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Substitution and transportation in non linear relations
The following sample material comes from the "Specialist Mathematics Teaching Notes" booklet by Antje Leigh-Lancaster and Michael Evans in the series "Supporting VCE Mathematics", published by the MAV. For further details, send an e-mail to office@mav.vic.edu.au.
Contents Introduction Sample course outline and assessment schedule Coordinate geometry Circular (trigonometric) functions Sample analysis task - assignment Algebra Vectors in two and three dimensions Calculus Solving Differential Equations with a graphics calculator An Analysis question using technology to solve differential equations Using Euler's method with a graphics calculator Explanation of the program Investigation of Euler's Method References and resources The changes to the Specialist Mathematics course for the revised VCE Mathematics study 2000 - 3 are summarised in the March edition of the VCE Bulletin, 1999. The requirements for coursework assessment are described in the mathematics study design, with further advice published in the Mathematics 'Assessment Guide Revised VCE 2000'. Most of the content for Specialist Mathematics remains the same as in the former study. The main change in the revised study has been to develop Specialist Mathematics Units 3 and 4 as a fully prescribed course with selected content from both of the previous Geometry and Mechanics modules incorporated within the course. Other sections of the revised course have also incorporated minor revisions. The following material provides advice on possible approaches to the teaching of new and revised material. Sample course outline and assessment schedule The outline given below provides a sample teaching sequence for the Specialist Mathematics course incorporating a possible assessment schedule. It should be noted that this sequence is based on weekly blocks with respect to the 1998 school year, to assist teachers in relating the new course to their implementation of the current course. In practice there would likely be variation in the number of periods taken to complete a topic or part of a topic, which would result in sections of work not necessarily starting or ending at the beginning or end of a given week. This will particularly be the case where timetables are constructed on a longer than 5 day cycle, and will also depend on the length of periods and the number of scheduled teaching periods in a week. For example, if there are 4 scheduled periods of 50 minutes duration in a week, 15 weeks will be needed to meet the unit requirement of a minimum of 50 hours of scheduled classroom instruction. Table 1- sample weekly content schedule
Table 1 (continued) - sample weekly content schedule
Each of the two analysis tasks in Unit 3 could, for example, be scheduled to take place over three consecutive periods (with possibly the equivalent of one period of homework time). The two tests in Unit 4 should each be designed to be completed in a single period, while the application task could be completed over 5 or 6 periods (all periods in one week and one or two periods in the second week, with possibly the equivalent of one or two periods of homework time).
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