Key ideas in the Numeracy Strategy

• Mental methods of calculation are stressed

• Standard written calculations are delayed until pupils have fundamental ideas about place value and have a repertoire of mental calculation strategies

How would you work out ….

23 + 24 =

45 + 46 =

68 – 34 =

101 – 59 =

Addition

• At Key Stage 1 ‘sums’ are usually written horizontally

• Number lines are often used to support informal methods and help build up imagery

24 + 58 =

Addition continued…

Children are introduced to ‘partitioning’

Early stage:

38 + 27 =

30 + 20 = 50

8 + 7 = 15

38 + 27 = 65

Then:

38 38

+ 87 + 87

110 15

15 110

125 125

Lastly:

236

+175

411

11

Subtraction at KS1

• Children use practical objects to carry out ‘take away’ and ‘find the difference’

• Number lines and 100 squares provide important modelsDifference ITP

Counting on and counting back25 – 3 26 – 21

_______________ _______________

Subtraction at KS2Children are taught to subtract by finding thedifference between the two numbers. This method involves counting on from the smaller

tothe larger number and is called ’complementaryaddition’

85 – 57 _85 57____________________________ 3 (60)

25 (85) 28

Subtraction with larger numbers

326 – 178 ______________________

326- 178 22 (200) 126 (326) 148

Subtraction at KS2• Finding the difference

continues to be an important informal method

• When children are ready, they are introduced to ‘decomposition’, which involves partitioning

245 – 123 =

200 40 5- 100 20 3 100 20 2

763 – 248

50 13

700 60 3 - 200 40 8 500 10 5

Leading to:

6 2 15

735 -248

487

Multiplication• Early work on

multiplication involves images of groups and arrays:

• Multiplication Facts ITP

Next children usepartitioningfor calculations:26 x 7 =

20 x 7 = 140 6 x 7 = 42

26 x 7 = 182

Multiplication – the ‘grid method’7 x 23 = 161

• Multiplication grid

x 20 3

7 140 21

Multiplication - continued

Another method of recording is taught to children who are ready

534 468x 6 x 52

DivisionEarly work on division involves

sharingand grouping

• Grouping

Next children are encouraged to understand

division as building up multiples (chunking)

84 ÷ 6 =

_________________________________

Division – the ‘chunking method’

305 ÷ 7 =(estimate: 40 x 7= 280 so the answer is

a bit more than 40)

305- 280 (40 x 7) 25 - 21 ( 3 x 7) 4

305 ÷ 7 = 43 r 4

Division continuedChildren who are ready, are

taught another method of recording

267 ÷ 8 = ____8) 267

In conclusion …

• Children are always encouraged to think which is the most appropriate and efficient method for the numbers involved

• Mental methods should be the first resort