math 2015
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Today in the Math Explorations workshop, the focus was probability, specifically situations that are characterized by their fractional probabilities. The class began online with the Interactivate website, and discussed probability with a simple coin toss model. The teachers asked the students to determine a formula for how often a certain result would occur, and also displayed a graph of that formula. The next topic of discussion was M&M’s. The students were all given a bag of M&M’s, a plastic cup, and a Styrofoam plate. They were then asked to do a simple task: put some M&M’s in the cup, pour them out on the plate, put the ones with their M facing up back into the cup, clear the plate, and repeat. This was repeated until no more M&M’s went back into the cup. During the whole process the “time step,” or which pour, was recorded, along with how many M&M’s were returned to the cup and how many not. When done with the tests, the students each gave their data to the teachers who entered it into an excel document and displayed for the class a graph of each student’s data. This graph also contained what the perfect “time step” to “M&M’s removed” ratio should be at any one “time step.” This allowed for a comparative display, to see ho close each student got to the perfect results. After the M&M’s there was a break, before returning and once again going on the Interactivate website. There, the models of a racing game which moves certain cars depending on the roll of a virtual die and the Monty Hall problem were played with and discussed. The cars one was not stuck with for long, but the Monty Hall problem was discussed for quite some time. It took a bit more time for the students to understand how the Monty Hall problem works, before they then moved on to the Advanced Monty Hall problem model. They proceeded to mess around with that for a bit. The class ended with discussion of what we can learn from the Monty Hall problem and how it can be useful in game show decisions.