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8.1 ConceptsMiddle grade students should learn and use appropriate terminology and should be able to compute probabilities for simple compound events, such as the number of expected occurrences of two heads when two coins are tossed 100 times. NCTM Standards 2000, page 51If two coins are tossed, the probability of obtaining exactly one head is 50%. However, if four coins are tossed, the probability of obtaining exactly two heads is not 50%. Use models or diagrams to determine the probability of exactly two heads and explain your reasoning. Discuss the probability of obtaining exactly half heads as greater and greater even numbers of coins are tossed. Does the probability get closer and closer to 50% or further away? 8.1 Teaching Misconceptions about probability have been held not only by many students but also by many adults (Konold 1989). To correct misconceptions, it is useful for students to make predictions and then compare the predictions with actual outcomes. NCTM Standards 2000, page 254Suppose you were teaching in elementary school and designed the following activity to introduce probability. Four blue tiles and 2 red tiles are placed in a sack by the students and one tile at a time is randomly selected, tallied, and returned to the sack. A common teaching practice is to ask students to predict what might happen before an experiment is carried out. Write some predictions you think school students might make regarding the outcomes for the selection of one tile. Now suppose this experiment is carried out 12 times and 7 red and 5 blue are recorded. Describe what you would do to help resolve this unexpected outcome. 8.1 Concepts Simulations afford students access to relatively large samples that can be generated quickly and modified easily. NCTM Standards 2000, page 254In a sports club with 12 students, 4 play soccer, 6 play tennis, 8 play basketball, 1 plays both soccer and tennis, 1 plays both soccer and basketball, and 4 play tennis and basketball. No member of the club plays all three sports. If three students are randomly selected from the club, what is the probability that each sport will be represented? Design and describe a simulation for approximating this probability. Predict the probability and then perform the simulation and compare the experimental probability you obtain to your prediction. |