Hunger Games

Hunger games is the name of a wildly popular book that was later made into a book.  Yes its been out a few years but its still one of those movies that can grab a students attention and keep it.

The basic story line for the story is 12 districts send a boy and a girl to compete in the nationally televised "Hunger Games". 

They fight it out until only one survives.  This time, the heroine must weigh love against survival.
The boy and girl who are selected to compete are randomly chosen during a ceremony from the 12 to 18 year old segment of the population.

A few years ago, the high school reading teacher used it in her class.  I didn't realize it at the time but it would have made a spectacular cross curricular unit between reading, math, social studies, and science.  From a mathematical point of view, Hunger Games provides a wonderful application of probability to a situation that students might relate to.

The selection process is actually a lottery in which the more times a name appears, the better the chance a person has of being selected but if their name has been selected, it is removed from the pot because they are either dead or won.  The reason a child has their name appear more than once is that it is put in again every year so at age 12, the name is entered for the first time, at 13 the name is put in again and it continues so at the age of 18 a person has multiple chances of being selected.

The above is a perfect example of arithmetic progression.  This means that when they are 12, the odds of being selected is low but by the time they are 18, the odds have increased tremendously. Wired has a beautiful article showing an example of how it works in this situation. It is well written and the example is easy to understand.  This contains a summary of the original one which has more detail and mathematical equations to use if students are interested.

The article points out that some children can have their names appear more if the family volunteers to have the name entered additional times for higher allotments of food, etc. One way to accomplish this is to create a random generator or even use a coin to choose a 1 or 0 representing the yes or no for another entry for more food.  The NCTM published an article on a Hunger Games activity in their Middle School Magazine Volume 17, issue 7 - the March 2012 publication that has the random generator.

In addition, this article looks at the probability of winning the event itself.  If you think about it, 2 contenders from 12 districts means there are 24 young adults trying to be the one winner.  That means each person as a chance of 23/24 of loosing the event.  Those are not good odds.

The other mathematical aspect is game theory or the theory of making independent choices based on the decisions of others.  The most famous of this type of theory is the prisoners dilemma.  The prisoners dilemma goes as follows - There are two suspects being questioned for a major crime but there is not enough evidence to arrest them on that but there is enough to get them on a minor crime. So the police offer them a choice. 

The one who confesses to the crime will be released while the other one will be convicted and spend 15 years in jail.  If neither confesses, they will be convicted of the minor crime and spend one year in jail. If they both confess, they will only spend 5 years instead of 15 in jail.

Although the best move is to stay quiet, the prisoners are under a lot of pressure to confess.  In the book and movie, contestants band together to form alliances or groups at the beginning.  But how much can they trust each other if they know the object is to kill the others.

I found the idea of creating a cross curricular unit quite appealing.  I don't know if we can do it but I'm going to propose it for next year.  Let me know what you think, I'd love to hear.