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Spatial Reasoning: Folding, Rotating & Views

Maths · Y4 OC Prep
Year 4 OC
Lesson Guide
Explanation
A classic folding question: a 10×10 paper is folded in half twice (making a 4-layer stack), some squares are cut from the stack, and the paper is unfolded — what area remains? The key: a cut through the stack removes one square from EVERY layer. Two folds = 4 layers, so each cut square costs 4. Cut 7 from the stack → 28 gone → 100 − 28 = 72 cm2. Folds multiply: once = 2 layers, twice = 4, thrice = 8.
Your Turn
A 6×6 paper folded once (2 layers) has 5 squares cut from the stack. Unfolded area? Check: 36 − 5×2 = 26.
Watch Out
Count the FOLDS to know the layers. And cuts on the folded EDGE behave differently — OC usually keeps cuts inside, but check the picture.
Explanation
Another folding question: one fold in a triangle of paper — which shape could NOT result? A single fold picks a fold line and mirrors everything on one side across it. So test each option: can one straight line + a mirror-flip produce that outline from this triangle? Folding never makes the paper BIGGER, and some outlines need two folds. It's a NEGATION question ('could not') — so eliminate the possibles; whatever survives is your answer.
Your Turn
Fold a real paper square once. Can you make: a rectangle? a triangle? a pentagon? Check: yes (edge to edge), yes (corner to corner), yes! (fold a corner partway — 5 sides).
Watch Out
On 'could NOT' questions, you're hunting the impossible one — catching yourself picking a possible shape is the #1 error.
Explanation
Glued-cube questions are a test favourite. The accounting: each cube has 6 faces; every glued JOIN hides 2 faces (one on each cube). Nine cubes in a 3×3 slab: 54 faces total; the grid has 12 joins (6 horizontal + 6 vertical), hiding 24 — so 30 are visible when you pick it up, and 24 can never be seen. The formula: visible = 6 × cubes − 2 × joins. Everything hangs on counting joins carefully — draw the grid and mark them.
Your Turn
Four cubes in a 2×2 square: joins? Visible faces? Check: 4 joins → 24 − 8 = 16.
Watch Out
'Can she NOT see' vs 'CAN she see' — same setup, opposite number. Read which side of the count they want.
Explanation
A typical symmetry question: shade squares so a dashed line becomes a line of symmetry, and give the answers as GRID REFERENCES. The mirror rule: each shaded square's twin sits at the same distance from the line, on the opposite side, in the same row. Count columns to the line, then the same count past it. Two skills chained: reflect correctly AND name the squares correctly (letter-then-number). Check by 'folding' the grid in your mind — every shaded square must land on a shaded square.
Your Turn
On paper, draw a 6-wide grid, shade B2, and mirror across the line between columns 3 and 4. Where is the twin? Check: E2 (B is 2 from the line; 2 past it is E).
Watch Out
Only the DISTANCE to the line flips — the row never changes in a vertical-line reflection.
Explanation
OC style: Ben walks 25 m north, 40 m east, 25 m south, 10 m east — how far from his start? Don't trace step by step; BALANCE the directions: north 25 vs south 25 cancels completely; east 40 + 10 = 50 with no west at all. He's exactly 50 m from his start. Opposite directions cancel — subtract them, and the leftovers tell you the displacement. (The trap answer 100 is the TOTAL distance walked — that's a different question!) Quiz and exercises now!
Your Turn
Walk: E 50, N 20, W 30, S 20. How far from start? Check: E−W = 20, N−S = 0 → 20 m.
Watch Out
'How far FROM THE START' ≠ 'how far did he walk'. Displacement vs distance — OC options include both numbers.
Step 1: Introduction
Step 1 of 5
Fold, cut, unfold A 10×10 paper is folded in half, then in half again (now 5×5, four layers). Squares are cut out of the folded stack and thrown away. KEY FACT: every cut square removes FOUR squares (one per layer!). Cut 7 squares from the stack → unfolded paper lost 7 × 4 = 28 squares. Area left = whole − removed: 100 − 28 = 72 cm2 ✓ Fold once = 2 layers. Twice = 4 layers. Three times = 8 layers. Whatever you do to the stack happens to EVERY layer.
One fold: possible results start: right triangle CAN make: smaller triangle ✓ (fold corner to corner) trapezium ✓ (fold a corner down) CANNOT make: anything BIGGER, or shapes needing two folds One fold takes part of the shape and mirrors it across the fold line. Test each option: "can ONE straight fold line produce this outline?" Eliminate the impossible ones — the leftover option is the answer. 'Could NOT be the result' — negation questions reward elimination!
Cube faces: hidden by the glue 9 cubes glued in a 3×3 slab Total faces: 9 × 6 = 54 Glued joins in a 3×3 grid: 12 Each join hides 2 faces: 24 hidden Visible (from all sides): 54 − 24 = 30 "Cannot see" = the 24 glued ones Method: total faces − 2 × (number of glued joins). Count joins carefully: a 3×3 slab has 6 + 6 = 12 joins.
Mirror the pattern given squares mirrored squares Each square's mirror sits the SAME distance from the line, opposite side, same row. Count columns to the line, count the same again past it.
Ben's walk ✗ end N 25 → E 40 → S 25 → E 10 N−S: 25 − 25 = 0 E: 40 + 10 = 50 E → 50 m from start Don't trace — BALANCE: total N vs S, total E vs W. The leftovers are the answer.
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