TGHS Maths

TGHS Maths Index

Term 1 Term 2 Term 3 Term 4

 

 

Level 3 Statistics: Teachers' page

 

Term 1

AS91580 Investigate Time Series Data
Internal 4 credits

Time Series

  •  

    Resources

    Time Scale (approx.)

    Introduction to Time Series

    2 lessons

    Smoothing and Recomposing

    2 lessons

    Describing trends etc

    (Students describe the given datasets in a document, and then peer-mark. They can be paired in a 'confidence line').

    2 lessons

    PPDAC

    Writing a report using the PPDAC framework. Includes an exemplar at Merit/Excellence.

    Most of these examples/datasets are from Jake Wills https://www.mathsnz.com/

    3 lessons

    Excellence

    Some issues for Excellence

    4 lessons

    How you will be assessed

    A practice assessment, which can be peer marked using the generic assessment schedule.

    4 lessons

    Practice assessment

     

    Working Out (password protected)
    Data (password protected - needs saving as .csv)

    3 lessons

    Real assessment

     

    document: assessment (password protected)
    dataset: asessment (password protected - needs saving as .csv)

    5 lessons

    Reassessment

    document: Extra teaching task (password protected)
    data (password protected - needs saving as .csv)

    document: Reassessment (password protected)
    data (password protected)

    		 

     

    Total:

    approx. 25 lessons

    •  

    The lessons require the use of NZGrapher

    AS91581 Investigate Bivariate Data
    Internal 4 credits

    Bivariate Data

     

    Resources

    Time Scale (approx.)

    Introduction to Bivariate Data
    What do you see?

    2 lessons

    Dependent/Independent

    The worksheet is taken fron the Nulake workbook IAS 3.9 Bivariate Data p5-6, and the answers can be found there.

    1 lesson

    Correlations

    Then, for each of the pairs of variables in the variables.doc worksheet (see last lesson), write a hypothesis using the given descriptions.

    1 lesson

    TARSOG

    For the datasets, choose a pair of variables which show a correlation, write a Problem (including a hypothesis) and a TARSOG analysis.
    Then fit a trendline, and make some predictions. What does the 'r value' tell you about the strength of the correlation?

    3 lessons

    PPDAC for Bivariate. Putting it all together.

    Follow the PPDAC document using the 'cars' dataset. The document introduces a few ideas needed for Excellence. Then produce a report for the kiwi data. In both cases, you should aim to introduce some of your own research. We have also provided a document: Achieved Essentials, which you should use as a checklist, and a document: For Excellence (which should be used as appropriate - it is not a checklist!).

    5 lessons

    Practice assessment

    4 lessons

    Extra Practice

    This exercise is provided as extra practice if necessary.

    (4 lessons- if necessary)

    Real assessment

    5 lessons

    Extra work

    		  

    Reassessment

    		  

     

    Total:

    approx. 21-25 lessons

     

    Term 2

    AS91586 Apply Probability Distributions in Solving Problems
    External 4 credits

    Probability Distributions

     

    Resources

    Time Scale (approx.)

    Probability Distributions

    • Modelling with a distribution
    • Expected value, variance and Standard Deviation
    • Gain
    • Discrete/Continuous distributions

    (Expectation Algebra is left until later)

    Document: student/teacher notes

    Powerpoint: introduction to distributions

    Powerpoint: Gain

    Up to this point we have been looking at discrete distributions only. Sigma p. 406 has an exrecise on the difference between discrete/continious distributions before we look at some specific examples of distributions (binomial etc).

    3 lessons

    Rectangular & Triangular distribution

    Powerpoint: rectangular distribution

    Powerpoint: triangular distribution

    		 4 lessons

    Binomial Distribution

    Powerpoint: binomial distribution

    		 4 lessons

    Poisson distribution

    Powerpoint: poisson distribution

    Inverse poisson. The teacher should work an example on the board. remember that students coming from the Maths Studies course will not have seen lnx or log x before.

    		 4 lessons

    Normal distribution

    Exercise H in the homework book, and Excercise J should be revision (don't do Exercise I). However, students in Year 12 are not normally taught GC methods, and may not have used the Difference Columns.

    		 4 lessons

    Expectation Algebra

    Document: student notes Introduction to Expectation Algebra
    HW book p8-9
    Document: student notes More Expectation Algebra
    Hw book p11-12

    		 4 lessons

    Excellence questions

    Combining distributions
          HW Book Exercise M p 53 onwards (but avoid Conditional Probability Questions)
    Justifying distributions
          Activity: Mix-and-match cards (answers)
          Activity: Kahoot Quiz
          HW book Exercise N p 58 onwards

    		 4 lessons
        approx. 27 lessons

    Revision resources:

    Document: Using your graphical calculator
    Document: Revision topics list
    Worksheet: Skills Revision

    Revision Questions:
    Distributions Revision 1
    Distributions Revision 2
    Distributions Revision 3
    Distributions Revision 4
    'Mainly Achieved' assessment practice

    Term 3

    AS91587 Apply systems of simultaneous equations in solving problems
    Internal 3 credits

    Simultaneous Equations

     

    Resources

    Time Scale (approx.)

    Revision: 2x2 equations

    DM: p. 417 by substitution AND elimination.
    Some students will not have done simultaneous since Year 11.
    It is worth drawing attention to Inconsistent and Dependent Equations. ThM Chapter 28 has more practice.

    		 2 lessons

    3x3 Equations

    DM: p. 425 by elimination.
    Students should also be taught to solve with GC.

    		 3 lessons
    Writing and Solving Equations

    Student notes: The Upholsterer. Continue to work through the example (from NuLake).
    Then NuLake p. 35-39, with more examples in DM: p. 439-441

    		 3 lessons
    Geometric Interpretations Ask students to solve (or attempt to solve) DM: p430 Q1-6, then:
    Introduce Student notes: Plane Geometry (print on A3).
    Then DM: p. 430-432    		 2 lessons
    Practice assessment Practice 3 lessons (including going through solutions)
    Real assessment Real 2 lessons
        approx. 15 lessons (3 weeks)

    Text book references:
    DM Delta Mathematics ThM Theta Mathematics(Orange/Climber)

    AS91585 Apply probability concepts in solving problems
    External 4 credits

    Probability Concepts

     

    Resources

    Time Scale (approx.)

    Introduction to Probability

    Student/Teacher notes: Covers experimental/theoretical probability.

    Sample spaces and distributions ESA book p. 4-8

    2 lessons

    Venn Diagrams

    Lesson 1: Worksheet: Introduction to venn diagrams
    Initially just hand out the first worksheet, and get the students to think/pair/share solutions. If they struggle, or when they finish, introduce the second page with the diagrams. Scaffold as necessary.
    Lesson 2: HW book p 10-13
    Lesson 3: Union and Intersection. p( A OR B). Mutually Exclusive. p. 14-19 (must do some of both sections).
    Lesson 4: Testing for independence. HW book p20-21
    Lesson 5-6: Conditional Probability. HW book p. 23-27. Go through Q1 - with a sample space diagram it gives a good introduction to using a sample space diagram, and then calculating a conditional probability using either a reduced space, or the formula.
    Test Out. Exam style question to test the concepts covered.

    		 6 lessons
    Two Way Tables

    This topic is generally covered well at Level 2. Independence is an important issue which will need emphasising.

    Lesson 1-3: Go through example on p. 31/32 as notes. Then p. 32-36
    Lesson 4-5: Relative Risk. p.36-40

    		 5 lessons
    Tree diagrams

    Lesson 1: Revision 10Ticks worksheet

    Lesson 2-3: Exercise J p.41-47

    		 3 lessons
    Revision Lesson 1-3: Exercise J and Practice Assessment Task p. 48-55 3 lessons
        approx. 19 lessons (4 weeks)

     

    Revision Questions:
    Concepts Revision 1

    Term 4

    Revision

    Week 0: Students should attempt the 2013 Distributions and the 2013 Concepts Papers, and record which questions they cannot complete.
    Week 1: Revision Week 1 Justifying models & comparing with data, and Venn diagram notation. Also 2014 papers.
         Kahoot: set notation
    Week 2: Revision Week 2. Inverse Normal, and Independent & Mutually Exclusive. Also 2015 papers
         Kahoot: choosing a distribution