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