2. If you were brought up on pages of ‘hard sums’ you may think maths is difficult and boring. Worse than that you may think you’re not very good at it!!! That’s a real shame because it is a fun subject and for most people, if they are taught to understand numbers, they should be reasonably easy to grasp and use.

3. When children are in years 1 and 2 they are not expected to do vertical sums 6 +4 10 but that doesn’t mean they won’t learn that 6+4=10. They will be doing a daily mixture of practical, mental and oral work including lots of counting, talking about numbers and using numbers in real life activities. They will begin to record what they’ve done with pictures and numbers. These recordings will help them to understand what is happening and to show how they’ve worked something out. Here are two examples of early recording.

4. + and -

5. This next example shows how different children have worked out and recorded the answer to the same problem about the children in the class. These diagrams and jottings help the children to see what is happening to the numbers and to use some facts they already know to help them work out others.

7. As the children move into the juniors they will carry on using horizontal recording of addition and subtraction to support their mental calculations and move on to column methods. The next example shows two ways of adding 76 and 93. The first splits the numbers into tens and ones (units) then adds the tens followed by the ones to give 169. The second example uses the idea of rounding to 100 by taking 7 from 76 and adding it to the 93 to make it 100 so making the addition easier.

9. Children will also continue to use drawings, diagrams and blank number lines to support their thinking, as below.

10. ‘Expanded methods’ are ways of recording that make the process of adding the different digits clear to children. These methods build on the mental methods they have been learning and should help children to understand what is happening. Here is an example of adding using an expanded method.

11. 235 + 37 12 60 200 272

12. This then becomes a more traditional compact method. 235 +37 272 1

13. Subtraction Children can find subtraction more difficult. Find the difference between 278 and 365 +2 +20 +60 +5 278 280 300 360 365 This turns a subtraction into an addition 60 + 20 + 5 + 2 = 87

14. 365-278 Expanded method 300 + 60 + 5 -200 + 70 + 8 Becomes 200 +150 + 15 200 + 70 + 8 0+ 80 + 7 = 87

15. Decomposition method. 2 15 1 365 -278 87

16. Multiplication Grid method 28 x 6 X 20 8 = 120 + 48 = 168 6 120 48

17. Long multiplication Grid Method 135 x 24 X 100 30 5 20 2000 600 100 4 400 120 20 2000 + 600 + 400 + 120 + 100 + 20 = 3240

18. Division 112 ÷ 4 Chunking method 112 10 x 4 =40 -40 72 10 x 4 = 40 - 40 32 8 x 4= 32 -32 0 A = 28

19. Short Division – Standard Method 128 ÷ 6 021r2 6 128

20. Long Division Standard Method 22 14 308 28 0