Backwell JuniorSchool

1. Backwell JuniorSchool Maths Parent Workshop Tuesday 14th October 2014 Before we begin, please try to solve the calculations on your table…..

2. Aims • To explain how we teach your children +, -, x, ÷ and Times Tables • To discuss our school focus of Conceptual Understanding • To give you ideas of how you can help your children at home.

3. How did you solve these? • 157+65= • 245-152= • 46x22= • 154÷7= • 278÷19=

4. How did you solve these? • 157+65= 222 • 245-152= 93 • 46x22= 1012 • 154÷7= 22 • 278÷19= 14.63

5. Maths lessons • Emphasis on mental calculation • Children are encouraged to work mentally, using jottings to support their thinking • Encouraged to use more formal written methods only for calculations they can not solve in their heads • Maths through problem solving/conceptual understanding

6. By the end of Key Stage 2 we want your children to… • Have good understanding of the 4 operations • Have an efficient, reliable method of written calculation for each operation • Be confident with mental calculations and times tables • Apply what they know to problems • Be happy and confident mathematicians

7. Addition

8. Addition Use of a number line 6+5= Use of a 100 square 34+12=

9. 25 + 16 = (20+5)+(10+6) 20+10=30 5+6=11 30+11=41 Addition by partitioning

10. Addition – Column Method 126+19=145 1 2 6 + 1 9 1 4 5 1

11. Addition – Column Method Development 12476+7369 12476 + 7369 19847 1 1 Extension through Decimals

12. Addition – Column Method Development Your turn: 67.75 + 21.50 =89.25

13. Subtraction

14. Subtraction Taking away practically. 3-2=

15. Use of a number line/100 square 12-6=6

16. Subtraction- Column Method 204-65= 139 129014 - 65 139 Your turn:708-89 = 619

17. Multiplication

18. Multiplication- repeated addition 3x5= (3 groups of 5) xx xx x xx xx x xx xx x 5 + 5 + 5 = 15

19. Multiplication using a blank number line 4x3= 12 _____________________ 0 3 6 9 12

20. Multiplication by Partitioning 32x3= 96 Your turn: 45x6 = 270

21. Multiplication - Written Method Short Multiplication 347 x 7 347 x7 2429 3 4 Your turn: 2746x 6 = 16,446

22. Multiplication - Written Method Long Multiplication 33x28 33 x28 264 2 660 924

23. Multiplication - Written Method Your turn: 36x57 =2052

24. Times Tables Awards Carrying out mental maths calculations quickly and accurately continues to be an important part of the maths curriculum. Times Tables tests are carried out each week (some children may begin on Number Bonds rather than Times Tables). Children progress through Bronze, Silver and Gold Awards. Children now need to know facts for 11 and 12 times tables as well (our new tests are out of 26).

25. Bronze Times Tables Awards Children know their times tables facts in order: Children need to achieve 26 out of 26 twice before they move onto the next times table. Class teachers will the children know which times tables they’re working on each week.

26. Silver Times Tables Awards Children know their times tables facts in random order:

27. Gold Times Tables Awards Children know their multiplication and division facts:

28. Next Steps… • If children achieve all of their awards, they will move onto our Extension Challenges. • These involve revising all times tables facts (45 Golden Facts and 75 Facts) • They then move onto working with Fractions and Percentages..

30. Division

31. Division Sharing The children are sharing out into a known number of groups but how many in each group is unknown, 12÷3= 12 apples are shared into 3 baskets. How many apples are in each basket?

32. Division Grouping It is known how many are in a group but the number of groups is not known. 12÷3= How many groups of 3 are there in 12? There are 12 apples. How many horses will get 3?

33. Division using a blank number line (How many groups of 5 are there in 25?) 25÷5= 5 _______________________ 0 5 10 15 20 25

34. Division Short Division 98÷7=14 1 4 7 92 8 Your turn: 98÷6 With a decimal remainder =16.33 Remainders 99÷7=14r1 or 1 4.142 7 92 9103020

35. Long Division 432÷15

36. Long Division 432 ÷ 15 becomes 15 ) 432

37. Long Division Calculate 4 ÷ 15 432 ÷ 15 15)4 3 2

38. Long Division We can’t do it, so we write the answer 0 here 432 ÷ 15 0 15 ) 4 3 2

39. Long Division So we next look at 43 ÷ 15 432 ÷ 15 0 15)4 32 Use repeated subtraction here if this helps

40. Long Division 2x 15 = 30 3 x 15 = 45 432 ÷ 15 0 2 15)4 3 2

41. Long Division 2 x 15 = 30 432 ÷ 15 We need to take off 13 from the 43 to get the remainder 0 2 15 ) 4 3 2 - 30 13

42. Long Division Now we are going to do 132 ÷ 15 and put the answer here 432 ÷ 15 0 28 15)4 3 2 - 30 1 3 2

43. Long Division Now we are going to do 132 - 120 to get the remainder 432 ÷ 15 0 2 8 15) 4 3 2 -3 0 1 3 2 1 2 0 1 2

44. Long Division 432 ÷ 15 0 2 8.8 15 ) 4 3 2120 - 3 0 1 3 2 1 2 0 1 2

45. Long Division = 28 r 12 432 ÷ 15 or 28.8

46. Long Division Your turn: 496 ÷ 11 = 45 r1 or 45.09

47. Conceptual Understanding Presenting problems and questions in different ways to deepen children’s understanding and reasoning in maths. Different to procedural teaching methods which practice processes – lists of calculations etc.

48. Conceptual Understanding Problems can be adapted by: • removing intermediate steps • reversing the problem • making the problem more open • asking for all possible solutions • asking why, so that pupils explain their reasoning • asking directly about a mathematical relationship.

49. Conceptual Understanding Which version involves deeper problem-solving skills and why? Version 1 Version 2

50. Conceptual Understanding Question 1 Jeans cost £13.95. They are reduced by 1/3 in a sale.What is their price in the sale? Dan buys the jeans. He pays with a £10 note. How much change does he get? Question 2 Jeans cost £13.95. They are reduced by 1/3 in a sale. Dan buys the jeans. He pays with a £10 note. How much change does he get?