Wednesday, August 22, 2012

An Olympic Look at Numbers

Locating open ended tasks can be difficult. I attempt to find as many free resources as possible, but many times those resources are not exactly what I am looking for, so tweaking must be done. In this case, I used something that occurred recently that the students had interest in, and turned it into a thirty minute activity. When talking with my students, almost all of them had a connection to the London Olympics in some way. Many families took this special event and turned it into a bonding experience. A few students sought out specific events or athletes, like volleyball, Usain Bolt, or Michael Phelps. I did not want to let the excitement of the Olympics pass, so I tried to think of a question to ask the students that would invoke discussion, and require my students to utilize past mathematical content in a unique situation. The question I chose was as follows:

Which country performed the best in the 2012 Olympics?

Most people would instantly think of the country with the most medals. While that could be one way to look at the situation, many other factors could come into play. My only requirement was that the ranking could not be done by total medals. Anything else was fair game. I wanted to make this open ended, but I also felt the need to provide a few starter resources to start the conversation. I gave my eighth graders twenty minutes, the following websites, and let them explore. 

My job in this process was to walk around the room, listening to conversations, and offering clarifying questions to either propel a group who was short on ideas, or help a group think through their current goals. After the twenty minutes, we discussed the findings.

Some ideas were simple, such as creating a weighted system, awarding gold, silver, and bronze medals a certain number of points. Those students were able to create a simple algebraic equation to display their learning. Many of the other options hinged on percentages, or unit rates. Here are a few examples:
  • Price per medal (GDP)
  • Medals per participant
  • Medal per person living in the country
  • Percent of participants winning medals
  • Percentage of gold medals out of the countries total
We discovered some interesting findings. Of the countries who at least won two medals, New Zealand and Jamaica had two of the highest medals per countries population ratios. Great Britain did as well, but we discussed how those numbers may be skewed because the host countries qualifies for events regardless of performance. We also talked about how Jamaica may not have as high of a ratio when focusing on Olympic participants and medals, because of the amount of relays Jamaica medaled in (the same goes for any country who won multiple team events).

Another surprising finding was that many African nations received the most medals for the money (GDP). Students were interested to see that China actually topped the list of medals per dollar of GDP because China is a bigger country, yet still relatively low on the GDP list. We were able to discuss cross curricular ideas by having a conversation dealing with communism and how economies can differ.

My goal was for students to be able to dig deeper into the numbers, not taking data at face value. I felt my students worked hard to uncover hidden anomalies in the data, using a context they enjoyed. I was also pleased to see that they had retained their knowledge dealing with rates and percentages, and were able to apply their previous understandings to a unique situation. 

Please feel free to comment on this activity, ask any questions pertaining to this activity, or leave ideas on how to expand on this activity. 

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