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Can you make five differently sized squares from the interactive tangram pieces?


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


Make a cube out of straws and have a go at this practical challenge.

Creating Cubes

Age 7 to 11
Challenge Level

Creating Cubes

Arrange nine red cubes, nine blue cubes and nine yellow cubes into a large $3$ by $3$ cube.

No row or column of cubes can contain two cubes of the same colour.

Why do this problem?

This activity is very good as a spatial challenge. Often having visual clues prompts pupils to have a go and helps them to make sense of the problem. This task also encourages them to be curious and wonder if it is possible to arrange cubes in this way.

Possible approach

You can lead up to this challenge by starting with a cube using two colours first. Having plenty of interlocking cubes available for children to try out their ideas will be essential. You could also begin by asking children if they think it is possible to create a cube with no two colours in the same row or column, using questions such as "I wonder ...? or 'Could I ...?' 

Key questions

How could you start the cube?
Is there only one way of doing it?
Have you all got the same solution?
Are some of the solutions similar?

Possible extension

Some children will be able to explain how they solved the problem. You could ask them to predict and then test if this is possible for a larger cube.

Possible support

Working in pairs would offer support for learners and also give them the opportunity to talk through their strategies.