Today we played the game "rock, paper, scissors." However, our play had a purpose. Before playing the game, I asked the kids if the game was a fair game. We turned to mathematics to find out. In order to determine if "Rock, Paper, Scissors" is a fair game, we needed to list all possible outcomes of the game. We did this by using the three visual models that we used with the 2 Coin Toss (t-chart, branches, and a matrix).
Using these three visuals, we were able to determine that Rock, Paper, Scissors IS a fair game. There are three ways to win, three ways to lose, and thee ways to tie.
Now, we needed to determine the theoretical probability (what SHOULD happen) when we played the game.
We discovered that each of the events should occur 1/3 of the time. Therefore, when we play the game, we should be able to gather our data and create a pie chart that is divided evenly into thirds.
Time to play.... I mean experiment! We each grabbed a partner and played until we had reached the end of one row. Once we finished the game we recorded our tallies in the form of fractions and compared our theoretical data with our experimental data. For example, the game I played with a student SHOULD have had us winning, losing, and tying 8 times each. Instead, I had 8 ties, 8 losses, and 15 wins. Therefore, my theoretical probability and my experimental probability were not compatible.
However, when we combined the data from all the students in a class, our data and our graph was MUCH closer!
- Mrs. Dittrich's class had a total of 420 games. Therefore, there should have been about 140 wins, 140losses, and 140 ties.
- Mrs. Dabbs' class had a total of 360 games. Therefore, there should have been about 120 wins, 120 losses, and 120 ties.
- Mrs. Johnson's class had a total of 420 games. Therefore, they should have had about 140 wins, 140 losses, and 140 ties.
Once again, the kids were thrilled to see that their graphs came out almost exactly as expected.....forgetting that this is what was SUPPOSED to happen! I love it!
Once again, I will combine the three class's data at the beginning of class. They can't wait to see if we have a perfect pie chart divided into three equal pieces!