Paul the Octopus died recently.

1. Paul the Octopus died recently. He achieved worldwide fame by correctly predicting the winner in seven matches in the World Cup this summer. He chose the winning team by choosing a mussel from one of two boxes – each decorated with the flag of the competing nations. Seven correct predictions in a row? There’s no way that could just be chance. That octopus must have been psychic or something? It’s just too unlikely otherwise I think it must have been chance. There were only two choices each time – it’s like flipping a coin seven times.

2. Imagine that Paul had a choice of two boxes, one that said ‘England’ and one that said ‘not England’ and he chooses the ‘England’ box. Paul backed the England bid to host the 2018 World Cup. England is competing against Russia, the United States, Australia, and joint bids from Spain and Portugal, and Holland and Belgiumto host the competition. The decision is being made by the FIFA committee on 2 December. Well, even if you think it’s just chance you’ve got to admit it’s likely that he’s right about this. He’s just got the last seven right after all. It’s more than a fifty-fifty chance. I think you’re both wrong! Because he’s got the last seven right he’s due a wrong prediction! I think it’s less likely that he gets this prediction right than the previous ones. No, I think that the chance that he gets this right is one half, just like all of the others.

3. The aquarium where Paul lived has unveiled its new octopus, also called Paul in honour of his predecessor. If there were claims that Paul II was psychic, how would you test these claims? How many matches would he have to predict correctly to convince you that it’s more than chance?

4. It’s in the News!Psychic Octopus Teacher Notes

5. Psychic Octopus Introduction: Do you remember Paul the Octopus? He achieved worldwide fame this summer during the football World Cup by correctly predicting the results of six of Germany’s matches, as well as picking Spain to win the final, leading to claims that he was psychic. Paul, who had been born in Dorset before moving to Germany, passed away peacefully in his tank at the end of October. Before he died, Paul had put his fame to good use, promoting the England bid to host the World Cup in 2018. The host will be announced by FIFA on 2 December this year. This resource uses the story of Paul as a context to generate discussion and debate around probability and chance. You might like to read this article from the BBC before using the resource with your class. Content objectives: This context provides the opportunity for teachers and students to explore a number of objectives. Some that may be addressed are: • compare experimental and theoretical probabilities in a range of contexts; appreciate the difference between mathematical explanation and experimental evidence • interpret the results of an experiment using the language of probability; appreciate that random processes are unpredictable. 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 the activity and highlighting the processes that this will allow on the diagram below:

6. Activity: There are three activities which build on and complement each other. The activities are based around misconceptions, with the first two slides offering contrasting opinions for students to discuss and decide who they agree with. These opinions will bring students’ misconceptions about probability to the fore and allow them to be challenged. You might choose to ask the students to provide a written explanation of why they agree with the opinion they decide is correct. The third activity asks students to explain how they would decide whether an octopus is psychic, how many results would the octopus have to predict to convince them that it was more than chance? Students are also invited to design an experiment to test any psychic octopus claims. Differentiation: The level of difficulty of this task is relatively low, the organisation and logic of the task can, however, end up being quite challenging. You may decide to change the level of challenge for your group. One of the objectives for this task might be for students to experiment with different approaches to a problem, to show resilience. It is worth considering what pedagogy would support this objective. To make the task easier you could consider: • assigning students to argue for a particular opinion, bringing out the issues but removing the personal from the opinion • providing coins or similar to help students experiment with the probabilities • providing information about the likelihood of various events in a familiar context to help students compare and decide what is likely by chance (Wolfram Alpha’s probability examples might be useful to illustrate this). To make the task more complex you could consider asking for a written report explaining the group’s thinking. This resource is designed to be adapted to your requirements. Working in groups: This activity lends itself to paired work 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. 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 use the APP model of assessment then you might use this activity to help you in building a picture of your students’ understanding. Assessment criteria to focus on might be • understand and use the probability scale from 0 to 1 (Handling data level 5) • find and record all possible mutually exclusive outcomes for single events and two successive events in a systematic way (Handling data level 6) • use tree diagrams to calculate probabilities of combinations of independent events (Handling data level 8).

7. Probing questions: These might include: • does Paul get better at predicting each time? • how is this like flipping a coin several times? • is flipping one coin seven times the same as flipping seven coins once? • what do you consider to be unlikely? Is it 1/100? 1/1 000? 1/1 000 000? Can you give an example for each of these? You will need: The PowerPoint presentation. There are just three slides: The first slide sets introduces Paul the Octopus and offers two opinions for students to discuss deciding whether seven correct results in a row could be chance or whether there was a skill involved. The second slide presents three opinions to discuss based around the misconception that the probability of each event is not independent of the previous events. The final slide allows the students the opportunity to decide what they consider to be possible through chance and what they consider to be through skill, asking them to decide how many games Paul II would have to predict the results for to convince them that it wasn’t just luck.