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Non-verbal Reasoning · Spatial

Track a paper fold

Predict the position or pattern produced by a stated paper fold or unfold.

Practise it now

Fold the paper, punch a hole, then predict what the sheet looks like opened out.

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A worked example

One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.

Unfolding one punched hole

The paper is opened out flat. How many holes are there, and where on the sheet do they sit?

A square of paper, folded twice and punched once, then opened out flat again.

1. right
2. down

Paper grid panels: panel 1, rows hole, empty; empty, empty. Folds: vertical right; horizontal down. Answer pictures: option 1, rows empty, empty, empty, empty; empty, hole, hole, empty; empty, hole, hole, empty; empty, empty, empty, empty. option 2, rows hole, empty, empty, hole; empty, empty, empty, empty; empty, empty, empty, empty; hole, empty, empty, hole. option 3, rows empty, empty, empty, empty; empty, hole, hole, empty; empty, empty, empty, empty; empty, empty, empty, empty. option 4, rows empty, empty, empty, empty; empty, hole, empty, empty; empty, empty, empty, empty; empty, empty, empty, empty.

Fold one: the square is folded in half from left to right.

Fold two: the folded paper is folded in half again, from top to bottom.

One hole is punched through every layer, close to the corner where the two folds meet.

  1. Four holes, one in each quarter, grouped close together around the centre
  2. Four holes, one near each corner of the sheet
  3. Two holes, side by side near the centre
  4. One hole in the centre

Answer: Four holes, one in each quarter, grouped close together around the centre

How you get there

Count the layers first. One fold makes two layers, and folding those in half again makes four, so the punch goes through four layers and there will be four holes. Now undo the folds one at a time. Opening the second fold mirrors the hole across the horizontal crease, which gives two. Opening the first mirrors both of those across the vertical crease, which gives four, one in each quarter. The punch was made close to the corner where the folds meet, and that corner is the middle of the whole sheet, so all four holes end up clustered around the centre.

Why the other answers tempt

"Four holes, one near each corner" gets the count right and the places wrong. A hole punched near the FOLDED corner unfolds inwards towards the middle. It is a hole punched near the loose, raw-edged corner that ends up out at the corners of the sheet.

If they are stuck, say this

Count the layers to get the number of holes, then open one fold at a time and mirror every hole across the crease you have just opened. Do not try to picture the finished sheet in a single jump.

Now do it live in Hole-Punch Unfolder

What this exercise is doing

Hole-Punch Unfolder

Fold the paper, punch a hole, then predict what the sheet looks like opened out.

A punch goes through every layer under it, so the number of holes doubles with each fold: two layers give two holes, four layers give four. When you open the paper, each hole reflects back across the crease it was folded over - so the finished pattern is symmetrical about every crease line, and you can work it out by mirroring backwards, last fold first.

  1. Step 1. Fold. Fold the sheet twice - drag the track or hit the fold button.
  2. Step 2. Punch. Tap a square on the folded stack to punch a hole straight through it.
  3. Step 3. Predict. Before you open it: tap every square you think will have a hole, then press Check.

What to say if they get stuck

  1. Every fold doubles the holes: one punch through two layers makes two holes.
  2. A hole always reappears as a mirror image across the crease you just opened.
  3. Undo the folds in reverse order in your head. Mirror the holes across the last crease first, then mirror EVERYTHING across the crease before it.

Open Hole-Punch Unfolder on its own page to share it

Where track a paper fold sits in the 11+

The 11+ does not test these skills in isolation, and practising one in the wrong order wastes the practice. These are the skills the curriculum map connects this one to.

Sits alongside

Validate a cube net

Both require folding representation, but generic paper folds and cube topology differ.

How track a paper fold differs from the skills beside it

The same exercise practises several skills, and telling them apart is often the difficulty rather than the exercise itself. On this page the skill is: predict the position or pattern produced by a stated paper fold or unfold, and it stops where one or more folds recorded as a difficulty dimension.

Related non-verbal reasoning skills

All non-verbal reasoning 11+ skills

Questions parents ask about track a paper fold

Answered from what the skill map records about this skill, not from a template. Every answer here is on the page, and the same questions are the page's FAQ structured data.

Predict the position or pattern produced by a stated paper fold or unfold. It is one of 22 named non-verbal reasoning skills in the 11+, in the spatial strand, and this page carries 1 interactive exercise that practises it.

Non-verbal reasoning is the paper families most often leave until last

A free diagnostic covers matrices, series, odd one out, rotation, reflection and the 3D questions, and shows where the time is worth spending.

Start the free 11+ diagnostic