This guidance paper details the key mental and written methods for calculations that are taught within Gunter School. It has been written to ensure consistency and progression and reflects a whole school agreement.
Although the focus is on written methods by the end of Key Stage 2, it is important to recognise how fundamental the ability to calculate mentally is. Mental methods are first introduced at Foundation Stage and develop through very regular planned opportunities throughout our school. Mental calculation is complementary to, and not separate from, written calculation methods. In every written method there is an element of mental processing.
Our children are introduced to calculations through a wide range of practical, concrete, oral and mental activities. As they begin to understand the underlying ideas they develop ways of recording to support their thinking and calculation methods, and learn to interpret and use the signs and symbols involved. Over time our children learn how to use models and images, such as empty number lines, to support their mental and informal written methods of calculation.
As children’s mental methods are strengthened and refined, so too are their informal written methods. These methods become more efficient and succinct and lead to efficient written methods that can be used more generally.
Our general aims are that by the time our children leave Gunter School they:
have a secure knowledge of number facts and a good understanding of the four operations;
are fluent in the fundamentals of mathematics and are able to use their knowledge of number facts to carry out basic calculations mentally;
can reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language;
make use of mathematical diagrams, models and informal notes as aids to solving problems;
can solve problems by applying their mathematics to a variety of problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions
have efficient, reliable, compact written methods of calculation for the four operations
‘Can I do this in my head?’
‘Can I do this in my head using drawings or jottings?’
‘Do I need to use a pencil and paper procedure?’
Mental methods of calculation
Early practical, oral and mental work must lay the foundations by providing children with a good understanding of how the four operations build on efficient counting strategies and a secure knowledge of place value and number facts. Later work must ensure that children recognise how the operations relate to one another and how the rules and laws of arithmetic are to be used and applied. Ongoing oral and mental work provides practice and consolidation of these ideas. It must give children the opportunity to apply what they have learned to particular cases, exemplifying how the rules and laws work, and to general cases where children make decisions and choices for themselves.
The ability to calculate mentally forms the basis of all methods of calculation. A good knowledge of numbers or a ‘feel’ for numbers is the product of structured practice and repetition. It requires an understanding of number patterns and relationships, use of models and images and the application of acquired number knowledge and skills. Secure mental calculation requires the ability to:
recall key number facts instantly – e.g. all +/- and facts to at least 20 (Year 2), sums and differences of multiples of 10 (Year 3) and x facts up to 12 × 12 (Year 4);
use taught strategies to work out the calculation – e.g. recognise that + can be done in any order (commutative), (Y1), partition 2-digit numbers in different ways including into multiples of 10 and 1 and + the 10s and units separately and then recombine (Y2);
understand how the rules and laws of arithmetic are used and applied – e.g. to +/- mentally combinations of 1-digit and 2-digit numbers (Y3), and to calculate mentally with whole numbers and decimals (Y6).
The Calculation Policy sets out the progression in written methods of calculation that highlights how children should move from informal methods, to expanded methods, to a compact written method for each of the four operations.
The aim is that by the end of Key Stage 2, the great majority of children should be able to use an efficient written method for each operation with confidence and understanding.
‘Standard’ written methods are compact and consequently help children to keep track of their recorded steps. Being able to use these written methods gives children an efficient set of tools they can use when they are unable to carry out the calculation in their heads or do not have access to a calculator. We want our children to know that they have such reliable, written methods to which they can turn when the need arises.
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