Today’s problem — free all day, every step. Every day has one.
Canvas — cut into a square and eight triangles
Ravi has a square piece of canvas of side 31 cm. He cuts along the dotted lines to get one small square of area 289 cm² and 8 identical right-angled triangles. Triangle XYZ is one such triangle. Find the length of XY.
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MathBrush is being tested with a few parent groups, and every solution on the site is open to them — one household, all children. If you were given a code, it goes in once and this device remembers it.
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65 worked examples are free without a code, two from every pattern. No account, either way.
The pattern behind it: Seeing it move
Work out where the pieces land after a fold, cut or stack.
In this one. The same two triangle legs give both a sum and a difference: their sum is the outer square’s side, while their difference is the small square’s side.
How to spot it
Words like 'folded', 'cut along the dotted line' or 'stacked' appear beside a shape, and the question asks for a length or angle that only makes sense once the pieces are in their new positions.
Common mistake
Children try to calculate the answer before working out where the pieces actually end up, skipping the visualisation step that the whole question depends on.
Try one like it
Challenging Devi's square — eight triangles Devi has a square of paper of side 23 cm. She cut along the dotted lines to get one small square of area 49 cm² and 8 identical ri…The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.