Level 8 operations research learning programme example
 The following learning programme example has three themes related to operations research that could for the basis of an alternative mathematics course.
 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 theme 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.
Operations research
Operations research focuses on the development of mathematical thinking and reasoning in patterns, relationships, equations, and expressions under three main themes. Linear models, critical paths and optimisation.
Theme 1 – Linear models
Ideas for teaching and learning activities  linear models

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)
Suggested achievement objectives  linear models
Select from below depending on the teaching and learning activities chosen.
Patterns and relationships
 M84 Use linear programming techniques.
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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Theme 2 – Critical paths
Ideas for teaching and learning activities  critical paths
 Interesting related websites:
Suggested achievement objectives  critical paths
Patterns and relationships
 M85 Develop network diagrams to find optimal solutions, including critical paths.
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Theme 3  Optimisation
Ideas for teaching and learning activities  optimisation
 Possible context elaborations for
AO M811
Suggested achievement objectives  optimisation
Calculus
 M811 Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods.
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Book resources
 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.
 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 range of achievement standards enabling teachers to select appropriate assessment programme to suit individual students within the class/school.
 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
 AS91578 Mathematics and statistics 3.6 Apply differentiation methods in solving problems  6 credits; external
 AS91587 Mathematics and statistics 3.15 Apply systems of simultaneous equations in solving problems  3 credits; internal
* Level 3 achievement standards registered and published in November 2016.
Last updated February 21, 2023
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