#### Background

Starting points are problems that teachers and students can explore. Over time the collection will grow to encompass mathematics being used – and useful – in a range of contexts and settings. The connecting thread will be purposeful use of mathematics to provide answers or insights into those contexts, whether they be personal, vocational, environmental or social in nature.

Very often, a systematic approach is helpful in addressing problems located in real world settings. Two variants are provided below; you may well have your own. However the process is rarely linear; checking, correcting, and reflecting means that there is usually movement to and fro between the stages.

While not specifically mentioned technology is relevant whenever it can enhance the total process – which is often. Also a given problem can often be addressed at different levels and different ways and use different tools (arithmetic, algebraic, geometric).

#### Real world problems – a method of attack

- Identify a (real world) problem
- Specify a related mathematical question
- Formulate a mathematical model to address the question (involves making assumptions, choosing variables, estimating magnitudes of inputs etc)
- Solve the mathematics
- Interpret the mathematical results in terms of their real world meanings
- Make a judgment as to the adequacy of the solution to the original question
- Either report a success or make adjustments and try for a better solution

#### The Modelling Process

(contributed by Jill Brown)

**And so to work...**