Hole-Punch Symmetry

Curriculum – Geometry and Spatial Sense 

  • Visualize how paper that has been folded and hole-punched will look when the paper is unfolded.
  • Complete and describe designs and pictures of images that have a vertical, horizontal, or diagonal line of symmetry.


  • Students should have previous experience with Hole-Punch Symmetry (Lesson found in Taking Shape: Activities to Develop Geometric and Spatial Thinking p. 94 “Hole-Punch Symmetry Challenge”)
  • students are sitting at desks or on a carpet facing the interactive whiteboard/projector. 


  • Interactive whiteboard or projector
  • Download: Hole-Punch Symmetry slides
  • Hole punch and square papers used for checking predictions


  • Hold a square piece of paper and clearly show children that you are folding it in half along the vertical midline with the fold at the left (as seen from the children’s perspective).
  • With the paper held in front of you, punch a hole in the middle of the side without the fold.
  • Project the Hole-Punch symmetry slide 1.
  • Explain to students that the bold line indicates the fold.
  • Challenge students to visualize what the piece of paper will look like when unfolded.
  • Invite children to select the best option.
  • Unfold the piece of paper to confirm students’ prediction.
  • Continue with next challenges. The challenges increase in complexity, both in terms of where the folds are in the paper (vertical, horizontal, or diagonal), and with increasing numbers of folds and/or holes  (Answers).


Moss, J., Bruce, C. D., Caswell, B., Flynn, T., & Hawes, Z. (2016). Taking Shape: Activities to Develop Geometric and Spatial Thinking. Toronto: Pearson Canada.

Adapted from Moss, Bruce, Caswell, Flynn & Hawes (2016)
By Dr. Joan Moss

To print detailed lesson plans and materials, please click here