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Advice for teachers -
Further Mathematics

Units 3 and 4

Developing a course

A course outlines the nature and sequence of teaching and learning necessary for students to demonstrate achievement of the set of outcomes for a unit. The areas of study specify the content to be studied and cover the key knowledge and key skills required for the demonstration of each outcome. Outcomes are introduced by summary statements and are followed by the key knowledge and key skills which relate to the outcomes. Together the areas of study and outcomes enable teachers and students to address the aims of the study.

Teachers must develop courses that include appropriate learning activities to enable students to cover the prescribed content and develop the knowledge and skills identified in the outcome statements in each unit. In Units 3 and 4, assessment is structured and for school-assessed coursework the assessment tasks are prescribed. The contribution that each task makes to the total school-assessed coursework is also specified.

In undertaking these units, students are expected to be able to apply techniques, routines and processes involving rational and real arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations, and graphs. They should have a facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic, financial and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout each unit as applicable. Students should develop a sense for the reasonableness or otherwise of results obtained using technology with respect to the context in which they are working mathematically.

The compulsory Core area of study comprising ‘Data analysis’ and ‘Recursion and financial modelling’ is to be completed in Unit 3 and the Applications area of study comprising two modules to be completed in their entirety, from a selection of four possible modules: ‘Matrices’, ‘Networks and decision mathematics’, ‘Geometry and measurement’ and ‘Graphs and relations’ is to be completed in Unit 4. There is flexibility at the local level in the design of a course and planning decisions need to be made about the order of topics, the time devoted to each topic, and connections between the content developed in particular topics and the outcomes for each unit. These decisions also need to take into account the timing of school-assessed coursework.

Sample course

The following sample course outlines one possible implementation across 27 weeks, including time for school-assessed coursework. Teachers are likely to present material covering content related to different topics in various ways, and should adjust time allocations accordingly. Schools and teachers are encouraged to develop their own sequences or variations to this sample sequence as applicable.