Three Sets of Cubes, Two Surfaces

Age 7 to 11

Challenge Level Yellow star

Three Sets of Cubes, Two Surfaces

This can be used as a follow-on from Two on Five.

You have interlocking cubes of three different colours - 2 of one colour, 3 of another colour and 4 of the third colour.

It could look like this;

This is slightly different from Two on Five but is seen as an extension for some pupils. You might like to go there first!
The nine cubes are to be connected in the usual way with the following rules being applied.
The two yellow cubes are not allowed to touch the wall or floor surfaces
The Three blue cubes must touch one surface only, the wall or the floor
The four red cubes must touch both wall and floor surfaces

Here are two examples that obey the rules;

See what others you can find.

How many will there be?

At some point ask yourself "I wonder what would happen if I ...?"

Possible approach

As this is designed for the highest attaining, it might be presented as on the website or in a one-to-one situation, encouraging discussion between adult and pupil. The pupils may need access to a computer program for drawing solutions.

Key questions

Tell me about what you have found.

Can you describe the ways that you arrived at these shape arrangements?

How did you construct these on the computer?

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners

Three Sets of Cubes, Two Surfaces