Session 2 Addition and Subtraction

1. Session 2Addition and Subtraction

2. Why is it all so different today? • A desire to do something different to counter the nations phobia around mathematics • Development of understanding of effective methods to teaching mathematics since mid 1990s • Exploration of effective approaches from some of the most successful education systems in the world • Extensive research and trialling

3. There is no “right” way to work! • Children exposed to a range of methods – if you get an answer, then the method works. • Methods selected will depend upon the situation and the numbers involved, including when to use calculators. Efficiency is as important as accuracy. • Children make decisions about methods and draw on a range of strategies and approaches when applying Maths is context. • Children in same class could be using different methods to others depending on their ability, confidence and stage of mathematical development.

5. Total of 11

6. 101 Down

7. Domino totals

8. The Numberline!! 16 + 8 16 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 16 17 18 19 20 21 22 23 24

9. The Numberline!! 16 + 8 16 + 2+ 2 + 2 + 2 16 17 18 19 20 21 22 23 24

10. The Numberline!! 16 + 8 16 + 4 + 4 16 17 18 19 20 21 22 23 24

11. 43 + 25 8 68 Expanded Addition 43+25 Try this method with these!! 54+67 123+241 60

12. Towards the Standard Method 63+39 6 3 + 3 9 1 2 9 0 1 0 2 6 3 + 3 9 2 1 6 3 + 3 9 1 0 2 1

13. The Standard Method - Decomposition • Linked initially with use of images and practical apparatus to secure understanding of how place value is being used in the calculation • Lots of stages where children can make errors • Not always the most efficient method to use • If children can obtain an answer using another method, that is OK.

14. 33 - 17 Which written method is most appropriate to use for these numbers? Shall I use a written method? Can I do this mentally?

15. 33 - 17 3 3 - 1 7

16. 33 - 17 3 3 - 1 7 I’m going to partition the numbers.

17. 33 - 17 3 3 - 1 7 30 and 3 - 10 and 7 =

18. 33 - 17 3 3 - 1 7 30 and 3 - 10 and 7 =

19. 33 - 17 3 3 - 1 7 30 and 3 - 10 and 7 I start with the units, so I need to take away 7 small cubes. But I only have 3 of them. I’ll break up one of the 10s into 10 units. =

20. 33 - 17 3 3 - 1 7 30 and 3 - 10 and 7 20 and 13 - 10 and 7 = = I’ve now got 2 lots of 10, so that’s 20, as well as 13 units, so let’s write it down to show what I am doing.

21. 33 - 17 3 3 - 1 7 30 and 3 - 10 and 7 20 and 13 - 10 and 7 = = Now I can take away 7!

22. 33 - 17 3 3 - 1 7 30 and 3 - 10 and 7 20 and 13 - 10 and 7 6 = =

23. 33 - 17 3 3 - 1 7 30 and 3 - 10 and 7 20 and 13 - 10 and 7 6 = = Now I can take away 10!

24. 33 - 17 3 3 - 1 7 30 and 3 - 10 and 7 20 and 13 - 10 and 7 10 and 6 = =

25. 33 - 17 3 3 - 1 7 30 and 3 - 10 and 7 20 and 13 - 10 and 7 10 and 6 = = = 1 6

26. There will be examples like this… 75 – 32 where no exchange is needed, but partitioning is still useful as children are more successful at working with tens and units separately. 7 5 7 0 + 5 3 2 3 0 + 2 - = 4 0 + 3 = 4 3

27. Next stages will involve increasing the number of digits in the numbers (HTU, the ThHTU), working with apparatus, then without, to ensure children are secure with place value before moving on to the final stage. Often this would be taught side by side with the more expanded method so that children can se how they relate.

28. 2 7 1 2 0 0 + 7 0 + 1 2 0 0 + 6 0 + 1 1 1 5 8 = 1 0 0 + 5 0 + 8 = 1 0 0 + 5 0 + 8 1 0 0 + 1 0 + 3 = 1 1 3 - 2 7 1 2 7 1 2 7 1 2 7 1 2 7 1 1 5 8 1 5 8 1 5 8 1 5 8 1 5 8 3 1 3 1 1 3 6 1 6 1 6 1 6 1 - - - - -

29. Why the additional steps? 2 1 1 6 3 0 4 1 6 3 0 4 3 2 0 7 3 2 0 7 1 3 0 0 7 - - 3 0 0 0 5 3 0 0 0 5 4 8 5 7 4 8 5 7 3 4 8 5 2 - -