MED 607/I2T2 Project—5 day lesson plan on geometric probability ...

2. Same game, but the opening to the container is twice as large.Instruction: Direct teaching format as we explore the answers generated as part of theanticipatory set.1. Answers will vary, but the point here is that the probability of winning isproportional to the size of the opening of the container.2. Since all that has changed is the size of the opening, they should be willing toaccept a prize that is half as large, so that the total expected winnings are the same.3. Play the game attached with the targets generated on GSP. Feel free to modify therules as needed. For example, I specified three roles for team members, but I wasconcerned about keeping all three members of my 6 th grade team engaged. The purposeof stepping back until misses begin to occur is to introduce errors, and errors that areprobabilistic. The ratio of the number of hits in two regions should be proportional to theareas of the regions. Score doesn’t matter; just the number of times a region is struck.Closure and assessment: For each target, have printout copies with areas displayed. Handeach group such a copy of their target. Compare the ratio of hits in a pair of regions tothe ratio of their areas on one target. Assign the following as Homework: Find at leastthree ratios of hits and corresponding areas. Compare these numbers and answer thequestion—How good is this technique in estimating areas? How would you improve it?----------------------------------------------------------------------------------------------------------Day 3—find pi by simulation on TI-83, circle inscribed in square.Learner Outcomes: the student will use technology to better assess the value of usingsimulation techniques to evaluate probabilities, and will be able to predict the number oftrials to get within a certain margin of error in such a probability.MST Standard #5—Students will use computers as tools for design, and for generatingideas.New York State Mathematics Standard #6D—Students will use simulation techniques toestimate probabilities.Materials: TI-83 calculator and “circleinsquare.GSP”, attached.