## A Wall of Symmetrical Shapes

### Barbara Johnson

#### Description

Students explore line(s) of symmetry in polygons during a hands-on activity and a Student Web Lesson. Information learned is used to build a wall of symmetrical shapes designed and drawn by students.

#### Objectives

The student understands the concepts of spatial relationships, symmetry, reflections, congruency, and similarity.

#### Materials

-Transparencies of symmetrical and non-symmetrical polygons
-Cutouts of symmetrical and non-symmetrical polygons
-Computer(s) to access the Student Web Lesson, Let's Learn Symmetry (See Weblinks)
-Butcher paper to hang on the wall for symmetrical shapes
-Construction paper
-Scissors
-Glue
-Pencils
-Rulers
-Math journals
-Stencils or templates of various shapes that students can trace (optional)

#### Preparations

1. Prepare several transparencies of examples and nonexamples of symmetry.
2. Prepare large constuction paper cutouts to use when showing line(s) of symmetry.
3. Make sure the computer is online. The Student Web Lesson, Let's Learn Symmetry, may be bookmarked for easy student access.
4. Place a strip of butcher paper on the wall where students will hang their shapes.
5. Prepare construction paper, pencils, rulers, and scissors for groups of four.

#### Procedures

INTRODUCTION: This lesson only addresses and assesses symmetry.
1. Use paper cutouts to show several examples of symmetrical polygons such as a square, circle, rectangle, heart, etc. Fold the cutouts along possible line(s) of symmetry--vertical, horizontal, and diagonal. Explain that a shape is symmetrical if it can be divided into two equal parts. On the overhead transparencies, draw the line(s) of symmetry while discussing each example.

2. Show non-symmetrical polygons such as a scalene triangle, a non-regular pentagon, or other non-regular polygons. Model with prepared cutouts that there is no way to symmetrically fold these shapes.

3. Ask students, “Can all figures be folded so that they have two matching parts?” (no) “What is a figure that can be folded more than one way into two matching parts?” (circle, rectangle, square) “Do all rectangles have a line of symmetry?” (yes) “Do all triangles have a line of symmetry?” (no) “What do we call the fold line of a figure that has two matching parts?” (a line of symmetry)

4. Discuss where the examples given and other symmetrical objects would occur in the real world. For real-world examples, you might consider a) store signs and symbols, b) country flags, and c) letters of the alphabet.

WORKSTATIONS
Use the following workstations to provide students with an opportunity to practice recognizing and drawing lines of symmetry. Four or five students may work at each station. The stations may be completed during center time. Note: Other workstations (reading, science, social studies) at the teacher's discretion may also occur at this time.

Station 1
Students explore symmetry in the Web lesson, Let's Learn Symmetry. (See Weblinks)

Station 2
a. Using construction paper, scissors, and optional stencils or templates, students draw and cut out a symmetrical shape. Shapes may come from their imagination or represent those earlier discussed.
b. The students fold their shape along as many lines of symmetry as possible, and then draw the line(s) of symmetry on their shape using a ruler.
c. They check with the rest of the group to see if the other students agree with the line(s) of symmetry drawn on the cutout.
d. When the group is in agreement, the student glues their shape on the Wall of Symmetrical Shapes.

WRAP-UP
Meet together again in a whole-group setting and discuss the wall of symmetry. Allow students to point out any patterns they observe between the shapes and the line(s) of symmetry.

*This activity can be divided into 2 days. Steps 1-4 can be taught on the first day, and after a quick review the workstations can be done on day 2.

#### Assessments

Formative Assessments: This lesson only addresses and assesses symmetry.

A. Teacher observes students' shapes and lines of symmetry drawn on the wall of symmetry to see if they have:
1. used materials provided in order to solve the problem of designing and drawing a symmetrical shape, and
2. identified and correctly labeled the line(s) of symmetry.

B. Have students answer the following questions in their math journals:
1. How would you explain symmetry to a second grader?
2. How do you know if a shape is symmetrical?

Review students' responses to see that their notes, comments, and observations reflect a comprehension of symmetry based on classroom experiences and discussion.

#### Extensions

This activity can lead into lessons on classifying geometric shapes, and identifying similar and congruent shapes. The wall of symmetry can be used to springboard discussions about how these shapes can be classified and labeled according to their properties and attributes.