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Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

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All in the Mind

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

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Reflecting Squarely

In how many ways can you fit all three pieces together to make shapes with line symmetry?

Rolling Around

Age 11 to 14 Challenge Level:

How about asking pupils to imagine this "in their mind's eye" - no paper, no body language and lots of discussion?

Alternatively this can be tackled through a practical activity involving a shape and a coin.

It is not necessary to be able to calculate the circumference of a circle.