**Extending patterns and structural reasoning**

The prompt invites students to extend a sequence of operations in order to derive rules about adding and subtracting (and multiplying) negative numbers. Indeed, extending a sequence and spotting the pattern is a requisite to ‘discover’ the rule. Consequently, there is a danger that the inquiry will restrict students to inductive thinking that involves them in comparing and describing the sequences. In such a circumstance, the teacher must encourage students towards structural reasoning that explains rather than just describes. To this end, the prompt below has proved effective.