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# Level 8 mathematics learning programme example

• The following learning programme example is divided into two semesters of work. Each semester has an overarching mathematics focus to support the learning.
• Semester 1 is common to all participants, calculus and mathematics introduction; semester 2 is split into two different options: (1) calculus or (2) applied mathematics.
• 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 semester 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.

## Semester 1 – Calculus and mathematics introduction

Calculus and mathematics introduction focuses on the development of mathematical thinking and reasoning in patterns, relationships, equations, and expressions.

### Ideas for teaching and learning activities

• Possible context elaborations for AO M8-1
• Possible context elaborations for AO M8-6
• Possible context elaborations for AO M8-9

### Suggested achievement objectives

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

Patterns and relationships

• M8-1 Apply the geometry of conic sections.

Equations and expressions

• M8-6 Manipulate trigonometric expressions.
• M8-9 Manipulate complex numbers and present them graphically.

## Semester 2 – Choice of: Calculus or applied mathematics

### Ideas for teaching and learning activities - Calculus

• Possible context elaborations for AO M8-2
• Possible context elaborations for AO M8-7
• Possible context elaborations for AO M8-10
• Possible context elaborations for AO M8-11
• Possible context elaborations for AO M8-12

### Suggested achievement objectives - calculus

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

Patterns and relationships

• M8-2 Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions.

Equations and expressions

• M8-7 Form and use trigonometric, polynomial, and other non-linear equations.

Calculus

• M8-10 Identify discontinuities and limits of functions.
• M8-11 Choose and apply a variety of differentiation, integration, and anti-differentiation techniques to functions and relations, using both analytical and numerical methods.
• M8-12 Form differential equations and interpret the solutions.

### Ideas for teaching and learning activities - Applied mathematics

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

• 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 - applied mathematics

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

#### Patterns and relationships

• M8-2 Use curve fitting, log modelling, and 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.

## 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.

Calculus focus

• AS91573 Mathematics and statistics 3.1 Apply the geometry of conic sections in solving problems - 3 credits; internal
• AS91575 Mathematics and statistics 3.3 Apply trigonometric methods in solving problems - 4 credits; internal
• AS91577 Mathematics and statistics 3.5 Apply the algebra of complex numbers in solving problems - 5 credits; external
• AS91578 Mathematics and statistics 3.6 Apply differentiation methods in solving problems - 6 credits; external
• AS91579 Mathematics and statistics 3.7 Apply integration methods in solving problems - 6 credits; external

Applied mathematics focus

• AS91573 Mathematics and statistics 3.1 Apply the geometry of conic sections in solving problems - 3 credits; internal
• AS91574 Mathematics and statistics 3.2 Apply linear programming methods in solving problems - 3 credits; internal
• AS91575 Mathematics and statistics 3.3 Apply trigonometric methods in solving problems - 4 credits; internal
• AS91576 Mathematics and statistics 3.4 Use critical path analysis in solving problems - 2 credits; internal
• AS91577 Mathematics and Statistics 3.5 Apply the algebra of complex numbers in solving problems - 5 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