Transcript Rautaki Tau

He Tirohanga ki te Uiui Poutama 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 āhinengaro 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?
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
1 – 1 counting
Te tatau panga tahi
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
Taumata
Tahi
Advanced Counting
Tatauria
Kaupae 2 Te tatau taonga mai i te kotahi
Nga Kaupae Rautaki
Taumata 2 ki te 5
Kaupae 5 Te pihinga o te wawahi tau tapiripiri
Early Additive
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
Kaupae 6 Te puanga o te wawahi tau tapiripiri
Kaupae 0 Te tatau pitomata
(Emergent)
(Taumata 1- Kaupae 1 ki te 3 hei te mutunga o te tau kotahi)
Karekau he rautaki hei tatau i te
maha o nga mea kei roto I tetahi
huinga.
1,2,3,5,8
...?
Kaore i taea e ratou te mahi i te
aha?
Te tatau pitomata
RAUTAKI TAU
Kaore 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)
Homai kia 7 nga patene?
1,2,3,4,5
,6,7,8.
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
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.
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•
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
E wha nga porotiti ki tenei
ringaringa e toru ki tenei. E hia
katoa nga porotiti?
Counts in head
1,2,3,4,5,6,
7,8.
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 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
Kaupae 4
Te puanga o te tatau
Advanced Counting
E iwa nga porotiti kei raro i tenei
kari, e waru kei raro i tenei kari. E
hia katoa nga porotiti?
9,
10, 11, 12,
13.
Counts on
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.
Arizona
Monica
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•
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
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
Kaupae 5 Te pihinga o te wawahi tau tapiripiri
Early Additive
E iwa nga porotiti kei raro i tenei
kari, e ono kei raro i tenei kari. E hia
katoa nga porotiti?
“I know that
If I take one off
the 6 and put it on
the 9 it =10. 10
+ 5 = 15”
The child uses simple strategies
to solve addition and subtraction
problems mentally
Te pihinga o te wawahi tau
tapiripiri
RAUTAKI TAU
MĀTAURANGA 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
Hannah
Kate
Louise
• 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
Kaupae 6 Te puanga o te wawahi tau tapiripiri
Advanced Additive/Early Multiplicative
63 people are on the bus and 39
people get off the bus. How many
people are left on the bus?
I think tidy numbers
would be smartest.
63 – 40 = 23
23 + 1 = 24
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
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•
•
•
•
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 whakarea
Advanced Multiplicative/Early Proportional
There are 28 fruit trees in each aisle of
the orchard.There are 6 aisles. How
many trees are there altogether?
Tidy Numbers would be
a smart strategy. 30 x 6
= 180
180 – (2 x 6) = 168
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 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
MĀTAURANGA TAU
• Choose appropriately from
a broad range of strategies
to +, -, x and ÷ fractions
and decimals.
• 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
•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
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 threequarters 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
Acknowledgements...
www.nzmaths.co.nz
Photos: Gray Clapham