1 / 37

Understanding the Numeracy Framework

Understanding the Numeracy Framework. Presented by Sheree Drummond sheree@gisborne.net.nzc. Strategy is about how children solve number problems, in particular the mental processes they use. Knowledge considers the key items of knowledge that children need to acquire. Strategy. Knowledge.

rowan-maddox
Télécharger la présentation

Understanding the Numeracy Framework

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Understanding the Numeracy Framework Presented by Sheree Drummond sheree@gisborne.net.nzc

  2. Strategy is about how children solve number problems, in particular the mental processes they use. Knowledge considers the key items of knowledge that children need to acquire. Strategy Knowledge Creates new knowledge through use Provides the foundation for strategies What is the difference between strategy and knowledge? Give some examples

  3. Knowledge and Strategy Examples • Knowledge – What they need • Number Identification, Number sequence and order, Grouping and place value, basic facts, written recording • Strategy – What they do in • Addition and Subtraction, Multiplication and Division, Fraction and Proportions

  4. UsingMaterials ImagingMaterials Working only with numbers Numeracy Teaching Model • Model and support children' understanding using a researched teaching model.Using materialsImaging -Thinking about what would happen on the materials Properties -Working only on numbers • Teach to achieve next learning steps.

  5. Stages of Development Counting Part-Whole Stage 0 Emergent Stage 1 1 – 1 counting Stage 2 Counting from 1 on Materials Stage 3 Counting from 1 by Imaging Stage 4 Advanced Counting Stage 5 Early Additive Stage 6 Advanced Additive/Early Multiplicative Stage 7 Advanced Multiplicative/Early Proportional Stage 8 Advanced Proportional Level One Level Two to Five

  6. Emergent – Stage 0(Level One - Stages 1 to 3 After one year at school ) Can you get me 7 counters from the pile please? 1,2,3,5,8...? What can’t emergent counters do?

  7. Emergent • KNOWLEDGE • Rote count to 5 at least. • STRATEGY • This child is unable to count a set of objects

  8. Can you get me 7 counters from the pile please? 1,2,3,4,5,6,7,8. What can this child do? One to One Counting -Stage One

  9. One To One Counting • KNOWLEDGE • Rote count to 10 at least • STRATEGY • Count a set of objects to 10 by one to one matching

  10. Counting or Adding? • One of the key progressions is when the students move from counting to adding. • Counters usually do not have basic number facts and /or do not know how to use them. • Counters usually have an incomplete understanding of place value.

  11. Count From One on Materials – Stage Two 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 . What else do they do?

  12. Counting from one on Materials • STRATEGY • Solve simple addition and subtraction problems to 20 by counting all the objects. • KNOWLEDGE • Rote count to 20 at least • Instant recognition of patterns to 5 including finger patterns • Forward and backward number word sequence 0 – 20 • Order numbers to 20 • Numbers before and after in the range 1 - 20

  13. Count From One By Imaging -Stage Three There are 4 counters and another 3 counters. How many are there altogether? Counts in head1,2,3,4,5,6,7,8. The child counts all the objects from one by imaging visual patterns of the objects in their mind.

  14. Counting From One By Imaging • KNOWLEDGE • Need … • Instant recognition of patterns/add/sub facts to 10 including finger patterns • Ordering numbers 0-20 • Forward and backward word sequence in the range 0 –20 • Doubles to 10 • Say the number before and after a given number in the range 0-20 • Record in pictures, diagrams, • 5 and 2 is 7, 5 minus 2 equals 7 or 7-2 =7 • STRATEGY • Can solve addition and subtraction problems to 20 by counting all the objects and or imaging numbers in my head.

  15. Advanced Counting – Stage Four(After two years at school) There are 9 counters under there and another 4 counters under there. How many are there altogether? What if I remove 4 counters? Counts on 9, 10, 11, 12, 13. The child counts on from the largest number. Is it OK to use their fingers at this stage?

  16. Advanced Counting • KNOWLEDGE • Need … • Recognising numbers 0 –100 • Ordering numbers 0-100 • Forward and backward word sequence 0-100 • Numbers before and after a given number from 0-100 • Skip count in 2s, 5,s 10s forwards and backwards. • Teen numbers 10+ • Doubles to 20 • BF to 20 • Compatable decade numbers to 100 • STRATEGY • Solve addition and subtraction problems by counting on or back in my head from the largest number using supporting materials then moving to imagery. • Solve addition and subtraction problems by counting on in 10’s and 1’s. • Solve multiplication problems by skip counting in 2s, 5s 10s. Arizona Monica

  17. The Reality? To become a Part-Whole thinker children need automatic recall of … • Facts to Ten • Doubles Facts • Ten and ….10 + 6 = 16 To Become a Multiplicative thinker children need to be able to recall the times tables

  18. There are 9 counters under there and another 6 counters under there. How many are there altogether? “I know that If I take one off the 6 and put it on the 9 it =10. 10 + 5 = 15” The child uses simple strategies to solve addition and subtraction problems mentally Early Additive Part-Whole - Stage 5 (Level Two After 3 years and/or End of Year 4)

  19. Early Additive Part Whole • STRATEGY • Solve addition and subtraction problems in their head by working out the answer from basic facts they know. • Solve addition and subtraction problems with 2 or 3 numbers using groupings of 10 and 100. • Use addition strategies to solve multiplication strategies • KNOWLEDGE • Recall doubles to 20 and corresponding halves • Recall the names for 10 • Recall the teen numbers • Skip count in 2s,5s, 10s forwards and backwards Hannah Kate Louise

  20. 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. How many strategies do they need to be functioning at stage 6? Advanced Additive Part-Whole -Stage 6(Level Three -End of year 5 and 6)

  21. Advanced Additive Part Whole • STRATEGY • Choose from: • Compensation • Place Value • Compatible numbers • Reversibility • Equal Additions for subtraction • Decomposition • to solve + and - problems. • Use pencil and paper or caluclator to work out answers where the numbers are large or untidy • Carry out column + and – with whole numbers of up to 4 digits (algorithms) • Solve multiplication and division problems using known strategies eg doubling, rounding. • KNOWLEDGE • Identify numbers 0-1000 • Forward and backward sequence by 1,10,100 to 1000 • Order numbers from 0-1000 • Recall + and - facts to 20 • Recall multiplication facts for 2, 5, and 10 times tables.

  22. There are 28 fruit trees in each aisle of the orchard. There are 6 aisles. 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. What other strategies could you use? Advanced Multiplicative - Stage Seven(Level Four- After Year 7 and 8)

  23. Advanced Multiplicative Part Whole • STRATEGY • Solve +, - , x and ÷ problems with whole numbers (and decimals) using a range of strategies. • Solve problems involving fractions, decimals, proportions and ratios using multiplication and division strategies • KNOWLEDGE • Identify, order and say forward and backward number sequence from 0 –1000000 • Recall multiplication and division facts. • Order fractions, including those greater than 1.

  24. Advanced Proportional – Stage Eight(Start Level 5 - Year nine) You can make 9 mittens from 15 balls of wool. How many mittens can you make from 10 balls of wool? I can see that 9:15 are both multiples of 3. I can 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. The brainbox of the framework!

  25. Advanced Proportional Part Whole • STRATEGY • Choose appropriately from a broad range of strategies to +, -, x and ÷ fractions and decimals. • KNOWLEDGE • Know equivalent proportions for unit fractions with numbers to 100 and 1000 • Know fraction, decimal, % conversion for unit fractions. • Order decimals to 3 places.

  26. What does this mean for you? • Assessment of all students in your class. • On going use of formative assessment methods. • Students grouped according to their numeracy strategy stages. • Planning and sharing learning intentions with students. • Use of equipment to reinforce teaching and learning. • Sharing learning intentions with students. • Encouraging students to talk about their learning. • Using modeling books with each group. • Students record in their own book • Sharing ideas and supporting colleagues

  27. EquipmentModel concepts with many physical representations • Place value equipment • - unifix cubes • - bean cannisters • - iceblock sticks • Number line • Empty numberline • Hundreds board • Money • Clip art and • 3D counters • Fly flip cards • Bead frame • Bead strings • Tens frames • Animal strips

  28. Assessing what children know. • Assess - where each child is at through oral interviewing and questioning • Group according to a Childs strategy stage using the New Zealand Number Framework • A useful tool - I CAN Portfolio Sheets • Encourage children to self assess (reflect) know and own their next learning steps.

  29. Grouping • Examine your Class Summary sheet and look at how you might group the students. • Strategy Stage for addition and subtraction is main indicator. • Transfer data to Class Grouping sheet. • With a partner discuss each other’s groupings.

  30. Classroom Management • The children need to be able to work in groups. • You need to be able to plan for groups. • Children must be able to work independently. • Spending time establishing routines, systems and expectations is crucial.

  31. Classroom Implementation • Long term planning • Weekly plan • Model for daily lesson • Learning outcomes/intentions • Modelling book • Taskboard

  32. 3-Way Rotation TPA Teacher Practice Practice Activity Activity Teacher

  33. Writes and Wrongs, Student Recording How do you want your children to record their working? • Why? • Records the process • Avoids mental overload • Encourages Imaging • Clarifies (and may extend) thinking • How? • Quality not quantity • Separate pages for thinking and formal working • Equipment sketched • Modelled by teacher

  34. Why is written recording important? We all need to learn and practise symbol and diagram literacy. They help to and to “park” information while you work on sub-tasks. Symbols and diagrams can ease the load on your working memory. Draw a diagram to help you solve this problem. Think about how the diagram helps you. Katy and Liam went shopping. At the start Liam had only three-quarters as much money as Katy. Liam spent $14 and Katy spent half her money. Then they both had the same amount of money. How much money did each person have left?

  35. Learning Intentions Teaching Model Modelling Book Resource Documents Materials Planning Learner Needs Assessment Information Task Board

  36. Acknowledgements... Acknowledgements... www.nzmaths.co.nz www.nzmaths.co.nz Photos: Gray Clapham Photos: Gray Clapham

More Related