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How do I teach mental and written calculation strategies in primary (KS1 & KS2) or secondary (KS3) mathematics?

Created on 03 October 2011 by ncetm_administrator
Updated on 05 September 2013 by ncetm_administrator


How do I teach mental and written calculation strategies in primary (KS1 & KS2) or secondary (KS3) mathematics?


The teaching of calculations is a core part of the curriculum for primary pupils and this extends into secondary schools too. By calculations we mean the four operations – addition, subtraction, multiplication and division. These four operations can be used to calculate with positive and negative numbers, fractions and decimals, numbers in standard form and indices.


In the past, the NCETM has provided funds to teachers and networks to explore effective teaching strategies. Take a look at the reports from these Funded Projects, all of which focus on some aspect of strategies for teaching calculations. For example, you could read about how Hexham Middle School developed their own CPD programme to raise standards in the teaching of division.

A wide range of research papers (many free to read) and articles about teaching calculations are available through the NCETM/ BEI Research Gateway.

Articles about teaching calculations can always be found in the NCETM’s sector magazines. If you are a registered user, then the latest editions arrive directly into your email inbox. But the archive also provides a good opportunity to browse.

And why not take a look at this document, that considers common misconceptions in addition, subtraction, multiplication and division.

Discussion Point

Should you teach a range of calculation strategies to all pupils or be selective?

Firstly, read this research paper about Calculation Strategies Used by Y5 Pupils which can be found on our Research Gateway to help you inform your thoughts.

Many pupils find division difficult to learn and understand. Why do you think this might be?

Look at this forum discussion about division to help you inform your thoughts.

Do you feel confident about what progression in understanding is required before teaching calculation strategies with fractions?

Look at this Mathemapedia entry on Preparing to Teach Fractions.

Explore a piece of mathematics

Have a go at multiplying the Ancient Egyptian way.

Use this link in the Primary Magazine Issue 4 to help you.

Learning from each other

It has been said by some recently that ‘teachers learn best when they learn from each other’. If you know of another link to an activity or resource on the NCETM website that you think would be useful or appropriate for readers of this guidance, please use the comments box below to let us and them know of your idea.

Courses and Networks

We have many courses and networks available, search in our Professional Development Calendar to find a suitable course or network.

Personal Learning

“Activity by itself is not enough; it is the sense that is made of it that matters” (DRIVER, R. (1983) The Pupil as Scientist?, Milton Keynes, Open University Press.

For the things you have tried out for yourself in your own classroom to become useful pieces of professional learning, there is a need to capture them, reflect upon them and remark on them. The NCETM Personal Learning Space (PLS) allows you to do this.

  • Use My Learning Journal to collect your thoughts and reflections as well as to log actions; documents can be attached to your entries. You could do this now by visiting your own PLS.
  • Use My Favourites and Notes to take note of and organise interesting things you have found (like this page) and want to return to easily in future.
  • Use the Sharing and Contacts facility to share elements of your PLS with colleagues, selecting them from your own list of contacts
  • Use the “Request a reminder” function

Find out more details of these and other functions of the PLS.




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