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Classroom Activities
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Author
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Level
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Technology
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Students discover the Central Limit Theorem by simulating rolls of two, four, and seven number cubes via the random number generator.
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- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
- TI-84 Plus C Silver Edition
- TI-84 Plus CE
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9272
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Students use a simulation to find the experimental probability of independent events.
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- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
- TI-84 Plus C Silver Edition
- TI-84 Plus CE
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9177
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Students use a tree diagram to find theoretical probabilities and use this information with lists to find the expected value.
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- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
- TI-84 Plus C Silver Edition
- TI-84 Plus CE
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9017
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Students investigate the fundamental counting principle, permutations, and combinations.
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- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
- TI-84 Plus C Silver Edition
- TI-84 Plus CE
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9285
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Students simulate a binomial distribution and calculate probabilities for a variety of situations involving binomial probability distributions.
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- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
- TI-84 Plus C Silver Edition
- TI-84 Plus CE
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9513
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In this activity, students use the random integer (randInt) command to simulate probability experiments. They also graph the number of trials and corresponding probabilities to observe the Law of Large Numbers. Simulated experiments involve tossing a coin, spinning a spinner, and observing the sex of children in a family.
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- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
- TI-84 Plus C Silver Edition
- TI-84 Plus CE
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8725
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Students explore Bernoulli Probabilities. They will use them to calculate the probabilities of various single and cumulative events.
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- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
- TI-84 Plus C Silver Edition
- TI-84 Plus CE
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8627
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Students use the RandInt() command to simulate the tossing of a coin and the rolling of a die. They will collect data for several trials and use the information to investigate the Law of Large Numbers.
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- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
- TI-84 Plus C Silver Edition
- TI-84 Plus CE
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9277
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Students simulate a geometric distribution of rolling a die to determine experimental probabilities and calculate theoretical probabilities.
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- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
- TI-84 Plus C Silver Edition
- TI-84 Plus CE
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8837
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Students use simulations and graphs to explore the common sense notion that repeatedly flipping a coin results in "heads up" about half of the time. First, they simulate an experiment by representing single coin flips with random numbers. Next, they use a given formula to simulate multiple coin flips at once, allowing them to perform a large number of trials easily. Lastly, they create a histogram of their data, observing that the data clusters around the mean.
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- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
- TI-89 / TI-89 Titanium
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4737
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It is believed that an unusually high occurrence of cancer in a small area may represent a "cancer cluster." Because this is rare, it is more likely to be a case of "Texas Sharpshooting." For example, suppose a person randomly shoots a gun several times at the side of a barn and draws a circle around the holes that are closest to each other. Since they fit in a 'cluster,' the person declares himself to be a Texas Sharpshooter.
Students will examine and simulate Texas Sharpshooting.
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- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
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4760
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In "The Art of Reckoning," Charlie discusses the security of a prison. "It's a hyper-secure system, but prisoners have nothing to do except think about how to crack it. Like two opposing armies." Charlie explains that analyzing such a situation involves determining the 'probabilities of penetration' by considering the ratio of vulnerable points to the resources required to defend that point.
In this activity, students analyze a game in which a spy is attempting to break into a fort.
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- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
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4810
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A young girl escaped from her "husband" and walked through the desert most of the night before collapsing. The FBI wants to reconstruct her path to determine where she was held, but she does not know what direction she walked. Don has some starting coordinates and asks Charlie to narrow the search area. He calculates the maximum distance she could have traveled in the night to estimate her starting location.
Students will simulate possible walks to narrow down the search area.
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- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
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4774
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In this episode, Don brings Charlie a notebook that was found on the body. It contains horse racing data and equations. Charlie determines that the equations were designed to pick the SECOND place winner, not first place. Parts of these equations use the "logit" function, a specific probability function that uses logarithms and odds ratios. Because the logit function can get pretty complicated, this activity lays its foundations, namely the relationship between probability, odds, and odds ratios.
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- TI-73 Explorer™
- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
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4957
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In "Longshot," Charlie explains that the racetrack uses a pari-mutual betting system - the odds of winning vary with the amount bet on each horse. This system not only calculates proportional payoffs for the bettors, but also guarantees a profit for the racetrack owners by removing a percentage of the money bet before the rest is split among the winners.
This activity examines the mathematical expectation of the player - the amount a person can expect to win (or lose) in the long run on average.
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- TI-83 Plus Family
- TI-84 Plus
- TI-84 Plus Silver Edition
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4847
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