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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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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.

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Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

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.