Paper folding
Strategy card
Unfolding is a sequence of reflections applied in reverse order.
- Step 1: Track the folds in order.
- Step 2: Reverse them: reflect every hole across the last fold line, then the one before.
- Step 3: Count expected holes: each fold doubles them.
- Step 4: Eliminate options with the wrong count or asymmetric positions.
Tip: Check symmetry: the final pattern must be symmetric across every fold line.
Worked example
The paper is folded, then a hole is punched through all the layers. What does it look like opened up?
Fold left half over onto the right, then top half down onto the bottom, then right half over onto the left. Then punch two holes.
- A: paper with 8 holes at row 3 column 1, row 3 column 2, row 3 column 3, row 3 column 4, row 4 column 1, row 4 column 2, row 4 column 3, row 4 column 4
- B: paper with 16 holes at row 1 column 1, row 1 column 2, row 1 column 3, row 1 column 4, row 2 column 1, row 2 column 2, row 2 column 3, row 2 column 4, row 3 column 1, row 3 column 2, row 3 column 3, row 3 column 4, row 4 column 1, row 4 column 2, row 4 column 3, row 4 column 4 (the answer)
- C: paper with 8 holes at row 1 column 3, row 1 column 4, row 2 column 3, row 2 column 4, row 3 column 3, row 3 column 4, row 4 column 3, row 4 column 4
- D: paper with 2 holes at row 3 column 3, row 4 column 3
- E: paper with 8 holes at row 1 column 2, row 1 column 3, row 2 column 2, row 2 column 3, row 3 column 2, row 3 column 3, row 4 column 2, row 4 column 3
Why: Every layer gets a hole. Unfold one step at a time: each fold line works like a mirror, so each hole gets a twin on the other side of the fold. 3 folds make 16 holes in all.
Your turn
Your turn 1 of 3
The paper is folded, then a hole is punched through all the layers. What does it look like opened up?
Fold right half over onto the left, then right half over onto the left, then bottom half up onto the top. Then punch two holes.
Your turn 2 of 3
The paper is folded, then a hole is punched through all the layers. What does it look like opened up?
Fold bottom half up onto the top, then top half down onto the bottom, then left half over onto the right. Then punch one hole.
Your turn 3 of 3
The paper is folded, then a hole is punched through all the layers. What does it look like opened up?
Fold bottom half up onto the top, then right half over onto the left. Then punch one hole.
Keep practicing
Grown-ups: Link this to symmetry in geometry class. Parent guide
Next lesson: Rule out wrong answers