assess students' prior knowledge, ask students to fold a piece of
colored paper in half and cut a heart shape, leaving the fold attached
as they would do to make Valentines to share with classmates. When they
are finished, direct students to open their folded piece of paper to
see that both sides are equal and are a reflection of the other. It may
be helpful to have mirrors available so that students can see how
dividing a figure with a line of symmetry creates a mirror image of the
An excellent way to connect seasonal holidays with mathematics
is to have students cut a shamrock, heart, Pilgrim’s hat, snowflake, or
other holiday symbol by folding paper and cutting symmetrical figures.
This activity engages students in problem solving that requires spatial
and visual thinking. The symmetrical figures can be used as the border
on a class bulletin board.
To begin the lesson, distribute one geoboard strung with rubber
bands to each student. Ask students to use one rubber band to create a
figure and use a second rubber band to divide it into two equal parts.
If you do not define how to divide the figure, students may
create many different lines of symmetry, which allows for a rich
discussion. The Rotations and Lines of Symmetry Teacher Resource Sheet
provides a reference.
It is important to note that some figures will not be able to
be divided into congruent shapes. As students are attempting to divide
their shapes, walk around the classroom to identify examples of shapes
which have line symmetry. Ask those students to share their examples.
Also talk about which examples do not have line symmetry and why. This
will allow for a rich discussion.
Next, have students compare their figure with those of a
partner and discuss how the figures are the same and how they are
different. They should be alike because they are equally divided and
one side is the reflection of the other.
Have a pair of students show their figures and share the
content of their conversation. Listen for students’ understanding of
the meaning of symmetry. Ask pairs of students to repeat this process
in order to hear the ideas of multiple students. This will help you
understand what students know as you begin the lesson so that you can
Discuss with the class the meaning of symmetry. It is
important to model line and reflectional symmetry and rotational
symmetry. Samples can be found in the Paper Quilts Unit.
Paper Quilts Unit
You may wish to project the Lines of Symmetry Overhead for students to discuss lines of symmetry in common geometric figures.
Lines of Symmetry Overhead
Encourage students to discuss what they learned by cutting figures
that were different from the figures on the geoboard. Discuss flips,
turns, and slides.
Next, give each student a copy of the Creating Lines of Symmetry Activity Sheet.
Creating Lines of Symmetry Activity Sheet
Ask students to use a pencil to draw as many lines of symmetry
as possible for each figure. Have students discuss their product. Then
place a transparent copy of the student learning guide on the overhead
and have students volunteer to draw lines of symmetry on each figure.
Have students cut out a shape of their choice from the student
learning guide. Ask them to cut along one of the lines of symmetry and
try to fit the two pieces one on top of the other. The pieces should
fit exactly. Flipping and rotating may be necessary to align the sides
Tell students that when two figures are the same size and
shape, they are said to be congruent. Repeat the activity once or
Model how to make a rectangle with one rubber band using the Virtual Geoboard E-Example.
Virtual Geoboard E-Example
Use a second rubber band to create a line of symmetry. Depending
on the experience of your students, it may be best to begin with
obvious and frequently presented lines of symmetry. This enables you to
accommodate the varying levels of knowledge of your students during
whole class instruction.
Now that students have experimented with creating symmetrical
figures with paper, distribute to each student a geoboard strung with
five rubber bands. Direct students to duplicate the same figures on
their geoboard that appear on the Creating Lines of Symmetry Activity Sheet. Ask them to use rubber bands to show lines of symmetry. Provide Dot Paper so that students may draw the figure as it appears on the geoboard. Keep these as a record of the student’s work.
Make notes about the level of understanding students demonstrate
on their recording. Use this information to determine the next
instructional activity that is appropriate for the students as
individuals or as a group.