Symmetry Game

Curriculum – Geometry and Spatial Sense 

For students to describe, sort, classify, and compare two-dimensional shapes and three-dimensional figures, and describe the location and movement of objects through investigation.


Students and the teacher begin by sitting on the floor in a circle. After the teacher has explained the game, students will go off in pairs.


  • Whiteboard with a line of symmetry and markers
    8.5 x 11 paper with different shapes on each paper, folded (Appendix A)
  • Magnetic board (cookie sheets work well) with a line of symmetry
  • Magnetic shapes

For appendix, download the lesson plan here.


  • Show students a half of a heart drawn on a sheet of paper. Ask students what they think would happen if you cut that shape out and opened it up.
  • After gathering some ideas, cut the shape out and show them the result.
  • Repeat these two steps with different shapes.


  • Turn their attention to the whiteboard with the line of symmetry on it. Draw attention to the line of symmetry.
  • Proceed by explaining that they are going to be playing a game where one person puts a shape down and the other person needs to put the same shape down in a way that follows the rules of the symmetry game.
  • Demonstrate this on the whiteboard.
  • After students have showed they understand how to play, explain that they will be getting their own board, and playing this game with a partner.
  • Have students play this game with their partner.


  • Gather the students in a circle again. Have them look at other designs made playing the symmetry game.

Extension Activities*

  • Take a picture of the design and see how it can be recreated using other pattern blocks (composing and decomposing 2D shapes)
  • Measure the area and describe your area in terms of triangles
  • Cut a piece of grid chart paper to fit on the cookie sheet. Design a symmetrical creation over top of the paper. Look at the negative space and try to figure out its area. Create questions involving negative space: How many triangles could you fit in the negative space?
  • Use your design to talk about slides and flips. Which shapes don’t have to be flipped to get the symmetrical image?
  • Exploring fractions by comparing shapes: What fraction of the hexagon is a trapezoid? Triangle? Rhombus?
  • Memory test: Look at another person’s design and try to reconstruct it
  • Puzzles: Create a base shape, trace the shape and give it to other students. Tell them how many pieces are required to fit the puzzle or give a list of the actual shapes used and ask students to fill in the shape.
  • Assigning a value to each 2D shape. For example, if the triangle is worth $1, what would the hexagon be worth? ($6). How much does your entire design add up to?
  • Stack the pieces in shape groups to create a 3D graph of how many of each type were used in the image.
  • Pattern identification: Are there repeating patterns?
  • Language Arts connection: Invite students to create personalities and names for the images/designs they’ve created and to make a story
  • Identifying larger shapes out of smaller shapes (e.g., a larger triangle made with four triangles; a trapezoid made with three triangles)
    • measure the perimeter of this new shape
    • See who has the biggest perimeter. How would need to move your pieces if you wanted to make your perimeter smaller or bigger without changing the number of pieces?

*These extension ideas were generated by OISE’s second-year Master of Teaching Students in Susan London McNab’s mathematics course. Thanks to you all!

  • Janna Barkman
  • Stephen Branston
  • Jacqueline Chiu
  • Mahshid Chowdhury
  • Sierra DeSouza
  • Chase Johnson
  • Sarah Kamrad
  • Claire Huang Kinsley
  • Stephanie Kocukov
  • Erin Lapp
  • Trami Thi Le
  • Morgan Mosher Lowe
  • Emma MacDonald
  • Madeleine MacGillivray
  • Velena Mackay
  • Lesley Marino
  • Karim Nahli
  • Samantha Napolitano
  • Victor Nosko
  • Dorothy Pau
  • Caileigh Prince
  • Sarah Raza
  • Lauren Alexandria Storer
  • Jennifer Szakall
  • Daphne Kerie Tam
  • Birdy Thanabalasingam
  • Yini Xie
  • Sean Yerzy
Created by OISE Mathematics Education Professor Dr. Joan Moss