shape fitting | don steward

the intention of this task is that students progressively fit shapes together
to form a rectangle at each stage

a while ago, Edward de Bono devised similar shape puzzles to encourage a view that when problem solving, sometimes you need to dismantle what you have done already and start again

there is a powerpoint that reveals the shapes, one at a time

alternatively two students could work together, revealing each new shape (in a column) one at a time (after the first two) holding another piece of paper over the rest

it is important that the shapes are encountered one at a time

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circle theorems meet 0.5absinC | don steward

another idea from Martin Wilson, in Harrogate, blending the circle theorems with area

you could use normal trigonometry (by bisecting chords) but Martin’s intention is that students use the (more efficient) method of calculating 0.5absinC

resources 2, 3 and 4 present an interesting relationship between sines
that is not easy to justify(?)
without involving the trig. formula sinA + sinB = 2sin(semi-sum).cos(semi-difference)
and noting that cosD = sin(90 – D)

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