Parent Workshop Addition and Subtraction

1. Parent WorkshopAddition and Subtraction October 4th, 2011

2. ? ? Visual Images ? Children should be selecting one of these three visual images before starting their work. These images reinforce the ‘what they are doing’, not ‘how are they doing it’.

3. Year 3-Hundreds to Thousands • Year 4-Thousands to Tens of Thousands, tenths, unit fractions • Year 5-Tens of Thousands, hundredths • Year 6-Tens of Thousands to Hundreds of Thousands, decimals Written methods then become basis for mental methods the following year.

4. ? Early Addition • Start by adding on a structured number line. • Start from larger number, count on in 1s • Progress to counting on, using number bonds and ‘bridging’ to nearest 10. 5 + 6 = 11 +1 +1 +1 +1 +1 +1 5 5 + 6 = 11, I know that 5 + 5 = 10, then +1 more on. +5 +1 5 10 11

5. ? Move to Partitioning • Partitioning means splitting a number into its place value components E.g. 674 = 600 + 70 + 4 • 57 + 33 Again, start from larger number: +30 +3 Some children will need to do three separate jumps of 10 here. 87 90 57

6. ? 227 + 532: 227 + 532 +7 +200 +20 732 752 759 532

7. Decimals • Children must have a good understanding of what happens between two ‘counting’ numbers (i.e. 33 and 34) before calculating with decimals. They will need to understand that each whole number is made up of ten tenths: 33.1 33.2 33.3 33.4 33.5 33.6 33.7 33.8 33.9 33.0 34.0

8. ? Number lines and Decimals • The same method can be used, again starting with the larger number: 18.2 + 57.4 +10 +8 +0.2 67.4 75.6 57.4 75.4

9. ? More Compact Methods • Drawing on the sound understanding of place value, more compact methods can then be used. 673 + 212 600 + 70 + 3 200 + 10 + 2 885 800 + 80 + 5

10. ? Bridging over a boundary • Some calculations may require the children to ‘bridge’ over a place value boundary: 367 + 284 = 300+ 60 + 7 200 + 80 + 4 500 + 140 + 11 = 500 + 100 + 40 + 10 + 1= 651

11. ? • Column Addition 6732 + 8673 6732 + 8673 15, 405 1 1

12. ? ? Subtraction • Two visual images: • Children will be able to select which image they need, based on either context or number size. Finding the Difference Counting Back

13. For example: • I have £4.75 and a DVD I want to buy costs £6.99. How much more money do I need to save? ? £4.75 £6.99

14. ? • I have 23 sweets and give 12 to my friends at playtime. How many have I got left?

15. Early Subtraction • Being able to count up or back from any number. What is the difference between 23 and 28? 5 +1 +1 +1 +1 +1 23 24 25 26 27 28 What is 21 - 6? -1 -1 -1 -1 -1 -1 21 – 6 = 15 15 16 17 18 19 20 21

16. ? Becoming more efficient 227-145 -40 -5 -100 87 82 127 227

17. ? Becoming more efficient Count up to the nearest multiple of 10 or 100 (or whole number if using decimals) 227-145 = 82 +27 +55 55 + 27 = 82 145 200 227 +50 Number bonds +27 +5 150 200 145 227

18. ? More Compact • Moving towards vertical methods, children should still be able to ‘see’ the visual image of what they are doing. 227 -145 150 + 5 +50 +27 200 227 227 - 145 = 82 82

19. ? 227-145 = ? 227 -145 227 - 145 = 82 -100 - 40 - 5 127 87 82