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

Lesson 1 of 2Spatial ReasoningEasy

Visual tile and rotation questions are among the most satisfying in OC TS Spatial Reasoning — because once you identify the single tile that builds the whole design and understand its rotation rule, the hidden region writes itself. Let's delve right into this type.

Tile rotation and hidden-pattern questions appear consistently in OC TS and are near-certain marks for students who approach them methodically. The question always comes down to the same insight: if a design is built from four identical tiles each rotated 90°, every cell in the hidden area can be deduced from the visible cells of the matching tile.

The examiner wants to know whether you can identify the single base tile, trace how it is rotated into each of the four positions, and then use the rotated version to predict what symbols are hidden under the covered area — cell by cell — without guessing.

A 2D design is assembled from four identical tiles, each rotated 90° clockwise from the previous. A grey mat or cover hides the central portion of the design, which contains exactly one corner from each tile. You are given four answer options (A–D), each showing a different possibility for what is under the mat.

Best approach: Pick one clearly visible tile and note the symbol in each of its four cells. Then mentally rotate that tile 90° clockwise to match the orientation of the tile whose hidden corner you are deducing. Read off the symbol at the relevant position. Repeat for each of the four hidden cells. Then eliminate answer options one by one — any option that contradicts even one of your deduced symbols is wrong.

Question

Jimmy made a design using four identical tiles, each rotated 90° from the previous. His mother placed a grey mat in the middle of the design, as shown in the image below. The grey mat covers the four inner corners — one corner from each tile.

Which option correctly shows what is hidden under the grey mat?

A $A$
B $B$
C $C$
D $D$

Decided on your answer? Check how you went below.

Correct Answer

B

Step-by-Step Explanation

Step 1: Identify the base tile and its rotation rule. The full design is a 4\times4 grid made from four identical 2\times2 tiles. Each tile is rotated 90° clockwise from the previous. The grey mat covers the central 2\times2 area — one inner corner from each tile. Step 2: Deduce each hidden symbol. By comparing the three visible cells of each tile to the same tile rotated to the hidden position: Hidden cell position Deduced symbol Top-left Hollow left arrow (\leftarrow) Top-right Hollow up arrow (↑) Bottom-left Double-headed arrow (\leftrightarrow) Bottom-right Bow-tie symbol Step 3: Eliminate wrong options. A: Top-right shows a down arrow (↓) — should be up (↑). ✗ B: Matches all four deduced symbols exactly. ✓ C: Top-left shows a right arrow (\to) — should be left (\leftarrow). ✗ D: Uses completely different symbols in multiple positions. ✗ The answer is B. The key insight: You never need to guess. Every hidden symbol is fully determined by the visible cells of the rotated tile — trust the rotation, not the appearance.

Lesson 2 of 2Spatial ReasoningDifficult

Cube net questions are the signature challenge of OC TS Spatial Reasoning — and the one type that students either love or dread. A 2D net folds into a 3D cube, and you must determine which of four 3D views is possible. The good news: a systematic three-step process removes all guesswork.

Cube net folding questions appear in every OC TS test and increase in difficulty based on how many faces are marked and how subtly the wrong options are constructed. Mastering the folding technique is one of the highest-value skill investments for OC Spatial Reasoning.

The examiner is testing whether you can mentally fold a 2D net into a 3D cube, track which faces end up opposite each other, and verify each 3D view by checking face relationships. Critically, the wrong options always exploit a specific misconception: showing two opposite-face symbols as adjacent, or placing a symbol with the wrong orientation.

A flat net with symbols or patterns on some faces is shown. Four 3D cube views (A–D) are given. Exactly one is a physically possible view when the net is folded. The other three are eliminated because they violate a face relationship — two opposite faces shown adjacent, or a symbol facing the wrong direction.

Best approach: Identify the three pairs of opposite faces from the net first — opposite faces can never appear side-by-side in a 3D view. Then test each answer option: check whether the visible face symbols and their orientations are consistent with the folded cube. Any option showing two opposite-face symbols as adjacent faces is immediately eliminated.

Question

A net of a cube is shown below. Study the pattern of symbols on each face of the net carefully.

Which of the following could be a possible view of the cube when the net is folded?

A $A$
B $B$
C $C$
D $D$

Decided on your answer? Check how you went below.

Correct Answer

C

Step-by-Step Explanation

Step 1: Identify the faces from the net. The net shows faces with grey and black semi-circles at various orientations. Number or label each face based on its position in the net — the centre square is typically the "base", and the arms fold upward to form the sides and lid. Step 2: Identify opposite face pairs. From the net layout, the grey and black semi-circle faces are opposite each other. This means they can never appear side-by-side in a valid 3D view. Step 3: Test each answer option. Option What it shows Problem A Grey semi-circle on side face; top face blank Top face should show the black semi-circle — but it's missing. ✗ B Black semi-circle on front-left face; adjacent face blank Adjacent face should show the grey semi-circle — it doesn't. ✗ C Grey semi-circle on top-right face with correct orientation Consistent with the folded cube — orientation and position match. ✓ D Grey and black semi-circles on adjacent faces, wrong orientations The curved edges point in inconsistent directions relative to each other. ✗ The answer is C. The two rules that eliminate wrong options every time: Opposite faces never appear adjacent in a 3D view — if the net has two symbols on opposite faces, no correct answer shows them side by side. Symbol orientation must be consistent with the fold direction — a symbol that faces "up" in the net cannot face "down" in the 3D view unless the fold specifically flips it.

Up next: Unit 14

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Hidden cell position	Deduced symbol
Top-left	Hollow left arrow (←)
Top-right	Hollow up arrow (↑)
Bottom-left	Double-headed arrow (↔)
Bottom-right	Bow-tie symbol

Option	What it shows	Problem
A	Grey semi-circle on side face; top face blank	Top face should show the black semi-circle — but it's missing. ✗
B	Black semi-circle on front-left face; adjacent face blank	Adjacent face should show the grey semi-circle — it doesn't. ✗
C	Grey semi-circle on top-right face with correct orientation	Consistent with the folded cube — orientation and position match. ✓
D	Grey and black semi-circles on adjacent faces, wrong orientations	The curved edges point in inconsistent directions relative to each other. ✗