Warm up activity. Using the first 3 problems as clues, what is the number represented as an “?”

1. Twyford School • Warm up activity. • Using the first 3 problems as clues, what is the number represented as an “?” • 1/3 of 12 = • 9 + 7 = • 100 – 36 = • 56 + ? = When are they going to start learning proper maths? 4 ? = 200 16 64 256 Maths Evening

2. Back to School time! 1. 127 + 125 = 2. 378 – 153 = 3. 9 x 49 = 4. 20 x 342 = 5. 408 ÷ 12 = 6. 37.5% of $80 =

3. Does this look familiar?

4. What about this? Do all the odd numbers!

5. Doesn’t it make sense to change it to 500+20 rather than doing all the renaming and carrying stuff? Solve by using working form 499 + 21 _______ Are algorithums outlawed? No. However students shouldn't be exposed to working form until they are “part wholing” (stage 6) Premature exposure to this may restrict the students ability and desire to use mental strategies.

6. Enter the Numeracy Project The Numeracy Development Project began with a pilot in 2000, since then its expanded to involve almost all of the primary schools in New Zealand. Its purpose is to promote quality teaching. It is designed to provide different experiences in learning mathematics. More emphasis is placed on the students making sense of mathematical ideas and to develop abstract thnking.

7. As part of the Numeracy Project your child will be learning to: • Enjoy working with numbers • Make sense of numbers - how big they are, how they relate to other numbers, and how they behave • Solve mathematical problems - whether real life or imaginary • Calculate in their heads whenever possible, rather than using a calculator or pen and paper • Show that they understand maths, using equipment, diagrams and pictures • Explain and record the methods they use to work out problems • Accept challenges and work at levels that stretch them • Work with others and by themselves • Discuss how they tackle mathematical problems - with other students, their teacher and you!

8. The Stages

9. 1,2,3,5,9 Stage Zero Students at this stage are unable to consistently count a given number of objects.

10. 6 Stage One Students can count a set of objects up to 10, but cant join two sets together

11. 5 and 3 more is 8 Stage Two Students can join two sets of objects, but rely on counting physical materials (including their fingers)

12. If I had 6 logs and carried in another 2, how many logs do I have? 1,2,3,4,5,6,7,8 Stage Three Students can count all of the objects in addition and subtraction problems in their mind

13. I counted 6 cars and 9 trucks. How many vehicles did I count? 9,10,11,12,13,14,15 Stage Four Students here are able to count on or back from the largest number rather than starting at zero

14. There are 7 in Team Red and 8 in Team White. How many players are there? 7+7=14, so 7+8=15 Stage Five Students are able to re-arrange numbers to make them easier to solve using their doubles or teen numbers

15. I had saved $63, but spent $29 on my new soccer boots. How much do I have left? 63-29=? 63-30+1=34 Stage Six Students can recombine numbers in a variety of ways to answer problems. They can also solve fraction problems by combining multiplication and addition facts

16. I divided an orange and ate 18 segments that equalled 2/3. How many pieces were there in total? 2/3 of __ = 18 ½ of 18 = 9 3 x 9 = 27 2/3 of 27 = 18 Stage Seven Students here have a vast range of strategies to call on and will use the “smartest” one. Some equations may require a combination of strategies in order to solve it

17. $75 - $50 = $25 25 is 1/3 of 75 The percentage discount is 33.3% Cayla’s Clothing Shop is giving a discount. For a $75 pair of jeans, you pay only $50. What percentage discount is that? Stage Eight Students are using estimations, fractions, proportions and ratios.

18. Knowledge and Strategy • Knowledge – Number identification, number sequence and order, grouping and place value, basic facts • Strategy – Addition and subtraction, Multiplication and Division, Fraction and Proportions. These are known as operations.

19. Creates new knowledge through use Knowledge Strategy Provides the foundation for strategies Knowledge and Strategy Strong knowledge is essential for students to broaden their strategies. There are several key elements to each stage that children must master to fully grasp the strategy. The Strategies build onto one and each other. These are used to solve problems throughout the stages

20. Are you ready?????? Lets break for a game! This is a great game you can play at home with children who are Stages 3-4, however it can be a challenge to anyone at any stage. I’m going to revel ‘x’ amount of counters for a short time. There wont be enough time to mental count them all so you’ll need to use another strategy.

22. ?

23. 7

25. ?

26. 9

28. ?

29. 13

31. ?

32. 15

33. A breakdown of some strategies There are slight variations of these in later stages! Doubles + - 1 8 + 9 = 8 + 8 = 16 16 + 1 = 17 Compensation 39 + 26 = 40 + 25 = 65 Skip Counting 4 x 6 = 6,12,18,24 Back through ten 84 – 8 84 – 4 = 80 80 – 4 = 76 Partitioning 43 + 25 = 40 + 20 = 60 3 + 5 = 8 60 + 8 = 68

34. Stage Six Strategy breakdown Compensation 324 – 86 = 324 – 100 = 224 224 + 14 = 238 Equal Addition 89 – 54 = 90 – 55 = 35 Round & Compensate 9 x 6 = 10 x 6 = 60 60 – 6 = 54 Reversibility 63 – 29 = 29 + 30 = 59 59 + 4 – 63 30 + 4 = 34 Doubling and Halving 8 x 25 4 x 50 = 200

35. What does this mean? • Your child will: • Enjoy working with numbers • Make sense of numbers • Solve mathematical problems • Calculate in their head rather than using a calculator or pen & paper • Explain and record the methods they used to work out problems • Accept challenges and work at levels that stretch them • Work with others and by themselves • Discuss how they tackle mathematical problems

36. Time to think!

37. Number Strategies (addition) There are 9 lollies in the jar, Mum gives me 8 more to put in the jar. How many are in the jar now? Solution: 9 + 8 = • How did you work it out? • What happened in your head Share your thinking with the people around you Can you think of any other ways to solve the problem?

38. Make sense of these strategies “I count on from the biggest number. I put 9 in my head and counted on. 10,11,12,13,14,15,16,17 “I use my doubles -1.” I know 9+9=18 so… 18-1=17 9 + 8 = “I can make a 10 by taking 1 from the 8 to make the 9 a 10… s0 10+7=17 “I use my doubles +1.” I know 8+8=16 so… 16+1=17

39. Number Strategies (subtraction) There are 53 people on the bus. 29 people get off. How many people are now on the bus? Solution: 53 – 29 = • How did you work it out? • What happened in your head Share your thinking with the people around you Can you think of any other ways to solve the problem?

40. I use a number line and reversibility 29 30 50 53 So… +1, +20, +3 = 24 Make sense of these strategies I use place value. 53-20=33. Minus another 9. I split 9 into 3 and 6. So… 33-3=30 30-6=24 I use tidy numbers: 53-30=23 23+1=24 53 – 29 = I use equal addition I change 53-29 to… 54-30=24

41. Number Strategies (multiplication) There are 4 packets of biscuits with 24 cookies in each pack. How many cookies are there altogether? Solution: 4 x 24 = • How did you work it out? • What happened in your head Share your thinking with the people around you Can you think of any other ways to solve the problem?

42. Make sense of these strategies I use tidy numbers: I know 4 x 25 = 100 so… 100-(1x4)=96 I used place value. 4 x 20 = 80, and 4 x 4 = 16. So… 80+16=96 4 x 24 = I know 24 + 24 = 48. So… 48 + 48 = 96 I used doubling and halving. Double 4 = 8, half 14 = 12. 8X12=96

43. Common Questions How important is equipment? When children meet new mathematical ideas for the first time, it is essential they explore those ideas using equipment. Once they understand an idea they should try to use it without the support of the equipment What about times tables? Children should be able to make sense of addition and multiplication before they try to memorise their tables. But when they do understand, it is important that they learn these basic facts and can recall them instantly

44. Common Questions What about calculators? Children should do most calculations in their heads. They should only use calculators when the numbers are hard. What about bookwork? Most children will have untidy sections in their maths books or maths scrapbooks, especially where they have been thinking about problems. They should also have tidy sections, where they have written out important ideas or results

45. How can I help my child? • Knowledge Building: • Counting: cars, shells on the beach, how many times you can run around the house, counting backwards etc • Numbers before and after: Letter boxes, number cards, keyboard numbers, dice etc • Identifying numbers: Letter boxes, number plates, speed signs, how many Km to go etc • Ordering numbers: Write some down on paper and order

46. How can I help my child? • Knowing groups to ten: using the tens frames, using fingers, cards, dice • Basic addition facts to ten • Recalling doubles

47. How can I help my child? To become a Part-Whole thinker (Stage 5+) children need automatic recall of… • Facts to ten • Doubles facts • Ten and … (10+6=16) To become a Multiplicative Thinker (Stage 7+), children need to be able to recall there times tables

48. Back to the start Now try and crack these questions using some of the strategies mentioned 127 + 125 = 378 – 153 = 9 x 49 = 408 ÷ 12 = 20 x 342 = 37.5% 0f $80 =

49. Pre Workshop Questions Here are some possible solutions. Can you name the strategies used? • 127 + 125 = • 125 x 2 + 2 = 252 • 200+40+12=252 • 130+125-3-252 • 378 – 153 = • 380-155=225 • 153+225=378 • 300-153+78=225 • 9 x 49 = • 9x40+(9x9)=441 • 10x49-49=441 • 9x50-9=441 • 20 x 342 • 2 x 342=684 so 20 x 342=6840 • 10x684=6840

50. Pre Workshop Questions • 408 ÷ 12 = • 408 ÷12 as 204 ÷6 as 102 ÷ 3 = 34 • 12 x 30 = 360, 4 x 12 = 48 so 30 + 4 = 34 • 12 ÷ 400 = 30r4, 12 ÷ 48 = 4. 30+4=34 37.5% of $80 10% of 80 = 8, so 30% = 24 5% of 80 is half of 10% so it must be 4 Half of 5 is 2.5 which is what we have left, so 2.5% of 80 must be 2 So… 24+4+2 = $30