Betting on the group winners using 2012 results

France is this year hosting football’s Euro 2016 competition and  I thought a number of teachers might find this resource useful (I’ve added more explanation on the sheet than I do in class e.g. the explanation for the Switzerland bet on p.2, for the benfit of reader’s in the hope it helps facilitate a better understanding of one way for running this activity). I’ve uploaded the activity in word to allow for easy tailoring to your particular needs (I’d appreciate a mention/reference). I’m posting this resource as a blog entry because it doesn’t really fit the style of our activities on the main topic pages - it's effectively a worksheet, but an activity/discussion based one (rather than independent practice). 

I use this resource each year (and tailor it to different sporting events at other times) and really enjoy teaching it. I tend to use it just after we’ve covered converting between fractions to decimals and percentages, introducing the activity with the question: “which is best: Fractions, Decimals or Percentages” (a good “display” opportunity or “court case” activity, with different groups preparing the “For and Against” arguments before battling it with one of their peers as the “judge” to maintain order). I tend only to use it with 14/15 year olds and above classes, and refer back to a nice activity we’ve generally covered in earlier years:   Fraction-decimal conversion debate “which is easier, converting fractions to decimals or decimals to fractions?”

Why do I like it?

• An application that genuinely engages and interests most students.
• International awareness – as with different country’s mains voltage levels, different plug sockets etc. it’s intriguing how different nations have developed different means for solving the same problem (US, UK and continental Europe betting odds).
• A good example of how fractions, decimals, percentages and ratio are used to measure and define proportions. Students often lose sight of, or never really understand, this aspect of what fractions, decimals etc. are used/designed for.
• Betting odds are an everyday example that seem so simple, yet actually require a lot of mathematical thinking to fully understand. In particular the extension where the understanding “chance of winning” is akin to the question “how does one break even on this bet” i.e. 2/9 odds means to be a “fair” game, the bookie would expect you to win your bet (and hence £2) for 9 games, but then lose your bet (hence lose £9) in the next two i.e. lose twice in every eleven bets and win nine times (chance of winning = 9/11).

However, it’s not a resource through which students can really “discover the mathematics for themselves”. To do this, I think you’d have to set up a simulation/game for them to play and record what happens each time and then leave it to them in pairs/groups/individually etc. to try and work out how the odds are working? I find it takes quite a bit of explanation, peer-to-peer help, and many students will need to understand the Pld, GF, GA, GD, Pts abbreviations used in the “Euro2012” pool matches tables – their sports interested peers can explain. There’s a lot of “explaining”, and discussion, required (but this doesn’t mean that by the end of it, they haven’t understood, only memorised!).

Why use this resource in a mathematics class?

So what’s the value of this resource in a mathematics classroom? As I often remind students, all of their parents are gambling, whether they see it like that or not: on their savings and investments, their pension plans, the insurance they do, and don’t, have etc. Gambling: sports, poker, is, rightly or wrongly, exciting to young people (because they know it’s not well seen in the adult world/it has an element of danger?) and glamorous – get rich quick with little effort . . (and equally easily end up on the street having lost years/decades of savings . . ). We can use this to educate more generally about risk assessment and management. It’s a context that gets them interested in relating the mathematics we’re covering in class to the world they're living in outside of class. I get a real sense of having communicated to students something that I think is essential . . and we have a lot of fun doing it! It would be great to hear from you if you use it: [email protected]