Consecutive sums/teaching approach

Tackling an extended problem is difficult. By definition, a problem is something that you do not immediately know how to solve, so learning how to solve something unfamiliar is not straightforward.

This lesson gives pupils an opportunity to engage in mathematical thinking⁽ⁱ⁾ through working on developing their problem solving⁽ⁱ⁾ skills using a problem that is accessible but which has a number of interesting features (such as the link between diagrammatical and numerical ways of presenting the problem).

This plan gives several ways of presenting and visualising⁽ⁱ⁾ what is the same underlying task. It should be useful for teachers to compare these different presentations and either to select the one that they feel will be most useful for their pupils or to explore ways of allowing the pupils to make links between them. The assessment⁽ⁱ⁾ ideas, using other pupils solutions from the nrich website (nrich.maths.org) are applicable to other problems and situations too.