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# Level 8 statistics learning programme example

• The following learning programme example is divided into three terms of work. Each term has an overarching statistics or probability focus to support the learning.
• Possible teaching and learning activities are given, from which teachers could select activities that best meet the needs of the students in their class/school. In addition teachers could select teaching and learning activities that they currently use, or source others that would meet student needs and address the focus.
• Each term has a list of possible achievement objectives to select from, the choice of which will depend on the selected teaching and learning activities.
• The intent is to be more holistic in the selection of achievement objects to allow for natural connections between and within strands.
• Some achievement objectives could be summatively assessed directly through achievement standards; others could be assessed through in-class formative or summative assessment. Not all achievement objectives need to be assessed.

## Term 1 – Surveys

This term focuses on the development of statistical thinking and reasoning with data from surveys and other sources. Integrated with this development will be aspects of statistical literacy and evaluation of statistical reports.

### Ideas for teaching and learning activities

• Maths for teenagers – the following themes have potential
• Smoking “Fag-ette It!” (pp. 72-78)
• Alcohol “None for the Road” (pp. 79-86)
• Getting a Licence (pp. 110-115)
• Practical statistics
• Samples (pp. 121-132)
• Estimating proportions (pp. 133- 144)
• Estimation: Sampling distributions and point estimates (pp. 145-163)
• Correlation (pp. 212-233)
• Linear regression (pp. 234-253)
• Practical investigations and longer projects (pp. 311-322)
• Possible context elaborations for AO S8-1
• Possible context elaborations for AO S8-2
• Possible context elaborations for AO S8-3

### Suggested achievement objectives

Select from below depending on the teaching and learning activities chosen.

Statistical investigation

• S 8-1 Carry out investigations of phenomena, using the statistical inquiry cycle:
• A – conducting experiments using experimental design principles, conducting surveys, and using existing data sets
• B – finding, using, and assessing appropriate models (including linear regression for bivariate data and additive models for time-series data), seeking explanations, and making predictions
• C – using informed contextual knowledge, exploratory data analysis, and statistical inference
• D – communicating findings and evaluating all stages of the cycle
• S8-2 Make inferences from surveys and experiments:
• A – determining estimates and confidence intervals for means, proportions, and differences, recognising the relevance of the central limit theorem
• B – using methods such as resampling or randomisation to assess the strength of evidence

Statistical literacy

• S8-3 Evaluate a wide range of statistically based reports, including surveys and polls, experiments, and observational studies:
• A – critiquing causal-relationship claims
• B – interpreting margins of error

## Term 2 – Experiments and statistical literacy

This term focuses on the development of statistical thinking and reasoning with through experiments, statistical literacy and evaluation of statistical reports.

### Ideas for teaching and learning activities

• Possible context elaborations for AO S8-1
• Possible context elaborations for AO S8-2
• Possible context elaborations for AO S8-3

### Suggested achievement objectives

Select from below depending on the teaching and learning activities chosen.

Statistical investigation

• S 8-1 Carry out investigations of phenomena, using the statistical inquiry cycle:
• A – conducting experiments using experimental design principles, conducting surveys, and using existing data sets
• B – finding, using, and assessing appropriate models (including linear regression for bivariate data and additive models for time-series data), seeking explanations, and making predictions
• C – using informed contextual knowledge, exploratory data analysis, and statistical inference
• D – communicating findings and evaluating all stages of the cycle
• S8-2 Make inferences from surveys and experiments:
• A – determining estimates and confidence intervals for means, proportions, and differences, recognising the relevance of the central limit theorem
• B – using methods such as resampling or randomisation to assess the strength of evidence

Statistical literacy

• S8-3 Evaluate a wide range of statistically based reports, including surveys and polls, experiments, and observational studies:
• A – critiquing causal-relationship claims
• B – interpreting margins of error

## Term 3 – Probability

This term focuses on the development of probabilistic thinking and reasoning.

### Ideas for teaching and learning activities

• Co-operative mathematics for level 8
• Mix and match activities
• Binomial, Normal and Poisson Distributions (1) (pp. 17-18)
• Binomial, Normal and Poisson Distributions (2) (pp. 19-20)
• Information-sharing activities (pp. 30-32)
• Probability trees q. 28-30
• Expected value q. 31
• Binomial distribution q. 32-33
• Poisson distribution q. 34-35
• Sequencing activities
• Standard Normal Distribution (pp. 43-44)
• Practical statistics
• Probability (pp. 39-70)
• The Binomial distribution (pp. 71-88)
• The Poisson distribution (pp. 89-104)
• The Normal distribution (pp. 105-120)
• MCTP Chance and data volume 2
• Winning streaks, matching, chocolate chip cookies (pp. 188-219)
• Sunsmart (pp. 342-353)
• How long is a rod, Colas (pp. 418-440)
• Possible context elaborations for AO S8-4

### Suggested achievement objectives

Select from below depending on the teaching and learning activities chosen.

Probability

• S8-4 Investigate situations that involve elements of chance:
• A – calculating probabilities of independent, combined, and conditional events
• B – calculating and interpreting expected values and standard deviations of discrete random variables
• C – applying distributions such as the Poisson, binomial, and normal

## Book resources

• Rouncefield, M and Holmes, P. (1989). Practical statistics. Macmillan Education Ltd: London.
• McIntyre, R. (1995). Cooperative mathematics for level eight. Masterton, New Zealand: Wairarapa Education Resource Centre.
• Fergusson, S., Jessup, E., Snow, P., Stewart, A., & Valente, F. (1990). Mathematics projects and investigations for years 11 & 12 (NZ Years 12 & 13). Nelson: Australia.
• Dengate, B. & Gill, K. (1989). Maths for teenagers. Longman: Australia.
• Lowe, I. (1991). Mathematics at Work: modelling your world – Volume 1. Australian Academy of Science: Canberra.
• Lowe, I. (1991). Mathematics at Work: modelling your world – Volume 2. Australian Academy of Science: Canberra.
• Lovitt, C. & Lowe, I. (1993).Chance and Data Investigations Volume 2. Curriculum Corporation: Australia

## Possible assessment programme

It is envisaged that this course could lead to assessment for a range of achievement standards enabling teachers to select appropriate assessment programme to suit individual students within the class/school.

• AS91581 Mathematics and statistics 3.9 Investigate bivariate measurement data - 4 credits; internal
• AS91582 Mathematics and statistics 3.10 Use statistical methods to make a formal inference - 4 credits; internal
• AS91583 Mathematics and statistics 3.11 Conduct an experiment to investigate a situation using experimental design principles - 4 credits; internal
• AS91584 Mathematics and statistics 3.12 Evaluate statistically based reports - 4 credits; external
• AS91585 Mathematics and statistics 3.13 Apply probability concepts in solving problems - 4 credits; external
• AS91586 Mathematics and statistics 3.14 Apply probability distributions in solving problems - 4 credits; external

OR

• AS91580 Mathematics and statistics 3.8 Investigate time series data - 4 credits; internal
• AS91582 Mathematics and statistics 3.10 Use statistical methods to make a formal inference - 4 credits; internal
• AS91583 Mathematics and statistics 3.11 Conduct an experiment to investigate a situation using experimental design principles - 4 credits; internal
• AS91584 Mathematics and statistics 3.12 Evaluate statistically based reports - 4 credits; external
• AS91585 Mathematics and statistics 3.13 Apply probability concepts in solving problems - 4 credits; external
• AS91586 Mathematics and statistics 3.14 Apply probability distributions in solving problems - 4 credits; external
• AS91587 Mathematics and statistics 3.15 Apply systems of simultaneous equations in solving problems -2 credits; internal

* Level 3 achievement standards registered and published in November 2016.

Last updated September 17, 2018