Calculation Policy

1

Addition

Beginning Developing Establishing Children begin to add/count on mentally using rhymes and begin to record in the context of play or practical activities e.g. Recording with marks, stamps or objects How many ways can you put 5 apples in 2 bowls. Use the language of 1 more by adding one to a group e.g. tower of cubes Use Numicon to investigate 1 more

Adding stories and role play, encouraging use of language for addition.

Use a numbered large number line (number tiles) to identify one more.

Adding by counting on. First by finding 1 more then in steps of 1.

Children can count on from the first number using fingers, objects, themselves etc.

Teacher should model drawing jumps on the numbered number line to support understanding of the mental method. Children are encouraged to use a number square to add by counting on, initially in units, then in tens and units. Example: 8 + 7=15

Children add single digit numbers. Children learn to count on in tens and ones on the number line and 100 square. Add 9 and 11 by adding 10 and adjusting by 1. Children add 2 digit numbers on the hundred square by counting on in tens down the hundred square and then across in ones. Example: 48 + 36=84

They then draw blank number lines and draw how many they are counting on.

Then helping children to become more efficient by adding the units in one jump (e.g.by using the known fact 3+5= 8). Followed by adding the tens in one jump and the units in one jump.

Calculation Policy

2

Children combine 2 groups of objects in practical activities in real contexts and role play 3 and 2 makes 5

Learn that addition can be done in any order and are taught that it is more efficient to put the larger number first. Children need to understand the concept of equality before using the = sign. Use bucket balances and number balances to explore the meaning and use of the = sign.

Calculations should be written either side of the equality sign so that the sign is not just interpreted as the „answer‟. E.g. 2 =1+1 and 2+3 = 4+1 Children begin to record addition number sentences using + and =. Missing numbers need to be placed in all possible places within the number sentence. 4+ = 7 + 2= 8 Also cover up operations as well as numbers. Use addition in terms of „how many more‟ to calculate the difference. Children learn number bonds to 10. Use a variety of visual models and resources including beads, cubes and Numicon.

Continue with using a range of equations, but with larger numbers such as multiples of 10. 70 + Children begin to round up to the nearest multiple of ten. Find the difference by counting on with larger numbers on the number line.

Know that subtraction is the inverse of addition and use known number facts to calculate mentally.

Begin to add by bridging through 10 where necessary. Children begin to add larger 3 digit numbers by partitioning and re-combining into hundreds, tens and ones.

Calculation Policy

3

Children begin to add 3 single digit numbers, by looking for pairs of numbers or doubles to aid mental calculation.

Children are taught to use the hundred square to find 10 more by looking at the number underneath.

Children begin to learn place value of 2 digit numbers to add in tens and ones.

12+27 = 10 + 20 = 30 = 2 + 7 = 9 = 30 + 9 = 39 extend to 112+ 27 = 100 + 10 + 20 = 130 = 2 + 7 = 9 = 139

Example: 47 + 76 40 + 70 = 110 7 + 6 = 13 110 + 13 = 123 which is then recorded in a shorter form below 47 + 76 = 110 + 13 = 123

Partitioned numbers are then written under one another:

Example: 47 = 40 +7 76 70 + 6 110 +13 =123

Adding nearest multiple of 10, 100, 1000 and adjusting. 24+19=24+20-1 +20

24 43 44 -1

Children use place value cards (arrow cards) to represent partitioning of a 2 digit number.

Calculation Policy

4

Subtraction

Beginning Developing Establishing Begin to record in the context of play or practical activities e.g. counting rhymes that count back. Remove objects from a group „I have 5 apples and a take one away how many are left?‟ Use the language of 1 less by taking 1 from a group e.g tower of cubes In take away stories such as role play encouraging use of language of subtraction.

Use a numbered, large number line (floor tiles) to identify one less. Picture representation of a subtraction sentence. For example: We had 5 balloons, we lost 2.

cross out 2 ‘Five take away two is three‟. 5 – 3 = 2 (modelled by teacher)

Counting back in steps of 1 then 10. Identify missing numbers in a number line. Adding by counting back. First by finding 1 less then in steps of 1. Children can count back 1 from the first number using fingers, objects, themselves etc.

Teacher should model drawing jumps on the numbered number line to support understanding of the mental method. Example: 15 – 7 = 8

Learn that subtraction must start with the larger number and count back the smaller number. Model on a 100 square: Example: 15 - 7=8

Children subtract single digit numbers, Children learn to count back in tens and ones on the number line and 100 squares. Subtract 9 and 11 by subtracting 10 and adjusting by 1 using the hundred square. Children subtract 2 digit numbers on the hundred square by counting back in tens up the hundred square and then back in ones. Example: 74-27=47

They then draw blank number lines and draw how many they are counting back. Example: 74 – 27 = 47

This would then progress to jumping in tens then ones. Subtract by bridging through 10 where necessary. Bridging through ten can help children become more efficient.

Calculation Policy

5

Children begin to record subtraction number sentences using - and =. Missing numbers need to be placed in all possible places within the number sentence.

Also cover up operations as well as numbers. Children should be taught to find the difference using subtraction.

8- 5=3 Children should experience difference in a context where quantities are compared and vocabulary such as more/less is used.

Continue with using a range of equations, but with larger numbers such as multiples of 10. 100 - = 40 Find the difference by counting on with larger numbers on the number line.

Know that subtraction is the inverse of addition and use known number facts to calculate mentally.

Children begin to subtract larger 2 digit numbers by partitioning the second number only. Keeping the first number whole. 37 – 12 = 37 – 10 = 27 = 27 – 2 = 25 Extending: Counting on method The mental method of counting up from the smaller to the larger number can be recorded using number lines. Children usually find it easiest to make the first jump to the next 10. The number of jumps will vary. For some children, they will find it comfortable to make only two jumps along the line. Others will need more. Children usually find it easiest to make the first jump to the next 10.

Calculation Policy

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Number lines and Numicon tiles are used to compare numbers and find the difference. Children are taught to use the hundred square to find 10 less by looking at the number above.

Children begin to subtract to solve simple word problems.

Begin to recognise that subtraction is the inverse of addition.

Example: 74 – 27=47

Others will need less jumps, especially when they become confident with the method.

For 3 digit numbers: Example: 326 – 178=148

leading to:

Calculation Policy

7

Multiplication

Beginning Developing Establishing Children begin to count in groups of 2, 5 and 10 using objects, recite counting, songs and rhymes. They count related groups of the same size in games and practical activities.

Links are also made to problem solving activities.

Children will develop their images of

multiplication from Foundation Stage and

on through Year 1 with the use of practical

equipment and activities so that they see

multiplication as increasing numbers by

repeated addition of the same number.

Children group objects in 2, 5 and 10. Model counting in groups using a counting stick.

Children start to use visual images as repeated addition.

use Numicon 2 + 2 + 2 + 2 + 2 = 10 Model this as jumps on a number line.

Children use repeated addition number sentences to calculate multiplication; 4x3 = 4+4+4 Say “you have 4, three times” Begin to show visual representation of this using an array. Successful written methods depend on visualising multiplication as a rectangular array. It also helps children to understand why 3 X 4 = 4 X 3

Explore the fact that multiplication, like addition, can be done in any order. Children are taught to calculate multiplication questions by jumping in groups on a number line.

Calculation Policy

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Practically double numbers to 10 and link this with multiplying by 2.

use cubes and Numicon

Solve practical problems involving multiplication such as; There are 4 bikes. Each bike has 2 wheels, how many wheels is that?

This number line shows “3, 4 times”: 3 x 4 = 12 Children begin to record multiplication number sentences using x and =. They are then taught to develop an understanding of the families of numbers to work out the missing numbers. = Use multiplication to solve more complex word problems.

Calculation Policy

9

Division

Beginning Developing Establishing Practical division as grouping e.g. buttons, beads etc Children share objects practically into equal groups e.g. “Share the cakes between the three bears. How many cakes will they each have?”

Links are made to problem solving activities.

Children will develop their images of division

through sharing and grouping in practical

activities in Foundation and Year 1 so that they

see dividing as repeated subtraction, sharing

amounts or objects equally and grouping sets.

Halving to match doubling and understand it is the

opposite. Sort a set of objects by grouping equally into 2‟s, 3‟s, 4‟s etc. Begin to use practical grouping to solve word problems. e.g. “There are 12 daffodil bulbs. Plant 3 in each pot. How many pots are there?”

Children continue to use grouping of objects practically and relate to real life situations. Children begin to relate division to fractions of numbers and shapes e.g. ½ and ¼ is the same as dividing by 2 and dividing by 4 respectively. There are 6 sweets, how many people can have 2 sweets each?

Division as an array

Introduce division as repeated subtraction.

Division ITP

Then begin to divide a number by counting back in equal steps model this on a number line.

Calculation Policy

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Children begin to record their practical division as a written calculation using ÷ and = in a number sentence. Children learn that division is the inverse of multiplication. They are then taught to use the multiplication and division facts to work out missing numbers. e.g. 12 ÷ = 4 Children use division to solve more complex word problems. Children will use an empty number line to support their calculation. Children should also move onto calculations

involving remainders. When there are some left over, the term remainder can be introduced. 13 ÷ 4 = 3 r 1

4 4 4 0 1 5 9 13 Using symbols to stand for unknown numbers to complete equations using inverse operations 26 ÷ 2 = 24 ÷ = 12 ÷ 10 = 8

Calculation Policy

11

The ability to calculate mentally forms the basis of all methods of calculation and has to be maintained and refined. 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 developed through directed enquiry, use of models and images and the application of acquired number knowledge and skills. This policy contains the key pencil and paper procedures that are to be taught throughout the school. It has been written to ensure consistency and progression throughout the school.

It is important to recognise that the ability to calculate mentally lies at the heart of numeracy.

Mental calculation is not at the exclusion of written recording and should be seen as complementary to and not as separate from it. In every

written method there is an element of mental processing.

Written recording both helps children to clarify their thinking and supports and extends the development of more fluent and sophisticated

mental strategies.

They should be working towards a method that helps them to calculate efficiently and one that can be understood by other people.

The long-term aim is for children to be able to select an efficient method of their choice that is appropriate for a given task. They should do

this by always asking themselves:

'Can I do this in my head?'

'Can I do this in my head using drawings or jottings?'

'Do I need to use a written method?'

Some children will not progress through all the methods shown here. Vocabulary The correct terminology should be used when referring to the value of digits to support the children’s understanding of place value. Eg. 68 + 47 should be read ‘sixty add forty’ not ‘six add four’ Foundation Stage At the Foundation Stage, children are not required to carry out formal written calculations. They will be learning to read and write numbers, understand and use the four operations and key vocabulary. Children’s understanding of number is developed through practical activities. This understanding may be recorded through pictures and informal jottings. When choosing numbers for calculation, follow this progression: Numbers crossing no boundaries. Numbers crossing only 10 boundary. Numbers crossing only 100 boundary. Numbers crossing both 10 and 100 boundary.

Calculation Policy

12

Special Educational Needs

The arrangements for children with special educational needs within mathematics lessons follows the guidelines set out in the school's SEN Policy. Wherever possible we endeavor to maintain an awareness of, and to provide for equal opportunities for all pupils in mathematics. We aim to fully include SEN pupils with appropriate IEP targets.

When planning, teachers will try to address the child's needs through simplified or modified tasks and/or the use of support staff for the most able as well as the less able.

Inclusion

We strive to create a sense of community and belonging for all our pupils. We have an inclusive ethos with high expectations and suitable targets, a broad and balanced curriculum for all children and systems for early identification of barriers to learning and participation.

Equal Opportunities

As a staff we endeavor to maintain an awareness of, and to provide for equal opportunities for all our pupils in mathematics. We aim to take into account cultural background, gender and special needs, both in our teaching attitudes and in the published materials we use with our pupils.