1. Multiplication and Division

2. 2 Key Messages – Mental Calculation Involves rapid recall Use of rapid recall facts and strategies to derive new facts May involve pencil and paper jottings Choice of strategy depends on the numbers involved, known facts and personal preference

3. What else do you know? 6 x 7 =42

4. Lemonade Mrs Jones bought 15 bottles of lemonade at 28p each. 15 x 28 = 420 So Mrs Jones paid £4.20

5. Lemonade Find the cost of 16 bottles of lemonade 15 x 28 = 420

6. Lemonade Find the cost of 8 bottles of lemonade 15 x 28 = 420

7. Lemonade Find the cost of 24 bottles of lemonade 15 x 28 = 420

8. Lemonade Find the cost of 15 bottles at 14p each 15 x 28 = 420

9. Lemonade Find the cost of 15 bottles at 7p each 15 x 28 = 420

10. Lemonade Find the cost of 15 bottles at 8p each 15 x 28 = 420

11. Lemonade Find the cost of 15 bottles at 29p each 15 x 28 = 420

12. Lemonade One tin of beans if 28 tins cost £4.20 15 x 28 = 420

13. Mental Calculation Strategies General Counting up and counting back Partitioning Particular Reordering Compensating Factorising Doubling and halving

14. 14 Progression: Mental with jottings Non -standard written methods Formal / compact / standard method

15. 250 x 3 1 4 3 x 3 2 3 6 x 7 Mental Jottings Grid method Write down What do I know? Partition into H, T and U the answer 143 x 2 = 286 200 + 30 + 6 750 What is the next step? Draw out a grid 286 + 143 What is the answer? Multiply each part by 7 280 + 140 = 420 420 + 9 = 429 Find the total 1400 + 210 + 42 = 1652 X200 30 6 7 x200306 7140021042

16. Directed task Read Thompson, I. (1999) Written Calculation in Thompson, I. (ed) (1999) Issues in teaching numeracy in primary schools Buckingham: OUP Girling, M. (2001) ‘Towards a definition of basic numeracy’, Mathematics Teaching, 174, March 2001, pp.12-13, reflect on the key points made in reference to the seminar content. Possible points to consider: What position does Girling take in the debate? Consider the extent to which you agree or disagree with his stance based on the reading you have undertaken so far and your personal experience.

17. Thompson ‘There are many studies which show that children's mental methods operate very differently from standard algorithms in several respects’ (Thompson, 1999, p. 170)

18. Multiplication x304 4012001601360 618024204 1564 3 4 3 4 x 4 6 4 6 2 4 (6 x 4) 2 0 4 1 8 0 (6 x 30) 1 3 6 0 1 6 0 (40 x 4) 1 5 6 4 1 2 0 0 (40 x 30) 1 5 6 4

19. Thompson Children are more likely to be able to understand these more ‘natural’ methods than the traditional standard algorithms which involve the automatic and unthinking manipulation of abstract symbols.’ (p.182)

20. Role of Calculators ‘At a time when a cheap calculator can be bought for the price of two good cabbages, we need to redefine our aims for numeracy. I suggest the following definition; Basic numeracy is the ability to use a four function calculator sensibly.’ (Girling, 2001, p.12)

21. Position in the debate ‘I am not going to suggest that pencil and paper methods should not be taught, but that they should only be taught as part of the armoury of techniques that we have to help in an understanding of number and not because they are useful’