Folding and Nets

Folding and nets questions test your ability to visualise in 3D. You might be asked what happens when a piece of paper is folded and a hole is punched, or which 3D shape a flat net would make when folded up. These are among the trickiest NVR question types, but with the right strategies you can tackle them confidently.

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Part 1: Paper Folding

In a paper-folding question, a piece of paper is folded one or more times, and then something happens to it (usually a hole is punched or a corner is cut off). You must work out what the paper looks like when it is unfolded again.

The Key Rule

Every fold creates a line of symmetry. When you unfold the paper, the holes or cuts are reflected across each fold line, just like a mirror.

How Many Holes?

Number of folds	Holes punched while folded	Total holes when unfolded
1 fold	1 hole	2 holes
2 folds	1 hole	4 holes
3 folds	1 hole	8 holes

The formula is: total holes = holes punched x 2 raised to the power of the number of folds. But do not worry about the formula — just remember that each fold doubles the number of holes.

Worked Example 1 — One Fold

1. Start with a square piece of paper.
2. Fold it in half from right to left (the right edge meets the left edge).
3. Punch a hole near the top-right corner of the folded paper.

Unfolding step: The fold line is vertical, down the middle. The hole on the right side has a mirror image on the left side.

Result: Two holes, one near the top-right and one near the top-left, both the same distance from the fold line.

Worked Example 2 — Two Folds

1. Start with a square piece of paper.
2. First fold: fold in half from right to left.
3. Second fold: fold in half from top to bottom.
4. Punch a hole near the bottom-right corner of the twice-folded paper.

Unfolding step 1: Undo the second fold (top to bottom). The hole reflects upward. Now there are 2 holes on the right side (one top, one bottom).

Unfolding step 2: Undo the first fold (right to left). Both holes reflect to the left side. Now there are 4 holes total — one near each corner.

Important: Always unfold in reverse order — undo the last fold first.

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Part 2: Nets

A net is a flat shape that can be folded up to make a 3D shape. The most common net question in 11+ exams involves cube nets.

Cube Nets

A cube has 6 faces, so a cube net is made of 6 connected squares. There are exactly 11 different valid cube nets.

How to Identify a Valid Cube Net

Rule	Explanation
Must have exactly 6 squares	Any more or fewer and it cannot be a cube
No more than 4 squares in a row	A line of 5 or more will overlap when folded
No 2x2 block of squares	A 2x2 block cannot fold into a cube without overlapping
All squares must be connected	Every square must share at least one full edge with another square

Worked Example 3 — Valid or Invalid?