Hole-Punch Symmetry

Age 6-9


Geometry and Spatial Sense

  • Identify and describe the locations and movements of shapes and objects.


  • 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 
  • Hole-Punch Symmetry slides (download)
  • 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.​
  • With the paper held in front of you, punch a hole in the middle of the side without the fold​.
  • Show children the Hole-Punch Symmetry page 1 of the Hole-Punch Symmetry slides​.
    • Explain to students that the bold line indicates the fold​.
  • Challenge students to visualize what the piece of paper will look like when unfolded​.
  • Present 4 possible options of what the square would look like unfolded​.
    • Invite children to select the best option.​
  • Unfold the piece of paper to confirm students’ predictions​.
  • Continue with next challenges which 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​.

Look Fors

  • How does the child describe the location of the holes?
    • Does the child use spatial language (over, under, top, bottom, right, left)?
  • Is the child able to consistently and accurately identify where the holes will be when the paper is opened?


  • The teacher can reverse the challenge by showing children the open hole-punched square paper.
    • Ask: If I could only make one hole-punch, how many times would this paper need to be folded to result in this design?
  • Children can create their own hole-punch symmetry challenges and challenge other classmates to solve it.

Share this lesson!