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Maths Calculation Policy

Written Methods of Calculation Policy September 2019

The National Curriculum for mathematics aims to ensure that all pupils:

  • become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems
  • reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
  • can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

This written calculations policy sets out how we teach the progression of children’s use of written methods of calculation.

Calculation strands of programmes of study for each year group as specified in ‘The national curriculum in England’, framework document (updated July 2014)

Calculating (Statutory Requirements)

  • Year 1 
  • Addition and Subtraction

    • read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs
    • represent and use number bonds and related subtraction facts within 20
    • add and subtract one-digit and two-digit numbers to 20, including zero
    • solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = - 9.

    Multiplication and Division

    • solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.
  • Year 2 
  • Year 3 
  • Year 4 
  • Year 5 
  • Year 6 

The Stages

It is recognised that prior to all written stages that a great deal of unwritten foundation work will have taken place and children gain a basic grasp of number. It is important that children have a clear and firm understanding of one stage before progressing fully to the next stage. In most cases it is vital that all stages are taught in order and that children have a secure understanding of the process before moving on. This will ensure children should always have a “fall back” written calculation method when faced with any problem. The very beginnings of calculation involves transferring the abstract concept of number to the physical and then to written numbers. Formation of numbers must be taught and should be reflected in the fonts that are used in school.

Early Understanding of Number

In the early stages (typically in Early Years, moving into Year 1) children should be introduced to numbers in a variety of ways. These will include:

Numicon Objects for representation
Number tracks and lines Number lines – 0 to 10 and 0 to 30
Introduction to the 100 square Children should be taught to look for patterns at every opportunity

Numbers as labels

The language of addition and subtraction (e.g. 6 and 4 more...)

Using Number Lines

The number line is a very useful tool to help all operations and should be introduced to children in a number of settings, both vertically and horizontally, numbered and blank. Bead sticks, metre rules, tape measures etc. can all help this introduce the concept.

It is important that children are able to distinguish between numbers that are set in place on the line and any calculations taking place. In order to ensure fidelity any numbers written below the line relate to set numbers on the number line. Those numbers written above the line should relate to calculations (e.g. an arrow +1). It is important to teach children to plan their calculation (estimate) in order to ensure sufficient space is allocated. This may involve steps in both directions.

number line

Mental Strategies

It is vital that mental strategies accompany written calculation strategies throughout the school. Children should be taught that mental strategies are different from compact written methods. Vital elements of this toolkit include a secure knowledge of number bonds, place value, partitioning and chunking. Counting strategies (age appropriate) should take place in all years to include counting on and backwards in various steps and starting points along with fractions and decimals. Times table facts should also be learned.