1. He Tirohanga ki te Uiui Poutama Tau

2. He aha ngā mea rerekē o te Rautaki Tau me Te Mātauranga Tau?
Te Reo
mā te rautaki e pakari ai te mātauranga
Rautaki
Mātauranga
mā te mātauranga e tutuki pai ai te rautaki
Ko ngā Rautaki Tau, koirā ngā momo whiriwhiringa ā-hinengaro e whakoti ai te ākonga i tētahi paheko tau (pērā i te tāpiri, te tango, te whakarea, me te wehe
Ko te Mātauranga Tau, koirā te mātauranga matua hei ako mā te ākonga, pērā i ngā meka matua me te pūnaha uara tū.
He aha ngā mea rerekē o te Rautaki Tau me Te Mātauranga Tau?

4. ‘Ma whero ma pango ka oti te mahi’
Te whakamārama
E haere tahi ana nga rautaki tau me te matauranga tau
‘Ma whero ma pango ka oti te mahi’
Ki te kore te akonga e mohio ki te meka rearua
= 26
Ka kore ia e whakamahi I te rautaki whakarearua hei whakaoti I te tapiritanga
= 27 ( )

5. Nga Kaupae Rautaki Kaupae 0 Te tatau pitomata - Emergent
Kaupae 1 Te tatau panga tahi 1 – 1 counting
Kaupae 2 Te tatau taonga mai i te kotahi
Counting from 1 on Materials
Kaupae 3 Te tatau a-hinengaro mai i te kotahi
Counting from 1 by Imaging
Kaupae 4 Te puanga o te tatau Advanced Counting
Tatauria
Taumata Tahi

6. Nga Kaupae Rautaki Taumata 2 ki te 5
Kaupae 5 Te pihinga o te wawahi tau tapiripiri Early Additive
Kaupae 6 Te puanga o te wawahi tau tapiripiri Advanced Additive/Early Multiplicative
Kaupae 7 Te wawahi tau whakarea Advanced Multiplicative/Early Proportional
Kaupae 8 Te wawahi tau panga riterite Advanced Proportional
Te wawahi tau

9. (Taumata 1- Kaupae 1 ki te 3 hei te mutunga o te tau kotahi)
Kaupae 0 Te tatau pitomata (Emergent)
(Taumata 1- Kaupae 1 ki te 3 hei te mutunga o te tau kotahi)
1,2,3,5,8...?
Karekau he rautaki hei tatau i te maha o nga mea kei roto I tetahi huinga.
Kaore i taea e ratou te mahi i te aha?

10. Te tatau pitomata MĀTAURANGA TAU RAUTAKI TAU Tatau ki te rima
Kaore he rautaki hei tatau i te maha o nga mea kei roto i tetahi huinga.
MĀTAURANGA TAU
Tatau ki te rima

11. 1,2,3,4,5,6,7,8. Kaupae 1 Te tatau panga tahi Homai kia 7 nga patene?
(1 – 1 counting)
1,2,3,4,5,6,7,8.
Homai kia 7 nga patene?
Ka taea e ia te aha?

12. Te tatau panga tahi MĀTAURANGA TAU RAUTAKI TAU Tatauria ki te 10
E mohio ana ki te tatau i te maha o tetahi huinga (tae atu ki te 10)
MĀTAURANGA TAU
Tatauria ki te 10

13. Kaupae 2 Te tatau taonga mai i te kotahi Counting from 1 on Materials
E wha nga porotiti ki tenei ringaringa e toru ki tenei. E hia katoa nga porotiti?
1,2,3,
4,5,6,7.
Ka tatau a ringaringa, a taputapu ranei ki te whakaoti i te rapanga. He aha atu?

14. Te tatau taonga mai i te kotahi
RAUTAKI TAU
Solve simple addition and subtraction problems to 20 by counting all the objects.
MĀTAURANGA TAU
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

15. Kaupae 3 Te tatau a-hinengaro mai i te kotahi
Counting from 1 by Imaging
Counts in head 1,2,3,4,5,6,7,8.
E wha nga porotiti ki tenei ringaringa e toru ki tenei. E hia katoa nga porotiti?
Mena he rapanga tapiri, tango ranei, ka puritia ki te hinengaro nga mea e tapira ana. He aha atu?

16. Te tatau a-hinengaro mai i te kotahi
MĀTAURANGA TAU
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
RAUTAKI TAU
Can solve addition and subtraction problems to 20 by counting all the objects and or imaging numbers in my head.

17. Kaupae 4 Te puanga o te tatau
Advanced Counting
Counts on 9, 10, 11, 12, 13.
E iwa nga porotiti kei raro i tenei kari, e waru kei raro i tenei kari. E hia katoa nga porotiti?
Ka timata kē te tatau mai i tetahi o nga tau e mohiotia ana
He pai ki te tatau ma nga ringaringa i tenei kaupae?

18. Kaupae 4 Te puanga o te tatau
MĀTAURANGA TAU
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
RAUTAKI TAU
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

19. 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

20. If I take one off the 6 and put it on the 9 it =10. 10 + 5 = 15”
Kaupae 5 Te pihinga o te wawahi tau tapiripiri Early Additive
“I know that
If I take one off the 6 and put it on the 9 it = = 15”
E iwa nga porotiti kei raro i tenei kari, e ono kei raro i tenei kari. E hia katoa nga porotiti?
The child uses simple strategies to solve addition and subtraction problems mentally

21. Te pihinga o te wawahi tau tapiripiri
RAUTAKI TAU
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
MĀTAURANGA TAU
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

22. I think tidy numbers would be smartest.
Kaupae 6 Te puanga o te wawahi tau tapiripiri Advanced Additive/Early Multiplicative
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?

23. Te puanga o te wawahi tau tapiripiri
RAUTAKI TAU
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.
MĀTAURANGA TAU
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.

24. Tidy Numbers would be a smart strategy. 30 x 6 = 180
Kaupae 7 Te wawahi tau whakarea Advanced Multiplicative/Early Proportional
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?

25. Te wawahi tau whakarea MĀTAURANGA TAU STRARAUTAKI TAU TEGY
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
MĀTAURANGA TAU
Identify, order and say forward and backward number sequence from 0 –
Recall multiplication and division facts.
Order fractions, including those greater than 1.

26. Kaupae 8 Te wawahi tau panga riterite Advanced Proportional
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!

27. Te wawahi tau panga riterite
RAUTAKI TAU
Choose appropriately from a broad range of strategies to +, -, x and ÷ fractions and decimals.
MĀTAURANGA TAU
Know equivalent proportions for unit fractions with numbers to 100 and 1000
Know fraction, decimal, % conversion for unit fractions.
Order decimals to 3 places.

28. 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

29. 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

30. 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.

31. 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.

32. 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.

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

34. 3-Way Rotation TPA
Teacher Practice
Practice Activity
Activity Teacher

35. 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

36. 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?

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

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