This article is part of our collection Great Expectations: Probability through Problems.

"Probability is fantastic!"

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.

So what's different about our approach:

• we start from a problem, not from a technique
• the progression is from the empirical to the theoretical, with the formal aspects of the curriculum introduced through the problems
• 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)
• 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
• data is recorded on a tree diagram and a 2-way table, using natural frequencies (whole numbers)
• we progress from what happened in the experiment (collating data from all groups in a classroom) to what we would expect to happen
• 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

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.

All the resources are based on interesting experimental contexts, which model real-life contexts: