Milking maths: Problem solving

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By John Dabell — Year 4 teacher at Forest Fields Primary and Nursery School in Nottingham

Encourage children to talk about shapes and numbers by breaking down sums in to manageable chunks


This is the third article in my ‘Milking maths’ series that aims to encourage children to develop an eye for numbers and shapes and all that they have to offer. When using and applying maths in the context of an investigation or puzzle, there are always maths moments there for the taking that extend beyond the actual problem that needs solving – in essence, opportunities to ‘milk’ the maths. It is also something that children can practise so that they see maths within maths – exploring properties and characteristics of numbers and shapes. They can begin to ‘see’ a sum and think around it, inside it and underneath it. This month, the focus is problem solving. The activities show children how to break sums down and give them the opportunities to talk about and discuss their reasons and conclusions.


  1. Getting started
  2. Magic 12
  3. Digit swaps
  4. New shapes
  5. Peri-surprise

1. Getting started

Mathematics Framework: Year 6, Block E – Ma1. Learning objective: Explain reasoning and conclusions, using words, symbols or diagrams as appropriate. Children’s learning outcome, ‘I can talk about how I solve problems’.

Let’s look at some magic rows and columns as a starting point. This problem-solving activity involves putting numbers in empty boxes so that the sums of the rows and columns are the same. This means adding and manipulating different combinations of numbers. For example, ask the children to place the numbers 1, 2, 3, 4 and 5 in squares to form a cross so that they add up to nine vertically and horizontally (answer shown below).

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