CHEQUERED FLAG

"In some ways race strategy is the same as chess. Ross Brawn, the strategist behind most of Michael Schumacher's 91 victories at Benetton and Ferrari Note: F1 Racing magazine estimated Brawn's salary being about $5 000 000 per season with Ferrari in 2000-2006 "In some ways race strategy is the same as chess. You know which direction you want to go in, and then try to be three or four moves ahead to try and outwit the opposition." Unlike in many other forms of auto racing, a Formula 1 race often has long periods in which very little track action appears to be taking place. But it's often during these apparently quiet moments that the biggest stakes are being played out in race strategy. And it is in following, or even second-guessing, that strategy that the spectator discovers a whole new, passionately interesting element to the race apart from track action. Strategy not only requires calculation from the team, it also requires perfect execution by the driver. At precisely the moment his team asks him to, he must speed up and pass straggling cars. His pit lane entry and exit must be perfect to reduce the time of his pit stop. The role of the race strategist is arguably as important as that of the driver.

If you think that looks fun and would like to be a race strategist. Part science, part magic – a decent strategy is essential to the business of winning races. Or, indeed, losing them. The basic variables of the equation are simple enough: fuel load and tyre wear. If you think that looks fun and would like to be a race strategist. Click onto the next slide The teams' race strategists are aware that at some circuits benefits could be gained from making two or three stops, rather than just one. This was because the car could run substantially quicker on a lower fuel load (with less weight to carry around) and using the grippier, but less durable, soft tyre compounds. A difference in performance that could be sufficient to offset the effect of the 30 or so seconds lost making a pit stop.

Are you a potential Race Strategist? Determine the optimum strategy for each of these three circuits. Monaco Number of Laps: 65 Circuit Length: 4.69 km Silverstone Number of Laps: 60 Circuit Length: 5.14 km Belgium Number of Laps: 44 Circuit Length: 7 km How much fuel do you need? How many scheduled pit stops are required? Will you have the winning strategy and beat your opponents?

Enter the initial amount of fuel required Note: The fuel tank will hold a maximum of 110 litres The more fuel you require during a pit stop, the longer it takes An additional 20 seconds is incurred when entering and leaving the pits Generally, the less fuel you have the faster you go Enter the lap distance and number of laps for your chosen circuit Find the best strategy to minimise your race time Enter ‘0’ litres for a one-stop race Enter the amount of fuel required during the pit stop

Use the lap data to inform your decision making

Up2d8 maths Chequered Flag Teacher Notes

Chequered Flag Introduction: A successful Formula One team relies on many factors working in harmony with each other; these include the skill of the driver, the car’s aerodynamics, engine power, tyres and a degree of luck. Nevertheless, no matter how advanced any of these factors are, in order to win the team must employ the optimum race strategy and outwit their opponents. Content objectives: use rounding to make estimates and to give solutions to problems to an appropriate degree of accuracy understand and use proportionality and calculate the result of any proportional change use systematic trial and improvement methods identify a range of strategies and appreciate that more than one approach may be necessary; explore the effects of varying values and look for invariance and covariance in models and representations show insight into the mathematical connections in the context or problem. 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.

Activity: Students will be asked to place themselves in the role of an F1 race strategist, whereby they must consider the fuel requirements for a selection of circuits. Consideration must be given to the weight of the car, its effect on speed, the number of pit stops and the length of the circuit in order to minimise the lap and race times. Differentiation: You may decide to change the level of challenge for your group. To make the task easier you could consider: investigating one circuit, initially limiting the number of possible variables, in order to make sense of the data – eg, find the shortest possible lap time allowing for only one pit stop within teams, develop a race strategy and comparing/analysing the results - eg, who was in the lead after the first pit stop? To make the task more complex you could consider: researching other factors which influence a race, and to what degree how rain affects the strategic planning of a race the causes and implications of tyre-wear and its effect on strategic planning the assumptions made within the theoretical exercise – eg, the weather conditions remain constant throughout the race. 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 the students according to their ability. This could be: a presentation, justifying the selected race strategy and decisions made in light of the information given teams racing each other virtually to find the fastest race time debate on the real-life scenarios which could occur within a race, and the planned measures taken to accommodate all eventualities. Working in groups: This activity lends itself to paired or 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.

What makes Formula One one of the most expensive sports? Probing questions: Initially students could brainstorm issues to consider. You may wish to introduce some points into the discussion which might include: What makes Formula One one of the most expensive sports? What factors make some drivers and teams better than others? What is meant by a ‘race strategy’? What makes one circuit different from another? What considerations must a team take into account when planning for a race? You will need: The PowerPoint display which you might read through with your class to set the scene at the beginning of the activity. There are six slides. The activity also requires computer access to run the Excel spreadsheet (Race Simulator). Estimating how many people you could fit inside The O2 Introduction to Michael Jackson story Circuit information and related questions. Introducing the race simulator. Race data. Title slide. What is meant by a race strategy. Describing what effect tyre wear and fuel load have on a car’s performance. Putting the size of The O2 into context Checking The O2 facts and trivia Creating your own trivia Estimating the volume of The O2

Up2d8 maths Chequered Flag Student resource sheets Click here to download the race simulator to accompany this Up2d8.