Symmetry Studio

What your child will figure out

• Predict and fold-check whether a proposed axis is a line of symmetry.
• Complete a mirror image by placing matching cells the same distance across an axis.
• Find and count every line of symmetry of familiar and generated shapes.
• Distinguish line symmetry from rotational symmetry in a novel shape.

The levels

1. The butterfly fold

   Predict the vertical fold, act on it, and observe every painted point meeting its partner.

2. Finish the print

   Complete a sparse half-painted tile design and fold-check the result.

3. Turn the fold

   Transfer the point-pair test from a vertical to a horizontal axis.

4. Four-fold frame

   Find all four symmetry lines of a square and explain that every point must pair across each line.

5. The stretched square

   Contrast a rectangle with a square and retain only its vertical and horizontal symmetry lines.

6. Reflect the skyline

   Complete a denser six-by-six mirror design across a horizontal axis.

7. One-fold chevron

   Prove that a shape can have exactly one symmetry line after testing four candidates.

8. Zero is an answer

   Reject every candidate line for an asymmetric shape instead of assuming a central line works.

9. Diamond folds

   Find two symmetry lines in a new orientation-rich shape without treating its sloping sides as axes.

10. Diagonal print

    Complete a seven-by-seven mirror image across a descending diagonal.

11. Four-line transfer

    Transfer the square's four-line structure to a decorated four-point star.

12. The turning trick

    Transfer the fold test to a parallelogram and distinguish zero line symmetries from half-turn rotational symmetry.