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www.everydaymathonline.com
eToolkitePresentations Interactive Teacher’s
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.
�
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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 �
812 Unit 10 Reflections and Symmetry
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
304-326_EMCS_B_MM_G4_U10_576965.indd 311 2/14/11 4:56 PM
Math Masters, p. 311
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]
PROBLEMBBBBBBBBBBOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEMMMBLLBLEBLEBLEBLELLLLBLEBLEBLEBLEBLEBLEEEMMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBLBLBLBLBBLLLLLLLLPROPROPROPROPROPROPROPROPROPROPROPRPRPROPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROROROOPPPPPPP MMMMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEELEEELEEEEEEEELLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRRPROBLEMSOLVING
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
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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
304-326_EMCS_B_MM_G4_U10_576965.indd 313 2/14/11 4:56 PM
Math Masters, p. 313
Teaching Master
LESSON
10�4
Name Date Time
Polygons F–J
pyg
gp
F
JI
G H
109
304-326_EMCS_B_MM_G4_U10_576965.indd 314 2/14/11 4:56 PM
Math Masters, p. 314
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
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814 Unit 10 Reflections and Symmetry
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 cups Equation: 4 ∗ 4 _
3 = 16
__ 3 , or 5 1 _
3
b. Cody should eat between cups of food in 4 days.
Circle the best answer.
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 cups Equation: 7 ∗ 3 _
4 = 21
__ 4 , or 5 1 _
4
b. The puppy should eat between cups of food in one week.
Circle the best answer.
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
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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
304-326_EMCS_B_MM_G4_U10_576965.indd 317 2/14/11 4:57 PM
Math Masters, p. 317
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.
304-326_EMCS_B_MM_G4_U10_576965.indd 316 2/14/11 4:57 PM
Math Masters, p. 316
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
304-326_EMCS_B_MM_G4_U10_576965.indd 315 2/14/11 4:56 PM
Math Masters, p. 315
Study Link Master
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