Because mathematics is sometimes messy and ambiguous, it is important to help children recognise these aspects of mathematics. Mathematics is also logical and conveys precise meanings. Take, for example, the notion of fallen leaves covering an area of ground. The leaves will have fallen in a ‘random’ fashion. Some leaves will overlap and there will also be gaps between them. This is an important discussion point in order to raise children’s awareness of the need for using like units in order to measure an area and convey this measurement to others. This leads eventually to using standard units that will cover the surface without gaps. This process of moving from a mess to a tidier structure is the process of formalising mathematics, of making sense of the world; this is the basis of mathematical modelling.

The two ideas offered here are aimed at children's understanding of area and perimeter. The essential ingredients are that the tasks, through their initial simplicity, are accessible to children at Key Stage 2 and above. Within the tasks we offer, there exist opportunities for ever-more complex and differentiated outcomes.