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# Mathematics Matters Lesson Accounts 12 - Probability Concepts (theoretical and experimental)

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Created on 27 May 2008 by ncetm_administrator
Updated on 16 June 2008 by ncetm_administrator
 Mathematics Matters Lesson Accounts A collection of memorable mathematics lessons that conference and colloquia delegates had observed or taught which they felt were successful.  Each account refers to one or more of the values and principles in the report.

# Lesson Account 12 - Probability Concepts (theoretical and experimental)

 Written by Dan Curran Organisation Norton College Age/Ability Range Year 7 class mixed boys and girls.

I had a slide of the old-fashioned “pinball” type toy where a ball can be dropped in from the top and the ball makes its way to bins at the bottom.

Several students recognised this type of equipment and we discussed what might happen to balls as they were dropped in to the pinball machine. The discussion was good with various ideas about how the bins might fill up; an equal distribution of balls in the slots was a common thought.

After generating interest in the outcomes. I showed them a virtual pinball simulator available as a Java type animation.

We experimented with the virtual pinball as a whole class activity, dropping balls of various sample sizes and with different numbers of bins at the bottom of the machine.

A helpful visual feature of the applet was the generation of a frequency diagram revealing the way in which the balls fell.

The distribution of balls wasn’t really what the class had generally expected. Claims of bad luck and fluke results were a general explanation for the distributions generated, so we re-ran the pinball simulator several times.

Amongst the class there was much debate about why the results were not as expected. Some students began to venture explanations for the distribution and started to talk about the “routes” that led to the bins at the bottom of the pinball machine.

Students suggested we reduce the simulator to a small number of bins and we then attempted to analyse the ways in which the balls could reach the bins. Within al short space of time explanations for the results yielded by the simulator were produced. We verified our thoughts with some attempts to predict the number of ball our theoretical models were predicting.

What were the critical moments?
When the students started to “list” the possible routes to the slots a connection to the structure of the pinball machine became apparent. They generated the routes themselves – albeit this was often attempted in a haphazard and unstructured way.

A second feature was the notion of experimental probability compared with the theoretical model. Lots of good discussion about ideas of luck and chance influencing deviations from our expectations. The ability to verify or discount ideas quickly made the debate manageable.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
Apart from the theoretical and experimental probability ideas there were opportunities for discussion of how the results were being represented the graphically.

An unexpected bonus was that the class was able to consider very large samples.

How was that mathematics learnt?
Mainly discussion and recording the “routes” through the pinball machine.

Other memorable outcomes

Resources
Very little apart from the slide of the pinball machine and the web reference to access the virtual pinball. They made some drawings / recording in their exercise books. The lesson was displayed through the data projector / IWB.

## Values & Principles

 Strategies for investigation and problem solving Encourages reasoning rather than ‘answer getting’ Creates connections between topics both within and beyond mathematics and with the real world

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