1. Welcome to Dingo State School Numeracy Afternoon

2. Our Aim Help children feel confident when working mathematically …

3. How is mathematics education different for this generation? Previously we were taught mainly facts and procedures. Lessons were about practise and recall Lessons ensure students have deep and connected understandings. Students are expected to explain, reason and justify.

4. In the Australian Curriculum, we expect students to have: Understanding (connecting, representing, identifying, describing, interpreting, sorting, …) Fluency (calculating, recognising, choosing, recalling, manipulating, …) Problem solving (applying, designing, planning, checking, imagining, …) Reasoning (explaining, justifying, comparing and contrasting, inferring, deducing, proving, …)

5. “But, I wasn’t good at Maths” When we focus too much on facts and procedures, students may develop misconceptions and inefficient methods. This quite often leads to maths anxiety, disengagement and poorer performance in all subjects that require mathematics.

6. Going mental first Mental computation and estimation account for approximately 80% of the calculations we do in real life Using a calculator 15-18% of the time Paper and pencil methods 3-5% of the time Most adults were not taught mental computation methods.

7. Discussion 30% of Australian adults are unable to use the procedure that was drilled into us. Most adults were shown one way to add and subtract, multiply and divide. Often, these adults have ‘ANXIETY’ in situations that involve calculation

8. Counting and Subitising The counting principles Each object must be counted only once Numbers must be said once Arrangement of objects does not affect how many there are in the collection The last number said tells how many in the collection

9. Key Terms Rainbow Facts or friends of 10 Doubles Near doubles Subitising Partitioning Compensating Jumping

10. Key Terms Rainbow Facts or friends of 10

11. Key Terms Doubles Near doubles 2+26+7 3+38+9 22+2222+23 46+4646+47

12. Counting and Subitising Subitising Students recognise numbers at a glance Familiar with collections or arrangements such as dice patterns Seeing smaller parts within collections Subitising assists students to quantify collections and build whole-part relationships and an understanding of decimal numbers.

14. Partitioning Breaking a number up into smaller numbers, usually hundreds, tens and ones. 156 100 + 50 + 6 50 + 50 + 50 + 6 9731 9000 + 700 + 30 + 1 Builds fluency and flexibility of thinking

15. [ ] = 7 + 5 + 3 + 5 + 6 How would you add these numbers?

16. [ ] = 7 + 5 + 3 + 5 + 6 Child A adds in order: 7,5,3,5 and then 6 (counting all on her fingers) Child B says ‘7 and 3 make 10’, ‘5 and 5 make 10’ and ‘6 more is 26’ Child C says ‘5+5 = 10’, then ‘6 + 3 = 9’, ‘so that’s 19’. He then counts on 7 more Child D takes 2 from 7 and adds it the 3 to make 4 lots of 5. She says, ‘Four fives are 20. 20 and 6 more is 26.’

17. 7 + 4 = [ ] + 5 1611611 & 16 Here are the four most common student responses (Years 2-7) Insight into misconceptions 55%20% 10%15% What is a typical response rate in Year 4? 6 is the correct answer.

18. 201-198

19. Jumped straight to a procedure and got it wrong Jumped straight to a procedure and got it correct Reasoned mentally Trusted Numbers 14%25%61% 25%35%40% 28%41%31% 2/3 4/5 6/7

20. 7 34 3 7 7 4 43 3 743 4 7 8 124 8 4 48 8 48 4 Give your child a number fact. Can they create the related number facts? To ensure they UNDERSTAND Ask your child to say or draw a problem that (USES) one of these facts

21. 24 83 8 3 38 3 83 8 3 124 3 4 43 3 43 4 LINK this to FRACTIONS Eg ⅓ of 12 = 4

22. NUMBER FACTSSTORY ( drawing or oral ) A chef made 10 cakes and I ate 2 of them. There are 8 cakes left. RELATED FACTSEXTENDED FACTS If I know 8 + 2 = 10 then I also know: 80 + 20 = 100 100 – 20 = 80 8 + 2 = 10 2 + 8 = 10 10 - 8 = 2 10 – 2 = 8 FOUR SQUARE

23. What methods do we use as adults? 38 + 57 72 - 28

24. JUMP- addition & subtraction

25. SPLIT: addition & subtraction Students must be confident and flexible with Place Value concepts to assist with mental computation.

26. Left to right adding and subtracting Students and adults naturally use left to right thinking for mental calculations. Left to right written methods connect to students’ mental strategies.

27. Compensating 38 + 57 72 - 28

28. What does Australian Curriculum expect? Addition and subtraction facts by Year 3 Multiplication and division facts by Year 3/4 A greater focus on mental methods to prepare students for real world situations A range of written methods (not just the one method) Students to choose methods and strategies to suit individual problems

29. How can you help at home? Talk about ways that you use to add and subtract mentally. Practise number facts in game situations. Don’t expect your children to naturally add and subtract like you do. Let your children discuss their ways for adding and subtracting with you.

30. Ask your child to explain their strategies for adding and subtracting Resist the temptation “ This is how you should do it” Ask your child for an estimate before they calculate the exact answer Ask “Is that answer reasonable?”

31. Adding number plates

32. Other Ideas Play board games with dice, spinners, dominoes and cards. Cook with the kids, scales, measuring cups and timers etc. Smarties or any sweets are great for counting large numbers, sharing….. Family bar of chocolate is great for fractions Shopping or travel challenges. How long, How much

34. 12345678910 80 8 40 16 32 64 24 48 72 56 If students are shown the links they are less likely to forget them The x1, x2, x5 and x10 facts can provide a foundation for all multiplication and division facts.

35. 45 How many multiplication facts are there? 2x34x22x59x22x610x22x78x22x2 3x54x33x103x68x39x37x33x3 4x109x44x74x85x44x64x4 10x67x69x68x66x6 8x77x107x97x7 10x89x88x8 9x55x67x55x108x55x5 10x99x9 10x10

36. I have forgotten 8 x 7? I know 7x2=14 Double 14 is 28 Double 28 is 56 10 x 7 = 70 Take two 7s (14) from 70 That’s 56 I know that 5 x 8 = 40 2 x 8 = 16 40+16 = 56 What do we do if my child doesn’t know a table fact?

37. Teaching Number Facts What is more important. To know your number facts or to understand strategies to solve number facts? 37

38. You need to know the basics 1’s 2’ 10s Term 1 2007 38 1 x 91 x 291 x 379 2 x 9 doubling 2 x 292 x 279 10 x 9 9 groups of 10 NOT add zero 10 x 29279 x 10

39. Number Facts 3X What strategies do you use? Term 1 2007 39 3 x 627 x 3231 x 3

40. Number Facts 3X (3x) double plus 1 Term 1 2007 40 3 x 6 Double 6 + 6 12 + 6 = 18 3 x 8 Double 8 + 8 16 + 8 = 24 What other strategies? 27 x 3 Double 27 + 27 54 + 27 = 81 231 x 3 Double 462 + 231 462+ 231 = 693 3 x 200 = 600 3 x30 = 90 3 x 1 = 3

41. Number Facts 3X Scan Think Do See Plan Do Check Term 1 2007 41 3 x 275

42. Number Facts 4X What strategies do you use? Term 1 2007 42 4 x 947 x 4135 x 4

43. Number Facts 4X (x4) Double Double Double the other number, then double again. Term 1 2007 43 4 x 6 Double 6 + Double 6 12 + 12 = 24 4 x 9 Double 9 + Double 9 18 + 18 = 36 What other strategies? 37 x 4 Double 37 + Double 37 74 + 74 = 148 135 x 4 Double 135 + Double 135 270 + 270 = 540 4 x 100 = 400 4 x 30 = 120 4 x 5 = 20

44. Number Facts 4X Scan Think Do See Plan Do Check Term 1 2007 44 4 x 128

45. Number Facts 5X What strategies do you use? Term 1 2007 45 5 x 637 x 5135 x 3

46. Number Facts 5X (x5) Multiply by 10 then half Term 1 2007 46 5 x 6 10 x 6 60 ÷ 2 = 30 5 x 9 10 x 9 then divide 2 90 ÷ 2 = 45 What other strategies? 37 x 5 10 x 37 then divide 2 370 ÷ 2 = 185 135 x 5 10 x 135 then divide 2 1350 ÷ 2 = 675 5 x 100 = 500 5 x 30 = 150 5 x 5 = 25

47. Number Facts 5X Scan Think Do See Plan Do Check Term 1 2007 47 5 x 246

48. Number Facts 6X What strategies do you use? Term 1 2007 48 6 x 734 x 6267 x 6

49. Number Facts 6X (x6) Multiply by 10 then half plus the numberOR Double the #, then add it one more time then double again Term 1 2007 49 6 x 7 ((Double 7) + 7) x 2 (14 + 7) x 2 21 x 2 = 42 6 x 7 10 x 7 then divide 2 + 6 70 ÷ 2 + 6 = 42 What other strategies? 34 x 6 ((Double 34) + 34) x 2 (68 + 34) x 2 102 x 2 = 204 34 x 6 10 x 34 then divide 2 + 34 340 ÷ 2 + 34 = 170 + 34 = 204 267 x 6 200 x 6 = 1200 60 x 6 = 360 7 x 6 = 42 1602

50. Number Facts 6X Scan Think Do See Plan Do Check Term 1 2007 50 6 x 262

51. Number Facts 7X What strategies do you use? Term 1 2007 51 7 x 724 x 7379 x 7

52. Number Facts 7X (x7) Multiply Fives strategies plus double strategies 52 7 x 7 7 x 10 ÷ 2 + (7 x 2) 70 ÷ 2 + 14 35 + 14 = 49 8’s -1? 9’s – double? Does anyone know a better mental strategy? 24 x 7 24 x 10 ÷ 2 + (24 x 2) 240 ÷ 2 + 48 168 138 x 7 138 x 10 ÷ 2 + (138 x 2) 1380 ÷ 2 + 276 690 + 276 966 379 x 7 300 x 7 = 2100 70 x 7 = 490 9 x 7 = 63 2653

53. Number Facts 7X Scan Think Do See Plan Do Check Term 1 2007 53 7 x 425

54. Number Facts 8X What strategies do you use? Term 1 2007 54 7 x 834 x 8154 x 8

55. Number Facts 8X (x8) Double + Double + Double When multiplying by 8 double the other #, double the result, and then double again. 55 6 x 8 Double 6 + Double 12 + Double 24 6 x 2 x 2 x 2 48 7 X 8 Double 7 + Double 14 + Double 28 7 x 2 x 2 x 2 56 Does anyone know a better mental strategy? 34 x 8 Double 34 + Double 68 + Double 136 34 x 2 x 2 x 2 = 272 154 x 8 Double 154 + Double 308 + Double 616 154 x 2 x 2 x 2 1232 278 x 8 200 x 8 = 1600 70 x 8 = 560 8x 8 = 64 2224

56. Number Facts 8X Scan Think Do See Plan Do Check Term 1 2007 56 8 x 256

57. Number Facts 9X What strategies do you use? Term 1 2007 57 3 x 927 x 9231 x 9

58. Number Facts 9X (x9) Multiply by 10 then subtract the number 58 6 x 9 6 x 10 then take 6 60 – 6 = 54 8 x 9 8 x 10 then take 8 80 – 8 = 72 ROTE 34 x 9 34 x 10 then take 34 340 – 34 = 306 156 x 9 156 x 10 then take 156 1560 – 156 = 1404 456 x 9 400 x 9 = 3600 50 x 9 = 450 6 x 9 = 54 4104

59. Number Facts 9X Scan Think Do See Plan Do Check Term 1 2007 59 9 x 455

60. Double Digit Multiplication What aspects of learning multiplication are the most important? 60

61. By the end of primary 27 x 33 =

62. Trusting the numbers In order for our students to do this they must TRUST the numbers. Thank you 62

63. Cheers