Spatial Reasoning
Spatial Reasoning on the NGAT tests whether you can hold a shape in mind and transform it without a physical model. Typical tasks include mental rotation, cube nets, folded paper, mirror images, plan views, and counting blocks. The items reward systematic tracking of edges, faces, and handedness rather than guessing.
Core rules
- Rotation preserves shape and handedness; reflection reverses handedness. Track one distinctive corner or mark.
- In a cube net, faces separated by one face in a straight line are opposite. Opposite faces can never be adjacent.
- When folding, keep the base fixed and fold each flap up; track which edges meet.
- Paper-folding punches create mirror-image holes across each fold line.
- Block-counting questions include hidden cubes that support visible ones; count by layers.
- For plan and elevation views, project the outline onto the named plane; do not rotate the object.
Worked example
A cube net is a row of four squares labelled 1, 2, 3, 4 from left to right. Square 5 is attached above square 2, and square 6 is attached below square 2. Which face is opposite square 5? In a four-square strip, 1 is opposite 3 and 2 is opposite 4. The remaining pair must be opposite: 5 and 6. Folding confirms it: 5 and 6 sit on opposite sides of the cube, both attached to 2 but on opposite edges. Answer: 6. A common wrong answer is 2, because 5 is drawn next to 2 on the net, but adjacency in the net does not mean adjacency on the cube.
Traps that cost marks
The first trap is treating a net as if neighbouring squares become neighbouring faces. The second is confusing a mirror image with a rotation: a rotated “R” is still an “R”, but a mirrored one is not. In cube-view questions, three faces meet at a corner, so two faces shown separately may still be adjacent. In paper folding, count the number of layers before punching; a punch through two layers produces two holes, mirrored across the fold. Finally, in block counts, do not count only visible cubes-hidden supports are part of the total.