Calculation Policy

Aims• To reduce the number of methods

being taught.

• To increase the links between the Infants and Junior school.

• To create a clear progression from reception to year 6.

A few notes

In year 3 children are encouraged to use jottings and work out calculations mentally.

Nearly all “traditional” methods are introduced in year 4 and 5.

The methods are not “set in stone” if a class or child is able to move onto the next stage

in a calculation they will be taught this.

Likewise, if a child is struggling an earlier method maybe used.

Mental Strategies

Written Strategies

Addition

• Counting on

14

19

+5

14 + 5 = 19

Addition

• Counting on

14

24

26

+10 +2

14 + 12 = 26

Addition

• Counting on

237

257

265

+20 +8

237 + 28 = 265

Addition

• Traditional method (from year 4)

129+ 22 151

Subtraction

• Counting up

37

45

+8

45 - 37 = 8

Subtraction

• Counting up

34 – 16 = 18

26 16 34

+10 +8

Subtraction

• Complementary addition

224 – 86 = 138

86 200 100 224

+14 +100 +24

Subtraction

• Written method (from year 5)

154 – 86 = 68

54 (100)14 (86)

68

Subtraction

• Written method – Borrowing• (from year 5)

754 – 286 = 468

754286

468

1146

Multiplication

• Using multiplication facts

You need to know your tables.

-Year 3 2,3,4,5,10-Year 4 6,7,8,9-Year 5 11,12

Multiplication

• Using multiplication facts

13 x 9 = 117

13 × 9 = ? 13 × 10 (-13)

Multiplication

• Using multiplication facts

13 x 11 = 143

13 × 11 = ? 13 × 10 (+13)

Multiplication

• Grid Method 12 6 = ?

x 10

2

6

100

20

x

Answer = 100 + 20

= 120

Multiplication

• Grid Method 132 5 = ?

x 100

30

5

500

150

x

Answer = 500 + 150 + 10

= 660

2

10

Multiplication

• Grid Method 132 12 = ?

x 100

30

10

1000

300

2 200 60

x

Answer = 1000 + 200 + 300 + 60 + 20 +4

2

20

4

Multiplication

• Traditional Method (from year 5)

Answer = 138

23 × 6 138 1

Division

• Sharing

13 ÷ 4 = 3 r 1

Division

• Grouping

41 ÷ 4 = 10 r 1

+1

+ 40

10 groups

Division

• Grouping

43 ÷ 4 = 10 r 3

0 3 43

-3

- 40

10 x 4

Division

• Traditional Method (from year 4)

81 ÷ 3 = 27

2 7

3 8 12

Summary of strategies

Children should always estimate first.

Children should decide whether a method is appropriate.

Children should be taught and reminded to use the correct language.

Children should always check their answer, preferably using a different method e.g. The inverse operation.

Children who make persistent mistakes should return to the method that they can use accurately.

Children still need to know number and multiplication facts by heart.