South Africa 2010 Introduction: The draw has been made for the 2010 FIFA World Cup South Africa. The first match starts on 11 June 2010. South Africa, as the host nation, is making thedraw preparations to host a major sporting event. Just what are Englands chances of winning this year? Does their place in the draw affect their chance of winning – or is it playing better football than any other team that will ensure their success? Football fans the length and breadth of the land will be starting to give us their opinion on Englands chances – but what do we think from a mathematical point of view? Content objectives: This context provides the opportunity for teachers and students to explore a number of objectives. Some that may be addressed are: when dealing with a combination of two experiments, they identify all the outcomes when solving problems, they use their knowledge that the total probability of all the mutually exclusive outcomes of an experiment is 1 they find and justify probabilities and approximations by selecting and using methods based on equally likely outcomes and experimental evidence, as appropriate in order to explore mathematical situations, they carry out tasks or tackle problems; pupils identify the mathematical aspects and obtain necessary information. Process objectives: These will depend on the amount of freedom you allow your class with the activity. It might be worth considering how youre going to deliver the activity and highlighting the processes that this will allow on the diagram below:
Activity: The activity uses the 2010 Football World Cup in South Africa as a context for discussing probabilities. The PowerPoint slides include2010 Football World Cup the misconception held by many students that the chance of winning a football match is 1/3 because there are three possible outcomes, and goes on to encourage pupils to consider other statements related to probability. Differentiation: You may decide to change the level of challenge for your group. To make the task easier you could consider focusing on only one statement. To make the task more complex you could consider asking pupils to make up their own statements and present the justifications for their arguments. This resource is designed to be adapted to your requirements. Outcomes: You may want to consider what the outcome of the task will be and share this with students according to their ability. This task would lend itself to a poster on which pupils put across their point of view for one or more of the statements – perhaps using the cartoon characters as their mouthpiece. Working in groups: This activity lends itself to paired and small group work and, by encouraging students to work collaboratively, it is likely that you will allow them access to more of the key processes than if they were to work individually. You will need to think about how your class will work on this task. Will they work in pairs, threes or larger groups? If pupils are not used to working in groups in mathematics, you may wish to spend some time talking about their rules and procedures to maximise the effectiveness and engagement of pupils in group work (you may wish to look at the SNS Pedagogy and practice pack Unit 10: Guidance for groupwork). You may wish to encourage the groups to delegate different areas of responsibility to specific group members – some of the group could look at the first task only, for example. Assessment: You may wish to consider how you will assess the task and how you will record your assessment. This could include developing the assessment criteria with your class. You might choose to focus on the content objectives or on the process objectives. You might decide that this activity lends itself to comment-only marking or to student self-assessment. If you decide that the outcome is to be a presentation or a poster, then you may find that this lends itself to peer assessment. Probing questions: You may wish to introduce some points into the discussion, which might include: what are the factors that affect who wins a football match? will a team which includes David Beckham beat your school team? are you equally likely to win or lose a football match? if you have just thrown a head with a coin, are you more likely to get a tail with the next throw? is this the same with football matches? If I have just won a match is it more likely that I lose the next one?
You will need: The PowerPoint presentation. There are four slides: The first slide introduces pupils to the misconception that you are equally likely to win, draw or lose a football match because there are three possible outcomes. The second slide asks pupils to consider whether Englands place in Pot 1 gives them a better chance of winning. The third slide asks pupils to consider whether England stand a better chance if they win their group. The final slide asks pupils to consider whether England are more likely to lose their second match if they have won their first.