Calculation Policy Trinity St Stephen First School (NC2014) November 2013 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 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 method For some this may still be supported by a number line Developing a Maths Concept Abstract ‘Just do it’ Visualise ‘With eyes closed’ Visual ‘With eyes open’ Language Concrete Using objects 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. Addition - Reception 3 + = 5 2 5 = 3 + 2 • • Record the outcome when two groups of objects are combined into one group • Estimate how many objects can they see • Say the number that is one more than a given number Record the outcome of physically moving along the number track 1 2 3 4 5 6 7 8 9 10 “Standing on three and moving forwards two spaces” Addition – Year 1 5 and 1 more is ? 6 • Combining sets to make a total 5 and 2 more is ? 6,7 • Add 3 single digits pictorially to make a total 5 and 3 more is ? 6, 7, 8 • 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 • Number bonds within 20 • Number bonds to 5, 6, 7, 8, 9 6 1 2 3 4 8 7 5 6 Count on one, two, three 7 8 9 10 Addition – Year 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 • Counting on in 10s then 1s on a number square and number line 48 + 35 = +10 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 48 +1 58 68 78 79 80 81 82 83 • 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 Addition – Year 3 • Use a number line Start from the largest number, partition the second and add the most significant digit first +4 +3 86 + 57 = +50 86 • 136 Partition both numbers and add the tens, then the units, finally recombining 86 + 57 = (80 + 50) + (6 + 7) = 130 = 143 + 13 • 140 143 Expanded vertical layout, adding the tens first 86 + 57 130 13 143 (80 + 50) (6 + 7) Addition – Year 4 • Use a number line, partitioning and adding the thousands first +30 +4 1387 + 1334 = +300 +1000 1387 • 2387 Expanded vertical layout, adding the hundreds first 1387 +1334 • Leading to expanded vertical layout adding the units first 1387 + 1334 600 110 11 11 110 600 2000 2721 2721 2000 2717 2721 2687 • Leading to formal written method 1387 + 1334 272 1 1 1 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?” • 1 2 3 4 5 6 7 8 9 10 Beginning to look at difference 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 Subtraction – Year 2 • • • Looking at appropriate times for counting back (taking away) and counting on (difference) Counting on and back finding differences on a 100 square Finding differences; recording on a number line 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Subtraction – Year 3 • Horizontal number line for HTU – TU 625 – 48 = -500 -50 -20 500 + 50 + 20 + 5 +2 = 577 -5 -2 48 • 100 50 600 620 625 Leading to formal columnar vertical layout 8 12 1 1 1 932 - 457 932 OR - 457 5 6 475 475 Subtraction – Year 4 • Use a formal written method of columnar subtraction to subtract Th H T U – TH T H U 8 12 1 1 1 2932 - 1457 1475 2932 OR - 1457 5 6 1475 Multiplication - Reception • Count in 2s 2 4 6 8 10 1 Five pairs of socks. Ten socks 2 3 Count on in 10s (and back) from a given tens number 5 6 7 8 9 10 Point to a number track, saying every other number aloud. 40 • 4 50 30 20 Multiplication – Year 1 • Count in 2s, 5s &10s 2 4 How many gloves in 3 pairs? 6 Double 4 is 8 8 10 • • Understand doubling • Recognise odd and even numbers up to 10 With help begin to understand arrays e.g. 3x2=6 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 0 • 5 10 15 2 hops of 4 20 4 Introducing arrays 4 x 2 = 8 2 x 4 = 8 4 8 0 2 2 2 4 hops of 2 2 Multiplication – Year 3 • • Arrays 8 x 5 = 40 5 x 8 = 40 • Count in 2s, 3s, 4s, 5s, 8s,10s, 50s, 100s, recording on a number line Know these as tables facts 0 • Multiplying by 10 and 100 1 2 3 4 5 10 20 30 40 50 100 200 300 400 500 600 4 8 12 16 Use partitioning to double numbers Double 18 Double 10 and double 8 18 10 + 8 20 + 16 = 36 Multiplication – Year 4 • Grid method for HTU x U – 324x6 x 6 20 4 1800 120 24 300 • 1800 + 120 24 324 x 6 1944 = 1944 • Expanded vertical method 324 x 6 24 120 1800 1944 • Recall multiplication and division facts for tables up to 12 x 12 Leading to the compact vertical method 1 1 2 • Informal jottings supporting mental multiplication using partitioning (factors) 17 x 3 = (10 x 3) + (7 x 3) = 30 = 51 + 21 Division – Reception & Year 1 • Practical sharing Half of 8 is 4 Can we share the cakes fairly between the four of us ? Put half of the animals into the ark. • Beginning to understand halves & quarters and equivalents • Identify own mathematical problems based on own interests Division – Year 2 • Sharing equally • Grouping 5 groups of 3 How many groups of 3 can we make from these 15 ? 2 groups of 4 Division – Year 3 • Grouping How many 3s in 15 ? 15 = 3 + 3 + 3 + 3 + 3 15 ÷ 3 = 5 15 divided by 3 = 5 0 6 3 12 9 15 • • Dividing by 10 and 100 Corresponding facts 3 x 4 = 12 implies that 12 ÷ 4 = 3 1 2 3 4 5 10 20 30 40 50 100 200 300 400 500 600 4 x 3 = 12 implies that 12 ÷ 3 = 4 • Dealing with remainders practically Division – Year 4 • Chunking TU ÷ U 98 ÷ 7 98 −70 ÷7 10 x 7 = 70 28 −28 0 • 4 x 7 = 28 14 Leading to short division TU ÷ U 98 ÷ 7 1 4 2 7 • • 9 8 Introducing TH H T U (Remainders Year 5 objective)