Figural Reasoning: Shapes, Folds, and Transformations
What Figural Reasoning asks
Figural Reasoning uses abstract shapes: squares, triangles, circles, lines, and folded paper. Level A tasks include Figure Classification, Figure Analogies, and Paper Folding. These items test geometric observation and the ability to hold a transformation in mind.
Core rules
- Count and compare properties: number of sides, number of corners, open versus closed, straight versus curved, filled versus outline, symmetry, and size.
- For Figure Classification, the group must share a consistent property. 'All have four sides' is a rule; 'all look big' is not reliable unless size is the only changing feature.
- For Figure Analogies, state the change from the first figure to the second: add one side, rotate a quarter turn, remove a dot, or change fill. Apply the identical change to the third figure.
- For Paper Folding, each fold creates layers. A punch through all layers makes one hole per layer when unfolded, mirrored across each fold line. A punch exactly on a fold line can make fewer holes because the halves meet.
Worked example
A square is folded in half vertically. One hole is punched through both layers, away from the fold. When the paper is opened, how many holes appear? The punch passes through two layers, so there are two holes. They sit at the same height and at equal distances from the vertical fold, one on each side. A single hole in the middle would mean the punch was on the fold line, which is not what the item states.
Traps that cost marks
Counting sides but not corners; treating a rotation as a reflection; forgetting that a fold doubles the layers; placing a hole on the fold and still counting two holes; and choosing a figure that matches only one property when the rule requires two.