Line Symmetry
Objective To guide exploration of the connection
between reflections and line symmetry.
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
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 Activities
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
ENRICHMENT
Multiplying a Fraction by a
Whole Number
Interpreting a Cartoon
Math Journal 2, pp. 280A and 280B
Students practice multiplying fractions
by whole numbers.
Math Masters, p. 316
Students interpret a cartoon involving
line symmetry.
Math Boxes 10 4
Math Journal 2, p. 280
Students practice and maintain skills
through Math Box problems.
Study Link 10 4
ENRICHMENT
Exploring Rotation or Turn Symmetry
Geometry Template pattern blocks tape
Students explore turn or rotation symmetry.
Math Masters, p. 315
Students practice and maintain skills
through Study Link activities.
Students 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.
EXTRA PRACTICE
Exploring Line Symmetry
Math Masters, p. 317
Geometry Template pattern blocks
Students use pattern blocks to create
shapes with line symmetry.
ELL SUPPORT
Creating a Line Symmetry Museum
magazines and newspapers scissors tape
Students create a Line Symmetry Museum.
Ongoing Assessment:
Recognizing Student Achievement
Use an Exit Slip (Math Masters, p. 389). [Patterns, Functions, and Algebra Goal 1]
Key Vocabulary
line of symmetry symmetric rotation (turn)
symmetry
Materials
Math 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
Advance Preparation
Teacher’s Reference Manual, Grades 4–6 pp. 180–185, 200
810
Unit 10
Reflections and Symmetry
810_EMCS_T_TLG1_G4_U10_L04_576906.indd 810
2/16/11 2:23 PM
Getting Started
Mental Math and Reflexes
Math Message
Write fraction addition problems on the board where tenths are
added to tenths, hundredths to hundredths, and tenths to hundredths.
Suggestions:
5
25
50
75
3
10
5
60
6
3
4
1
1
_
_
_
+_
=_
, or _
+_
=_
, or _
+_
=_
, or _
, or _
What is symmetry? Be
ready to name an object
in the classroom that has line
symmetry.
10
10
10
2
100
100
100
4
100
10
100
10
5
6
3
9
_
+_
=_
10
40
20
60
3
_
+_
=_
, or _
5
40
80
8
4
4
_
+_
=_
, or _
, or _
5
2
7
_
+_
=_
75
5
80
4
_
+_
=_
, or _
90
100
10
1
_
+_
=_
, or _
, or 1
10
10
3
_
10
10
+
10
1
_
10
=
10
4
_
10 ,
100
2
or _
5
100
65
_
100
100
+
100
35
_
100
100
=
100
100
_
100 ,
5
or 1
10
100
100
25
_
100
+
10
5
_
10
100
=
100
75
_
100 ,
10
or
5
Study Link 10 3
Follow-Up
10
3
_
4
Have partners compare
answers and describe how they
know each image is a reflection of
the preimage.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
Adjusting
the Activity
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.
English language learners may find it helpful
if you use page 109 in the Student Reference
Book to summarize the discussion of line
symmetry.
Tell students that in this lesson they will investigate how
symmetry and reflections are related.
Completing Symmetric Pictures
AUDITORY
PARTNER
ACTIVITY
(Math Journal 2, p. 279; Math Masters, p. 311)
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.
KINESTHETIC
Date
TACTILE
VISUAL
Time
10 4
Line Symmetry
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?
3.
Polygon
B
C
D
E
4.
Bow
Number of Lines
of Symmetry
3
1
4
2
2
Polygon
Number of Lines
of Symmetry
0
1
0
5
6
F
G
H
I
J
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
Math Journal 2, p. 279
274-285_EMCS_S_MJ2_G4_U10_576426.indd 279
2/15/11 6:15 PM
Lesson 10 4
811-815_EMCS_T_TLG1_G4_U10_L04_576906.indd 811
109
Cut out each polygon on Math Masters, pages 313 and 314. Find all the lines of
symmetry for each polygon. Record the results below.
A
●
Student Page
LESSON
Ask students to turn to journal page 279. Partners share a
transparent mirror while working on the activities.
ELL
811
3/16/11 4:19 PM
Teaching Master
Name
Date
LESSON
10 4
Time
Half-Pictures
NOTE 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.
109
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
Math Masters, p. 311
304-326_EMCS_B_MM_G4_U10_576965.indd 311
of Polygons
2/14/11 4:56 PM
PARTNER
ACTIVITY
PROBLEM
PR
PRO
P
RO
R
OBL
BLE
B
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
VING
VIN
IIN
NG
(Math Journal 2, p. 279; Math Masters, pp. 313 and 314)
Adjusting the Activity
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.
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
Ongoing Assessment: Informing Instruction
VISUAL
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.
Teaching Master
Name
LESSON
10 4
Date
Symmetric Pictures
Time
109
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
Exit Slip
py g
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.
g
p
[Patterns, Functions, and Algebra Goal 1]
Math Masters, p. 312
304-326_EMCS_B_MM_G4_U10_576965.indd 312
812
2/14/11 4:56 PM
Unit 10 Reflections and Symmetry
811-815_EMCS_T_TLG1_G4_U10_L04_576906.indd 812
3/16/11 4:19 PM
Teaching Master
Name
2 Ongoing Learning & Practice
Multiplying a Fraction by
Date
LESSON
10 4
Time
Polygons A–E
INDEPENDENT
ACTIVITY
109
E
a Whole Number
(Math Journal 2, pp. 280A and 280B)
B
Students practice multiplying fractions by whole numbers.
C
Math Boxes 10 4
INDEPENDENT
ACTIVITY
(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
INDEPENDENT
ACTIVITY
D
A
Math Masters, p. 313
304-326_EMCS_B_MM_G4_U10_576965.indd 313
2/14/11 4:56 PM
(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.
Teaching Master
Student Page
10 4
Date Name
Time
LESSON
LESSON
10 4
Multiplying Fractions by Whole Numbers
10 4
Date
Polygons F–J
Time
109
Write an equation to describe each number line.
1.
1
5
1
5
1
5
0
1
3
Equation:
∗
2.
_1
5
_3
=
5
J
4
6
6
6
0
2
Equation:
∗
I
4
6
_4
6
12
6
_8, or 1_2, or 1_1
=
6
6
3
Use the number lines to help you solve the problems.
8
, or = 4 ∗ _2
3. 5
5
3
15
2
2
2
_
F
_
5
5
2
5
5
5
5
0
_ or _3
4
10
5
py g
6
,
2
_
4. 3 ∗ 8 = 8
2
8
2
8
g
2
8
p
__
__
_
__
G
8
8
0
Solve. You may draw a visual fraction model such as a number line if you wish.
16
6
, or= 8 ∗ _
1
2
_
7
5. 6 ∗ 7 =
6. 10
10
6
3
110, or 15
15
3
1
8
1
12 , or 1 12 , or
3 4
2
_
9
=5∗_
7.
8. 4 ∗ 9 =
12
__
_
_
_
280A
Math Journal 2, p. 280A
280A-280B_EMCS_S_MJ2_G4_U10_576426.indd 280A
H
3/30/11 12:56 PM
Math Masters, p. 314
304-326_EMCS_B_MM_G4_U10_576965.indd 314
2/14/11 4:56 PM
Lesson 10 4
811-815_EMCS_T_TLG1_G4_U10_L04_576906.indd 813
813
3/31/11 11:37 AM
Student Page
Date
Time
LESSON
3 Differentiation Options
Solving Number Stories
10 4
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)
1
6 –11 Weeks
1
_
2
3
5
b.
1
_
5
_
2
_
4
4
4
13
_
4
Interpreting a Cartoon
2
4
3
5
_
4
3
3
4
10
_
ENRICHMENT
4
2
2
11
_
3
1
2
1
Buddy should eat between
Circle the best answer.
3 and 4
Cody is 8 weeks old and weighs about 5 pounds. How much food should
he eat in 4 days?
16
1
4
_1
5_3 cups
4 ∗ _3 = __
3 , or 5 3
Equation:
Cody should eat between
Circle the best answer.
ENRICHMENT
Exploring Rotation or
cups of food in 4 days.
4 and 5
5 and 6
The puppy should eat between
Circle the best answer.
cups of food in one week.
4 and 5
SMALL-GROUP
ACTIVITY
15–30 Min
Turn Symmetry
A puppy weighs 5 pounds and is 6 months old. How much food should
the puppy eat in one week?
3
1
21
_1
5_4 cups
7 ∗ _4 = __
4 , or 5 4
Equation:
3 and 4
5–15 Min
To apply students’ understanding of line symmetry, have
them interpret a cartoon.
cups of food in 5 days.
2 and 3
INDEPENDENT
ACTIVITY
(Math Masters, p. 316)
Buddy weighs 3 pounds and is 9 months old. According to the guidelines,
1
he should eat about _
3 cup of food per day. How much food should Buddy
eat in 5 days?
5
1
2
_2
13 cups
5 ∗ _3 = _3, or 1_3
Equation:
3 and 4
3. a.
3
_
3
2
11
_
1 and 2
b.
1
_
5
_
4
20
2. a.
8–12 Months
1
_
1
_
3
15
b.
5–7 Months
1
_
3
_
1
4
_
10
1. a.
3–4 Months
1
_
5 and 6
Math Journal 2, p. 280B
280A-280B_EMCS_S_MJ2_G4_U10_576426.indd 280B
3/16/11 11:13 AM
To 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:
Math Boxes
10 4
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
preimage
image
3.
a.
What is the median?
b.
Mode?
12
8
24
7
17
c.
Maximum?
d.
Minimum?
e.
Range?
106
Order the fractions from least to greatest.
a.
8 _
4 1 9 3
_
, , _, _, _
9 9 9 9 9
b.
4 _
4 4 4 4
_
, , _, _, _
4 9 12 3 2
c.
3 _
1 7 1 4
_
, , _, _, _
7 2 8 5 4
_1 , _3, _4, _8, _9
9 9 9 9 9
4 4 4 4
4 _
_
, , _, _, _
12 9 4 3 2
_1 , _3 , _1 , _7, _4
5 7 2 8 4
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
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.
73
4.
Sample answers:
Insert the decimal point in each product.
2 6• 8
a.
4 ∗ 6.7 =
b.
1 4 5 • 6 = 28 ∗ 5.2
3 3 5• 8
c.
7.3 ∗ 46 =
d.
2 2 • 2 5 = 0.25 ∗ 89
53 54
5.
●
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 use
pattern blocks and tape to make their own turn-symmetric shapes.
Have them use their Geometry Templates to record the shapes
they make.
Time
LESSON
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.
●
Student Page
Date
●
18 19
6.
What are the perimeter and area of the
rectangle? Include the correct units.
22 m
15 m
74 m
330 m2
1
-turn symmetry
2
Perimeter =
38
39 62
Area =
131 134
1
-turn symmetry
3
1
-turn symmetry
4
Math Journal 2, p. 280
274-285_EMCS_S_MJ2_G4_U10_576426.indd 280
814
2/18/11 9:15 AM
Unit 10 Reflections and Symmetry
811-815_EMCS_T_TLG1_G4_U10_L04_576906.indd 814
3/16/11 4:19 PM
Study Link Master
Name
PARTNER
ACTIVITY
EXTRA PRACTICE
Exploring Line Symmetry
Date
STUDY LINK
10 4
Time
Line Symmetry in the Alphabet
Print the 26 capital letters of the alphabet below.
109
15–30 Min
(Math Masters, p. 317)
2. The capital letter A has a vertical line of symmetry.
The capital letter B has a horizontal line of symmetry.
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.
Use the letters of the alphabet to complete the Venn diagram.
Capital Letters of the Alphabet
Vertical Line
of Symmetry
SMALL-GROUP
ACTIVITY
ELL SUPPORT
Creating a Line
15–30 Min
3. The word BED has a horizontal line of symmetry.
Symmetry Museum
The word HIT has a vertical line of symmetry.
Use capital letters to list words that have
horizontal or vertical line symmetry.
To 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.
Sample answers:
horizontal
Practice
4. 86 ÷ 9 =
_
6. 6 742 =
10 4
5.
7.
17
122 _17
= 68 / 4
= 855 / 7
315
304-326_EMCS_B_MM_G4_U10_576965.indd 315
2/14/11 4:56 PM
Teaching Master
Date
Name
Time
LESSON
Line Symmetry
9 R5
123 _46
vertical
Math Masters, p. 315
Teaching Master
Name
LESSON
Horizontal Line
of Symmetry
10 4
109
Date
Time
Interpreting a Cartoon
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 lines of symmetry
2.
Sample
answer:
3.
2 red trapezoids
6 lines of symmetry
1 orange square, 4 green triangles
0 lines of symmetry
Sample answer:
By permission of Rick Detorie and Creators Syndicate, Inc.
4.
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.”
5 orange squares
1 line of symmetry
“Across, it’s zero.”
Name
Sample answer
4
1.
LESSON
10 4
Date
Time
Interpreting a Cartoon
Try This
5.
5 red trapezoids
1 line of symmetry
Show two different ways.
By permission of Rick Detorie and Creators Syndicate, Inc.
6.
1.
What answer does Ruthie’s brother expect?
2.
Explain and draw pictures to show why both of Ruthie’s answers are correct.
On the back of this page, make up a problem of your own. Give it to a partner to solve.
Math Masters, p. 316
Math Masters, p. 317
304-326_EMCS_B_MM_G4_U10_576965.indd 317
2/14/11 4:57 PM
304-326_EMCS_B_MM_G4_U10_576965.indd 316
2/14/11 4:57 PM
Lesson 10 4
811-815_EMCS_T_TLG1_G4_U10_L04_576906.indd 815
815
2/16/11 2:23 PM