This activity is based on using very special dice that seem to contradict common sense. Carefully analysing the situation that exists when using any pair of these special dice helps to show why the result makes sense.

Summary

This activity is based on using very special dice that seem to contradict common sense. Carefully analysing the situation that exists when using any pair of these special dice helps to show why the result makes sense.

Mathematical strand:

Probability

Prior knowledge

It requires students to have an understanding of how probability works, but this activity will require a rather different sort of analysis.

Relevance to Core Maths qualifications

•AQA

•C&G

•Eduqas

•Pearson / Edexcel

•OCR

Suggested approaches

The context described in the handout works well with either yourself or a senior staff member (or school visitor) playing the professor role. You could first ask for challengers and play the game with two or three of your students before asking them to prove or refute the professor’s claim of never losing.

Resources/documentation

In addition to this overview there are:

- Teacher guidance notes
- Handout

Relevant digital technologies

No need for any use of digital technologies (although writing a simulation of the situation would prove illuminating).

Possible extensions

Another special dice could be added in, as the winning pattern works with four dice.

Acknowledgement

This is a resource developed for the CMSP by David Burghes (CIMT, Plymouth University).