A low-floor, high-ceiling investigation about combining additions of two coprime numbers.

Encourages conjecture, justification, and generalisation, and builds into algebra.

Forming and understanding basic expressions such as:

$n + 4$ and $n + 7$ .

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

2. You may wish to explain the basic premise of the investigation perhaps modelling how you could deduce reachable squares in the first (3, 7) example of the game.

3. Otherwise pupils should be able to work through the tasks at their own pace. On their sheet, pupils have been instructed to check their answers to questions 6 and 12 with their teacher.

*It is suggested that you print off a copy of the teacher sheet for your reference whilst pupils work.