Suggest a CBM Problem

One aspect of developing a CBM curriculum is finding interesting problems from all subject areas for which maths can help to find solutions. We'd like your help!

Try coming up with a CBM problem in your area of experience or expertise. Here is some guidance as to how we hone our ideas, which we hope can help you to help us.

What makes a good module?

When thinking of new modules in your area, please consider the following:

Is the title a question?
Is it suitable for mathematical treatment and analysis?
Can someone of the target age group understand the idea of the question without explanation?
Is it clear what would be worked out?
Are there useful solutions?
Are the concepts used in the solution accessible, with help, by the target age group?
Will it be fun to do?

Examples of module titles

1. "Am I normal?"

An introductory module for statistics. Students collect and look at ways of visualising data about themselves. They learn about how a number can be used to describe aspects of the dataset. They see how different characteristics lead to different results for normality and learn how to combine two or three characteristics to define normality.

2. "Should I insure my laptop?"

Students begin by playing lotteries and calculating the costs and probabilities of winning. They learn how insurance works and then determine their personal utility curves for their laptop and compare the losses and gains made from insuring or playing a lottery. They role–play a competitive insurance market, with student insurance agents determining policy premiums to offer to their student clients. The teacher is able to see the big picture and determine an overall winning insurance agent.

3. "Can I spot a cheat?"

Students attempt to visually spot fraudulent results from a 200–coin–flip experiment. They learn about patterns and distributions that theory predicts and see how a hypothesis test can be used formally to provide evidence of fraud. Students investigate various datasets and provide evidence to support a hypothesis they make.

Criteria to see if a topic or problem is CBM

The reason for teaching a topic must be: (a) it's useful for a technical job; (b) it's useful for everyday living; or (c) it trains the brain in logical reasoning.
The context should be in real-world problem solving.
A computer is assumed to be available to use for problem solving.
Manual computation is only taught if: (a) it explains a practical concept; or (b) it's important to be able to perform it without a computer.
The emphasis is on problem setup and interpretation—not the mechanics of the calculation.
Concepts are applied with as complicated examples as can be computed.
The aim of the solution is for a practical truth rather than a formal proof.
Explicit validation, critique and judgements upon the reliability of results.