Why do this problem?
This problem offers an engaging context for planning and carrying out a data-handling activity. Many problems that students meet are "tidy"; this activity prepares students for the messy nature of real-world data-handling. Students will need to make decisions about the data they need, and to search for that data.
Show the medal table from the 2012 Olympics.
"Here are the results from the 2012 Olympics. Can we conclude from this that China and the USA have the most naturally athletic populations?"
Allow some time for students to talk about this in pairs. Then bring the class together and collect ideas about other factors they think should be taken into account when deciding which nations are most naturally athletic.
Next, split the class into groups of 3 or 4 and set them the task of developing a method for deciding which nations are most naturally athletic. This may be spread over a couple of lessons and homework time, as students will need to decide on the criteria they wish to use, carry out some research, and then present their findings.
When groups present their findings, encourage the other groups to offer constructive feedback on the decisions they chose to make, the evidence they chose to include in their analysis, and the parts of the presentation they found most convincing. One way to do this is for each group to make a short presentation with time for comments and questions afterwards. Alternatively, groups could prepare a
poster presentation and then time could be allowed for everyone to go round and look at each poster, writing feedback on post-it notes.
Does the Olympic table rank countries according to their natural athleticism?
What other factors apart from natural athleticism might affect a country's ranking at the Olympics?
Students could use data from previous Olympics to see the extent to which their criteria give a constant list of most athletic nations over time.
Some simple and quantifiable criteria that students could use in their analysis could be population size and wealth of the nation. It may be worth finding out some of this data in advance in order to guide the students' searches.