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All in the Mind

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface of the water make around the cube?

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Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

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Instant Insanity

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Rolling Around

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.