Maths - Head to head

Make a mathematical model of how nits spread by rolling dice

Jonny Griffiths

"There is no topic on Earth that doesn't lead to mathematics," we maths teachers often say. Head lice are no exception.

So how do we model the spread of head lice mathematically? The epidemiology of head lice is about as simple as it gets: they have only one host (humans) and can only spread from human to human. Pupils can simulate this scattering of the population by using dice. Each pupil is responsible for one "head" and monitors the presence or absence of head lice over 10 weeks. There are a number of probabilities we can vary: (a) the starting chance of being infested; (b) the chance of picking up the infestation if you are currently clear; and (c) the chance of recovery once you are infested. The conclusion upon collecting together the class results? The proportion of the population infested tends to a limit as time goes by, and the limit depends on (b) and (c) but not (a). (The limit is in fact b(b+c).)

Dice may seem a little old-fashioned these days. The temptation is to click on a spreadsheet to introduce randomness. Indeed, that is how this activity ends - the donkey work for counting thousands of throws can only sensibly be done with a computer. Yet rolling dice at the start gives pupils a genuine feel for the random nature of the activity - and it's fun.

It gently introduces the idea of a limit, a vital idea for later work on calculus, as well as sequences and series. The spreadsheet models 100 people. How many people would be enough to make a good stab at the limiting value? Pupils can now be invited to research some statistics for themselves, such as how prevalent head lice are in the population.

Jonny Griffiths teaches maths at a sixth-form college


Download Jonny Griffiths' Lousey-Lousey lesson from TES Resources to try it for yourself.

For a basic introduction to spreadsheet modelling, try elizabrown's muffin-making task.

In the forums

Maths teachers look at a 1986 O-level maths paper to see if it was more rigorous than GCSEs.

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Jonny Griffiths

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