I estimate that more than 2/3 of the class declared it their “worst lesson ever” and I loved every minute of it!
The Worst Lesson Ever…an Idea is Born
I can’t lie, I am a little behind pacing wise and am working to get in the rest of the very important 7th grade probability unit before state testing and the end of the school year. I don’t have tons of time to teach a lot of direct instruction type lessons on different aspects of probability and if you know me you know that isn’t my style anyway so I wrapped about 1/2 of the probability content into this one lesson. Last week students were exposed to basic probability, probability on a number line and my favorite sample space and the fundamental counting principle through the amazing Mathalicious lesson “Pair-Alysis”. They have no previous exposure to theoretical vs. experimental probability or the concept of a fair game and this is where today’s lesson comes into play.
It Started So Innocently
Our lesson started so innocently with a game of rock, paper, scissors. Students played 20 rounds of the game in pairs and kept data on how many times each player won in addition to the number of ties the group had.
Once students completed their data collection they submitted it via their clicker so we had class data to examine. Results were fairly evenly distributed and students quickly jumped to the conclusion that it must have been a “fair game” but when I asked them to prove why their arguments were week. This led us to a rich discussion about how what we had just done was the “experimental probability ” but in order to prove the game fair we had to have the”theoretical probability”. Students listed the sample space and determined that each player had a 1/3 chance of winning with the other 1/3 going to the “tie” category.
That’s Not Fair
So far this seems like a pretty boring lesson and rather unmemorable so I spiced it up in the next step by changing their groups to three people and having the groups identify a player A, B, and C. This time scoring goes as follows:
Player A receives a point if all three players pick the same item
Player B receives a point if all three players pick a different item
Player C receives the point if two players pick the same item
After reviewing the rules most students thought this would also be a “fair game” assuming that player C assumed the “tie” probability from before and each person would have a 1/3 chance of winning. As groups got finished I awarded the winning player (player C in every group every period) $500 in our team money.
Once all the groups were done we compiled all the data again and a riot nearly broke out. Students quickly figured out, if they hadn’t already, that this was anything but a fair game. They worked in their group to identify the sample space and compare their theoretical and experimental probabilities of the game.
The Worst Lessons are the Most Memorable
To say they were upset with me over their classmates winning $500 e-bucks in an “unfair” game was an understatement. I think they really thought at the end of the day that I would give them all $500 e-bucks but that would have defeated the purpose of the unfairness. In the end we had fun and although they may have declared this as the worst lesson ever I would bet it will also be the one they remember most. I don’t foresee them forgetting the concept of fair games anytime soon.