Free resources · Spatial reasoning
Fold & Punch
Fold a sheet of paper, then punch holes of different shapes through the folded layers.
What will I be asked?
Questions first present (in a series of boxes) how a square of paper has been folded up. In the last box, some holes are punched through the folded paper. You are required to select the answer option that shows what the paper would look like when it has been unfolded.
These are trussed up reflection questions — that’s all!
Variations
Some holes are circular; these questions are easiest. If other shapes are used, they will likely have an orientation to consider as well. If the paper is folded along a horizontal line and an arrow is punched into it pointing down, the arrow will be reflected when the paper is unfolded.
If diagonal folds are used, remember: rotate your head and think of it as a vertical mirror line.
When working on paper
Start on the rightmost box. Look at where the holes have been punched.
Go left one box. Look at the fold line. The fold line is your mirror line, and in it you must reflect the holes.
Repeat until the paper is fully unfolded.
Missing layers
Take care. Sometimes holes may be punched that do not go all the way through the paper. If the paper is folded incompletely (where the edges do not meet) it is not guaranteed that the number of holes will double on each reflection. Holes may miss layers of the paper and be unaffected by one or more reflections.
Where it comes up
Hole punch questions appear in non-verbal reasoning sections of independent school entrance exams, in the ISEB Pre-Test, and in GL-style 11+ papers. Simpler single-fold versions can appear at 7+ and 8+. Gulp!
How to use this tool
Fold the sheet, punch a shape through the layers, then unfold it one step at a time rather than all at once.
Attempt each reflection first, unfolding when you have an idea what the result of that action will be.
Ensure to explore why you went wrong — check each resulting hole against your expectation.
If you’re still learning, get a few squares of paper too so you can explore practically, but this tool goes some way to emulate it.
A note on when to use it
Predict before unfolding, every time. The tool shows the answer immediately if you let it, which does not count as practice.