The Olympic Games, taking place in Rio de Janeiro this year, are a celebration of athletic prowess, diverse cultures, and global unity. Athletes competing in the Olympics have spent the last few years of their lives training – trying, failing, and retrying – for a chance to win a gold medal in their chosen sport. Not every athlete will succeed in winning a gold medal, but that does not mark the end for them. Instead, these athletes will continue training – trying, failing, and retrying – to better themselves for the next Olympic Games.
Succeeding in math, like sports, requires consistent practice, learning from failure, and an attitude of determination. In the spirit of the Rio Olympics, we’ve prepared a series of activities to exercise the math mind. Start at the bronze level and go for the gold!
Challenge 1: The Road to Rio
The torch relay carries the Olympic tradition from its birthplace in Olympia, Greece to the host city. During the relay, it is not the torch that is being passed, but rather the Olympic flame.
This year, the torch was lit on April 21 in Olympia and made its way across Greece and Switzerland before arriving in Brazil on May 3. The torch then traveled across Brazil until it reached Maracanã Stadium in Rio, where the flame was used to light the Olympic cauldron, signaling the start of the 2016 games.
The 2016 Torch relay, by the numbers:
- Over 12,000 people took part in the relay in Brazil across a route that covers 20,000 kilometers by land.
- The flame traveled to over 300 cities in 27 states across Brazil.
- Each torch-bearer carried the flame for approximately 200 meters.
How many miles did the Olympic torch travel across Brazil and how many miles did each torch-bearer run?
If the torch were to travel directly from Olympia to Rio by foot, what would be the distance of this journey? How long would it take? How many people would have to partake in this journey, assuming each person runs 300 meters?
Go for the Gold
In 2020, the Olympics will be held in your country. The torch will only have 60 days to travel across the country. 15,000 people will be involved and they each, at maximum, can run 300 meters. Pick your host city. Then, plan a route for the torch-bearers that passes through the top ten most populated cities in your country, ending at the host city.
Challenge 2: Ticket Sales
Brazil projected a $14.4 billion cost to host the 2016 Olympics in its bid proposal. Aside from increased tourism, corporate sponsorships, and broadcasting licensing fees, one of the other main ways to these costs is through ticket sales.
Ticket sales and prices, by the numbers:
- 7.5 million tickets are available during 717 sessions.
- 55% of these tickets will cost $30 or less in an effort to make the Olympics affordable for locals.
- 2 million tickets will cost less than $20.
- 6 million tickets will have an average price of $36.
Can you determine if the Brazil can recoup the cost of hosting the Olympics from ticket sales alone based on the given information? If yes, how would you calculate it? If not, what other information would you want to know?
If Brazil will operate the Olympics at a loss, how much would tickets have to sell for in order to break even?
Go for the Gold
Assume you are a single person living in Rio in a rental apartment. Your monthly wage is that of the average worker, or 1,902 Brazilian Real. Based on the cost of living standards in Rio listed here, can you afford to attend the Olympics? If attending the Olympics is the top of your bucket list, can you build a monthly budget, without sacrificing any essentials, that will allow you to purchase two tickets?
Challenge 3: Who’s the best?
Their people, the food, and the economy are just a few things that countries love to be competitive about. Now, add Olympic medals to that list. Winning an Olympic medal reflects upon a country’s athleticism, training facilities, coaching talent, endurance, and more.
This table provides a list of the medals that each country has won in every single summer and winter olympics.
Simply, who’s the best? Can the claim, “most athletic country” be made based solely on the number of Olympic medals a country has won? What are some other factors that need to be taken into consideration?
Based on the table, the United States has won 2,399 medals from just summer Olympic games. However, the US also sends a larger amount of athletes to compete. In fact, this year, the US is sending the most athletes out of any other country, at 554. Should the number of athletes a country sends be considered in comparison to their medal count, since more athletes means more opportunities to win a medal? Can you calculate the ratio of athletes to medals? Who comes out on top now?
Go for the Gold
Can you predict how many medals each country will win this year based on their past performance? What models can you build with the medal information? Compare your predictions with the actual results of the Rio Olympics. How did you fare?