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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

• Interesting related websites:

### 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
• Interesting related websites:

### Suggested achievement objectives - optimisation

#### Calculus

• 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 September 17, 2018