Once or twice a year, students in Years 8 to 12 complete an extended problem-solving and modelling task as part of their mathematics assessment. These tasks are conducted over a number of weeks, and are based in an authentic context in which students must apply mathematical techniques they have learned to solve a real-life problem. Students are typically required to present their solution in the form of a clear and concise report.
Examples of tasks that students in junior year levels have completed include modelling the trajectory of a basketball using parabolas, comparing two mobile phone plans by creating linear models for each, and predicting how long an irregular-shaped pool will take to fill.
The level of mathematical sophistication required to complete these tasks increases as students progress through the Year levels and learn how to wield more powerful mathematical tools.
The current cohort of Year 12 Mathematics C students have already completed two tasks of this nature. The first involved applying matrix techniques to decrypt a secret message that had been encrypted using a well-known modern cipher (Hill Cipher), while the second involved using the Leslie Population Model to make predictions about the size and structure of a population of foxes. Currently, girls are using their knowledge and understanding of conics—the class of two-dimensional curves formed by intersection of a plane and a cone—to create a computer model of a planet moving in an elliptical orbit. Students are required to use a specialised piece of dynamic geometry software to incorporate this law and predict the time at which their planet will reach a particular location.
Although the extended modelling and problem-solving tasks are challenging, students find them extremely worthwhile. Unlike a supervised examination, these tasks allow students to take their time exploring the problems in great depth and be imaginative in how they solve them. They also provide students with a sense of the power of mathematics to represent complex real-life phenomena and solve associated problems.
Dr Pete Jenkins
Head of Mathematics C and Specialists Mathematics
Mathematics C students, Sarah Pyman (12O) and Abigail Clacher (12H).
