Geometry
5
Symmetrical Figures
Objective
Common Core
State Standards
■ 4.G.3
In this lesson, students solve problems involving symmetry. Because
relationships across a line of symmetry correspond exactly in terms of size,
form, and arrangement, students can begin to develop a sense of formal
balance, which will serve as a foundation for geometric equations.
Talk About It
Discuss the Try It! activity.
■ Say: An image that has symmetry can be divided into two halves that are
mirror images of each other. Ask: What is a mirror image?
■ Draw two shapes on the board, one that is symmetrical and one that is not.
Point to the symmetrical shape. Ask: Is this shape symmetrical? How can you
tell? Point to the asymmetrical shape. Ask: Is this shape symmetrical? How
can you tell?
Solve It
With students, reread the problem. Have students decorate their own
symmetrical masks by folding construction paper in the center and tracing
a Pattern Block design along the fold to make the first half of the mask.
Students then unfold the paper and complete the other half of the mask,
tracing blocks so that it is symmetrical.
More Ideas
For other ways to teach about symmetry—
■ Have students use a GeoReflector™ Mirror on the shapes they made in the
lesson. With one half of the shape in place, students can place the mirror
along the line of symmetry and observe the reflection.
■ Have students work in pairs. Students should divide a Geoboard in half
with a rubber band. One student then makes a shape or pattern on one
half of the Geoboard. The other student must then make a mirror image of
the first shape or pattern on the second half of the Geoboard so that the
design is symmetrical. Students then switch roles and repeat the activity.
■ Have students make symmetrical designs out of Centimeter Cubes. Students
can then use crayons to draw their designs on a Centimeter Grid (BLM 12).
Formative Assessment
Have students try the following problem.
Which shows a line of symmetry?
A.
B.
C.
D.
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Try It!
30 minutes | Pairs
Here is a problem about symmetry.
Introduce the problem. Then have students do the
activity to solve the problem. Give Pattern Blocks,
crayons, and blank sheets of paper to each pair.
Introduce and model the concept of symmetry.
1. Take the blue rhombus. Use the green
triangles to show a line of symmetry. Invite
students to trace the blue rhombus and draw
other lines of symmetry. Do the same with the
yellow hexagon and red trapezoid.
3. Students should trace their figures onto
the paper and color the shapes. Have students
check to make sure that they can draw a line of
symmetry that will divide the design into two
halves that are mirror images of each other.
Partners then switch roles and repeat the activity.
Geometry
Andrew wants to decorate a face mask like his favorite action hero to wear
on the night of his class costume party. The mask he wore last year was torn
in half, but Andrew is hoping to use it as a pattern. How can symmetry help
Andrew create a whole face mask from the half he has?
Materials
•
•
•
•
Pattern Blocks (50 assorted per pair)
crayons (10 per pair)
paper (5 sheets per pair)
pencils (1 per student)
2. Say: We can make a group of shapes that
has symmetry, too. Have one student in each
pair create one half of a shape; then the other
student should complete a symmetrical side.
Have students draw a vertical line on their
paper to help.
Some students may try to complete the
pattern by repeating the shapes (i.e., triangle,
trapezoid, triangle, trapezoid) instead of
creating mirror images. You may wish to use a
hand mirror or GeoReflector™ Mirror to help
students check their design for symmetry. Hold
the mirror so that students can see half their
design reflected along the line of symmetry.
Then remove the mirror and have students
check that the other half of the design matches
what they just saw in the mirror.
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Lesson
5
Geometry
Name
Answer Key
Use Pattern Blocks to model the symmetrical figure. Name the figure and
the two parts.
(Check students’ work.)
1.
2.
hexagon; trapezoid
____________________________
rectangle; square
____________________________
Using Pattern Blocks, model a symmetrical figure. Sketch the shape. Name
the shape that you sketched. Name the shape formed by
both sides together.
(Check students’ work.)
3.
4.
square; rectangle
____________________________
triangle; rhombus
____________________________
Sketch the other half of each shape to make a symmetrical figure.
5.
6.
7.
8.
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146
Hands-On Standards, Common Core Math
Download student pages at hand2mind.com/hosstudent.
Name Key
Answer
Challenge! If a shape is drawn on a piece of paper, explain how
you can tell if the shape is symmetrical. Draw a picture to help.
Challenge: (Sample) Fold the paper so that the fold line is along the center line of the
shape. If the two halves of the shape match, the shape is symmetrical.
© ETA hand2mind®
Download student pages at hand2mind.com/hosstudent.
Hands-On Standards, Common Core Math
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