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 top half down onto the bottom, then left half over onto the right. Then punch one hole.
- A: paper with 2 holes at row 1 column 4, row 4 column 4
- B: paper with 2 holes at row 4 column 1, row 4 column 4
- C: paper with 4 holes at row 1 column 3, row 1 column 4, row 2 column 4, row 4 column 2
- D: paper with 1 hole at row 4 column 4
- E: paper with 4 holes at row 1 column 1, row 1 column 4, row 4 column 1, row 4 column 4 (the answer)
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. 2 folds make 4 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 left half over onto the right, then bottom half up onto the top, then right half over onto the left. Then punch one hole.
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 top half down onto the bottom, then right half over onto the left, then top half down onto the bottom. Then punch two holes.
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 right half over onto the left, then top half down onto the bottom, then top half down onto the bottom. Then punch two holes.
Keep practicing
Grown-ups: Link this to symmetry in geometry class. Parent guide
Next lesson: Rule out wrong answers