What Do You Expect
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File Size: | 334 kb |
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Goals of What Do You Expect
Students should...
- Understand experimental and theoretical probabilities
- Explore and develop probability models by identifying possible outcomes and analyze probabilities to solve problems
Investigation 1
Vocabulary | |
File Size: | 160 kb |
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Investigation 1 introduces students to experimental probabilities as a way to predict the chance that an event will occur. Students will have many opportunities to collect data through experimentation using such items as coins and paper cups. Then, they will use the data collected to assign experimental probabilities to the results. This Investigation also introduces students to the notion of equally likely outcomes and that the range of probabilities for a situation is from 0 to 1.
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Investigation 2
Vocabulary | |
File Size: | 179 kb |
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This Investigation continues students’ work with finding experimental probabilities and formally introduces the term theoretical probability. The colors of identically shaped objects chosen from a bag are analyzed both theoretically and experimentally. Students also consider the difference between a particular outcome being possible and being likely (or probable) and determine if a game or probabilistic situation is fair. Making an organized list and making a tree diagram are two strategies for finding all the theoretical outcomes.
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Investigation 3
Vocabulary | |
File Size: | 161 kb |
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Investigation 3 introduces spinners as a new context for thinking about probabilities. The crucial difference between spinners and the other objects studied so far is that a spinner has a continuous range of possibilities. The 360° angle at the end of a spinner can be subdivided into any number of angles. Students also analyze various methods for making fair decisions and devise a simulation to find experimental probabilities.
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Investigation 4
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File Size: | 173 kb |
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Investigation 4 uses an area model as a way to analyze the theoretical probability of two-stage (compound) events. Two-stage events analyzed are choosing a marble at random from a container, spinning two spinners, and a one-and-one free-throw situation. For example, the player attempts the first free throw and then either takes a second free throw (if the first one was made) or does not get a second chance (if the first free throw was missed). Students use a simulation, such as a spinner, to determine frequencies of compound events, such as creating purple or making free throws in basketball. After determining experimental probabilities that the player will get a score of 0, 1, or 2, students find the theoretical probability by using an area model. Students determine the long-term average (expected value) for the situation and explore expected value in a variety of different probability settings.
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Investigation 5
Vocabulary | |
File Size: | 160 kb |
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Students are introduced to binomial situations by taking a four-item true-false quiz in which each answer is determined by tossing a coin. Students then find the expected value (or average score) for guessing the answers. Students also use lists or tree diagrams to determine outcomes. The situations lead naturally to Pascal’s Triangle, which is explored in ACE. Students use lists or tree diagrams to determine binomial probabilities in other situations, such as the number of children of each gender in a family with five children or the winning of a baseball series between two evenly matched teams. Students recognize that once they have analyzed one binomial situation, they can use this knowledge to answer questions about different binomial situations. For example, once they have analyzed families with five children, they are able to use their knowledge to answer questions about a five-game baseball series in which each team has an equally likely chance of winning.
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