An investigation where pupils explore how to maximise a product given a fixed sum. The activity requires pupils to tabulate results, consider a geometric context (area) and then interpret their findings.

Area of a rectangle.

1. Distribute one copy of A3 sheet to each pupil, or pair if preferred.

2. Important: explain the basics of the investigation to pupils in that we are trying to find which split of numbers maximises a product for a given sum, but let the pupils discover the key insight themselves.

3. Pupils can then work through the task at their own pace.