Example problems

To help participants conceptualise and develop a greater understanding of mathematical modelling, example problems that are contained in the Guidebook are also available for download and distribution.

Each modelling problem contains data sets and information sources. These help to illustrate the 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, make obtaining data part of the modelling task.

Download all example problems (zip file)

Junior modelling problems for upper primary, junior or middle secondary

These junior 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.

Intermediate modelling problems for junior or middle secondary

Modelling problems are often in the eyes of the beholder – if those eyes are open. The intermediate modelling problems provided include examples drawn from two sources available to us all: things we do and what we read. 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.

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.

Senior modelling problems for middle or senior secondary

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 used. These problems contain scope for individuals and groups to exercise initiative and demonstrate attention to detail.