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Maths - Dotty thinking

Create a data set that delivers big results in the blink of an eye

Create a data set that delivers big results in the blink of an eye

Have a very quick look at the dots above, then look away. How many dots do you think there are? No cheating, just write down your first estimate.

Now get your class to do the same. Show them the image of the dots for less than a second, get them each to write down their guess, make them promise not to change it, and then quickly go around the class and collect their guesses together, recording them on the board.

In less than three minutes you have created a data set. It may not look like the most interesting data set, but to your pupils it is, for the simple reason that they have created it. Perhaps more importantly - and you will have to trust me on this until you try it for yourself - your pupils will be desperate to know how many dots there are and will do almost anything to find out.

But you do not tell them yet, as you have hooked them in and there is plenty of important maths to do with this little set of data. First, we can work out the mean, median, mode and range of the guesses. In my experience, the range is one of the least understood concepts in maths, but in this case your pupils have a clear understanding of what the range is: it is the difference between their lowest guess and their highest guess; it is a measure of the spread of the class's guesses.

Once you have done this, why not compare the results with another class that has carried out the same experiment? Which class had the better estimators? How can we tell? Your pupils will be arguing about whether the mean or median is a better measure of average in ways they would not have previously done, simply because they own their guesses and they own the data set. They will be interpreting data and, more importantly, understanding what they are saying.

Finally comes my favourite. Without revealing anything, offer your pupils the opportunity to stick with their original guess or change it to something else. Record this new data set on the board and ask pupils to predict how the mean, median, mode and range might change. The results are fascinating. The range tends to diminish rapidly as over- and under-estimators sheepishly converge to the norm, and the mean tends to rise or fall in line with the guesses of the most vocal students. Perhaps most interestingly of all, due to a phenomenon known as "The Wisdom of the Crowds", the mean of this second data set tends to be further away from the true number of dots than the first set.

By the time you have created stem and leaf diagrams, histograms and cumulative frequency curves from the class's data, you have filled several lessons and covered most of the handling data requirements for the GCSE syllabus, all with a single set of dots. Oh, and there are 58, by the way.

Craig Barton is an advanced skills teacher at Thornleigh Salesian College in Bolton. He is the creator of and TES secondary maths adviser. He can be found on Twitter at @TESMaths

What else?

For a colourful step-by-step guide to finding the mean, try Ben Cooper's worksheet.


Help pupils to remember mean, mode and median with Danny Barthorpe's 3M cowboys. bit.ly3Mcowboys.

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