Example problems

To help participants conceptualise and develop a greater understanding of mathematical modelling, example problems are available for download and distribution.

Throughout out these problems, example data sets and information sources are provided. This has been necessary to illustrate workings and development of models. In general, in real-world modelling scenarios, finding appropriate data sources are part of the task. When using these example problems, teachers or mentors may choose to withhold the example data sets provided, and instead direct student activity to make obtaining data part of the modelling task.

 

Simple modelling activities

These simple modelling problems involve the sorts of mathematical processes that we often undertake automatically. In doing so, we can overlook that we have made assumptions that are so ‘obvious’ that we did not realise that we had made them. Students should be encouraged to articulate the assumptions and processes required. Those already familiar with basic modelling approaches might wish to skip to later material.

Download 'Adapting a recipe'

Download 'Hyperthermia'

Download 'Köchel numbers'

 

Self-generated modelling activities

Modelling problems are often in the eyes of the beholder – if those eyes are open. The self-generated modelling problems provided include examples drawn from two sources available to us all: things we do and what we read. The problems are intermediate in demand. Application of the modelling process in these problems involves more initiative and persistence. Mathematics is often initially absent, and needs to be introduced by the modeller.

Download 'Evacuating'

Download 'Howzat!'

Download 'Newspaper'

Download 'Bushwalking'

Download 'Fifteen–forty'

Download 'Nuclear blast'

 

Suggestions for self-generated modelling activities

We encourage students to invent their own problems and to outline their approach to solutions. These problems should be related to things that students find interesting and important.
Some topics with the potential to give rise to good modelling projects are provided here.

 

Harder modelling activities

The problems at this level are designed to bridge from students’ previous learning into the more substantial and complex demands of IM2C-style problems. These examples call upon initiative, persistence, decisions about the type of mathematics to apply and how technology might be utilised. These problems contain scope for individuals and groups to exercise initiative and demonstrate attention to detail.

Download 'Population growth'

Download 'Farm dams: Middle secondary'

Download 'Farm dams: Senior secondary'

Download 'Super Size Me'

Download 'Temporary traffic lights'