Martin Bamber, AC for Cheshire West, Chester, Halton, Knowsley, Liverpool, Sefton, St Helens, Warrington, Wigan, and Wirral

Recent enrichment activities, designed to help students engage more meaningfully with the mathematics they study and promote level 3 maths, highlighted certain features in the design that appeared to generate an additional ‘premium’ in terms of student engagement and motivation. To explain, consider a task with which many teachers will be familiar:

“Can the entire population of the world fit on the Isle of Wight?”

This is generally thought to be a reasonably engaging mathematical activity. However, in presenting it in the past, I tend to be asked, “Isle of What?” Students have little idea where the Isle of Wight actually is – especially in our region – and almost none of how big it might be. Of course, we give them a map with a scale, and a ruler, and tell them to get working. But as the Isle of Wight is a rather arbitrary choice in any case, why not start off with a locality that is familiar? Schools on the Wirral (Merseyside) were therefore given the task,

“Can the entire population of the world fit on the Wirral?”

The answer to this question is ‘no’, at least not if we assume people are to stand ‘shoulder-to-shoulder’. And that’s fine: a problem involving lots of useful concepts, approximations and reasoning is localised, and that is probably a good thing. It is also a useful introduction to the study of Core Maths, and I have used it to promote Core Maths regularly.

Is it a ‘plausible’ problem? I don’t think it is always necessary to achieve plausibility in setting problems: sometimes, ‘fun’ trumps everything, including in mathematics. And it is ‘plausible’ in one sense: large numbers of humans do sometimes stand together ‘shoulder-to-shoulder’, at festivals, or during protests (both of which phenomena can be studied at degree level – see MMU’s ‘Crowd Science’ degree course, for example). But we don’t usually do this just to see if we will fit in a particular space.

A more plausible (but still not ‘realistic’) problem is to ask,

“Can the entire population of the world LIVE on the Wirral?”

or more realistically, in Merseyside, as the Wirral is still too small. This raises new and interesting ideas, inspired by the notion of a ‘mega-city’. How do people actually live in densely-packed locations such as Hong Kong? How much ‘ground space’ is taken up by a typical high-rise housing estate, and how many people live there? Transferring this mode of living to Merseyside, how high would our skyscrapers have to be, and would we like living there?

Students’ reactions to this alternative to the ‘Isle of Wight problem’ suggest that locality and plausibility enhance their engagement. And it is usually not too difficult to localise a problem from its original context. Adding in ‘plausibility’ can sometimes be more challenging …