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

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

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

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

  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. Addition 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) pictures 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) symbols

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

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

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

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

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

  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? Subtraction (Take away) Drawing a picture helps children to visualise the problem (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? Using dots or tally marks is quicker than drawing a detailed picture (Take away) (Find the difference)

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

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

  18. Number lines - taking away 74 – 26 = 48 − 20 − 4 − 2 48 50 54 74

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

  20. 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 89 = 80 + 9 - 5750 + 7 30 + 2 = 32

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

  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. Progression for multiplicationand division • Counting • Doubling and halving • Multiplication as repeated addition anddescribing an array • Division as groupingandsharing • Understand that multiplication and division are inverses • Recall of multiplication and division facts • Multiply two / three-digit numbers by 10 / 100 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. pictures symbols Multiplication 2 x 3or3 x 2 3 plates, 2 cakes on each plate (Children could draw a picture to help them work out the answer) 2 x 3or3 x 2 3 plates, 2 cakes on each plate (Children could use dots or tally marks to represent objects – quicker than drawing a picture)

  29. 4 0 2 6 Number tracks and number lines (modelled using bead strings) 2 x 3or3 x 2 [two, three times] or [three groups of two]

  30. Arrays 5 x 3or3 x 5 14 x 2 = 28 Array creator

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

  32. TU x TU (Short multiplication - multiplication by more than a single digit) 64 x 34 1800 240 120 + 16 2176 HTU x TU (Short multiplication - multiplication by more than a single digit) 6000 372 x 24 1400 40 1200 280 8 8928

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

  34. DIVISION

  35. Division 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

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

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

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

  39. Sharing equally8 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. 24 ÷ 4 = 6 8 12 4 20 24 0 16

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

  44. 97 ÷ 9 = 10 r 7

  45. Efficient methods . . . . 754 ÷ 6 Approximation: Answer lies between 100 (600 ÷ 6) and 150 (900 ÷ 6) Answer = 125 r 4 Extend to U.t ÷ U and HTU ÷ TU

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

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

  48. Useful websites and resources • Transumhttp://www.transum.org/Software/ - provides a mathematics challenge for every day of the year! • Nrichhttp://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. • Woodlandshttp://resources.woodlands-junior.kent.sch.uk/maths/ • - interactive maths games and activities for both KS1 and 2 • BBC Bitesizehttp://www.bbc.co.uk/bitesize/ - useful summary of KS1/KS2 content with interactive activities [also has KS3/KS4 materials] • I Love Maths Games – games, puzzles and investigations http://www.ilovemathsgames.com/ • Professor Kageyama’s maths training for DS consoles

  49. Maths for mums and dads – Rob Eastaway Rob 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

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