To Be Numerate ……

1. To Be Numerate …… Maths Information for Parents

2. Numeracy Project Goal “to be numerate is to have the ability and inclination to use mathematics effectively – at home, at work and in the community” Published in Curriculum Update 45:

3. Goals – We want our students to: • Developmultiple flexible thinking strategies • Use mental strategies and confidently explain orally before written standard vertical forms • Use a range of strategies and makedecisions about using the most effective strategy to work out any given problem. • Achieveand develop a positive attitude towards learning mathematics while enjoying the challenge of problem solving

4. The Big Picture of Numeracy and Maths

5. Maths Strands

6. Number

7. Number and Algebra is the most important strand. The balance shifts as students progress through the stages. A guide to this is: The Balance of Strand

8. Strategy Knowledge The NZ Numeracy Framework • Each Numeracy Stage highlights key knowledge and strategy that a child should know. • Strong knowledge is essential for students to broaden their strategies across a full range of numbers. Creates new knowledge through use Provides the foundation for strategies

9. Knowledge and Strategy • Knowledge – • Number Identification • Number Sequence and Order • Grouping and Place Value • Basic Facts • Strategy – Three domains • Addition and Subtraction • Multiplication and Division • Ratios and Proportions

10. Knowledge Before StrategyIt is essential that students have sound knowledge for the strategies they are developing; e.g.

11. Developmental Stage Progression The New Zealand Number Framework

12. Number Framework

13. Number Identification & Ordering Stages 6 - 8 1- 1 000 000 & decimals to 3 places Stages 0-1 1-10 Stages 2-3 1-20 Stage 4 1-100 & ½, 1/3, ¼, 1/5 Stage 5 1-1000 & improper fractions

14. Grouping and Place Value Stages 1- 3 within 5, with 5, within 10, patterns to10. Stages 6 groupings within 1000, groupings of 2, 3, 5 and 10 in 100, groupings of 2, 3, 5, & 10 in 4 digit numbers (& remainders) tenths and hundredths in decimals to (2 places) Stage 4 groupings with 10 and 20, number of tens in decades Stage 5 groupings within 100, groups of 10s, 100s & 1000s in 4 digit numbers Stages 7groupings of all numbers up to 10 in 100 (& remainders) groupings of 10s,100s &1000s in (up to) 7 digit numbers equivalent fractions

15. Basic Facts Stages1- 3 addition and subtraction facts to 5, doubles to 10 Stage 4 addition and subtraction facts to 10, doubles to 20, ten and facts, multiples of ten that add to 100 Stages 6 addition & subtraction facts to 20 multiplication facts up to 10x (& some corresponding division facts) multiplication facts with 10s, 100s & 1000s Stage 5 addition facts to 20, subtraction facts to10, 2x, 5x and 10x timetables, hundreds that add to 1000 Stages 7/8division facts up to 10x tables conversions (fractions/decimal/percentage) factors, common multiples, divisibility rules & square roots

16. How is maths taught differently now?

17. UsingMaterials ImagingMaterials Working only with numbers Teaching Model • Model and support children’s understanding using a researched teaching model • Steps for when a new strategy is introduced i. Using materials ii. Thinking about what would happen on the materials iii. Working only on numbers and applying strategy to higher numbers • Teach to achieve next learning steps

18. Using EquipmentThe use of equipment is essential when developing new strategies Bridging to Ten Happy Hundreds

19. Numeracy Strategy Stages Counting Strategies Non - Counting Strategies • Emergent • One to One Counting • Count from one on Materials • Count from one by Imaging • Advanced Counting • Early Additive Part-Whole • Advanced Additive Part-Whole • Advanced Multiplicative • Advanced Proportional

20. Examples of Strategies for each Stage

21. Can you get me 7 counters from the pile please? 1,2,3,5,8...? The child can not consistently count a collection of objects. Emergent Stage 0

22. Can you get me 7 counters from the pile please? 1,2,3,4,5,6,7 The child can count a set of objects up to ten but can’t join and separate sets like 4 + 3 = One to One Counting Stage 1

23. Count From One on MaterialsStage 2 There are 4 counters and another 3 counters. How many are there altogether? 1,2,3,4,5,6,7 The child solves the problem by using their fingers or other materials and counts from one.

24. There are 4 counters and another 3 counters. How many are there altogether? Counts in head1,2,3,4,5,67 The child counts all the objects from one by imaging visual patterns of the objects in their mind. Count From One By ImagingStage 3

25. There are 9 counters under there and another 4 counters under there. How many are there altogether? Counts on 9, 10, 11, 12, 13. The child counts on from the largest number. To be achieving at Stage 4 a child needs to be able to solve problems such as 49 + 4 = Advanced CountingStage 4

26. There are 9 counters under there and another 6 counters under there. How many are there altogether? Take one off the 6 and put it on the 9 it =10 so 10 + 5 = 15 The child uses simple strategies to solve addition and subtraction problems mentally Early Part-WholeStage 5 (Early Stage 5)

27. 63 people are on the bus and 39 people get off the bus. How many people are left on the bus? I think tidy numbers would be smartest. 63 – 40 = 23 23 + 1 = 24 The child can select from a wide range of strategies to solve various addition and subtraction problems mentally Advanced Part-WholeStage 6

28. There are 28 fruit trees in each row of the orchard. There are 6 rows. How many trees are there altogether? Tidy Numbers would be a smart strategy. 30 x 6 = 180 180 – (2 x 6) = 168 The child can select from a wide range of strategies to solve various multiplication and division problems mentally. Advanced MultiplicativeStage 7

29. Advanced ProportionalStage 8 You can make 9 mittens from 15 balls of wool. How many mittens can you make from 10 balls of wool? The child sees that 9:15 are both multiples of 3. They simplify by ÷3 and get a ratio of 3:5 ?:10 = 6 The child can select from a wide range of strategies to solve challenging problems involving, decimals, fraction percentages and ratios.

30. Assessing what children know • Teachers use a variety of tasks (informal and formal) to form our Overall Teacher Judgements (OTJs) • Group according to a child’s strategy stage using the New Zealand Number Framework • Encourage children to self assess (reflect) know and own their next learning steps. (Personalised Learning)

31. National Standards • Maths illustrations • JAM

32. National Standards Expectations

33. National Standardsare based on all areas of the Maths Curriculum • Number and Algebra - Knowledge -Addition/ Subtraction -Multiplication and Division -Ratios and Proportions (Fractions) -Patterning (Algebra) • Geometry and Measurement • Statistics

34. After One Year

35. After Two Years

36. After Three Years

37. At the End of Year 4

38. At the End of Year 5

39. At the End of Year 6

40. How do we cater for individual learning needs in Maths? • Using a variety of assessments and analyse data • Grouping and teaching according to learning needs • Individual Learning Goals • Cross grouping in the middle and senior classes • Personalised Learning Programmes

41. How can parents help? Developing a child’s knowledgeis a key to their success and development in mathematics This is the perfect area for you to help and support your child at home Knowledge lists for each stage and activities are on our school website Encourage your child to spend 10 minutes a day or 3x 20 minutes a week on Mathletics

42. Knowledge Building These activities can be used at all levels – just use different range of numbers for different levels • Counting(cars, shells on beach, pegs, run around the house, how many steps you walk, count backwards, start from different numbers, skip counting groups of objects; e.g. pairs of shoes ) • Numbers before and after(Letter boxes, say a number, use a number line, use number cards, write a number down, ladder game, keyboard numbers, using dice) • Identifying numbers(Letter boxes, number plates, speed signs, how many km to go, number cards, combine numbers, odometers, metres) • Ordering numbers(Number cards, write some numbers down, cut up calendars)

43. Knowledge Building cont.. • Knowing Groups of ten (Using ten frames, using fingers, abacus, ice- block sticks) • Recalling Doubles and Halves(ten frames, fingers, flashcards) • Basic addition & subtraction facts to 5, then 10, then 20 (Buttons, ten frames, fingers, flashcards, number boggle, playing cards)

44. Finger patterns

45. The Reality? To become a Part-Whole thinker (stage 5 plus) children need automatic recall of… • Facts to Ten (addition and subtraction) • Doubles Facts • Ten and ….10 + 6 = 16 • Groups of ten (Place Value) To become a Multiplicative thinker (stage 7) children need automatic recall of … • All of the above • The times tables

46. It may surprise you to know…. Algorithms are okay but only when… • A student shows an understanding of how they work e.g. 73 - 59 involves renaming 73 as 60+13 • A student reaches end of Stage 6 • It is an effective method for the problem posed. e.g. Try working out this out as an algorithm 10004 or 199 - 9998+ 99 • They also know other strategies they can use • They are achieving at Stage 6

47. It may surprise you… • In Stage 1-4: We focus on learning our addition and subtraction facts to 10 • At Stage 3-4: We focus on developing understanding of multiplication and division (not learning the multiplication & division facts) • At Stage 5 Students learn addition facts to 20 & subtraction facts to 10 • 2x, 5x and 10x multiplication facts

48. Support Material • www.nzmaths.co.nz/families • Video, Maths at Our House (cooking, maps, shopping, newspapers) • Number Knowledge Activities (games, activities and flashcards) School Website: Knowledge Lists Knowledge activities • Student-led conferences/reports: It will identify you child’s next learning step.