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