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Green Cube, Yellow Cube
There are eight small cubes. Each face of each cube is to be painted either green or yellow but each cube must use each of the two colours somehow.
Work out how to paint the faces so that the cubes can be put together to make a $2$ by $2$ cube that is green all over AND can be rearranged to make a $2$ by $2$ cube that is yellow all over.
Now work out how to paint the faces to make a $3$ by $3$ green cube and a $3$ by $3$ yellow cube.
Why do this problem?
This activity is very good for giving pupils the opportunity to explore spatial properties, particularly properties of cubes. It is also an opportunity to develop their skills in perseverance and extending challenges for themselves.
Possible approach
For some pupils there will be a need to show how a cube can be coloured in different ways. So, you may find it useful to have a large cube made out of cardboard as an example, or a blank dice and coloured stickers.
Key questions
Tell me about the cubes you've got.
What colours are the faces of this cube?
How many yellows here?
Possible extension
Children could change the 'rules' slightly and decide on some simple patterns of colours that should show on each face. Like this one:
Possible support
Little cubes with small coloured squares available for pupils to choose to use may be helpful for some.