The chance of England winning the 2010 World Cup is 1/3.They can win, draw or lose.

What do you think Dave?

Well, that’s right isn’t it John?

England were in Pot 1 with the other seeded teams. This gives them a good chance of winning.

If England come top of their group they will have a better chance of winning.

If England win their first match against USA, they are more likely to lose their second match

against Algeria.

Up2d8 mathsSouth Africa 2010

Teacher Notes

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 thepreparations to host a major sporting event. Just what are England’s 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 theiropinion on England’s 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 you’re going to deliver theactivity 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 includethe misconception held by many students that the chance of winning a football match is 1/3 because there are three possible outcomes, andgoes 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 onlyone statement. To make the task more complex you could consider asking pupils to make up their own statements and present the justificationsfor 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 taskwould lend itself to a poster on which pupils put across their point of view for one or more of the statements – perhaps using the cartooncharacters 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 thatyou 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 toworking in groups in mathematics, you may wish to spend some time talking about their rules and procedures to maximise the effectiveness andengagement of pupils in group work (you may wish to look at the SNS Pedagogy and practice pack Unit 10: Guidance for groupwork). You maywish to encourage the groups to delegate different areas of responsibility to specific group members – some of the group could look at the firsttask 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 developingthe assessment criteria with your class. You might choose to focus on the content objectives or on the process objectives. You might decide

thatthis activity lends itself to comment-only marking or to student self-assessment. If you decide that the outcome is to be a presentation or aposter, 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 England’s 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.