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 methodFor some this may still be supported by a number line

Developing a Maths Concept

ConcreteUsing objects

Visualise‘With eyes closed’

Abstract‘Just do it’

Visual‘With eyes open’

Language

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• Record the outcome when

two groups of objects are combined into one group

1 2 3 4 5 6 7 8 9 10

• Record the outcome of physically moving along the number track

“Standing on three and moving forwards two spaces”

3

5 = 3 + 2

2 = 5+

• Estimate how many objects can they see

• Say the number that is one more than a given number

Addition – Year 1• Combining sets to

make a total5 and 1 more is ?

5 and 2 more is ?

5 and 3 more is ?

6

6,7

6, 7, 8

1 2 3 4 5 6 7 8 9 10

6 7 8

Count on one, two, three

• Number bonds within 20

• Number bonds to 5, 6, 7, 8, 9

• 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

Addition – Year 2

• Counting on in 10s then 1s on a number square and number line

48 + 35 =

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

4848 58 68 78 79 80 81 8382

+10+1

• Number bonds to 10 and 20

• Number bonds to 11, 12, 13, 14, 15, 16, 17, 18 and 19

• Addition of three numbers

E.g. 7 + 6 + 3 =

• Use a number lineStart from the largest number, partition the second and add the most significant digit first

86 + 57 =

Addition – Year 3

86 136

+50

140

+4

143

+3

• Partition both numbers and add the tens, then the units, finally recombining

86 + 57 = (80 + 50) + (6 + 7)

= 130 + 13

= 143

• Expanded vertical layout, adding the tens first

1 3 01 3

1 4 3

8 6 + 5 7

(80 + 50)(6 + 7)

• Use a number line, partitioning and adding the thousands first

1387 + 1334 =

Addition – Year 4

1387 2687

+300

2717

+30

2721

+4

• Expanded vertical layout, adding the hundreds first

6 0 0 1 1 0

2 7 2 1

1 3 8 7 + 1 3 3 4

1 1

• Leading to expanded vertical layout adding the units first

6 0 0 1 1 0

2 7 2 1

1 3 8 7 + 1 3 3 4

1 1

• Leading to formal written method

1 3 8 7 + 1 3 3 4

1

1

+1000

2387

2 0 0 0

2 0 0 0

22 7

1

Subtraction - Reception10 grapes, eat one, how many

left? 9.And another? 8.Another, 7 . . .

10 grapes, eat two. How many left?

9,88 left

• 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

• Finding the difference between 3 and 5

• 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

Subtraction – Year 2• Finding differences;

recording on a number line

• Counting on and back finding differences on a 100 square

• Looking at appropriate times for counting back (taking away) and counting on (difference)

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 =

• Leading to formal columnar vertical layout

62548 50 600

-2-50 -500

100 620

-20 -5

500 + 50 + 20 + 5 +2

= 577

9 3 2

4 5 7 -

4 7 5

8 12 1

9 3 2

4 5 7

4 7 5

-

1 1

OR 5 6

Subtraction – Year 4

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

2 9 3 2

1 4 5 7 -

1

1 2 9 3 2

1 4 5 7

1 4 7 5

- 5 6

1 1

OR 4 7 5

2

1

8

Multiplication - Reception

1 2 3 4 5 6 7 8 9 10

• Count in 2s2 4 6 8 10

Five pairs of socks. Ten socks Point to a number track, saying every other number aloud.

• Count on in 10s (and back) from a given tens number

50 20

3040

Multiplication – Year 1• Count in 2s, 5s &10s

6 10842

Double 4 is 8

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

5 + 5 + 5 + 5 = 20

5 x 4 = 20

5 multiplied by 4 is 20

0 5 10 15 20

4 x 2 = 8

2 x 4 = 8

0 8

4 4

2222

2 hops of 4

4 hops of 2

• Count in 2s, 3s, 5s and 10s from 0, recording on a number line

• Recall of 2, 5 and 10 times table

• Introducing arrays

Multiplication – Year 3• Count in 2s, 3s, 4s, 5s, 8s,10s,

50s, 100s, recording on a number lineKnow these as tables facts

• Multiplying by 10 and 100

600500400300200100

5040302010

5 4321

8 x 5 = 40

5 x 8 = 40

• Arrays

0 4 8 12 16

• Use partitioning to double numbersDouble 18

10 + 8

18

20 + 16 = 36

Double 10 and

double 8

Multiplication – Year 4• Grid method for HTU x U – 324x6

• Recall multiplication and division facts for tables up to 12 x 12

x 300 20

6 1800 120

4

24= 1944

1 8 0 0 1 2 0

1 9 4 4

3 2 4 x 6

2 4

1 1 9 4 4

3 2 4 x 6

2 1 • Expanded vertical method

• Leading to the compact vertical method

• Informal jottings supporting mental multiplication using partitioning (factors)

17 x 3 = (10 x 3) + (7 x 3)

= 30 + 21

= 51

1800 + 120

24

Division – Reception & Year 1

Can we share the cakes fairly between

the four of us ?

Put half of the animals into

the ark.

• Practical sharing

• Beginning to understand halves & quarters and equivalents

Half of 8 is 4

• 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

How many 3s in 15 ?

Division – Year 3

0 3 12 156 9

• Grouping

15 = 3 + 3 + 3 + 3 + 3

15 ÷ 3 = 5

15 divided by 3 = 5

• Dividing by 10 and 100

600500400300200100

5040302010

5 4321

• 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 498

−70

28

−28

0

4 x 7 = 28

10 x 7 = 70

14

• Chunking TU ÷ U

98 ÷ 7÷ 7

• Leading to short division TU ÷ U

98 ÷ 7

7 9 8

1 4

2

• Introducing TH H T U

• (Remainders Year 5 objective)