Calculation Policy

1. Calculation Policy Trinity St Stephen First School (NC2014) November 2013

2. Aims • To support greater consistency in the teaching of written calculation across the school • To strengthen continuity and progression in children’s understanding of the development of written calculation • To form a ‘spine’ or ‘core’ set of methods which every child will experience and can be built upon.Once children acquire mastery of these, other calculation methods can be introduced • To build on models and images introduced to promote conceptual understanding • To provide reference and guidance on the teaching of calculation skills for teaching staff and teaching assistants

3. The Place of Writing in Maths Lessons • Recording of calculations takes place throughout KS1 and KS2 • Development of formal written calculation methods follows development of mental methods • Early stages of formal written calculations begin in the summer term of Year 3 • By end of Year 6, children should have a reliable written method for tackling all four operations – not necessarily a ‘standard’ written methodFor some this may still be supported by a number line

4. Abstract ‘Just do it’ Visualise ‘With eyes closed’ Visual ‘With eyes open’ Language Developing a Maths Concept Concrete Using objects

5. Good Practice in Calculation • Establish mental methods, based on good understanding of place value in numbers and tables facts. • Show children how to set out written calculations vertically, initially using expanded layouts (starting without adjustments of 'carrying', and introducing this adjustment slowly and systematically). • Make sure that the children always look out for special cases that can still be done entirely mentally. • Gradually refine the written record into a more compact standard method. • Extend to larger numbers and to decimals. • Ensure that mental approximations are carried out before written methods are used. • Ensure that the understanding of remainders and what to do with them in context is taught alongside division throughout. • Once written methods are introduced, keep mental skills sharp by continuing to develop and apply them to appropriate examples. Encourage children always to use mental methods as a first resort.

6. 1 2 3 4 5 6 7 8 9 10 Addition - Reception + = 5 3 2 • Record the outcome when two groups of objects are combined into one group • Estimate how many objects can they see 5 = 3 + 2 • Say the number that is one more than a given number • Record the outcome of physically moving along the number track “Standing on three and moving forwards two spaces”

7. 1 2 3 4 5 6 7 8 9 10 Addition – Year 1 6 5 and 1 more is ? • Combining sets to make a total 6,7 • Add 3 single digits pictorially to make a total 5 and 2 more is ? 6, 7, 8 5 and 3 more is ? • Counting along a number track, then number line in 1s and 10s • Patterns using known facts e.g. 4+3 = 7, so we know • 24-3 = 27 & 44+3 = 47 etc 8 6 7 • Number bonds within 20 • Number bonds to 5, 6, 7, 8, 9 Count on one, two, three

8. Addition – Year 2 • Counting on in 10s then 1s on a number square and number line 48 + 35 = +10 +1 48 83 81 80 78 79 68 58 82 48 • Addition of three numbers • E.g. 7 + 6 + 3 = • Number bonds to 10 and 20 • Number bonds to 11, 12, 13, 14, 15, 16, 17, 18 and 19

9. Addition – Year 3 • Use a number lineStart from the largest number, partition the second and add the most significant digit first 86 + 57 = +4 +3 +50 140 143 86 136 • Expanded vertical layout, adding the tens first • Partition both numbers and add the tens, then the units, finally recombining • 86 + 57 = (80 + 50) + (6 + 7) • = 130 + 13 • = 143 8 6 + 5 7 1 3 0 (80 + 50) 1 3 (6 + 7) 1 4 3

10. Addition – Year 4 +30 +4 • Use a number line, partitioning and adding the thousands first 1387 + 1334 = +300 +1000 2717 2721 1387 2387 2687 • Leading to expanded vertical layout adding the units first • Leading to formal written method • Expanded vertical layout, adding the hundreds first 1 3 8 7 1 3 8 7 1 3 8 7 + 1 3 3 4 + 1 3 3 4 + 1 3 3 4 2 2 1 7 1 1 2 0 0 0 1 1 1 1 0 6 0 0 6 0 0 1 1 0 2 0 0 0 1 1 2 7 2 1 2 7 2 1

11. 1 2 3 4 5 6 7 8 9 10 Subtraction - Reception 10 grapes, eat one, how many left? 9.And another? 8. Another, 7 . . . 10 grapes, eat two. How many left? • Establishing take away 9,8 8 left • Show their calculation on a numbered track • “Sophie has 5 sweets. She eats 2 of them. How many sweets are left?” • Beginning to look at difference

12. Subtraction – Year 1 • Counting back along a number line when taking away • Counting back in 10’s e.g. 53-20 as 53,43,33 • Patterns using known facts e.g. 7-3=4, so we know 27-3=24 & 47-3=43 etc • Finding the difference between 3 and 5

13. Subtraction – Year 2 • Finding differences; recording on a number line • Looking at appropriate times for counting back (taking away) and counting on (difference) • Counting on and back finding differences on a 100 square

14. Subtraction – Year 3 • Horizontal number line for HTU – TU • 625 – 48 = 500 + 50 + 20 + 5 +2 = 577 -500 -20 -5 -50 -2 625 620 600 100 48 50 • Leading to formal columnar vertical layout 1 1 8 12 1 9 3 2 4 5 7 9 3 2 4 5 7 - - OR 5 6 4 7 5 4 7 5

15. Subtraction – Year 4 • Use a formal written method of columnar subtraction to subtract Th H T U – TH T H U 8 1 1 2 1 1 2 9 3 2 1 4 5 7 2 9 3 2 1 4 5 7 - - OR 5 6 5 1 4 7 1 4 7 5

16. 1 2 3 4 5 6 7 8 9 10 Multiplication - Reception • Count in 2s 4 6 10 2 8 Five pairs of socks. Ten socks Point to a number track, saying every other number aloud. 40 30 • Count on in 10s (and back) from a given tens number 50 20

17. Multiplication – Year 1 Double 4 is 8 • Count in 2s, 5s &10s 10 2 8 6 4 • Understand doubling • Recognise odd and even numbers up to 10 How many gloves in 3 pairs? • With help begin to understand arrays e.g. 3x2=6

18. 0 10 20 5 15 Multiplication – Year 2 • Count in 2s, 3s, 5s and 10s from 0, recording on a number line • Recall of 2, 5 and 10 times table 5 + 5 + 5 + 5 = 20 5 x 4 = 20 5 multiplied by 4 is 20 2 hops of 4 4 4 • Introducing arrays 8 0 4 x 2 = 8 2 2 2 2 2 x 4 = 8 4 hops of 2

19. 1 2 3 4 5 10 20 30 40 50 100 200 300 400 500 600 Multiplication – Year 3 • Arrays • Count in 2s, 3s, 4s, 5s, 8s,10s, 50s, 100s, recording on a number lineKnowthese as tables facts 8 x 5 = 40 5 x 8 = 40 0 16 4 8 12 • Use partitioning to double numbersDouble 18 • Multiplying by 10 and 100 Double 10 and double 8 18 10 + 8 20 + 16 = 36

20. Multiplication – Year 4 • Leading to the compact vertical method • Grid method for HTU x U – 324x6 20 4 300 1800 x + 120 3 2 4 24 6 1800 120 24 x 6 = 1944 1 9 4 4 1 2 1 • Expanded vertical method • Informal jottings supporting mental multiplication using partitioning (factors) 3 2 4 x 6 2 4 1 2 0 17 x 3 = (10 x 3) + (7 x 3) = 30 + 21 = 51 1 8 0 0 1 9 4 4 • Recall multiplication and division facts for tables up to 12 x 12

21. Division – Reception & Year 1 Half of 8 is 4 • Practical sharing Can we share the cakes fairly between the four of us ? • Beginning to understand halves & quarters and equivalents Put half of the animals into the ark. • Identify own mathematical problems based on own interests

22. Division – Year 2 • Sharing equally 5 groups of 3 • Grouping How many groups of 3 can we make from these 15 ? 2 groups of 4

23. 1 2 3 4 5 10 20 30 40 50 100 200 300 400 500 600 Division – Year 3 How many 3s in 15 ? • Grouping 15 = 3 + 3 + 3 + 3 + 3 15 ÷ 3 = 5 15 divided by 3 = 5 0 6 12 3 15 9 • Corresponding facts • Dividing by 10 and 100 3 x 4 = 12 implies that 12 ÷ 4 = 3 4 x 3 = 12 implies that 12 ÷ 3 = 4 • Dealing with remainders practically

24. Division – Year 4 • Chunking TU ÷ U • 98 ÷ 7 98 ÷ 7 10 x 7 = 70 −70 28 −28 4 x 7 = 28 0 14 • Leading to short division TU ÷ U • 98 ÷ 7 4 1 2 7 9 8 • Introducing TH H T U • (Remainders Year 5 objective)