Section 3: Ways to solve number problems

Key Focus Question: How can you develop pupils’ problem-solving skills using number problems?

Keywords: meta-cognition; differentiation; tasks; creativity; ‘thinking about thinking’; problem solving; number

Learning Outcomes

By the end of this section, you will have:

  • used strategies to explore pupils’ ways of solving mathematical problems;
  • distinguished between deep and superficial features of mathematical problems;
  • used techniques to develop thinking about thinking in your pupils.


Problem solving is an interesting way to develop your pupils’ mathematical thinking. Pupils have to work out what calculations need to be done before they can find the answer. This means sorting the information given to establish what it is they need to find out and how to do it.

This will help them make explicit their mathematical thinking, and understand and recognise the deep features of a mathematical problem. You might find it useful to think of why problem solving is important. Some reasons are given in Resource 1: Why problem solving is important.

1. Helping pupils think