He Tirohanga ki te Uiui Poutama Tau

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?

‘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 13 + 13 = 26 Ka kore ia e whakamahi I te rautaki whakarearua hei whakaoti I te tapiritanga 13 + 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 Tatauria Taumata Tahi

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

(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?

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

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?

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

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?

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 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.

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 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

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

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 =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. Kaupae 6 Te puanga o te wawahi tau tapiripiri Advanced Additive/Early Multiplicative 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?

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 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.

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?

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 –1000000 Recall multiplication and division facts. Order fractions, including those greater than 1.

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!

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

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

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 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

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?

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

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