Maths

1. Maths How do we teach it? Why do we teach it like that? What do the written methods look like? What can you do at home to help?

2. How do our children learn in Maths lessons at Orleans? • Encouraged to use mental calculation methods • Practise recall of number facts to become quicker and more accurate • They are more aware of the strategies they use to calculate • Focus on correct use of vocabulary and talk for learning • Real-life, contextual learning • Practical and engaging lessons – fascinators!CB's

3. ‘I hear and I forget. I see and I remember. • I do and I understand.’ • (A Chinese proverb) ‘It just doesn’t look like it did in my day.’

4. Until fairly recently, maths was taught using Victorian era methods. Were you one of the lucky ones? Logical and strong with numbers?

5. Victorian Times Vast numbers of clerks to perform calculations every day. • Today, calculators and spreadsheets can do this car quicker, so the need for everybody to be able to do big calculations by hand has largely disappeared That’s not to say we don’t need strong number skills!

6. We are inundated by numbers all the time…

7. Do we all need to be able to work out 27 x 43 precisely with a pen and paper? Probably not…but we do need to know that: 27 x 43 is roughly 30 x 40 and… that this is roughly 1,200 It's partly the need to have a good feel for numbers that is behind the modern methods.

8. National Numeracy Strategy 1999 • The revolution in the teaching of maths at primary school kicked in with this strategy. • The emphasis moved away from blindly following rules (remember borrowing one from the next column and paying back?) towards techniques a child understood

9. The Aim • for children to do mathematics in their heads, and if the numbers are too large, to use pencil and paper to avoid losing track. • To do this children need to learn quick and efficient methods, including mental methods and appropriate written methods.

10. Learning written methods is notthe ultimate aim. Mathematics is foremost an activity of the mind; written calculations are an aid to that mental activity.

11. We want children to ask themselves: Can I do this in my head? Can I do this in my head with the help of drawings or jottings? Do I need to use an expanded or compact written method? Do I need a calculator?

12. 97 x 100 9 9 1 16 0 1 1 1 00 0 1 0 0 0 - 7 9 9 3 - 9 000 9700 7 9700 0 8 0 5 7 5 6 A sledgehammer to crack a nut!

13. Addition

14. Addition – progression • Y3 Programme: • To add mentally combinations of 1-digit and 2-digit numbers • Develop written methods to record, support or explain addition of 2-digit and 3-digit numbers • Y4 Programme: • To add mentally pairs of 2-digit numbers • To refine and use efficient written methods to add 2-digit and 3-digit numbers and £.p

15. How would you solve these? • 25 + 42 • 25 + 27 • 25 + 49 • 145 +127

16. Partitioning Your turn… 53 + 46 = • 48 + 33 • 8 30 3 • 70 + 11 = 81

17. Number line + 10 +1 +1 36 37 26 38 38 26 + 12 = + 100 +6 + 30 242 + 136 = 378 242 342 372 378

18. Use the number line to work these out… • 67 + 48 = • 346 + 237 = • 3241 + 1471 = 242 + 136 = 378 + 30 + 100 +6 242 342 372 378

19. Column Method Compact Expanded 358 + 33 358 + 33 Leading to 11 80 300 391 1 391

20. Subtraction

21. Subtraction - progression • Y3 Programme: • To subtract mentally combinations of 1-digit and 2-digit numbers • Develop written methods to record, support or explain subtraction of 2-digit and 3-digit numbers • Y4 Programme: • To subtract mentally pairs of 2-digit numbers • To refine and use efficient written methods to subtract 2-digit and 3-digit numbers and £.p

22. How would you solve these? • 67 - 45 • 67 – 59 • 178 - 99 • 3241 - 2167

23. Number line • Subtraction as taking away - 10 - 5 - 2 30 15 20 13 30 – 17 = 13

24. Subtraction as finding the difference Difference 5 12

25. Number line • Subtraction as finding the difference 34 – 18 = + 4 + 10 +2 34 18 20 30 • Jump to next multiple of 10 • Count the jumps 10 + 4 + 2 = 16

26. Column Method 1 7 82 - 57 25 547 134 413

27. Use the number line to work these out… • 48 – 31 = • 256 - 167 = + 4 + 10 +2 18 20 30 34

28. Multiplication

29. Multiplication - progression Y3 Programme: • Multiply one digit and two digit numbers by 10 or 100 and describe the effect; • Derive and recall multiplication facts for the 2, 3, 4, 5, 6, and 10 times tables; • Use informal and practical methods to multiply two digit numbers e.g. 13 x 3. Y4 Programme: • Multiply numbers to 1000 by 10 and then 100 and describe the effect; • Derive and recall multiplication facts up to 10 x 10; • Use written methods to multiply a two digit number by a one digit number e.g. 15 x 9.

30. How would you solve these? • 24  50 • 24  4 • 24  15 • 136  9

31. Number line Multiplication as repeated addition 4 x 2 +2 +2 +2 +2 0 2 4 6 8 4 x 2 = 2 + 2 + 2 + 2 So, 2 x 4 = 8

32. Arrays 3 x 6 Or Add the dots

33. What multiplication are these arrays showing?

34. Partitioning 24 x 5 20 x 5 = 100 4 x 5 = 20 100 + 20 = 120

35. Grid Method 24 x 5 20 4 x 5 100 20 100 + 20 = 120 BBC News Video Link

36. Expanded Multiplication 38 x 7 210 56 (30 x 7) (8 x 7) 266

37. Use the grid method to work these out: 24 x 7 142 x 3 24 x 5 20 4 x 5 100 20 100 + 20 = 120

38. Division

39. Division - progression Y3 Programme: Use practical and informal written methods to divide two-digit numbers (e.g. 50 ÷ 4); Y4 Programme: Develop and use written methods to record, support and explain division of two-digit numbers by a one-digit number, including division with remainders (e.g. 98 ÷ 6)

40. How would you solve these? • 123  3 • 165  10 • 325  25 • 623  24

41. Division Sharing Grouping

42. Arrays First group of 3 12 ÷ 3 = 4

43. Repeated subtraction • ÷ 3 = 4 - 3 - 3 - 3 - 3 12 0 3 6 9 12 - 3 – 3 – 3 – 3

44. Counting in steps • ÷ 3 = 4 Add the jumps + 3 + 3 + 3 + 3 Fingers 12 0 3 6 9 “3” “6 “9 “12”

45. Chunking 75 ÷ 5 5 x 5 10 x 5 25 0 75 75 - 50 (10 x 5) 25 - 25 (5 x 5) 0 Need to know tables! 75 ÷ 5 = 15 BBC News Video Link