National Workshop Mathematics and Statistics

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National WorkshopMathematics and Statistics

• BACKMAPPING A LEARNING PROGRAMME

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Entree

• This session is about designing a way to assure
  success for students at NCEA L2.
• Hogans Plan is to have each standard at L2
  backmapped to Year 7/8.
• Firstly an example, then you will do one standard
  each in groups. Ham, Rot and EIT all collated and
  sent back to you.

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Focus Ideas

• Backward design means starting with the end in
  mind and planning for it, step by step.
• Deep Knowledge focuses on the concepts and their
  relationships
• Deep Understanding is about demonstrating
  profound meaning

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Outcome
I will collect all your work and put it in a
spreadsheet for you to use.
AS91256 AS91257 AS91258
Y12 Method
Y11
Y10
Y9
Y7/8

Each row will describe a YEAR of building blocks
for learning, to meet goal. Resources, key ideas,
skills.
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Key Question

• To achieve NCEA L2 what is it a student has to
  learn in previous years?
• I want a description of what must be learned in
  Year 7/8, Year 9, Year 10 so that a particular
  topic can be accessed by students in Year 11 and
  12.
• NCEA L2 is the 85 PS Goal

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The Learning Programme

• We should be able to inform/check a learning
  programme for a year level as a result.
• Other factors like building problem solving
  ability, literacy and need to be considered

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What do we need?

• NZC these are the AOs.
• National Standard Descriptions, Exemplars
• Internet
• to see supporting SSTLG
• to access C_at_S
• to access nzmaths.co.nz
• to access math dictionary
• your knowledge
• two heads are better than one!

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Learn by Doing

• I have selected AS 91264 as a starter because it
  is probably familiar to us and it is a popular
  choice.

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AS91264methods

• Using the statistical enquiry cycle to make an
  inference involves
• posing an appropriate investigative comparison
  question from a given set of population data
• selecting random samples
• selecting and using appropriate displays and
  measures
• discussing sample distributions
• discussing sampling variability, including the
  variability of estimates
• making an inference
• communicating findings in a conclusion.

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1st Task - 3 minits

• posing an appropriate investigative comparison
  question from a given set of population data
• Just focusing on this method fill in
• gt for Year 11
• gt for Year 10
• gt for Year 9
• gt for Year 7/8

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My Attempt

• gt for Year 11
• That AS 91035 has been attempted. Students can
  write conclusions to investigative questions.
• gt for Year 10
• That comparison questions have been practiced as
  part of PPDAC. The C_at_S analyser has been used to
  answer a question.

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and

• gt for Year 9
• That comparison questions have been practiced as
  part of PPDAC and the data cards have been used.
  See Stats nzmaths
• gt for Year 7/8. Students have asked
  investigative questions from familiar data sets.
  This means they have taken part in the C_at_S
  survey. They own the data.

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2nd Task- 3 minits

• selecting random samples
• Just focusing on this method fill in
• gt for Year 11
• gt for Year 10
• gt for Year 9
• gt for Year 7/8

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My Attempt

• gt for Year 11
• Students use random ideas to select a sample.
  The idea of sample to population is understood
  for making an inference. Non random ideas can be
  identified.
• Chance language including bias, likely, outcome
  are used.

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and

• gt for Year 10
• Students use random sampler on C_at_S to find a
  sample. Biased samples, cleaning data,
  non-representative samples are identified.
• gt for Year 9
• Use a spreadsheet to generate random numbers
• gt for Year 7/8
• Sampling by hand, using dice and knowing what
  random means. Using random in language correctly.
  

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3rd Task 3 minit

• selecting and using appropriate displays and
  measures
• discussing sample distributions
• Just focusing on this method fill in
• gt for Year 11
• gt for Year 10
• gt for Year 9
• gt for Year 7/8

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My Attempt

• selecting and using appropriate displays and
  measures
• discussing sample distributions
• gt for Year 11
• Uses dot plots and box and whisker to show the
  information comparatively . Finds measures of
  middle and spread, IQR, shift and OVS. Clear
  diagrams. Labels. Writes correct statements about
  shape of distribution.

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and

• gt for Year 10
• Becomes fluent in interpreting box and whisker,
  making and describing dot plots. Use this
  information to help describe distribution of the
  data.
• gt for Year 9 and Year 7/8
• Draws dot plots and describes the data. Finds
  middle measures. Notices spread. Writes and
  speaks about the shape. Notices unusual data
  points.

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4th Task 3 minit

• discussing sampling variability, including the
  variability of estimates

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My Attempt

• discussing sampling variability,
• including the variability of estimates
• gt for Year 11
• This means noticing different samples usually
  give a different result but most samples will
  show the same trend. Knowing a sample of around
  20 to 30 is not a bad choice for size.

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and

• gt for Year 10
• Noticing different samples will look different as
  well. Explores visual spread and sample size
  relationship. Notices middle 50 is a good
  indicator of being typical. Can explain why some
  data supports a different conclusion.

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and

• gt for Year 9 and gt for Year 7/8
• Noticing different samples look different and can
  explain why. States that this is usual and can be
  expected. Is not phased by having a different
  answer to the same question.

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5th and Final Task 3 minit

• making an inference
• communicating findings in a conclusion.
• Just focusing on this method fill in
• gt for Year 11
• gt for Year 10
• gt for Year 9
• gt for Year 7/8

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My attempt cf

• making an inference
• communicating findings in a conclusion.
• gt for Year 11
• Uses middle 50, OVS, Shift and other supporting
  evidence in making an inference. Can write clear
  correct statements using statistical language.
  Does not contradict findings with waffle or
  wobble.

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and

• gt for Year 10
• Uses ½ to ¾ rule for establishing validity of
  inference. Uses shape of distribution when
  appropriate. Makes and communicates clearly an
  inference.
• gt for Year 9 and Year 7/8
• Answers the question posed with supporting
  evidence based on shape and position.

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Now

• Collect each Year level
• Decide if inference is part of the learning
  programme for that year.
• Compare with exisiting learning plans
• Allocate time, resources, order of learning, pre
  and post test tasks.
• Organise resources!

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Organising

• So I decide that inference is indeed going to be
  taught in Year 10. I will call the unit Making
  an Inference and allocate 3 weeks of time in
  Term 1.
• Broad Content
• That comparison questions have been practiced as
  part of PPDAC. The C_at_S analyser has been used to
  answer a question.

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Content cont

• Students use random sampler on C_at_S to find a
  sample. Cleaning data.
• Becomes fluent in interpreting box and whisker,
  making and describing dot plots.
• Noticing different samples will look different as
  well. Explores visual spread and sample size
  relationship.
• Can explain why some data supports a different
  conclusion.

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Content more!!!

• Uses ½ to ¾ rule for establishing validity of
  inference. Uses shape of distribution when
  appropriate.
• Makes and communicates clearly an inference.

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Key Learning

• Key Learning
• ½ to ¾ inference idea
• Box and whisker plots
• Measures of centre
• Measures of spread

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Resources

• Census _at_ School data viewer
• Using Census at School data from surveys
• Writing frames for conclusions
• For Imagination
• http//www.bigkidsmagazine.com/
• http//www.mathscentre.co.nz
• http//www.youcubed.org

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Your Turn

• Select a standard
• List methods one at a time
• Break down Learning at Y 11 to 7
• Make sure I have a copy
• AS and method
• Who?
• Each Level Key ideas

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Hope that was useful

• Thank you
• Morning Tea
• or
• Coffee
• and
• Talk
• Back at 11am