👁️ Spatial Thinking
Visualise shapes, views, folds, and arrangements
👁️ Seeing in your mind
Spatial thinking is about imagining how shapes look from different angles, how they fit together, and what happens when you fold, rotate, or flip them.
🧊 Views from different angles
A 3D object looks different from the front, back, top, and sides. The back view is like a mirror of the front — left and right swap, but up and down stay the same.
Try it: Hold your hand up, palm facing you. Now turn it around. Your thumb switches sides! That's what happens with "from the back" problems.
📐 Folding and flaps
When a piece of paper folds over, the content on the flap mirrors along the fold line. Transparent windows let you see through to what's underneath.
Key insight: When a left flap folds right, the left column of numbers now sits on top of the right column — but reversed left-to-right.
🧩 Fitting pieces together
When filling a shape with puzzle pieces:
- Count the total squares in the shape
- Count the squares in each piece type
- Start with corners and edges — they're the most constrained
- The biggest pieces first = fewer total pieces needed
📏 Rectangle-to-square puzzles
If a rectangle (length 27) is cut into two pieces that form a square, the square's area = rectangle's area. If width = w, then 27 × w = side². Also, the side of the square must be related to both 27 and w. Since 27 = 1.5 × 18, and 27 × 18 = 486... but actually, the zigzag cut means the square side = 18 and the rectangle is 27 × 18. Check: we need 27 × w = s², and the pieces must rearrange. The answer is 18 cm.