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Non-Verbal Reasoning · Guide 8 of 8

Paper folding and hidden shapes

Two spatial skills: unfolding a punched piece of paper in your head, and finding a small shape hiding inside a busy picture.

  • Ages 9 to 11
  • 11+ Non-Verbal Reasoning
  • Worked examples

What is it?

In a paper folding question, a square of paper is folded once or twice, then a hole is punched through every layer. You choose what the paper looks like when it's opened out.

In a hidden shape question, you find which picture contains a given shape, exactly the same size and the same way round, hidden among other lines.

Folded in half, punched, then unfolded

Fold
Punch
Unfold

How to spot it

  • Paper folding: pictures of a square with dashed fold lines and arrows, then a punched shape.
  • Hidden shapes: a small shape on its own, and several larger patterns to search.

Step-by-step method

  1. Step 1: Paper folding: unfold one fold at a time, in the reverse order to the folding.
  2. Step 2: Each time you unfold, every hole is reflected in that fold line, so the number of holes doubles.
  3. Step 3: A hole near the fold stays near the fold on the other side; a hole near the edge stays near the edge.
  4. Step 4: Hidden shapes: note the shape's size and the angle of each side.
  5. Step 5: Look for its most unusual part first (a sharp corner or a slanted line), then trace the rest.
  6. Step 6: The hidden shape must be the same size and the same way round, not turned or flipped.

Worked examples

Example 1: one fold

Question: A square is folded in half (left onto right) and a hole is punched near the top. What does it look like unfolded? (above)
  1. Step 1: There are two layers, so the punch makes two holes.
  2. Step 2: Unfold: the hole is reflected in the fold line. It was 8 units right of the fold, so the new hole is 8 units left of it, at the same height.

Answer: Two holes near the top, one each side of the fold, the same distance from it

Example 2: two folds

Question: A square is folded in half, then in half again, and one hole is punched near the folded corner. How does it look unfolded?
Punch
Unfold
  1. Step 1: Two folds make four layers, so there will be four holes.
  2. Step 2: Undo the second fold: the hole is reflected in the horizontal fold, giving two holes.
  3. Step 3: Undo the first fold: both are reflected in the vertical fold, giving four holes around the centre.

Answer: Four holes, one in each quarter, all close to the centre

Example 3: a hidden shape

Question: Which pattern hides the triangle exactly (same size, same way round)?
Shape
A
B
  1. Step 1: The shape is a right-angled triangle with its square corner at the bottom left, and a slanted side from top left to bottom right.
  2. Step 2: A: the diagonal goes from top left to bottom right. With the left and bottom edges it makes exactly the triangle.
  3. Step 3: B: the diagonal slopes the other way, so the triangles in B have their square corners at the top left and bottom right.

Answer: A

Common traps

  • Forgetting a layer

    Count the layers: one fold makes 2, two folds make 4, three folds make 8. That's how many holes you'll get.

  • Reflecting the wrong way

    Holes reflect across the fold line, like a mirror. They don't slide across.

  • A turned hidden shape

    A shape that's the right size but rotated or flipped doesn't count in hidden shape questions.

Top tips

  • Practise with real paper and a hole punch (or a sharp pencil with a grown-up).
  • Trace the hidden shape with your finger, side by side, to check every line is there.

Practice questions

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4 practice questions on this topic, from easy to 11+ level. Reading the guide is free for everyone; practice is for members, and signing up is free.

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