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P6 Seeing it move

Today’s problem — free all day, every step. Every day has one.

Kite paper — triangle LMN

Farhan has a square kite paper of side 28 cm. He cuts along the dotted lines to get one small square of area 16 cm² and 8 identical right-angled triangles. Triangle LMN is one such triangle. Find the length of LM.

One step of the worked solution to Kite paper — triangle LMN, drawn in pencil.
7 steps, drawn in pencil

See all 7 steps

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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 side, while their difference is the small square’s side.

ABCDEFa straight strip of three: the two ends land opposite

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 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 iden…
All 9 with this pattern →

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.