Going for gold in 2012
Problem
Here are the top ten nations in the table of medal winners for the 2012 Olympic Games:
Is your own nation in the list?
If not find the data on the internet and compare it with the table.
How do you think the positions have been decided?
Could the results be presented differently to give another nation the top place?
How would this affect other results in the table?
Getting Started
Look at the totals. Any surprises there?
Look at the numbers in each medal category. What do you notice?
Student Solutions
I am breaking with tradition here and showing just one submission. We did also get solutions from St. John the Baptist School naming Tom, Niamh, Erin and Hayden, Kim, Abi and Laura, TC and Emily, Josh and Isobel, Ben and Oscar, Miah and Ali, Olivia and Eva, Joel Tom and Abigail, Kyle and Rio. We also had some good thoughts from Zain and Walail from St. Philips School, as well as Adam from Kings Chester. From Scotland Nicholas and Angus at St. Andrews.
So, from Ben Aditya and Megan at St. Nicolas School Newbury we had this grand submission.
Going for Gold
Ben H., Aditya and Megan from the Extension Maths Group.
The Extension maths group at St Nicolas CE Junior School, Newbury really enjoyed this problem. Our own country, Great Britain, was placed $4$th. We looked on the internet and found out that there were $87$ countries listed in the complete $2008$ medal table and $204$ countries took part.
The positions have been decided on the amount of gold medals won by the country. Ben H thought there were better ways of doing it as the silver and bronze medal holders would be disheartened if it was just on gold because they wouldn't have helped their country in the medal table.
Aditya said it would be more fair to decide top place on the total number of medals because it judges second and third place as well. The table would then look like this.
He noticed that:
* the top nation used to be China but now it's the United States;
* Russia and Great Britain stay in the same place;
* France has been lifted off the bottom up to sixth place with Germany.
Ben thought the best way would be to give $3$ points for a gold medal, $2$ for silver and $1$ for bronze because that would reward medals differently but everybody that won a medal would help their country move up the medal table. Megan created the table:
She noticed that with this method, compared to the given medal table, the top places are quite similar. The first four are the same but after that they begin to change more and more and by the time you've got to the bottom four, it is quite different. Compared to Aditya's table, China is now top and South Korea and France have swapped places.
Well done all of you who sent in these thoughtful contributions. I hope to see your names again with next month's activities.
Teachers' Resources
Going for Gold in 2012
Here are the top ten nations in the table of medal winners for the 2012 Olympic Games:
Is your own nation in the list?
If not find the data on the internet and compare it with the table.
How do you think the positions have been decided?
Could the results be presented differently to give another nation the top place?
How would this affect other results in the table?
Why do this problem?
This problem is intended to encourage children to develop their skills in data analysis and to be critical of the way in which data are presented to them.
Possible approach
Present the children with the table to look at and invite them to tell you about what it shows. Explain where it comes from and why it might have been made. Encourage the children to look at the variation in the numbers of medals of different types or the totals or both.
Key questions
How are the nations ordered?
Are there nations that have the same numbers of gold medals? Of silver medals? Of bronze medals?
Are they next to each other in the table? Why do you think this is so?
Do you think the system for ordering the nations is fair? Why?
Possible extension
Encourage the children to think creatively about scoring systems such as 3 points for a gold, 2 for a silver and 1 for a bronze and investigate the impact this would have on the order.
Further investigations might help the children to offer each nation advice about the sports they should focus on to maximise their position in the table. They would need to find and examine further data to do this.
Can you work out a system that is 'fair' but puts your favourite nation at the top?
It might be interesting to consider other factors that affect perception of performance at the Olympics, such as population and wealth - see this Plus article for further discussion.
Possible support
Get children to tell you and each other about the meaning of the data in the table. Ask straightforward questions such as:
How many gold medals does China have?
Which country is top of the table?
Once they have a good idea of the meaning of the data, they may be able to go on to consider the main task.