Te Kete Ipurangi Navigation:

Te Kete Ipurangi
Communities
Schools

Te Kete Ipurangi user options:


Senior Secondary navigation


RSS

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

  1. 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.)
  2. 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.
  3. Lowe, I. (1991). Mathematics at Work: modelling your world – Volume 1. Australian Academy of Science: Canberra.
  4. 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 December 2012.

Last updated July 30, 2015



Footer: