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’

Language Visual

‘With eyes open’

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.

•

3

Addition

= 5 + 2

- Reception

• 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 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 ?

5 and 2

more

is ?

5 and 3

more

is ?

6 7 8 6 6,7 6, 7, 8 • • Combining sets to make a total Add 3 single digits pictorially to make a total • • 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 1 2 3 4 5 Count on one, two, three 6 7 8 9 10 • Number bonds to 5, 6, 7, 8, 9

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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 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 • Counting on in 10s then 1s on a number square and number line 48 + 35 = +10 +1 48 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 86 + 57 = +50 +4 +3 86 • Partition both numbers and add the tens, then the units, finally recombining 86 + 57 = (80 + 50) + (6 + 7) = 130 + 13 = 143 136 140 143 • Expanded vertical layout, adding the tens first 8 6 + 5 7 1 3 0 1 3 (80 + 50) (6 + 7) 1 4 3

•

Addition – Year 4

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

9,8 8 left

Subtraction - Reception

10 grapes, eat two. How many left? 10 grapes, eat one, how many left? 9.

And another? 8.

Another, 7 . . . • Establishing take away • 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

• 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 1 11 21 31 41 51 61 71 81 91 3 13 23 33 43 53 63 73 83 2 12 22 32 42 52 62 72 82 92 93 5 15 25 35 45 55 65 75 85 4 14 24 34 44 54 64 74 84 94 95 7 17 27 37 47 57 67 77 87 6 16 26 36 46 56 66 76 86 96 97 8 18 28 38 48 58 68 78 88 98 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100

•

Subtraction

Horizontal number line for HTU – TU 625 – 48 = -2 -50 -500 -20

– Year 3

-5 500 + 50 + 20 + 5 +2 =

577

• 48 100 600 620 50 Leading to formal columnar vertical layout 8 12 1

9 3 2 4 5 7

OR 625

4 7 5

1 1

9 3 2 4 5 7

5 6

4 7 5

Subtraction – Year 4 -

• Use a formal written method of columnar subtraction to subtract Th H T U – TH T H U 8 1

2 9 3 2

1 1

2 9 3 2 1 4 5 7 1 4 7 5

OR

1 4 5 7

5 6

1 4 7 5

Multiplication - Reception

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

40 30 20

Multiplication – Year 1

• Count in 2s, 5s &10s Double 4 is 8 2 4 6 8 10 How many gloves in 3 pairs?

• 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 Introducing arrays 15 20 4 x 2 = 8 0 2 x 4 = 8 2 4 2 hops of 4 4 2 2 4 hops of 2 2 8

•

Multiplication – Year 3

•      Arrays                                    8 x 5 = 40 • Count in 2s, 3s, 4s, 5s, 8s,10s , 50s, 100s, recording on a number line Know these as tables facts 5 x 8 = 40 0 4 8 12 16 • Multiplying by 10 and 100 1 10 100 2 20 200 3 30 300 4 40 400 5 50 500 600 Use partitioning to double numbers Double 18 18 Double 10 and double 8 10 + 8 20 + 16 = 36

• • • x 6

Multiplication – Year 4

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

•

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

• Sharing equally

Division – Year 2

• Grouping 2 groups of 4 How many groups of 3 can we make from these 15 ?

5 groups of 3

• Grouping

Division – Year 3

How many 3s in 15 ?

0 3 6 9 12 • Dividing by 10 and 100 1 10 100 2 20 200 3 30 300 4 40 400 5 50 500 600 15 = 3 + 3 + 3 + 3 + 3 15 ÷ 3 = 5 15 divided by 3 = 5 15 • Corresponding facts 3 x 4 = 12 implies that 12 ÷ 4 = 3 4 x 3 = 12 implies that 12 ÷ 3 = 4 • Dealing with remainders practically

•

Division – Year 4

Chunking TU ÷ U 98 ÷ 7 98 ÷ 7 −70 10 x 7 =

70

28 −28 4 x 7 =

28 14

0 • Leading to short division TU ÷ U 98 ÷ 7 1 4 7 2 9 8 • • Introducing TH H T U (Remainders Year 5 objective)