _ 3

8 _ 5 , or

1 3 _ 5

6 _ 8 , or 3 _ 4

16

__ 10 , or

1 6 __ 10 , or 1 3 _ 5 15

__ 12 , or 1 3 __ 12 , or 1 1 _ 4

280A-280B_EMCS_S_MJ2_G4_U10_576426.indd 280A 3/30/11 12:56 PM

Math Journal 2, p. 280A

Student Page

811-815_EMCS_T_TLG1_G4_U10_L04_576906.indd 813811-815_EMCS_T_TLG1_G4_U10_L04_576906.indd 813 3/31/11 11:37 AM3/31/11 11:37 AM


Math Boxes LESSON

10 �4

Date Time

4. Insert the decimal point in each product.

a. 4 ∗ 6.7 = 2 6 • 8

b. 1 4 5• 6 = 28 ∗ 5.2

c. 7.3 ∗ 46 = 3 3 5• 8

d. 2 2 • 2 5 = 0.25 ∗ 89

1. Use your Geometry Template to draw the

image of the figure that is shown above

the line of reflection.

2. Use the following list of numbers to answer

the questions.

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

a. What is the median? 12

b. Mode? 8

c. Maximum? 24

d. Minimum? 7

e. Range? 17

3. Order the fractions from least to greatest.

a. 8

_

9 ,

4

_

9 ,

1

_

9 ,

9

_

9 ,

3

_

9

b. 4

_

4 ,

4

_

9 ,

4

_

12 ,

4

_

3 ,

4

_

2

c. 3

_

7 ,

1

_

2 ,

7

_

8 ,

1

_

5 ,

4

_

4

5. Jaleel missed 20% of the 30 problems

on his science test. How many problems

did he miss? Fill in the circle next to the

best answer.

A. 5

B. 20

C. 3

D. 6

6. What are the perimeter and area of the

rectangle? Include the correct units.

Perimeter =

Area = 330 m2

74 m

preimage

image

4

_ 12 , 4

_ 9 ,

4

_ 4 ,

4

_ 3 ,

4

_ 2

1

_ 5 , 3

_ 7 , 1

_ 2 , 7

_ 8 ,

4

_ 4

1

_ 9 , 3

_ 9 , 4

_ 9 ,

8

_ 9 ,

9

_ 9

73106

131 1343839 62

18 1953 54

22 m

15 m

274-285_EMCS_S_MJ2_G4_U10_576426.indd 280 2/18/11 9:15 AM

Math Journal 2, p. 280

Student Page

Date Time

A manufacturer of dry puppy food has the following feeding guidelines. All

measurements are given in cups per day. Use the information in the table to

answer the questions below. Write an equation to show what you did.

Weight (lb) 6 –11 Weeks 3–4 Months 5–7 Months 8–12 Months

1 1 _ 2 1

_ 3 1 _ 4 1

_ 4

3 1 3

_ 4 1 _ 2 1

_ 3

5 4 _ 3

5

_ 4 3

_ 4 1 _ 2

10 2 2 5

_ 4 2 _ 3

15 11

_ 4 11

_ 4 5

_ 3 1

20 10

_ 3

13

_ 4 2 1

1. a. Buddy weighs 3 pounds and is 9 months old. According to the guidelines,

he should eat about 1 _ 3 cup of food per day. How much food should Buddy

eat in 5 days?

1 2 _

3 cups Equation: 5 ∗ 1 _

3 = 5 _ 3 , or 1 2 _

3

b. Buddy should eat between cups of food in 5 days.

Circle the best answer.

1 and 2 2 and 3 3 and 4

2. a. Cody is 8 weeks old and weighs about 5 pounds. How much food should

he eat in 4 days?

5 1 _


3 = 16

__ 3 , or 5 1 _

3

b. Cody should eat between cups of food in 4 days.


3 and 4 4 and 5 5 and 6

3. a. A puppy weighs 5 pounds and is 6 months old. How much food should

the puppy eat in one week?

5 1 _


4 = 21

__ 4 , or 5 1 _

4

b. The puppy should eat between cups of food in one week.


3 and 4 4 and 5 5 and 6

Solving Number StoriesLESSON

10�4

280A-280B_EMCS_S_MJ2_G4_U10_576426.indd 280B 3/16/11 11:13 AM

Math Journal 2, p. 280B

Student Page

3 Differentiation Options

ENRICHMENT INDEPENDENTACTIVITY

� Interpreting a Cartoon 5–15 Min(Math Masters, p. 316)

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

ENRICHMENT SMALL-GROUP ACTIVITY

� Exploring Rotation or 15–30 Min

Turn SymmetryTo further explore symmetry, have students use combinations of pattern blocks to perform and analyze transformations. Ask students to tape together a trapezoid and an equilateral triangle pattern 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 will slant to the left after the flip.

● Does the parallelogram have line symmetry? No. Students have already 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 1 _ 2 -turn? yes Have students trace the parallelogram

and show that after a 1 _ 2 -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 use pattern blocks and tape to make their own turn-symmetric shapes. Have them use their Geometry Templates to record the shapes they make.

Sample answers:

12 -turn symmetry

13 -turn symmetry

14 -turn symmetry


EXTRA PRACTICE PARTNER ACTIVITY

� Exploring Line Symmetry 15–30 Min

(Math Masters, p. 317)

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

ELL SUPPORT SMALL-GROUP ACTIVITY

� Creating a Line 15–30 Min

Symmetry MuseumTo provide language support for symmetry, have students bring in pictures of objects with line symmetry to create a Line Symmetry Museum. Have students describe the objects in the pictures and the lines of symmetry they see. They may even draw the lines of symmetry on the pictures. If some of the pictured objects are not perfectly symmetric, consider setting up a section of the museum called Almost Symmetric.

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 triangles

2 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 trapezoids

1 line of symmetry

Show 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



Teaching MasterLESSON

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? 4

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

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.”

By permission of Rick Detorie and Creators Syndicate, Inc.

By permission of Rick Detorie and Creators Syndicate, Inc.



Teaching Master

STUDY LINK

10�4 Line Symmetry in the Alphabet

315

109

Name Date Time

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 have

horizontal or vertical line symmetry.

horizontal vertical

Sample answers:

Practice

4. 86 ÷ 9 = 9 R5 5. 17 = 68 / 4

6. 6 � _

742 = 123 4 _ 6 7. 122 1 _ 7 = 855 / 7

Capital Letters of the Alphabet

Vertical Line of Symmetry

Horizontal Line of Symmetry



Study Link Master


810 emcs t tlg1 g4 u10 l04 576906 - everyday math · line symmetry objective to guide exploration...

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