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This activity investigates how you might make squares and pentominoes from Polydron.

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Multilink Cubes

If you had 36 cubes, what different cuboids could you make?

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Cereal Packets

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

It Figures

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Why do this problem?

This activity makes interesting use of multiplication facts. The challenge can easily be used without the connection with fractions and by just dealing with the denominators.

Key questions

Tell me about the numbers you've found.

Possible extension

For more advanced/experienced/older pupils, challenge them to find the number of different combinations according to:-
the number of fractions that are allowed to be multiplied together;
the range of numbers that are allowed to be used.
If you pursue this you may come across the addition of triangular numbers [to make pyramid numbers] and then the addition of these [pyramid] numbers, and so on!

Possible support

Calculators may be supportive for those pupils without fast recall of facts.