This investigation begins with opportunities to explore the factors of 36 through rectangular boxes. Note that 36, as well as being a square, is also a triangular number so that pupils can be encouraged to explore triangular boxes too.

Supply squared and (if possible) isometric paper.

When investigating the arrangements of the colours counters could prove useful. These can be stacked when the sweets are in layers.

Get pupils to find good ways of recording their work so that it can be displayed and allow comparison with other pupils' solutions. Take the opportunity to have pupils explain their strategies.

This investigation can be extended in several ways:

When placing the sweets in layers try cuboids or pyramids or ...?

Use triangular or hexagonal cells, rather than squares, for the sweets.

Draw 'boxes' for different numbers, to help when exploring factors, rectangular, square and triangular numbers among others.

Try arranging the sweets with only 3 differently coloured sweets in each box, 12 of each colour.

Explore the '4 colour map problem'. Can they draw a 'map' for which it is necessary to have more than 4 colours so that no two 'countries' which share a border are the same colour?