The Isles of What If…? is an inquiry approach to teaching maths in primary schools. It views mathematics as a continuous and collaborative game of asking ‘what if…?’ questions to create rules and investigating the consequences. Once created, the learner is invited to imagine that the exploration that follows is akin to exploring an island in search of treasure. Each island represents a set of ‘what if…?’ questions.

For example, we might ask, what if we wanted to create an addition with an answer of 5,555 and what if, for each unique digit that we used in the addends, a point is scored. What possible points values can be scored?

The children are assisted through the inquiry through the use of a range of reasoning skills that are clearly defined across six posters.

Whilst we begin an inquiry in an accessible focused way, only focusing on a small area of possible exploration (the Landing Spot), through further ‘what if…?’ questions, we can expand our investigation.

For example:

- What if we used decimals?
- What if we used more than two addends?
- What if we had a different target number? Would it be easier to score points?

These further ‘what if…?’ questions represent a new area of search, a different part of the island or possibly a new island completely. Once children start asking their own ‘what if…?’ questions, with the teacher the arbitrator of genuine mathematical investigation, children see maths as an ever-expanding world full of possibilities.