TEACHING WRITTEN CALCULATIONS

St. Augustine’s Catholic Primary

Introduction

• Common approach – so the children don’t get confused

• Mainly start recording fromY1 onwards• Stages relate to year groups but not all

children at year group level• Cover all calculations today – am available

afterwards, or speak to class teacher• Presentation on school website

ADDITIONStage 1 –Teachers demonstrate

number lines8 + 5 = 13

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Stage 2 – Children use empty number lines starting with the

largest number and counting on

34+23 = 57

34 44 54 55 56 57

34 44 54 57

34 54 57

Stage 3

Make sure children count from largest number first.

Example

38 + 86 = swap to

86 + 38 =

Children begin to work in columns

6 7

+ 2 4

1 1 (7+4)

8 0 (60 + 20)

9 1

Stage 4 – Children begin to carry below the line

7 8 3

+ 4 2

8 2 5

1

Stages 5 and 6

Children use larger numbersChildren use decimal numbers

Have a go!!

How would you use a number line to demonstrate 28 + 54 =

Use the column method to calculate345 + 67 =

SUBTRACTIONStage 1 – Teachers demonstrate

number lines

13 – 5 = 8

0 1 2 3 4 5 6 7 8 9 1011 12 131415

Stage 2 – Children use empty number lines

47-23 =

24 25 26 27 37 47

24 27 37 47

24 27 47

Counting on

82-47 =

47 48 49 50 60 70 80 81 82

Stage 3 – Children use column method71 – 46 =

7 0 1

- 4 0 6

Stages 4,5 and 6 – Larger numbers, leading to short method

7 5 4

- 2 8 6

Have a go!!

How would you use a number line to demonstrate 58 – 24 =

Use the short column method to calculate 654 – 482 =

MULTIPLICATION – Stage 1 and 2Children must understand that

multiplication is repeated addition

5x3 =5+5+5

0 5 10 15

Need to understand that:

3x5 is the same as 5x3

0 3 6 9 12 15

Stages 3 and 4 – Children continue to use number lines and arrays

X 1 0 4

6

Grid method

23 x 8 =

x 2 0 3

8 1 6 0 2 4

1 6 0

+ 2 4

1 8 4

Short method38 x 7 =

3 8

x 7

2 6 6

5

Grid method for TU X TU

X 5 0 6

2 0 1 0 0 0 1 2 0

7 3 5 0 4 2

1 3 5 0 1 6 2

1 3 5 0

+ 1 6 2

1 5 1 2

1

Stages 5 and 6 – Short method

56 x 27 =Children approximate first:

60 x 30 = 1800

5 6

X 2 7

3 9 2 56x7

1 1 2 0 56x20

1 5 1 2

1

Have a go!!!

Use the grid method to calculate43 x 6

Try the short method

Calculate 56 x 43 using the grid method and short method

DIVISION – Stage 1 and 2 –Children understand that division

is repeated subtraction -4 groups of 3 in 12

12 3 = 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Stage 3 – Children continue to use repeated addition on number lines

including remainders13 4 = 3 r 1

0 1 5 9 13

Stage 4 – Short division using chunking method72 3 = 24

3)72 - 30 10 x 42 - 30 10 x 12 - 6 2 x 6

6 2 x Answer = 24 0

Stages 5 and 6 – Children use larger multiples and numbers

864 24 = 36

24)864- 720 30 x

144 - 72 3 x 72 - 72 3 x Answer = 36 0

Other Year 6 methods

Please look at the leaflets/website. These are used if children are having difficulties with the chunking method

Have a go!!

Use a number line to demonstrate 14 7 = 2

Use the chunking method to work out

65 5 =210 15 =