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Child's Play

Age 7 to 11
Challenge Level

Child's Play

A toy has a regular tetrahedron, a cube and a base with triangular and square hollows.

If you press the start button and fit the tetrahedron into the triangular hollow or the cube into the square hollow, it rings a bell.

It only rings the bell again if you then fit the tetrahedron or the cube into its hollow in a different way from any you have done before.

When you have fitted the shapes into the hollows in all the possible ways, the game is complete.

How many times does the bell ring in a complete game?

Why do this problem?

This problem encourages children to consolidate their knowledge of the properties of regular 3D shapes.

Key questions

Can you put that shape in the hollow in a different way?
How many faces does that shape have?
Can you fit the same face in the hollow in a different way?

Possible extension

Some learners may like to consider a similar toy involving all five platonic solids. How many times does the bell ring in a complete five-solid game?

Possible support

Using real solid shapes will help children work on this problem.