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 inclass 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 nonlinear) 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. 121132)
 Estimating Proportions (pp. 133 144)
 Estimation: Sampling Distributions and Point Estimates (pp. 145163)
 Correlation (pp. 212233)
 Linear Regression (pp. 234253)
 Practical Investigations and Longer Projects (pp. 311322)
Suggested achievement objectives
Select from below depending on the teaching and learning activities chosen.
Statistical investigation
 S81 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 timeseries 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
 S82 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
 S83 Evaluate a wide range of statistically based reports, including surveys and polls, experiments, and observational studies:
 A – critiquing causalrelationship claims
 B – interpreting margins of error
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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

Cooperative mathematics for level 8:
 Mix and match activities
 Simultaneous equations with inconsistent solutions (p. 6)
 Informationsharing activities
 Simultaneous equations (q. 22, 23)
 Double sequencing activities
 Simultaneous equations (p. 39)
 Linear programming (p. 41)
 Possible context elaborations for
AO M84
 Possible context elaborations for
AO M85
 Possible context elaborations for
AO M88
Suggested achievement objectives
Select from below depending on the teaching and learning activities chosen.
Patterns and relationships
 M84 Use linear programming techniques
 M85 Develop network diagrams to find optimal solutions, including critical paths
Equations and expressions
 M88 Form and use systems of simultaneous equations, including three linear equations and three variables, and interpret the solutions in context
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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 S81
 Possible context elaborations for
AO S82
 Possible context elaborations for
AO S83
Suggested achievement objectives
Select from below depending on the teaching and learning activities chosen.
Statistical investigation
 S81 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 timeseries 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
 S82 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
 S83 Evaluate a wide range of statistically based reports, including surveys and polls, experiments, and observational studies:
 A – critiquing causalrelationship claims
 B – interpreting margins of error
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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.
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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
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