Transcript Te Tauanga Statistics 2009 WMA teacher only day presentation

Statistics
Kia ora ai i tènei rà, me
mòhio te tangata ki te
kaupapa o nga tikanga
pàngarau.
One needs to
understand basic
mathematics to survive
in today's world.
Te Tauanga.
http://www.biomotionlab.ca/Demos/BMLwalker.html?GXHC_GX_jst=8258c07950ea6164
Simon Morris
Learning Outcomes
Students will be able to:


Develop an understanding to how
probability relates to number
Key competencies...
What
Building confidence with probability
through developing understanding
Why
Probability concepts can be
misunderstood
How
Through the use of language activities,
examples and contexts
What is the purpose of probability?
When or how do you use Probability?
What is probability?
What is most important in teaching/learning probability?
Two ways of thinking:
Deterministic thinking
proceeds from a position
of certainty and
precision.
Stochastic thinking
proceeds from a
position of
uncertainty and
variation.
The New Zealand Curriculum 2007.
Where does probability vocabulary fit into the curriculum?
Āwhai
Maybe
Tērā
Might
Tērā pea
Perhaps
Kare e kore
Without a
doubt
Taunga kore
Impossible
Kārangirangi
Doubtful
Mōhio
Tūturu
Sure
Tautanga iho
Odds Against
I ngā wā katoa
Always
Taurite te
Tūpono
Even Chance
(Tūpono)
Kore rawa
Never
Tika Tonu
Certain
Mehemea
Unlikely
Kore mōhio
tūturu
Unsure
Heipū
Definite
Tērā tonu
pea
Likely
Haurua
50-50
Tautanga ake
Odds-ON
Puta noa
Unexpected
Waimarie noa
lucky
He Kōtuku
Rerenga Tahi
One in a
Million
Korekore
rawa
Buckley’s
Chance
Āhei
Possible
Tāu whiwhi
Lucky
Parau
Incredible (Not
believable)
Whakaharahara Wow
Āe pea
Could
Tataunga kore
Odds off
Mīharo kē
tinny
Ka taea pea
Conceivable
Kāore pea e hua
mai
Less likely
Development of associated language:
Will/Might/Won’t happen/Certain/Possible/Impossible etc.
Can be
expressed
as a fraction
Probability =
number of “desired” outcomes
total number of “possible” outcomes
Work
out
Theoretical
Work out all possible ways to
get the ‘desired” outcomes
Work out all possible outcomes
Impossible
(0)
(0%)
Can be
placed on a
number line
Certain
(1)
(100%)
Birth month

My best friend and I have our birthdays
in the same month.

In my family of five, none of us have
our birthdays in the same month.
Problem

To explore the different combinations
of birth months in groups of five
people, to see how likely it is that two
or more people have the same birth
month.
On a scale of 1 – 5
1 being easy and 5 being very hard
1
2
3
4
5
Question: Which Sudoku would you rank 1 ~ 5?
9
1
2
8
4
7
5
3
6
6
7
5
2
9
3
8
1
4
3
8
1
6
5
9
7
2
11
33
66
44
88
99
77
22
55
77
22
88
33
55
66
11
44
99
44
55
99
77
22
1
33
66
88
22
66
77
55
33
88
44
99
11
55
44
33
99
11
22
66
88
77
88
99
11
66
77
44
22
55
33
http://www.nzmaths.co.nz/numeracy/2006numPDFs/NumBk9.pdf
Volunteers Please…
A quizmaster
A lovely assistant
Some contestants
http://www.nzmaths.co.nz/numeracy/2006numPDFs/NumBk9.pdf
1. The quizmaster places a chocolate bar under one of
the three cups while the contestant is not watching.
2. The contestant points at a cup that the chocolate
bar might be under
3. The quizmaster turns over one of the cups that they
know doesn’t cover the chocolate bar
4. The contestant decides whether to change their
choice
5. The quizmaster shows the cup which is hiding the
chocolate bar
The Monty Hall problem is a puzzle based
on the American game show Let's Make a
Deal. Suppose you're on a game show, and
you're given the choice of three doors:
Behind one door is a car; behind the others,
goats. You pick a door, say No. 1, and the
host, who knows what's behind the doors,
opens another door, say No. 3, which has a
goat. He then says to you, "Do you want to
pick door No. 2?" Is it to your advantage to
switch your choice?
http://www.letsmakeadeal.com/problem.htm
http://www.dcity.org/braingames/3doors/index.htm
KEY COMPETENCIES
•managing self
•relating to others
•participating and contributing
•thinking
•using language, symbols, and texts.
Thinking
•Ask questions: teacher → student, student → student, student → teacher
•Reflect on learning
•Make deductions
•Think logically
•Co-construct knowledge
•Justify and verify
•Use mathematics to model real life and hypothetical situations
•Investigate
•Deal with uncertainty and variation
•
Want to know ‘why’
•Prove
•Make connections
•Hypothesise
•Estimate
•Deduce
Using Language, Symbols and Texts
Understand mathematics as a language
•Understand and communicate information and ideas using mathematics
•Interpret and use mathematical symbols
•Interpret statistical information
•Know and use mathematical conventions
•Process and communicate mathematical ideas
•Know, use and interpret specialised vocabulary
•Communicate findings
•Record mathematical ideas
•Capture thought processes
•Explore different representations
Relating to Others
•Listen actively
•Accept and value differing viewpoints
•Share ideas
•Negotiate meaning
•
Understand others’ thinking
•Accept being wrong as part of learning
•Explore the approaches, ideas and ways of thinking of others
•Co-operate
•Work in groups
•Communicate thinking
•Work cooperatively
•Debate solutions
•Compare and contrast ideas
•Remain open to learning from others
•Collaborate
Managing self
•Work independently
•Remain open to continuous learning
•Take responsible risks
•Make decisions
•Reflect
•Know own strengths and weaknesses
•Persevere
•Demonstrate rigour
•Take ownership of own learning
•Rise to new challenges – using appropriate strategies and skills
•Seek understanding
•
Ask for help if you don’t understand
•Focus on goal / objective
Participating and Contributing
•Share strategies and thinking
•Work in groups with everyone contributing
•Empower and enable others
•Assist others
•Contribute to shared vision (learning intentions)
•Build on prior knowledge
•Share equipment / resources