9837 /www/nrich/html/content/id/9837/ 3 2013-01-22T17:56:13 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><h3> <mdo:image alt="adding data elements to a Venn diagram" src="ProbLaunch-website3.png" style="width: 265px; height: 300px; margin: 10px; float: right;"></mdo:image><br></br> "Probability is fantastic!"</h3> <br></br> Perhaps not the usual reaction!  But this was the heading of a forum post written by a South African teacher who met our resources recently.<br></br> <br></br> So what&#39;s different about our approach:<br></br> <ul> <li>we start from a problem, not from a technique</li> <li>the progression is from the empirical to the theoretical, with the formal aspects of the curriculum introduced through the problems</li> <li>we start each problem with an experiment (using eg. multi-link cubes, specially adapted dice, as well as counters, numbered dice and coins) so that in watching the data accumulate, then analysing it, students can gain a sense of what is happening before being asked to make predictions (which are so often totally ill-informed)</li> <li>where dice are used in a model, data is typically collected from 36 trials to make the initial analysis transparent, and so that it is straight-forward to compare what actually happens with what we expect to happen</li> <li><mdo:image alt="practical 2-way table" src="ProbLaunch-website1.png" style="width: 300px; height: 171px; margin: 10px; float: right;"></mdo:image>data is recorded on a tree diagram and a 2-way table, using natural frequencies (whole numbers)</li> <li>we progress from what happened in the experiment (collating data from all groups in a classroom) to what we would expect to happen</li> <li>we then progress from expectation,  expressed as a proportion of the number of trials, to probabilities expressed as fractions, using a tree diagram to derive the multiplication rule</li> </ul> We have a collection of resources which can be used as a basis for the whole of the probability curriculum for 11-16 year-old students, which will take them from a first introduction right through to independent and dependent probabilities, and conditional probability.  In addition, we have a further set of problems providing a wider range of contexts in which students can investigate the mathematisation of probability and allied topics.<br></br> <br></br> All the resources are based on interesting experimental contexts, which model real-life contexts:<br></br> <br></br> <div> </div> <div style="margin-left: 40px;"><a href="http://nrich.maths.org/9546">Which team will win?</a> - introducing tree diagrams and the method of collecting data which is then interpreted in terms of what we would expect if we could collect enough data<br></br> <a href="http://nrich.maths.org/9525">The dog ate my homework</a> - building on this, expressing expected results in the form of proportions, and hence answering questions about how likely an event is<br></br> <a href="http://nrich.maths.org/9840">Who is cheating?</a> - from expected results to probabilities in the form of fractions, and the multiplication rule (and onto conditional probability)<br></br> <a href="http://nrich.maths.org/9843">Being Representative</a> - from experiment to sampling with and without replacement<br></br>  </div> <div style="text-align: center;"><mdo:image alt="flow chart of curriculum resources" src="curriculum_resources.png" style="width: 600px; height: 398px;"></mdo:image></div> <div><br></br> <br></br> We have a further set of resources which provide additional contexts for exploring the mathematisation of uncertainty and risk: </div> <div style="text-align: center;"><br></br>  </div> <div style="margin-left: 40px;"><a href="http://nrich.maths.org/9601">The Wisdom of the Crowds</a> - exploring averages in the context of skewed data, histograms<br></br> <a href="http://nrich.maths.org/9685">How confident are you?</a> - testing people&#39;s confidence levels<br></br> <a href="http://nrich.maths.org/9609">Capture and re-capture</a> - proportional reasoning through sampling<br></br> Luigi&#39;s Ice Cream Business (still being worked on) - what effect does risk have on assessment of likely outcomes<br></br> To insure or not to insure (still being worked on) - risk from the perspective of the owner of a mobile phone and a company that wants to make money out of insurance</div> <br></br> <div style="text-align: center;"><mdo:image alt="supplementary probability resources" src="ProbLaunch_SupplementaryResources.png" style="width: 500px; height: 356px;"></mdo:image></div></mdoxml> 2 0 0 0 1 1 0 jag55 Probability - modelling approach