Folding & 3D Visualisation

Folding questions show you a flat shape (a net) and ask you to imagine folding it up into a 3D shape — like folding a cardboard box. 3D Visualisation questions test your ability to imagine how a shape looks from different angles, or how a piece of paper looks after being folded and hole-punched.

These questions test your spatial reasoning — your ability to picture shapes in your mind and mentally move them around.

---

Part 1: Paper Folding and Punching

How It Works

1. You start with a flat piece of paper (usually square).
2. The paper is folded one or more times (the question shows you the fold lines and arrows).
3. A hole is punched through the folded paper.
4. You must work out what the paper looks like when it is unfolded.

Key Principle

Every fold creates a MIRROR IMAGE of the hole on the other side of the fold line.

When you unfold, the hole "reflects" across each fold line. If the paper was folded twice, you need to unfold in reverse order — undo the last fold first, then the first fold.

Worked Example 1: Single Fold

Step 1: A square piece of paper.

+--------+
|        |
|        |
|        |
+--------+

Step 2: Folded in half from right to left (right side folds onto left side).

+----+
|    |
|    |
|    |
+----+

Step 3: A hole is punched in the top-right corner of the folded paper.

+----+
|   O|
|    |
|    |
+----+

Question: What does the paper look like when unfolded?

Solution:

When we unfold (left to right), the hole in the top-right of the folded paper was punched through both layers. So there are two holes: one where we punched, and one that is its mirror image across the fold line.

+--------+
| O    O |
|        |
|        |
+--------+

The holes appear in the top-left and top-right (symmetrical across the centre fold line).

Worked Example 2: Two Folds

Step 1: Start with a square piece of paper.
Step 2: Fold in half from bottom to top.
Step 3: Fold in half again from right to left.
Step 4: A hole is punched in the centre of the folded paper.

Question: What does it look like when fully unfolded?

Solution:

Unfold in reverse order:

Undo the second fold (right to left): The single hole becomes 2 holes — the original and its mirror image across the vertical fold line.

Undo the first fold (bottom to top): Each of those 2 holes becomes 2, giving 4 holes — mirrored across the horizontal fold line.

+--------+
| O    O |
|        |
| O    O |
+--------+

Four holes, one in each quarter — symmetrical both horizontally and vertically.

Quick Rule for Paper Folding

Number of folds	Maximum holes from 1 punch
0 folds	1 hole
1 fold	2 holes
2 folds	4 holes
3 folds	8 holes

Each fold doubles the number of holes (because each hole is mirrored).

---

Part 2: Nets and 3D Shapes

What Is a Net?

A net is a flat shape that can be folded up to make a 3D shape. For example, a cube net is a flat arrangement of 6 squares that folds up into a cube.

Common Nets

Cube Net (6 squares):

    +--+
    |  |
 +--+--+--+--+
 |  |  |  |  |
 +--+--+--+--+
    |  |
    +--+

This is a cross-shaped net. When folded, each square becomes one face of the cube.

Other 3D shapes and their nets:

3D Shape	Net description	Faces
Cube	6 connected squares	6
Cuboid	6 connected rectangles (3 pairs)	6
Triangular prism	2 triangles + 3 rectangles	5
Square-based pyramid	1 square + 4 triangles	5
Tetrahedron	4 connected equilateral triangles	4

Cube Net Questions

The most common net question asks: "Which of these nets will fold up to make a cube?" or "When this net is folded, which face is opposite which?"

Key Rules for Cube Nets