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 inclass 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 M81
 Possible context elaborations for
AO M86
 Possible context elaborations for
AO M89
Suggested achievement objectives
Select from below depending on the teaching and learning activities chosen.
Patterns and relationships
 M81 Apply the geometry of conic sections.
Equations and expressions
 M86 Manipulate trigonometric expressions.
 M89 Manipulate complex numbers and present them graphically.
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Semester 2 – Choice of: Calculus or applied mathematics
Ideas for teaching and learning activities  Calculus
 Possible context elaborations for
AO M82
 Possible context elaborations for
AO M87
 Possible context elaborations for
AO M810
 Possible context elaborations for
AO M811
 Possible context elaborations for
AO M812
Suggested achievement objectives  calculus
Select from below depending on the teaching and learning activities chosen.
Patterns and relationships
 M82 Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions.
Equations and expressions
 M87 Form and use trigonometric, polynomial, and other nonlinear equations.
Calculus
 M810 Identify discontinuities and limits of functions.
 M811 Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods.
 M812 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.

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  applied mathematics
Select from below depending on the teaching and learning activities chosen.
Patterns and relationships
 M82 Use curve fitting, log modelling, and 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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Book resources

McIntyre, R. (1994). Cooperative mathematics for level eight. (This book is out of print but PDF versions are available on
Wikispaces: Auck SNP 2011 with the author’s permission for distribution and use.)

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.
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 December 2012.
Last updated July 30, 2015
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