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Make a skeletal cube.
How many ways are there from one vertex, S to another, F?
Experiment with different ways of recording the journeys made.
Thread cotton from each vertex to opposite midpoints.
Try to anticipate what will happen as more and more threads are attached.
Finally what do you get?
Attach rods to vertices that are opposite.
What will happen when the cube is spun?
Spin between the fingers and see - were you right?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?