1. This policy was created with the requirements of the National Curriculum in England and the 2016 SATs in mind. 1 Lady Bay Primary School Written Calculation Policy July 2015 + - x ÷ Guidance for staff and parents

2. Contents Page 2 3 – 4Addition 5 – 6Subtraction 7 – 8 Multiplication 9 – 10Division Please note that the ‘steps’ in this policy are not associated with year groups but are designed to be taught when individual children are ready for them.

3. Addition - Step 1Addition - Step 2Addition - Step 3 Use apparatus (such as Numicon) to identify one more/less. Combine Numicon pieces to add. Children to record by printing/drawing around numicon. Solve simple problems using fingers. + = signs and missing numbers Children need to understand the concept of equality before using the ‘=’ sign. Calculations should be written either side of the equality sign so that the sign is not just interpreted as ‘the answer’. 2 = 1+ 1 2 + 3 = 4 + 1 Counting and Combining sets of Objects Combining two sets of objects (aggregation) which will progress onto adding on to a set (augmentation) Missing numbers need to be placed in all possible places. 3 + 4 = = 3 + 4 3 + = 7 7 = + 4 Understanding of counting on with a number track. Understanding of counting on with a number line (labelled numbers). E.g. 7+ 4 = 11 Number line methods Use of the number line s and blank number lines for the following additions Counting on in tens and ones 23 + 12 = 23 + 10 + 2 = 35 Partitioning and bridging through 10. The steps in addition often bridge through a multiple of 10 e.g. Children should be able to partition the 7 to relate adding the 2 and then the 5. 8 + 7 = 15 Adding 9 or 11 by adding 10 and adjusting by 1 e.g. Add 9 by adding 10 and adjusting by 1 35 + 9 = 44 Use of a number line to solve missing number puzzles: e.g 14 + 5 = 10 + 32 + + = 100 35 = 1 + + 5 Written methods Partition the numbers into tens and ones, add the tens together and then add the ones together. Recombine to give the answer. Always model and encourage the use of one number in every square. 3a) Partitioning E.g. 43 + 25 = 68 Progressing onto to expanded method (shown below) Partition the numbers to hundreds, tens and ones. Add the hundreds, tens and ones together. Recombine to give the answer. Always model and encourage the use of 1 digit per square. 3b) E.g. 236 + 73 = 309 3

4. Addition - Step 4Addition - Step 5Addition - Step 6 – Extending Written methods (progressing to 4-digits) Add the least significant digits (ones in a whole number), then the tens and finally the hundreds. Use the language of place value to ensure understanding. E.g. seven + five =twelve, forty + twenty = 60 NOT four add two. Always model and encourage the use of one digit per square. Progressing to setting out without partitioning (but maybe bracketing the partitioned bits) E.g. 236 + 73 = 309 An example involving decimals E.g. 27.2 + 24.3 = 51.5 Written methods (progressing to more than 4-digits) Progress to this when understanding of the expanded method is secure, children will move on to the formal columnar method for whole numbers and decimal numbers as an efficient written algorithm (including carrying). Use similar language of place value as in step 4. Any numbers carried should must be written underneath the tens column (as shown below) to represent the extra ten. E.g. 436 + 347 = 783 Ensure that when using decimals, the decimal points are lined up. E.g. 35.26 + 27.28 = 62.54 4

5. Subtraction - Step 1Subtraction - Step 2Subtraction - Step 3 Use concrete objects and pictorial representations. If appropriate, progress from using a number track, to a number line with every number shown. Understand subtraction as take-away: Use of concrete apparatus Pictorial representations, e.g. 5 – 2 = 3 Use of fingers Use of number track for counting back. Use of number line to count back. Moving onto understanding subtraction as finding the difference. Other apparatus, such as: Numicon, bundles of straws, Dienes apparatus, multi-link cubes, bead strings can be used to support understanding. Missing number problems e.g. 7 = □ - 9; 20 - □ = 9; 15 – 9 = □; □ - □ = 11; 16 – 0 = □ Subtraction on a number line to count back Use of the number line to count back in ones and tens initially. When this is embedded, count back in more efficient steps (as shown below). Subtraction on a number line to count on As children progress and their understanding of the link between subtraction and difference is more secure, they should be developing the idea of using a n empty number line to count on from the smaller number. E.g.1) 42 – 39 E.g. 2) 126 - = 45 Notes: It is important to consider the type of question when choosing whether to count on or back. I.e. is the numbers are close, as it example 1, counting on is more time-efficient. 5

6. Subtraction - Step 4Subtraction - Step 5 Subtraction - Step 6 – Extending Written methods (Standard compact method with exchange) The use of language is very important to ensure consistency. We will not use the term’ borrow a ten/hundred. We will speak of ‘taking’ a ten/hundred and exchanging it for tens and hundreds. E.g. 84 – 47 = 37 When learning to exchange, explore partitioning in different ways so that pupils understand that when you exchange the value is the same. I.e. 80 + 4 = 70 + 14 (as in the example above) An example involving decimals Written methods This progresses to larger numbers (e.g. with 3 or 4 digits). Use the language of place value to ensure understanding. See Step 4 for notes regarding correct use of terminology. E.g. 852 – 427 = 425 An example involving decimals E.g. 35.26 – 27.28 = 7.98 Notes: 6

7. Multiplication - Step 1Multiplication - Step 2Multiplication - Step 3 Understand multiplication is related to doubling and combing groups of the same size (repeated addition) Washing line, and other practical resources for counting. Concrete objects. Numicon; bundles of straws, bead strings Problem solving with concrete objects (including money and measures. Children formally using a number line to record jumps on a number line. E.g. Use arrays to understand multiplication can be done in any order (commutative) Notes: Show the link between multiplication and repeated addition. Expressing multiplication as a number sentence using multiplication symbol. Using understanding of the inverse and practical resources to solve missing number problems. 7 x 2 = = 2 x 7 7 x = 14 14 = x 7 x 2 = 14 14 = 2 x x ⃝ = 14 14 = x ⃝ Written methods (progressing to 2d x 1d) Developing written methods using understanding of visual images. Develop onto the grid method 7

8. Multiplication - Step 4Multiplication - Step 5Multiplication - Step 6 Grid method Development of the grid method for TO x O, HTO x O and TO x TO (O means ones!) Notes: Ensure the children include a column addition method to add the numbers accurately at the end. Ensure the correct language and understanding of place value for products such as 17 x 40. NB – Children will NOT receive a mark in KS2 SATs for using this method if the answer incorrect. Therefore, in Year 6, they should use the formal written methods of stage 5 and 6. For SEN pupils, teacher discretion is required. Expanded Short multiplication Long multiplication Notes: Multiply the least significant digits first. Using brackets to record working out reinforces understanding of place value. Refer back to addition calculation policy where it is necessary to carry. Compact - Short Long Notes: Only move this stage when children are absolutely secure in all of the previous stages. This process should not be rushed. Do not tell the children to ‘add a zero’ at the start of the second line of working out. An understanding of the previous stage will ensure that children see as 30 x 8 = 240 and not 3 x 8 = 24. 8

9. Division - Step 1Division - Step 2Division - Step 3 Children must have secure counting skills- being able to confidently count in 2s, 5s and 10s. Children should be given opportunities to reason about what they notice in number patterns. Sharing Children should be taught to share using concrete apparatus. Grouping Children should apply their counting skills to develop some understanding of grouping. Children should be able to find ½ and ¼ and simple fractions of objects, numbers and quantities. Know and understand sharing and grouping- introducing children to the ÷ sign. Use of arrays as a pictorial representation for division. 15 ÷ 3 = 5 There are 5 groups of 3. 15 ÷ 5 = 3 There are 3 groups of 5. Grouping using a number line (make the link with repeated subtraction). Use an empty number line to count forwards/backwards How many 6’s are in 30? 30 ÷ 6 can be modelled as: Progress to more efficient methods using the number line. Children need to be able to partition the dividend in different ways. Show on number line using repeated subtraction. Note here, it may be appropriate to count back in small steps of the same size initially. 48 ÷ 4 = 12 2 groups 10 groups 0 8 48 Progress to quotients with remainders, e.g: 49 ÷ 4 = 12 r1 -8 10 groups Sharing – 49 shared between 4. How many left over? Grouping – How many 4s make 49. How many are left over? - 40 -8 49 9 - 40 1 0 9 2 groups

10. Division - Step 4Division - Step 5Division - Step 6 Short division involving TU without remainders: E.g. 69 ÷ 3 = 23 Always remind children of the correct place value. Pose the questions: How many 3s in 6? Record above the 6 tens. How many 3s in 9? Record above the 9 ones NB – Always ensure that you use the correct numbers for calculations at step 4. E.g. Each digit must be a multiple of the divisor. Progressing to: E.g. 98 ÷ 7 = 14 Short division involving larger numbers (including remainders) where the divisor can be taken out of the starting number. E.g. 3016 ÷ 13 = 232 (From Sample arithmetic paper 2016 SAT) Once children demonstrate a full understanding of remainders, they can be taught how to use the short division method when remainders do occur within the calculation. In such quotients, they need to ‘carry’ the remainder onto the next digit. When the answer for the first column is zero, children should write a zero above to acknowledge its place and then must ‘carry’ the number (4) over to the next column. Beginning to express answers to divisions as decimals, fractions or a rounded number. Pupils need to consider the meaning of the remainder and how to express it (e.g. as a fraction, decimal or a rounded number) Long division – For calculations such as 2331 ÷ 37 (Taken from Sample arithmetic paper 2016 SAT) where the divisor cannot easily be taken ‘out’ of the starting number. Use of a column addition/multiplication to support. Note here – like with multiplication, the children will NOT gain marks in the arithmetic test when using an informal method to calculate a division. Formal methods must be used – i.e. Short or long division (chunking). 10