15 000 seems like a really round number. It can’t be accurate can it? A marathon is 42.195 km (26 miles and 385 yards). How inaccurate is 15 000 km? Does it matter? 15 000 seems like a really round number. It can’t be accurate can it?

My best time was 2 hours and 56 minutes My best time was 2 hours and 56 minutes. I averaged about 4 hours for each marathon. What might my slowest time have been?

Which of these distances makes most sense to you? How far is 15 000 km ? How far is 15000km anyway? It’s the same as going from Land’s End to John O’Groats 11 times! It’s the same as going from London to New York three times! It’s the same as running around the M25 80 times! Which of these distances makes most sense to you? Which do you feel illustrates the distance in the most understandable way? How would you illustrate 15 000 km so that someone in your school was able to ‘get a feel’ for the distance?

It’s in the News! A marathon a day… Teacher Notes

A marathon a day… Introduction: Content objectives: During 2010 and into 2011, Belgian Stefaan Engels completed an extraordinary feat of endurance, running 365 marathons in 365 days! The races, in the UK, Spain, Portugal, Belgium, Canada, Mexico and the US, mean that Stefaan Engels ran more than 15 000 km in a year, averaging around four hours for each marathon. This resource uses this extraordinary feat as a context for exploring notions of distance and allows the opportunity for students to practice proportional reasoning in a number of contexts. Content objectives: This context provides the opportunity for teachers and students to explore a number of objectives. Some that may be addressed are: apply understanding of the relationship between ratio and proportion; simplify ratios, including those expressed in different units enter numbers [into a calculator] and interpret the display in different contexts choose and use units of measurement to measure, estimate, calculate and solve problems in a range of contexts; know rough metric equivalents of imperial measures in common use, such as miles. 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: Differentiation: Working in groups: Assessment: This is a set of activities which might be used as separate short activities or run together as one longer lesson. The first activity looks at the error in reporting the distance run by Stefaan Engels in a year. Students are asked whether this rounding is important in this context and could be led to a conversation about appropriate degrees of accuracy and rounding. The second activity could be a very short discussion activity or could be used to begin a discussion about different types of average. Students are given information about the fastest marathon run and the average and are asked what the slowest time might be. The third activity gives an opportunity for students to use their imagination in exploring a proportional relationship. They are offered three examples of the distance travelled by Stefaan Engels and are asked which of them is most useful to them and to offer some other comparisons which will mean something to people in their school. These might include, how many times they’d need to travel from home to school to cover 15 000 km, how many times they’d travel from school to the nearest large town or how many times they’d have to travel from home to their last holiday destination Differentiation: To make the task easier you could consider: using just one of the discussion activities preparing some distances from the school for students to work with for the third activity asking students only for an informal, verbal justification of their opinion in the second activity. To make the task more complex you could consider: asking the students to offer a written justification of their opinion for the first or second activity encouraging students to work with percentage error in the first activity and to decide when this sort of percentage error is acceptable and when it’s not asking students to offer a general rule for the slowest time if the average and fastest time remain fixed – maybe extending this to a general rule for each type of average. Working in groups: This activity lends itself to paired discussion 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. 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: present information and results in a clear and organised way (using and applying mathematics level 4) solve simple problems involving ratio and direct proportion (calculating level 5) communicate interpretations and results of a statistical survey using selected tables, graphs and diagrams in support (handling data level 6) show understanding of situations by describing them mathematically using symbols, words and diagrams (using and applying mathematics level 5).

Probing questions: You will need: These might include: When does accuracy matter? Why do you think the BBC have rounded? How much further would he have needed to travel for the rounding to give a different answer? Is this percentage accuracy always appropriate? What type of average is he talking about? Does the type of average impact on the possible slowest times? If it’s the mean average, is there a slowest time that would make an average of four hours impossible? How far is 15 000 km from the school? The moon is around 384 400 km from Earth. How many times this distance did Stefaan Engels run? How long would it take you to travel 15 000 km if you followed your normal routine for a year? You will need: The PowerPoint. There are three slides: The first slide introduces the story and offers the opportunity to explore rounding and percentage error in context. The second slide asks, if the best time was two hours and 56 minutes with an average of about four hours for each marathon, what might the slowest time have been? The third slide offers students the chance to compare familiar journeys and distance with 15 000 km to help get a feel for the distance and, in doing so, provides a context for some proportional reasoning.