paper-fold-and-cut-symmetry
A square (or other shape) is folded one or more times, a piece is cut out of the folded stack, and the unfolded result must be predicted. The underlying mechanic is that each fold creates a reflection axis, so the cut is reflected back across every fold line on unfold. Solving without physically folding requires mentally composing reflections about each fold axis.
How to solve
- Fold once vs twice — single fold gives mirror image, double fold gives 4-fold symmetry
- Move a triangular cut from a corner to an edge — answer changes from rhombus to bow-tie
- Use a fold diagonal to introduce 45° rotation into the reflected shape
Sub-archetype mix (3)
Click a row to see member problems.
- fold-cut-unfold-shape 40% (2)
The student folds a sheet one or more times, makes a straight cut through all layers, and unfolds. The task is to identify the resulting shape, hole pattern, or piece dimensions. Each fold line acts as a mirror; tracking which edges contain a fold (and stay connected) versus which were outer edges (and separate after cutting) is the load-bearing move.
- fold-maps-point-to-point 40% (2)
A fold is described as carrying one labeled point of the figure exactly onto another labeled point. The student recognizes the fold crease as the perpendicular bisector of the segment joining the two points, then uses equidistance to set up the missing length — typically a triangle height, a side length, or a coordinate.
- compose-reflections-of-figure 20% (1)
A pictured figure (letter, arrow, polygon) is reflected over a given line, then the result is reflected over a second given line. The student must identify both the final position and the final orientation. Two reflections over intersecting lines compose to a rotation about the intersection by twice the angle between the lines — the standard shortcut for checking.
More data (year-over-year, tool fingerprint, grade distribution, all members)
Tool fingerprint (1–17)
Grade distribution
- Gr 4 2
- Gr 8 3