Probability with the usual suspects

Each time we cover probability in the classroom I warm more to the topic.  Not just because it offers an opportunity for the learners to get hands-on experience with simple equipment and addresses a variety of learning styles, but also because it forces discussion, and we can bring in so much simple mathematics that would otherwise be rather dry and dull. 

My first resource then is a large tin of equipment – dice of every shape and size (all the regular Platonic solids, to be precise), playing cards, lots of coins of different value, spinners, a Bingo machine with ninety numbered balls, coloured counters and cubes, and so on – and a healthy imagination. 

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My next resources (all available on the TES resources site) consist of lots of sets of cards for problems, discussion and ordering. The first set I made were True/False cards, with some obvious answers and some not so obvious – results of tossing one coin, two coins (are two heads, two tails and one of each equally likely?), lottery results, outcomes of dice, weather events, football results, and so forth.  We’ve enjoyed discussing these over the years, but I often feel my input has been greater than that of the learners. So I introduced matching cards – the event on one card and the probability, as a percentage, on another card.  Ordering these were simple once the probability was determined, and big displays with number lines were produced for classroom decoration.  Then I introduced some experiment cards – the results from two coins, adding two dice, looking at football results, etc., so that the learners have to actually do it, rather than guess at the answer, which is often the case.   Finally I developed the A4 cards, duly laminated, with fifteen scenarios that covered possible natural events like snow in June (I can add snow in October to that this year) and experimental events, like scoring a double six with two dice, picking the ace of Spades from a pack, any ace, any Heart, and so on, ranging from impossible to certain, with some unlikely, some very unlikely, and some very likely, along with those for which it is possible to calculate a value.  These are my favourites, since it involves fifteen people trying to arrange themselves in order of likelihood, with any spare learners helping the proceedings. There is nothing I like better than taking them into a big space and watching as they do the work and I sit back and take a photograph, for display and checking back in the classroom.  (It always impresses management too – seeing the learners taking responsibility in what one described last week as ‘warm and supportive atmosphere.’)

It is so easy with probability to think the learner has grasped a concept, but the teacher can easily set up scenarios in the classroom and ask the learners to decide if it is fair, or true, and make sure they have the resources to answer it.  Are more boys than girls born each year in the UK?  Is a draw in football less likely than a win/lose result?  Is seven the most likely score when adding two dice?  Teachers too often think because they have said something the learner has grasped it – the first fallacy of teaching.

And finally it can bring in so much. The obvious things are being able to convert between common fractions, decimals and percentages, and between equivalent fractions if one fiddles the answers a bit.  Being able to compare and order fractions is something the learners have to do to align themselves on an imaginary number line. And then the whole area of combinations – the possible results from two successive events, for example.  For years I would entreat my learners to be systematic, until the day I asked if anyone knew what ‘systematic’ meant – not a single response.  All skills required by the National Curriculum and GCSE, and useful skills for life, being able to consider and enumerate the whole set of possibilities.  And of course, and understanding of likelihood really is a skill for life – how many times do we make stupid mistakes by simply not considering the likely outcomes?

Do try some of these things yourself, and keep it active and meaningful. It might also be rather fun.

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About Colin Billett

Maths teacher, among other things. View all posts by Colin Billett

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