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He Tirohanga ki te Uiui Poutama Tau
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
mā te rautaki e pakari ai te mātauranga
Ko te Mātauranga Tau, koirā te mātauranga matua hei
ako mā te ākonga, pērā i ngā meka matua me te pūnaha
uara tū.
Rautaki Mātauranga
mā te mātauranga e tutuki pai ai te rautaki
He aha ngā mea rerekē o te Rautaki Tau me Te Mātauranga Tau?
Te Reo
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 13 + 13 = 26
Ka kore ia e whakamahi I te rautaki whakarearua hei whakaoti I te tapiritanga13 + 14 = 27 (13 + 13 + 1)
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
Tata
uria
Taumata Tahi
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 whakareaAdvanced Multiplicative/Early Proportional
Kaupae 8 Te wawahi tau panga riteriteAdvanced Proportional
Taumata 2 ki te 5
Te w
aw
ah
i ta
uNga Kaupae Rautaki
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?
Te tatau pitomata
RAUTAKI TAUKaore he rautaki hei
tatau i te maha o nga mea kei roto i
tetahi huinga.
MĀTAURANGA TAU• Tatau ki te rima
Kaupae 1 Te tatau panga tahi(1 – 1 counting)
1,2,3,4,5,6,7,
8.
Homai kia 7 nga patene?
Ka taea e ia te aha?
Te tatau panga tahi
RAUTAKI TAU• E mohio ana ki te
tatau i te maha o tetahi huinga (tae atu ki te 10)
MĀTAURANGA TAU• Tatauria ki te 10
Kaupae 2 Te tatau taonga mai i te kotahi Counting from 1 on Materials
1,2,3, 4,5,6,7
.
E wha nga porotiti ki tenei ringaringa e toru ki tenei. E hia katoa nga porotiti?
Ka tatau a ringaringa, a taputapu ranei ki te whakaoti i te rapanga. He aha atu?
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 1 - 20
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?
Te tatau a-hinengaro mai i te kotahi
RAUTAKI TAU• Can solve addition and
subtraction problems to 20 by counting all the objects and or imaging numbers in my head.
MĀTAURANGA TAUNeed …
• 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
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?
Kaupae 4 Te puanga o te tatau
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.
MĀTAURANGA TAUNeed …
• 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
100Arizona Monica
The Reality?
To become a Part-Whole thinker children needautomatic recall of …
• Facts to Ten• Doubles Facts• Ten and ….10 + 6 = 16
To Become a Multiplicative thinker children needto be able to recall the times tables
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 =10. 10 + 5 = 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
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
I think tidy numbers would be smartest.
63 – 40 = 23 23 + 1 = 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?
Kaupae 6 Te puanga o te wawahi tau tapiripiriAdvanced Additive/Early Multiplicative
Te puanga o te wawahi tau tapiripiri
RAUTAKI TAUChoose 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 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.
Kaupae 7 Te wawahi tau whakareaAdvanced Multiplicative/Early Proportional
Tidy Numbers would be a smart strategy. 30 x 6
= 180180 – (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?
Te wawahi tau whakarea
STRARAUTAKI TAUTEGY• 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 –1000000
• Recall multiplication and division facts.
• Order fractions, including those greater than 1.
Kaupae 8 Te wawahi tau panga riteriteAdvanced Proportional
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
You can make 9 mittens from 15 balls of wool. How many mittens can you make from 10 balls of wool?
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!
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.
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
•Clip art and 3D counters•Fly flip cards•Bead frame•Bead strings•Tens frames•Animal strips
•Place value equipment - unifix cubes - bean cannisters - iceblock sticks•Number line•Empty numberline•Hundreds board•Money
EquipmentModel concepts with many physical representations
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.
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.
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.
Classroom Implementation
• Long term planning
• Weekly plan
• Model for daily lesson
• Learning outcomes/intentions
• Modelling book • Taskboard
3-Way Rotation TPA
Teacher Practice
Practice Activity
Activity Teacher
Writes and Wrongs, Student Recording
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
How do you want your children to record their working?
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?
Planning
Materials
Resource Documents
Assessment Information
Learner Needs
Teaching Model
Learning Intentions
Modelling Book
Task Board
Acknowledgements...
www.nzmaths.co.nz
Photos: Gray Clapham
Acknowledgements...
www.nzmaths.co.nz
Photos: Gray Clapham