1. Understanding the Numeracy Framework
Presented by Sheree Drummond

2. What is the difference between strategy and knowledge?
Creates new knowledge through use
Strategy
Knowledge
Provides the foundation for strategies
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.
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. Working only with numbers
Numeracy Teaching Model
Working only with numbers
Imaging Materials
Using Materials
Model and support children' understanding using a researched teaching model. Using materials Imaging -Thinking about what would happen on the materials Properties -Working only on numbers
Teach to achieve next learning steps.

5. Stages of Development 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
Counting
Level One
Level Two to Five
Part-Whole

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

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

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

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

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

13. Count From One By Imaging -Stage Three
Counts in head 1,2,3,4,5,6,7,8.
There are 4 counters and another 3 counters. How many are there altogether?
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)
Counts on 9, 10, 11, 12, 13.
There are 9 counters under there and another 4 counters under there. How many are there altogether? What if I remove 4 counters?
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 … = 16
To Become a Multiplicative thinker children need
to be able to recall the times tables

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

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. I think tidy numbers would be smartest.
Advanced Additive Part-Whole -Stage 6 (Level Three -End of year 5 and 6)
I think tidy numbers would be smartest.
63 – 40 = 23
= 24
63 people are on the bus and 39 people get off the bus. How many people are left on the bus?
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?

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
Forward and backward sequence by 1,10,100 to 1000
Order numbers from
Recall + and - facts to 20
Recall multiplication facts for 2, 5, and 10 times tables.

22. Advanced Multiplicative - Stage Seven (Level Four- After Year 7 and 8)
Tidy Numbers would be a smart strategy. 30 x 6 = 180
180 – (2 x 6) = 168
There are 28 fruit trees in each aisle of the orchard. There are 6 aisles. How many trees are there altogether?
The child can select from a wide range of strategies to solve various multiplication and division problems mentally. What other strategies could you use?

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 –
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. Equipment Model 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

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