Symmetry
Objectives To review symmetry; and to provide opportunities
to
t explore properties of symmetric shapes.
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Identify equal parts of shapes. [Number and Numeration Goal 3]
• Draw line segments to connect points. [Geometry Goal 1]
• Draw missing parts of symmetric figures. [Geometry Goal 3]
• Locate lines of symmetry in
2-dimensional shapes. [Geometry Goal 3]
Key Activities
Children fold and cut out a symmetric
figure, explore the properties of symmetric
figures, connect matching points on mirror
images, and draw the missing parts of
symmetric shapes.
Ongoing Assessment:
Recognizing Student Achievement
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Angle Race
Math Masters, p. 430 (optional); p. 441
Student Reference Book, pp. 271
and 272
per partnership: 24-pin circular
geoboard and 15 rubber bands or
Math Masters, p. 430, straightedge,
and pencil
Children practice measurement skills.
Math Boxes 6 9
Math Journal 1, p. 147
Children practice and maintain skills
through Math Box problems.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Reviewing Symmetry
pattern blocks paper
Children fold paper into halves and copy
pattern-block designs.
ENRICHMENT
Solving Pattern-Block Symmetry Riddles
Math Masters, p. 187
pattern blocks Pattern-Block Template
Children solve pattern-block puzzles
involving shapes with symmetry.
ELL SUPPORT
Home Link 6 9
Building a Math Word Bank
Math Masters, p. 186
Children practice and maintain skills
through Home Link activities.
Differentiation Handbook, p. 132
Children add the term symmetry to their
Math Word Banks.
Use journal page 146. [Geometry Goal 3]
Key Vocabulary
symmetric symmetry mirror image line
of symmetry
Materials
Math Journal 1, p. 146
Student Reference Book, pp. 122 and 123
Home Link 68
Math Masters, p. 185
scissors straightedge cm ruler hand
mirror (optional) hole punch (optional)
Advance Preparation
Copy and cut out Angle Race degree-measure cards from Math Masters, page 441.
Teacher’s Reference Manual, Grades 1–3 pp. 149, 150
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Getting Started
Mental Math and Reflexes
Math Message
Pose equal-sharing and equal-grouping number
stories. Children share solution strategies. Suggestions:
Take one Math Masters, page 185. Use a
straightedge to draw line segments to connect the
dots in order: A to B, B to C, and so on. Fold along
the dotted line, keeping the picture on the outside.
Keep it folded. Cut along the solid lines.
2 children share 7 sweet pickles equally. How many
pickles does each child get? 3 pickles How many pickles
are left over? 1 pickle
4 children share 14 envelopes equally. How many
envelopes does each child get? 3 envelopes How many
envelopes are left over? 2 envelopes
4 children share 33 crayons equally. How many crayons
does each child get? 8 crayons How many crayons are left
over? 1 crayon
PROBLEM
PRO
PR
P
RO
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OBL
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B
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SOLVING
SO
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Home Link 6 8 Follow-Up
Briefly go over the answers. Make sure children
understand that the curved arrow shows the
path and the direction of the rotation.
1 Teaching the Lesson
Math Message Follow-Up
(Math Masters, p. 185)
WHOLE-CLASS
ACTIVITY
ELL
Ask children to name the unfolded cutout figure. kite Remind
children that kite has 2 meanings: it can be a toy or a
mathematical shape. It is important to distinguish this kite from
the polygons discussed in Lesson 6-5. Ask children to explain why
we can say that the kite is symmetric, or has symmetry. When
the shape is folded, the two halves match. To support English
language learners, discuss when to use the adjective symmetric
versus the noun symmetry.
Exploring Properties of
Teaching Master
WHOLE-CLASS
ACTIVITY
Symmetric Figures
Name
LESSON
69
Date
Time
Mirror Image
(Math Masters, p. 185)
B
Ask children to refold their cutout kites. Explain that now they
will make their kite symmetric. Show them how to hold the kite
up to a light source and mark the points on the unmarked half
with a pencil or marker. They may also punch a hole with a pencil
point or hole puncher through both halves at each of the labeled
points, except A and J.
A
G
E
F
Children then use a straightedge to connect the holes or dots on
the blank half of the kite in the same pattern as on the printed
half.
When they unfold their kites, children will notice that they have
drawn a pattern like the existing pattern. If you have a hand
mirror, place it upright along the fold line. Ask a volunteer to
describe what is in the mirror. The pattern is called the mirror
image of the existing pattern. Discuss the relationship between
the printed pattern and its mirror image. Ask: How are they alike?
D
C
I
H
J
Math Masters, p. 185
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They are the same size and have the same shape. How are they
different? They face in opposite directions.
B
A
D
G
C
E
IF
H
J
A line connects point B to its mirror image point.
NOTE For practice
decomposing polygons, go to
www.everydaymathonline.com.
Have children use a straightedge to connect a pair of matching
points (a point on the right side to its corresponding point on the
left side). Repeat for two other pairs of matching points.
For each pair of matching points, children measure the distance in
centimeters from each point to the fold line. Children share their
observations. The distance from one point to the fold line is the
same as the distance from its matching point to the fold line. Some
children may mention that the line segments connecting pairs of
matching points form right angles with the fold line.
After children have connected all pairs of matching points and
measured each point’s distance to the fold line, discuss the
following concepts:
A shape is symmetric about a line if it can be folded in half
along that line so the two halves match.
The fold line is called the line of symmetry.
The mirror image of a design is the same size and shape as the
design, but it faces in the opposite direction.
Completing Symmetric Figures
PARTNER
ACTIVITY
(Math Journal 1, p. 146; Student Reference Book,
pp. 122 and 123)
PROBLEM
PRO
P
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RO
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BLE
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SO
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SOLVING
OL
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Partners draw the missing halves of symmetric figures.
Have children describe how they solved Problem 9.
Children can read more about line symmetry on pages 122 and
123 of the Student Reference Book.
Student Page
Date
Time
LESSON
6 9
䉬
Symmetric Shapes
夹 夹 夹 夹
Each picture shows one-half of a letter. The dashed line is the line of
symmetry. Guess what the letter is. Then draw the other half of the letter.
1.
2.
3.
4.
Adjusting the Activity
Children use hand mirrors to see the missing parts of the figures and
complete the drawings. They may also check that the missing parts of the figures
are completed correctly.
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
Draw the other half of each symmetric shape below.
5.
6.
7.
8.
9. The picture at the right shows one-fourth
of a symmetric shape, and two lines of
symmetry. Draw the mirror image for each
line of symmetry.
Ongoing Assessment:
Recognizing Student Achievement
Journal
page 146
Use journal page 146, Problems 1–4 to assess children’s ability to complete
symmetric shapes. Children are making adequate progress if they are able to
draw the other half of the letters in Problems 1–4. Some children may be able to
complete the remaining problems.
[Geometry Goal 3]
Try This
10. The finished figure in Problem 9 has 2 more lines of symmetry. Draw them.
Math Journal 1, p. 146
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Student Page
2 Ongoing Learning & Practice
Playing Angle Race
PARTNER
ACTIVITY
(Math Masters, pp. 430 and 441; Student Reference Book,
pp. 271 and 272)
Children practice measurement skills by playing Angle Race.
They make angles on geoboards or on Math Masters, page 430.
For detailed instructions, read the directions on Student Reference
Book, pages 271 and 272 with the children.
Math Boxes 6 9
Games
Angle Race
Materials □ 24-pin circular geoboard or a sheet
of Circular-Geoboard Paper (Math
Masters, p. 430)
□ 15 rubber bands, or a straightedge
and a pencil
□ deck of Angle Race Degree-Measure
ure
Cards (Math Masters, p. 441)
Players
2
Skill
Recognizing angle measures
Object of the game To complete an angle exactly
ly
at the 360° mark on a circular geoboard.
Directions
circular geoboard
1. Shuffle the cards. Place the deck
number-side down on the table.
2. If you have a circular geoboard, stretch
a rubber band from the center peg to
the 0° peg.
If you do not have a circular geoboard,
use a sheet of Circular-Geoboard Paper.
Draw a line segment from the center
dot to the 0° dot. Instead of stretching
rubber bands, you will draw line segments.
INDEPENDENT
ACTIVITY
Circular-Geoboard
Paper
(Math Journal 1, p. 147)
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 6-11. The skill in Problem 6
previews Unit 7 content.
Student Reference Book, p. 271
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Writing/Reasoning Have children write an answer to the
following: Explain why the quadrangle you drew in
Problem 3 is not a square, a rhombus, or a rectangle.
Sample answer: A square and a rhombus have 4 equal sides.
A square, a rhombus, and a rectangle have pairs of parallel sides.
A rectangle and a square have 4 right angles. My quadrangle does
not have 4 equal sides, pairs of parallel sides, or 4 right angles.
Home Link 6 9
INDEPENDENT
ACTIVITY
(Math Masters, p. 186)
Home Connection Children fold sheets of paper to create
lines of symmetry and answer questions about the shapes
that they create.
Student Page
Date
Time
LESSON
69
Math Boxes
1. 3 people share 14 pennies.
Each person gets
There are
2
4
2. A baker packed 8 boxes of cup-
pennies.
pennies left.
cakes. She packed 4 chocolate and
4 white cupcakes in each box. How
many cupcakes did she pack in all?
64 cupcakes
(unit)
250–253
73 74
3. Draw a quadrangle with exactly one
right angle. Label the vertices A, B,
C, D. Which letter names the right
angle?
Sample answer:
Angle
B
A
C
4. Draw a quadrangle that is not a
square, a rectangle, or a rhombus.
Sample answers:
A
D
98
108 109
5. Describe the angle.
108 109
6. Estimate. A package of cookies
costs $2.09. About how much do
3 packages cost? Show the
number model for your estimate.
Fill in the circle for the best answer.
A.
1
greater than a _
4 turn
B.
1
less than a _
4 turn
$6.00
$2.00 × 3 = $6.00
Sample answer
1
C. greater than a _
2 turn
D. one full turn
About
Number model:
191 193
194
168
Math Journal 1, p. 147
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3 Differentiation Options
Home Link Master
Name
Date
HOME LINK
69
Family
Note
Time
Symmetric Shapes
Our class has been studying lines of symmetry—lines that divide figures into mirror images.
Help your child look for symmetric shapes in books, newspapers, and magazines, and in
objects around the house, such as windows, pieces of furniture, dishes, and so on.
122 123
Please return this Home Link and your cutouts to school tomorrow.
1. Fold a sheet of paper in half. Cut off the folded corner, as
shown. Before you unfold the cutoff piece, guess its shape.
READINESS
Reviewing Symmetry
a. Unfold the cutoff piece.
What shape is it?
5–15 Min
To explore the concept of symmetry, have children use pattern
blocks to create designs. First, children fold a blank sheet of paper
in half to create a line of symmetry. They unfold the paper and lay
it flat on the table.
triangle
b. How many sides of the cutoff
piece are the same length?
INDEPENDENT
ACTIVITY
2 sides
2 angles
c. How many angles are the same size?
d. The fold is a line of symmetry. Does the cutoff
no
piece have any other lines of symmetry?
Next children make a simple design with pattern blocks on the
right side of the paper. Then they use pattern blocks to create the
other half of the design on the left side of the paper.
2. Fold another sheet of paper in half. Fold it in half again.
Make a mark on both folded edges 2 inches from
the folded corner. Cut off the folded corner. Before
you unfold the cutoff piece, guess its shape.
a. Unfold the cutoff piece. What shape is it?
b. Are there any other lines of
symmetry besides the fold lines?
square
2 in.
2 in.
yes
c. On the back of this paper, draw a picture of the
cutoff shape. Draw all of its lines of symmetry.
Math Masters, p. 186
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Folded paper provides the background for a symmetric design.
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One-half of design
The child completes the design.
454
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SMALL-GROUP
ACTIVITY
ENRICHMENT
Solving Pattern-Block
15–30 Min
Symmetry Riddles
PROBLEM
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SOLVING
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(Math Masters, p. 187)
To apply children’s understanding of symmetry, have
them solve pattern-block puzzles involving shapes with
symmetry. Children complete Math Masters, page 187.
Have children describe the blocks they used to solve each riddle.
For example, “I used two red trapezoids and six green triangles
to solve the first riddle.”
SMALL-GROUP
ACTIVITY
ELL SUPPORT
Building a Math Word Bank
5–15 Min
(Differentiation Handbook, p. 132)
To provide language support for symmetry, have children use the
Math Word Bank template found on Differentiation Handbook,
page 132. Ask children to write the term symmetry, draw a
picture to represent the term, and write other related words.
See the Differentiation Handbook for more information.
Teaching Master
Name
Date
LESSON
69
Time
Pattern-Block Symmetry Riddles
Use your Pattern-Block Template to record your solution to each
problem on another piece of paper. Check that each solution
works for all the clues in the problem. Sample answers:
1. Build a symmetrical shape using these clues:
Use exactly 2 red trapezoids and put them
together to make a hexagon.
Use exactly 6 green triangles around
the outside of the hexagon.
Use exactly 8 blocks.
2. Build a symmetrical shape using these clues:
Use exactly 2 red trapezoids.
Use exactly 5 tan rhombuses.
Use exactly 7 blocks.
3. Build a symmetrical shape using these clues:
Build a large triangle.
Use a yellow hexagon in the center at the
bottom of the large triangle.
Use at least 3 different colors of blocks.
Try This
4. Build a shape that has more than 1 line
of symmetry using these clues:
Use exactly 2 red trapezoids.
Do not use yellow hexagons.
The longer sides of the red trapezoids
touch and line up together.
Use a green triangle at the top and at
the bottom of the shape.
Use exactly 10 blocks.
Math Masters, p. 187
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