Unit 13
Spatial Reasoning
About this unit
Develop your ability to visualise, manipulate, and reason about shapes and space in your mind. Questions cover cube net folding, 3D views from different angles, compass direction navigation, paper folding, grid shading patterns, and completing visual sequences — all without physically touching anything.
What types of questions will you face?
- 1Cube net folding: given a 2D net, identify which 3D cube view is possible
- 2Cube/die faces: three views of a die are shown — determine what face is opposite another
- 3Paper folding: a paper is folded and a hole is punched — determine the hole pattern when unfolded
- 43D view matching: given front and side views, find the top view or identify the 3D object
- 5Compass direction navigation: trace a journey with N/S/E/W turns and find the final position or direction
- 6Grid shading patterns: a rule determines which cells are shaded — count shaded cells in a grid
- 7Visual pattern completion: identify which figure comes next in a rotating/transforming sequence
Skills you will build
- Mentally rotating and folding 3D objects from their 2D representations
- Tracking face relationships on a cube (opposite faces, adjacent faces)
- Mapping compass movements onto a mental grid and tracking final position
- Applying symmetry rules to folded paper problems
- Identifying transformation rules (rotation, reflection, translation) in visual sequences
- Applying arithmetic rules to grid shading counts
By the end of this unit, you will be able to
- Fold any cube net mentally and verify any given 3D view
- Navigate complex compass direction problems and state the final displacement
- Predict the hole pattern in any folded-paper hole-punch problem
- Complete any visual rotation or transformation sequence
- Count shaded cells in a grid using a mathematical rule
Difficulty profile
Difficult (avg 3.65) — the 3rd hardest unit. Grid shading and simple compass problems are Medium; cube net folding with complex symbol faces and 3D multi-layer view matching are Very Difficult. This unit requires the most practice for most students.
Exam tip: Spatial Reasoning
For cube nets: identify the centre square first, then mentally fold the arms upward. For each face in the question, ask "which arm folds up to face me?" For compass: draw a mini grid and mark each move as a vector — then calculate net displacement.
Sample Questions
Tile-and-mat questions are a Selective spatial staple: four identical tiles rotated 90°, with the centre covered — deduce what is hidden, not what looks plausible.
Hidden-corner rotation puzzles appear regularly on Selective TS — near-certain marks when you trace one tile’s symbols through each rotation instead of guessing from the options.
The examiner checks whether you can identify the base 2×2 tile, apply consistent 90° rotations to each quadrant, and read off the four hidden inner cells without contradicting any visible symbol.
A 4×4 design is built from four identical tiles. A mat covers the four inner corners (one corner from each tile). Four 2×2 answer grids (A–D) show possible hidden patterns.
Best approach: Pick one fully visible tile and list its four cells. Rotate that tile mentally to match each hidden corner’s orientation. Fill the 2×2 hidden region cell by cell, then eliminate any option that disagrees on even one symbol.
Question
Anisha made a design using four identical tiles. Her mother put a black colour mat in the middle of the design as shown below.
Which option correctly shows what is hidden under the black mat?
- AA
- BB
- CC
- DD
Decided on your answer? Check how you went below.
Cube nets fold into 3D shapes — your job is to find the one view that could actually happen when the net is folded, using opposite-face rules.
Net-to-view questions appear on most Selective TS papers; wrong options usually show opposite faces side by side or flip a symbol’s orientation.
The examiner tests whether you can pair opposite faces from the flat net and reject any 3D view where those opposites touch, or where a symbol faces the wrong way after folding.
A labelled cube net is shown with four 3D cube views (A–D). Exactly one view matches the net; the others break an opposite-face or orientation rule.
Best approach: List the three opposite pairs from the net first. For each option, check adjacent faces — if two opposites appear beside each other, eliminate it. Among survivors, verify symbol orientation matches the fold direction.
Question
A net of a cube is shown below.
Which of the following could be a possible view of the cube?
- AA
- BB
- CC
- DD
Decided on your answer? Check how you went below.
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