# Teacher Notes

### London Marathon

Introduction:

The first London Marathon took place on 29 March 1981, with 6 625 runners completing the course. The American Dick Beardsley and Norwegian Inge Simonsen won the men’s event dramatically, holding hands as they crossed the finish line in a dead heat. The marathon has since grown enormously with many runners raising money for charity. The sponsors claim that the London Marathon is the biggest fundraising event in the world.

This resource uses the context of the London Marathon to pose two questions for students to work on: firstly, students are asked to consider how long the fastest runner in your class could keep up with a marathon runner; and then they are asked to predict whether running or driving is a faster way to travel around London.

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Content objectives:

This context provides the opportunity for teachers and students to explore a number of objectives. Some that may be addressed are: • interpret results involving uncertainty and prediction interpret graphs and diagrams and make inferences to support or cast doubt on initial conjecture interpret and use compound measures, including from other subjects and real life.

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:

The activity asks students to estimate and make predications based on a few facts about times taken to complete the London Marathon. In the first activity, they are given the course record (2 hours 5 minutes and 9 seconds) and are asked to estimate for how long the fastest runner in the class could keep up with the runner that set this time (Kenyan Samuel Wanjiru in 2009). They are likely to offer a number of strategies which may or may not be practical in your school or classroom so you might like to set further restrictions, ask them to make assumptions about their maximum running speed or coordinate with the PE department (a treadmill would be very useful!). The second activity might follow on from this or may be run as a separate activity. Students are given the fact that, according to Jeremy Clarkson, the average driving speed in London is 10.6mph and are asked to predict whether an amateur marathon runner will be able to complete the course faster than a car. During this activity, students will need to create a mathematical model, making assumptions and considering variables to come up with a reasoned solution. There is a 13-minute video of the race from Top Gear which you might like to share with the class.

Differentiation:

You may decide to change the level of challenge for your group. To make the task easier you could consider: • scaffolding the task – breaking the analysis into manageable chunks to focus on for short lesson episodes • asking only for an oral justification rather than a written one • converting the distances and times into easier units. Maybe give the time in minutes or the distance in kilometres.

To make the task more complex you could consider: • reducing the scaffolding for the task – leaving the students to decide independently how to go about making their predictions • asking for a written justification of the students’ prediction for keeping up with Wanjiru • asking for a written justification explaining the mathematical model that the students have developed This task offers plenty of opportunities for developing students’ skills in justifying, and this might be a priority objective for the lesson 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: • use their own strategies within mathematics and in applying mathematics to practical contexts (Using and Applying Mathematics level 4) • draw simple conclusions of their own and give an explanation of their reasoning (Using and Applying Mathematics level 5) • solve problems and carry through substantial tasks by breaking them into smaller, more manageable tasks, using a range of efficient techniques, methods and resources, including ICT; give solutions to an appropriate degree of accuracy (Using and Applying Mathematics level 6) • • • •

Probing questions:

You may wish to introduce some points into the discussion which might include: • what was Wanjiru’s average speed? where do you think a marathon runner is going at their slowest? At their fastest?

how much slower is an amateur runner likely to be than a world record holder?

what factors influenced Clarkson’s drive that were not ‘average’?

if the car vs runner were to happen again, who would you predict would win?

You will need:

The PowerPoint presentation (and some idea about how fast someone in your class can run. If impractical then, if your school has a sports day, maybe the records from this or a conversation with the PE dept about expected times). There are three slides: The first slide sets the scene The second slide sets the first activity, asking students to estimate for how long they could keep up with Olympic Champion Samuel Wanjiru The final slide sets the second task, asking students to construct and interpret a mathematical model to predict whether a marathon runner or a car is faster around the marathon route.