Nonverbal Reasoning: Figure Matrices, Paper Folding, and Figure Classification
The CogAT Level 8 Nonverbal battery measures reasoning with shapes and spatial patterns and does not require reading or arithmetic. Its three subtests are Figure Matrices, Paper Folding, and Figure Classification.
Core rules
- Figure Matrices: Read the rule across each row and down each column. Track several attributes at once: number of sides, size, shading, rotation, number of objects, and position. The rule must hold for every complete row or column, not just one example.
- Paper Folding: Each fold creates a mirror line. When the paper is unfolded, every punched hole appears again on the opposite side of each fold line it crosses. A single punch through one fold gives two holes; through two folds it gives four, unless the punch lies on a fold line, where holes merge.
- Figure Classification: Identify one attribute shared by all three figures, such as symmetry, curved versus straight sides, open versus closed shapes, or shading. The answer must have that attribute; distractors often match only one example.
Worked example
A 2×2 matrix has a square in the top-left and a triangle in the top-right. The bottom-left is a pentagon, and the bottom-right is blank. The row rule is "lose one side": 4 sides → 3 sides, so 5 sides → 4 sides. The answer is a four-sided figure. A triangle is a trap because it copies the top-right shape instead of applying the rule to the pentagon.
Traps that cost marks
- In Paper Folding, counting only the holes visible in the folded picture. Each fold doubles the hole pattern; a punch through one fold produces two holes.
- Treating a fold as a rotation. Unfolding reflects the hole across the fold line, so the mirror image is on the opposite side.
- Forgetting that a punch exactly on a fold line produces one merged hole, not two.
- In Figure Classification, choosing a figure that matches only one of the three examples (same color, for instance) while ignoring the shared attribute.
- In matrices, tracking only one feature when two change at once.