## Focus on Mathematical Modelling: Cornering

Written by Kaye Stacey

A rite of passage for many students in Years 9 and 10 is preparing to obtain a drivers’ licence or learning how to cycle in traffic. The Cornering unit from the Mathematical Modelling Special Topic provides insight into the complex situation of long vehicles turning corners and builds understanding of road safety for drivers, cyclists and even pedestrians standing at corners. The motion of turning vehicles is difficult to visualise and prone to misconceptions, yet it makes an excellent context for developing students’ modelling skills. Students start from a very simple paper scale model and gradually build their understanding from practical experiments with scooters and bicycles, and increasingly complex pre-made dynamic geometry models. The main insight is that the rear wheels of a long vehicle do not follow the path of the front wheels, but ‘cut the corner’.

The central question is to find the space (size and shape) that is required for turning vehicles. At each stage of the investigation, students find new questions to ask, and consider how a different or improved model might better approximate the real situation and provide useful answers. There are two products–presentation of a short road safety message, and a report to a local council on an aspect of road design (such as the size of roundabouts or width of parking bays). There is a continual need to move back and forth between understanding the real situation and interpretation of the mathematical models, constraints and results.

The unit highlights the power of an iterative approach of mathematical modelling. While students do not make all the models themselves, they experience the cyclic stages of understanding, using, critiquing, and recommending refinements to models.

The Special Topic Mathematical Modelling provides 5 units suitable for students in Years 9 and 10 and based on real world situations of cornering, queuing at a theme park, pricing, designing packaging, and examining ‘How Risky is Life’. The Special Topic was prepared in conjunction with a Shell Centre team consisting of Professor Hugh Burkhardt, Rita Crust, Daniel Pead and Professor Geoff Wake from the University of Nottingham, U.K.