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Reasoning about the number of matches needed to build squares that share their sides.

Little Boxes

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Two Squared

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?


Age 7 to 11
Challenge Level

Make a skeletal cube.

How many ways are there from one vertex, S to another, F?

cube made of 8 balls and 12 straws with one vertex marked as S and diagonally opposite vertex as 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?

cube made of balls and straws with cotton strings drawn in

Attach rods to vertices that are opposite.

What will happen when the cube is spun?

Spin between the fingers and see - were you right?