1. Berkeley Primary School Calculation Evening, May 2013 Please sit anywhere for the moment

2. Objectives for the evening: To share how we teach calculation at Berkeley. To give an understanding of progression in calculation. To let adults experience what their children experience. To have FUN! Don’t be shy – get stuck in

3. Our children... are all different (believe it or not). They are not widgets at exactly the same point on the ‘production line’. That’s why we teach them as individuals and tailor maths to suit them. They are all on individual journeys and at varying stages in their progression.

4. The Four Rules Understanding Mental calculations Rapid recall Efficient written methods Models, images & concrete materials Stories / rhymes Problem solving and role play Use of ICT

5. ADDITION AND SUBTRACTION

6. PROGRESSION FOR ADDITION AND SUBTRACTION Counting One more / less Addition as combining two groups, then counting on Subtraction as take away or difference (eg how many more is … than …?) Ten more/less Recall of addition/subtraction facts to 10, 20 and beyond Understand that subtraction and addition are inverses

7. 2 + 3 = I buy 2 cakes and my friend buys 3 cakes. How many cakes did we buy altogether? (Children could draw a picture to help them work out the answer) 8 + 5 = 8 people are on the bus. 5 more get on at the next stop. How many people are on the bus now? (Children could use dots or tally marks to represent objects – quicker than drawing a picture) Addition pictures symbols

8. Counting on – jumps of 1 (modelled using bead strings) 18 + 5 = 23 18 19 20 21 22 23 24 +1 +1 +1 +1 +1

9. 47 77 80 82 (+ 2) (+ 3) (+ 30) 35 + 47 = 47 + 30 + 5 = 77 + (3 + 2) = 82 35 + 47 = 82 No number line

10. 74 + 48 Addition by partitioning 70 + 40 = 110 4 + 8 = 12 122

11. 374 + 248 Addition by partitioning 70 + 40 = 110 4 + 8 = 12 300 + 200 = 500 622 300 + 70 + 4 200 + 40 + 8 500 + 110 + 12

12. 1 COLUMN ADDITION Extended to: 1247 + 367 £2.36 + £6.48 3.5 + 4.8 7.48 + 2.6 12.5 km + 6.08 km 1 + 248 374 622 MORE TRADITIONAL METHODS ARE STILL USED!

13. SUBTRACTION

14. Earlier work involves taking away objects from groups, counting back on a number line or using number beads. Counting on fingers etc

15. 5 – 2 = I have five cakes. I eat two of them. How many do I have left? A teddy bear costs £5 and a doll costs £2. How much more does the bear cost? (Take away) (Find the difference) 13 – 5 = Mum baked 13 biscuits. I ate 5. How many were left? Lisa has 13 felt tip pens and Tom has 5. How many more does Lisa have? Drawing a picture helps children to visualise the problem Using dots or tally marks is quicker than drawing a detailed picture (Take away) (Find the difference) Subtraction

16. Taking away – jumps of 1 (modelled using bead strings) 13 – 5 = 8 8 9 10 11 12 13 -1 -1 -1 -1 -1

17. Counting on – jumps of 1 (modelled using bead strings) 11 – 8 = 3 0 1 2 3 4 5 6 7 8 9 10 11 +1 +1 +1

18. 74 4850 54 − 2 − 4 − 20 Number lines - taking away 74 – 26 = 48

19. Number lines - counting on 74 – 26 = 48 0 26 30 70 74 + 4 + 40

20. 89= 80 + 9 - 57 50 + 7 30 + 2 = 32 As they move up into KS2, the children will begin to use partitioning to subtract too- breaking down the numbers into Hundreds, Ten’s, Units etc

21. We then move onto the RED ALERT questions (or decomposition) where borrowing is introduced: 352 = 300 50 40 12 - 136 = 100 30 6 200 10 6 = 216

22. 7 1 6867 - 2684 4183 MORE TRADITIONAL METHODS ARE STILL USED! Does this look more familiar?!

23. Our children are always encouraged to have a go and to not be afraid of making mistakes. That’s how we learn. OK… If you’re still awake, time to head for a maths group and try an activity or two.

24. MULTIPLICATION AND DIVISION

25. Counting Doubling and halving Multiplication as repeated addition and describing an array Division as grouping and sharing Understand that multiplication and division are inverses Recall of multiplication and division facts Multiply two / three-digit numbers by 10 / 100 Progression for multiplication and division context Dice race game

26. COUNTING IN CONTEXT How many 10p coins are here? How much money is that? How many toes are there on 2 feet? How many gloves in 3 pairs? If Sarah counts in 2s and Nigel counts in 5s, when will they reach the same number? How many lengths of 10m can you cut from 80m of rope?

27. DOUBLING AND HALVING IN CONTEXT There are 8 raisins. Take half of them. How many have you taken? One snake is 20cm long. Another snake is double that length. How long is the longer snake? I double a number and then double the answer. I now have the number 32. What number did I start with?

28. 2 x 3 or 3 x 2 3 plates, 2 cakes on each plate (Children could draw a picture to help them work out the answer) 2 x 3 or 3 x 2 3 plates, 2 cakes on each plate (Children could use dots or tally marks to represent objects – quicker than drawing a picture) Multiplication pictures symbols

29. Number tracks and number lines (modelled using bead strings) 2 x 3 or 3 x 2 4 620 [two, three times] or [three groups of two]

30. Arrays 5 x 3 or 3 x 5 14 x 2 = 28 x 104 2208 Array creator

31. 43 x 6 258 1 40 x 6 = 240 3 x 6 = 18 X403 624018 43 x 6 Arrays then can lead into what we call grid multiplication- partitioning numbers for multiplication

32. TU x TU (Short multiplication - multiplication by more than a single digit) 64 x 34 HTU x TU (Short multiplication - multiplication by more than a single digit) 372 x 24 X 60 4 301800120 4 24016 1800 240 120 + 1 6 2176 X 300 70 2 206000 1400 40 41200 280 8 6000 1400 40 1200 280 8 8928

33. HTU x TU (Standard Method for long multiplication) 372 x 24 372 24 x 8 280 1200 40 1400 6000 8928 372 x 1488 + 7440 8928 Multiplying 4 x 2 then 4 x 70 then 4 x 300 etc ( 372 x 20) ( 372 x 4) 1

34. DIVISION

35. 6 ÷ 2 6 cakes shared between 2 6 cakes put into groups of 2 (Children could draw a picture to help them work out the answer) pictures Division

36. 6 ÷ 2 6 cakes shared between 2 6 cakes put into groups of 2 (Children could use dots or tally marks to represent objects – quicker than drawing a picture) symbols

37. Number tracks and number lines - grouping (modelled using bead strings) 8 ÷ 2 = 4 6 ÷ 2 = 3 0 2 4 6

38. Number lines / Arrays 15 ÷ 5 = 3 0 5 10 15

39. Sharing equally 8 sweets are shared between 2 people. How many do they each receive?

40. GROUPING OR REPEATED SUBTRACTION- ASKING IN A DIFFERENT WAY! There are 8 sweets. How many people can have two sweets each?

41. As children progress in division, they will continue to use: repeated subtraction using a number line. They may use an empty number line or a hand drawn jumping line. e.g. 24 ÷ 4 = 6 - children will start at 0 and jump forwards in 4’s to find how many 4’s go into 24 or they may do a multiplication (repeated addition from earlier) Children will also move onto remainders e.g. 13 ÷ 4 = 3 r 1

42. 0 4 812 16 2024 24 ÷ 4 = 6

43. As children continue with their progress, they will learn methods such as chunking! This is chunking! This is chunking! http://www.bbc.co.uk/news/11260872

44. 97 ÷ 9 = 10 r 7

45. EFFICIENT METHODS.... Answer = 125 r 4 Approximation: Answer lies between 100 (600 ÷ 6) and 150 (900 ÷ 6) 754 - 600 (6 x 100) 154 - 120 (6 x 20) 34 - 30 (6 x 5) 4 Extend to U.t ÷ U and HTU ÷ TU 754 ÷ 6

46. Efficient methods.... Short division 291 ÷ 3 = 97 Estimation: 270 ÷ 3 = 90 3 291 97 2 7 43.4 6.2 1 43.4 ÷ 7 = 6.2 Estimation: 42 ÷ 7 = 6 2 4

47. OK… Time to try some multiplication and division activities.

48. Transum http://www.transum.org/Software/ - provides a mathematics challenge for every day of the year!http://www.transum.org/Software/ Nrich http://nrich.maths.org/public/ - thousands of FREE mathematics enrichment materials for ages 5 to 19 years. The resources are designed to develop problem-solving and mathematical thinking skills.http://nrich.maths.org/public/ Woodlands http://resources.woodlands-junior.kent.sch.uk/maths/http://resources.woodlands-junior.kent.sch.uk/maths/ - interactive maths games and activities for both KS1 and 2 BBC Bitesize http://www.bbc.co.uk/bitesize/ - useful summary of KS1/KS2 content with interactive activities [also has KS3/KS4 materials]http://www.bbc.co.uk/bitesize/ I Love Maths Games – games, puzzles and investigations http://www.ilovemathsgames.com/ http://www.ilovemathsgames.com/ Professor Kageyama’s maths training for DS consoles Useful websites and resources

50. Maths for mums and dads – Rob Eastaway Rob EastawayRob Eastaway has been Director of Maths Inspiration since it began in 2004. He is an author whose books on everyday maths include the bestselling Why Do Buses Come In Threes? and The Hidden Maths of Sport. He appears regularly on BBC Radio 4 and 5 Live to talk about the maths of everyday life and has given maths talks across the world to audiences of all ages http://www.bbc.co.uk/news/11260872

51. 31142016 246525 30291836 117131 14 20 21 34 39 45 50 Three in a row Choose two numbers from the row of numbers above the grid. Find the difference between these numbers. If the answer is on the grid, cover that number with a counter.

52. A Square of Numbers http://nrich.maths.org/public/viewer.php?obj_id=2005 Y3