Calculation Policy

Calculation Policy

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St Blaise Church of England Primary School

Achieving together

Aims of the National Curriculum in Mathematics and at St Blaise CE Primary School

Children of St Blaise CE Primary School become fluent in the fundamentals of mathematics through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.

Children follow the acquisition of calculation progressively and over time, as set out below, to develop different methods and approaches to calculation.

They reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.

Children reason in mathematics regularly in a variety of different ways, as a part of daily teaching and in stand-alone teaching sessions. They explore, discuss and analyse solutions to different problems which are both calculation and non-calculation based.

They 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.

Children solve problems in a variety of different ways, through written, practical, visual and exploratory mathematics based activities.

Children use a variety of computing based mathematics, including websites and apps both in and out of school, to encourage problem solving and develop a range of mathematics problem solving skills.

In Reception, mathematics follows the aims of the Early learning Goals and involves providing children with opportunities to develop and improve their skills in counting, understanding and using numbers, calculating, simple addition and subtraction problems; and to describe shapes, spaces, and measure.

Progression in calculation of addition

Agreed calculation in Reception

Children develop on skills learned in Nursery and add numbers to 10 in terms 1a and 1b. From term 2a they begin to add numbers to 20.

Children begin by adding practically and then continue to add using equipment to support and reinforce the skills and concepts of addition.

They calculate and record initially using a tens frame, supported by blank numbers or with numbers in place. Counters and practical equipment reinforce the skills and concept of addition.

When secure and before the end of reception, children progress to using a number track, with clear counters to secure number knowledge.

Agreed calculation in Years 1 and 2

Children in Years 1 and 2 who have a secure understanding of the place value of tens and ones should be taught the column method for addition.

Children add the numbers in the ones column and then the tens. Children “carry” the ten underneath the calculation.

Presentation supports this method with children lining up the columns using the “one number in each square” approach. Aids such as Dienes blocks, Numicon and tens and units grids are used to reinforce place value.

Agreed calculation in Years 3 and 4

Children in Years 3 and 4 continue to acquire knowledge of place value of tens and ones, as well as knowledge of hundreds, thousands and tens of thousands.

With secure place value knowledge they continue to add larger numbers using the column method, calculation from right to left and “carrying” tens, hundreds and thousands. Children are supported by Dienes blocks and become confident to rely on this apparatus less and less, moving increasingly to mental calculation.

Agreed calculation in Years 5 and 6

Children have secured their understanding of place value and are able to securely add two or more numbers using the column method. Children apply the column method calculation to assist them in other areas of their maths learning.

Progression in calculation of subtraction

Agreed calculation in Reception

Children develop on skills learned in Nursery and subtract numbers within 10 in terms 1a and 1b. From term 2a they begin to subtract numbers within 20.

Children begin by subtracting practically and then continue to subtract using equipment to support and reinforce the skills and concepts of subtraction.

They calculate and record initially using a tens frame, supported by blank numbers or with numbers in place. Counters and practical equipment reinforce the skills and concept of subtraction.

When secure and before the end of reception, children progress to a number track, with clear counters to secure number knowledge.

Agreed calculation in Years 1 and 2

Children in Years 1 and 2 who have a secure understanding of the place value of tens and ones should be taught the column method for subtraction.

Children subtract the numbers in the ones column and then the tens. Presentation supports this method with children lining up the columns using the “one number in each square” approach. For more able children “regrouping” of tens may be taught.

Agreed calculation in Years 3 and 4

Children in Years 3 and 4 who have a secure understanding of the place value of tens and ones and hundreds, tens and ones continue be taught the column method for subtraction. Children subtract the numbers in the ones column and then the tens.

For those children who are secure in this concept subtraction by regrouping/exchanging should be taught.

It is essential that children are taught visually to exchange ten ones for a ten, before moving the ten to the tens column, using Dienes blocks or other equipment when subtracting.

Presentation supports this method with children lining up the columns using the “one number in each square” approach.

Agreed calculation in Years 5 and 6

Children have secured their understanding of place value and are able to securely subtract two or more numbers using the column method. Children apply the column method calculation to assist them in other areas of their maths learning and may have developed their own methods.

Progression in calculation of multiplication

Agreed calculation in Reception

Multiplication is referred to in terms of grouping. In readiness for Year 1 children experience practical examples of grouping. They count in 2s, 5s and 10s, using real objects, body and pairs, etc.

They experience activities such as discovering and calculating “how many pairs of eyes do 4 children have?” and “count 2 objects in each of the bowls”.

Evidence is recorded as pictures and symbols and photographs support evidence of this teaching and calculation.

Agreed calculation in Years 1 and 2

Year 1

Practical activities and visual representations of repeated addition. This stage is key in securing knowledge of multiplication as groups of. Multiplication vocabulary must be used.

Year 2

Children record multiplications they are familiar with formally.

2 x 2 = 4

Calculation of multiplication using repeated jumps on a number line or using arrays. Children may also be supported with equipment such as multi-link.

Agreed calculation in Years 3 and 4

Children in Years 3 and 4 with a secure understanding of multiplication as groups of begin to calculate multiplication using visual multiplication grids.

Leading to compact/efficient methods.

Number lines and arrays are used to support understanding and visual addition/place value methods.

Agreed calculation in Years 5 and 6

Children have secured their understanding of multiplication of larger numbers and are able to calculate two-digit multiplications using initially visual and partitioning approaches.

Moving onto compact methods once secure.

Children may also be able to complete this mentally or using jottings.

Progression in calculation of division

Agreed calculation in reception

Division is referred to in terms of sharing. In readiness for Year 1 children experience practical examples of sharing. They share practically one by one to ensure and check that their calculations are fair and equal. They share in 2s, 5s and 10s, using real objects.

They experience activities such as discovering and calculating “8 sweets are shared between 2 children, how many does each have?” and “Share the counters one by one into bowls. How many counters each?”

Evidence is recorded as pictures and symbols and photographs support evidence of this teaching and calculation.

Agreed calculation in Years 1 and 2

Year 1

Practical activities involving sharing amounts and visual representations of division. This stage is essential in securing knowledge of division as groups of. This includes sharing between groups and use of questioning.

Year 2: As per main teaching methods.

Agreed calculation in Years 3 and 4

Children in Years 3 and 4 with a secure understanding of division as groups of begin to calculate division using the bus stop method.

Children who secure this method begin to find remainders.

Agreed calculation in Years 5 and 6

Bus stop method continues to be taught with increasingly complex numbers.

Children may also be able to complete these calculations mentally or using jottings.

N Lyne January 2018