TACHS: Ability: paper folding

A method you can use

1. Read fold arrows in order, then undo the folds in reverse order. A punch goes through the layers actually present at its location. When unfolding, reflect every existing hole across the last fold before reversing the previous fold.
2. Original coordinate model: a vertical fold lies on x = 0, and a punched point lies at (2, 1) in the folded layer. Unfolding creates the reflected point (−2, 1), with the same distance from the fold and the same vertical position. Moving the point to (−2, −1) incorrectly changes a coordinate the vertical fold does not affect.
3. A point on a crease can coincide with its reflection; a fold need not always double the number of distinct holes. For diagonal folds, identify the mirror line first rather than treating the transformation as a rotation. Follow the drawing’s layer boundaries and punch location.
4. Transfer: after folding across x = 0 and then y = 0, a punch at (2, 1) unfolds to (2, 1), (2, −1), (−2, 1) and (−2, −1). Undoing the horizontal fold first creates the second point; undoing the vertical fold reflects both. Check symmetry across both fold lines. Coordinate language teaches the relationship; official Ability practice must respect the no-scratch-paper rule.

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Related section practice

30 practice questions cover this skill. Try a set below or use the question bank for more.