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# Level 8 optimisation and data analysis learning programme example

• The following learning programme example is divided into three terms of work. Each term has an overarching mathematics 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 – Data analysis

Data analysis focuses on the presentation of data using appropriate table and graphs and modelling trends with linear (and non-linear) models. This is extended by using these to make calculations and continues by considering the appropriateness of the models and how they might be used.

### Ideas for teaching and learning activities

• 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)

### Suggested achievement objectives

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

Statistical investigation

• S8-1 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 - Optimisation

Optimisation focuses on the use of linear equations, inequations and networks to optimise situations and processes.

### Ideas for teaching and learning activities

• Co-operative mathematics for level 8:
• Mix and match activities
• Simultaneous equations with inconsistent solutions (p. 6)
• Information-sharing activities
•  Simultaneous equations (q. 22, 23)
• Double sequencing activities
• Simultaneous equations (p. 39)
• Linear programming (p. 41)
• Possible context elaborations for AO M8-4
• Possible context elaborations for AO M8-5
• Possible context elaborations for AO M8-8

### Suggested achievement objectives

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

Patterns and relationships

• M8-4 Use linear programming techniques
• M8-5 Develop network diagrams to find optimal solutions, including critical paths

Equations and expressions

• M8-8 Form and use systems of simultaneous equations, including three linear equations and three variables, and interpret the solutions in context

## Term 3 – Experiments and statistical literacy

This term focuses on the development of statistical thinking and reasoning 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

• S8-1 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

## 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.

## Possible assessment programme

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

Selection from:

• AS91574 Mathematics and statistics 3.2 Apply linear programming methods in solving problems - 3 credits; internal
• AS91576 Mathematics and statistics 3.4 Use critical path analysis in solving problems - 2 credits; internal
• AS91587 Mathematics and statistics 3.15 Apply systems of simultaneous equations in solving problems - 3 credits; internal

Selection from:

• AS91580 Mathematics and statistics 3.8 Investigate time series data - 4 credits; internal
• 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

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

Last updated September 17, 2018