1. Numeracy Across the Curriculum Chris Olley

2. Written Arithmetic On your own use written methods to add, subtract, multiply and divide the largest numbers you can handle (at least 2/3 digits). Be ready to explain the details of your method. Go round the group each time starting with a different person, to find all of the different details in your methods for each arithmetic operation. Include all methods: including long division, short division, gelosia, Russian/Egyptian multiplication,…(look them up if you need to) 1 =10min 2 =25min 3 =15min each choose one method to ‘teach’ how it works to your group

3. 27 x 34

4. 27 x 34 The Russian or Ancient Egyptian Method

5. 2734 27 x 34 The Russian or Ancient Egyptian Method

6. 2734 Halve the left hand column rounding down until your reach 1. 27 x 34 The Russian or Ancient Egyptian Method

7. 2734 13 Halve the left hand column rounding down until your reach 1. 27 x 34 The Russian or Ancient Egyptian Method

8. 2734 13 Halve the left hand column rounding down until your reach 1. 6 27 x 34 The Russian or Ancient Egyptian Method

9. 2734 13 Halve the left hand column rounding down until your reach 1. 6 3 1 27 x 34 The Russian or Ancient Egyptian Method

10. 2734 13 Halve the left hand column rounding down until your reach 1. 6 Now double the right hand side up to the line with 1. 3 1 27 x 34 The Russian or Ancient Egyptian Method

11. 2734 1368 Halve the left hand column rounding down until your reach 1. 6 Now double the right hand side up to the line with 1. 3 1 27 x 34 The Russian or Ancient Egyptian Method

12. 2734 1368 Halve the left hand column rounding down until your reach 1. 6136 Now double the right hand side up to the line with 1. 3 1 27 x 34 The Russian or Ancient Egyptian Method

13. 2734 1368 Halve the left hand column rounding down until your reach 1. 6136 Now double the right hand side up to the line with 1. 3272 1 27 x 34 The Russian or Ancient Egyptian Method

14. 2734 1368 Halve the left hand column rounding down until your reach 1. 6136 Now double the right hand side up to the line with 1. 3272 1544 27 x 34 The Russian or Ancient Egyptian Method

15. 2734 1368 Halve the left hand column rounding down until your reach 1. 6136 Now double the right hand side up to the line with 1. 3272 Cross out the lines with an even number on the left hand side. 1544 27 x 34 The Russian or Ancient Egyptian Method

16. 2734 1368 Halve the left hand column rounding down until your reach 1. 6136 Now double the right hand side up to the line with 1. 3272 Cross out the lines with an even number on the left hand side. 1544 27 x 34 The Russian or Ancient Egyptian Method

17. 2734 1368 Halve the left hand column rounding down until your reach 1. 6136 Now double the right hand side up to the line with 1. 3272 Cross out the lines with an even number on the left hand side. 1544 Add up the remaining numbers in the right hand side. 27 x 34 The Russian or Ancient Egyptian Method

18. 2734 1368 Halve the left hand column rounding down until your reach 1. 6136 Now double the right hand side up to the line with 1. 3272 Cross out the lines with an even number on the left hand side. 1544 Add up the remaining numbers in the right hand side. 918 27 x 34 The Russian or Ancient Egyptian Method

19. 2734 1368 Halve the left hand column rounding down until your reach 1. 6136 Now double the right hand side up to the line with 1. 3272 Cross out the lines with an even number on the left hand side. 1544 Add up the remaining numbers in the right hand side. 918 27 x 34 The Russian or Ancient Egyptian Method 27 x 34 = 918

20. Numeracy Across the Curriculum Chris Olley

21. What does it amount to? 1. A consistent approach across the school to support all students develop their (mental) numeracy. 2. A consistent mathematics across the school 3. Integrated problem solving involving mathematical methods

22. What does it amount to? 1. A consistent approach across the school to support all students develop their (mental) numeracy. 2. A consistent mathematics across the school 3. Integrated problem solving involving mathematical methods

23. Albert Einstein (1879-1955) Do not worry about your difficulties in mathematics, I assure you that mine are greater.

24. Bistromathics itself is simply a revolutionary new way of understanding the behaviour of numbers. Just as Einstein observed that space was not an absolute but depended on the observer's movement in space, and that time was not an absolute, but depended on the observer's movement in time, so it is now realized that numbers are not absolute, but depend on the observer's movement in restaurants. Adams, Douglas Life, the Universe and Everything.

26. Work these out 2037  12.6 34012  1362 14.7²+8.6³

27. I am ill at these numbers. William Shakespeare, (1564-1616) Hamlet.

30. I'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it. Malcom X

31. Effective primary school teaching has ensured that pupils arrive at secondary school with secure number skills. Secondary school maths departments effectively develop these skills so that they are fluently applied in all secondary subject studies. Olley, C.J. (1961-) A Statement

32. A good calculator does not need artificial aids. Lao Tze (604-531 B.C.) Tao Te Ching

33. Hardy, Godfrey H. (1877-1947) Ramanujan, London: Cambridge University Press, 1940. I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.“

34. Which numbers are you happy with? (Work these out!) 147 + 149 224 ÷ 4 54 + 77 162 – 28 87  6

35. Choosing calculating tools Mental methods Mental + thinking tools + jottings Written methods Calculators

36. Taught Numeracy Strategies Number Facts: Doubles and Halves Number Bonds Times tables facts Number Techniques: Decomposition Multiply and divide by 10, 100, 1000 etc. Change the order Equivalences Nearest 10 and adjust … but also … Square numbers Triangle numbers Prime numbers Pascal’s (Chinese) triangle

37. How to deal with number problems 1. Change the problem into one with numbers you are happy with 2. Deal with these numbers 3. Modify your answer to take account of the changes you made Work it out in your head Use a method that suits what you know Support with Numeracy facts and techniques Use jottings to support your thinking Use written methods as a last resort Only use a calculator when you have to

38. Questions/Prompts “Can you see numbers close to these that would be easier to deal with?” “Would it be easier the other way round?” “Could you break it up and work on the bits separately?” “Could you use doubles or halves?” “Can you see an easier problem with the same answer as this one?” “Would it help to jot down a number half way?” “Would it help to use a number line?”

39. What does it amount to? 1. A consistent approach across the school to support all students develop their (mental) numeracy. 2. A consistent mathematics across the school 3. Integrated problem solving involving mathematical methods

40. We hate bad maths! Which department does the most maths? To what extent is maths done the same? What bad maths do we want to sort out round the school?

41. The Deptford Green Guide 1. Read through the final section. Can you agree to these conventions? Would you need anymore. 2. Find an interesting numeracy strategy. Share how it works to your neighbour. Choose one to explain to your group.

42. What does it amount to? 1. A consistent approach across the school to support all students develop their (mental) numeracy. 2. A consistent mathematics across the school 3. Integrated problem solving involving mathematical methods

43. Projects The Pizza Problem (Bowland) by KCL … develop the skills of constructing the model. Why do penguins huddle? See the Australian Antarctic Survey … to see how mammals vary their volume to surface area ratio. Work with biology. (Also: fridges vs radiators) Is the Chinese New Year animal designation (or star sign) accurate? Construct a statistical model. Designing an efficient car park for the school (and other packing problems) School finance (capitation in … salaries, buildings, equipment, … out). Work with Business Studies. Islamic Patterns (17 unique tesselations of the plain, start to develop a taxonomy, …)(Also, Escher tessellations for transformational geometry). Work with Art/Textiles. The Finances of the School Play. Work with Drama. Readability tests (well known readability models are available in MS Word … how is the model constructed and what is it good/bad for?) Work with English. What is the relationship between words and symbols for numbers in different languages? Why are some numbers special? What number base is being used? (Four score year and ten = Quatre-vingt dix) Work with MFL.