The children in Miles’s class were about to go on a residential trip and were planning to stop for a picnic on the way. Their teacher used the opportunity this provided for the children to solve problem, showing them a pack of three nectarines she had bought and inviting them to work out:

Seven-year old Miles decided to use pen and paper to help him think about how to calculate the total number of packs they would need.

He chose to orientate his paper in ‘portrait’ format (thereby limiting the length of the empty number line he drew) but quickly understood that he would run out of space. His highly adaptive solution was to double several of the jumps that he made as he worked from right to left.

Providing a real context for mathematics helps young children’s understanding and leads to increased levels of involvement. After the children had discussed how they had worked out their calculations and their findings, their teacher bought 9 packs of nectarines to add to the food for their picnic the next day – and the additional nectarine was enjoyed by their teacher!

Early operations: development of children’s own written methods

• Calculating with larger numbers supported by jottings