Year 9 bottom set today. 25 pupils in the room. Question "How many boys in the room?" "13". "What is the probability of choosing a boy at random from the class?" "13/25". "What does that mean?" Blank stares...
Fortunately this was anticipated, and the point of the lesson - what does it actually mean to write down a probability? What information does that fraction give us? To help illustrate the idea I used the random name generator that I have for each of my classes and we did some basic probability experiments, cycling the random name generator 25 times and seeing how many times a boy came out (actually happened 14 times, which was lucky!). We then did some further fun data collection - pupils had to find out which of their classmates, could roll their tongue, had ever broken a bone, won a competition or similar. Having done this activity before I had learnt from previous mistakes - I only had 6 pieces of data collection where previously I might have done 10 (understanding that 6 bits of data x 24 pupils = 144 data points altogether for each pupils to collect), I structured their time a little more so that they had certain time around the room, then time at their own tables to share the data they have gathered, then separate time to write down the probabilities - whereas before I had previously just given time for the whole activity without the structure. We then did the same sort of experiments again, looking at how many times in the random name generator produced the names of people that did or did not meet the criteria, and compared to the probability that the data had given us (thankfully they compared favourably). By the end pupils did have an understanding of the idea of probability as a measure of chance when outcomes could be selected at random, that this also told us about how many times outcomes occurred when a number of events are possible and they also gained more comfort with the idea of probability telling us if something is biasing an experiment if the experimental results are significantly different to those that the probability suggests. Although there are still things to tweak, particularly with the data collection, I think that overall this lesson was a success in generating an extra level of understanding about probability in pupils.
Fortunately this was anticipated, and the point of the lesson - what does it actually mean to write down a probability? What information does that fraction give us? To help illustrate the idea I used the random name generator that I have for each of my classes and we did some basic probability experiments, cycling the random name generator 25 times and seeing how many times a boy came out (actually happened 14 times, which was lucky!). We then did some further fun data collection - pupils had to find out which of their classmates, could roll their tongue, had ever broken a bone, won a competition or similar. Having done this activity before I had learnt from previous mistakes - I only had 6 pieces of data collection where previously I might have done 10 (understanding that 6 bits of data x 24 pupils = 144 data points altogether for each pupils to collect), I structured their time a little more so that they had certain time around the room, then time at their own tables to share the data they have gathered, then separate time to write down the probabilities - whereas before I had previously just given time for the whole activity without the structure. We then did the same sort of experiments again, looking at how many times in the random name generator produced the names of people that did or did not meet the criteria, and compared to the probability that the data had given us (thankfully they compared favourably). By the end pupils did have an understanding of the idea of probability as a measure of chance when outcomes could be selected at random, that this also told us about how many times outcomes occurred when a number of events are possible and they also gained more comfort with the idea of probability telling us if something is biasing an experiment if the experimental results are significantly different to those that the probability suggests. Although there are still things to tweak, particularly with the data collection, I think that overall this lesson was a success in generating an extra level of understanding about probability in pupils.
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