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Probability of Childhood Games Objective: Students will find probability of several different events theoretically and experimentally. This lesson is intended for junior high students. Materials Needed: 1. 5 or 6 spinners evenly divided into 6 colors. 2. Three-color spinner divided into a half and two quarters. 3. A bag of fifteen marbles (five of one color, four of another, etc.). 4. A set of dice and a Monopoly board. Strategy: Students in groups will migrate from one station to another during the period with about ten minutes given to each task. Each group should have a recorder to write down the results of each experiment. The following is a description of each experiment and what to do for each: Experiment 1: The four color spinner experiment involves a spinner for each participant and the participants will spin the spinner twenty times and record on which color the spinner landed. Experiment 2: The six color spinner follows the same procedure as the four color spinner of Experiment 1. A total of twenty spins per group is again suggested. Experiment 3: When I did this experiment as my mini-teach, I used a unique spinner. The spinner with marbles is a spinner from the game The Magnificent Race, a favorite game of my childhood. Unfortunately, the game is no longer being made. However, you can simulate the results using a bag of marbles with five of one color, four of another, three of a third, two of a fourth and one of a fifth. This will give you a total of 15 marbles. Have each group draw a marble from the bag, replace it, and draw again until they have drawn a total of twenty times. Record the results. Experiment 4: The Monopoly board task is for students to determine which space on the Monopoly board is landed on the most. To do this, starting at Go, roll the dice and record where on the board the player would land. Continue doing this starting at Go each time until the dice have been rolled twenty times. After students have finished all the experiments and recorded them, the next step is to compare the experimental probability from the results of the experiment to the theoretical probability. The theoretical probability can be determined for each of the experiments in this way: Experiment 1: This spinner is broken up into one half and two fourths, so theoretically, the probability for landing in each of the spaces should be one half, one fourth, and one fourth. This means that theoretically the spinner should land in the half space half the time and so on. Experiment 2: This spinner has evenly divided spaces, so theoretically the spinner should land in each space the same number of times. This may or may not happen in reality. You need a whole lot of trials to match the theoretical probability. Experiment 3: This spinner holds a a total of fifteen marbles with more of some marbles than others so the theoretical probability depends on the number of marbles of each color. The theoretical probability is the number of marbles of a particular color over the total number of marbles. For example, if you have five marbles of one color, the probability of that color being picked is five over fifteen. Experiment 4: The Monopoly experiment is rooted in the classic probability experiment of rolling two dice. Students can make a chart to determine which rolls come up more frequently than others and then match the rolls to the spaces on the Monopoly board. The most common roll should be seven. After the groups have finished with their individual experiments, compile the data for each experiment from all the groups. You should find that the compiled data of the entire class should be closer to the theoretical probability than the data of the individual groups.
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