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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 in-class 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

  • 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)

Suggested achievement objectives - linear models

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

Patterns and relationships

  • M8-4 Use linear programming techniques.

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.

Theme 2 – Critical paths

Ideas for teaching and learning activities - critical paths

Suggested achievement objectives - critical paths

Patterns and relationships

  • M8-5 Develop network diagrams to find optimal solutions, including critical paths.

Theme 3 - Optimisation

Ideas for teaching and learning activities - optimisation

  • Possible context elaborations for AO M8-11

Suggested achievement objectives - optimisation


  • M8-11 Choose and apply a variety of differentiation, integration, and anti-differentiation techniques to functions and relations, using both analytical and numerical methods.

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.

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