Recall ideas they’ve already learned about probability and get excited about learning more.
This section is intended to activate students’ prior knowledge of probability. The activities in this section are intended to create an intellectual need for the more precise terminology to be developed in the unit. Depending on time constraints, one, two, or three of these activities could be used to achieve the goals of this section.
WHAT: Given a set of three non-transitive dice and the rules of a simple game, students are asked to predict which die is more likely to win. It appears that no die has an advantage, but the relative advantages are made clear by creating and inspecting the sample space.
WHY: This task provides a foundation for a discussion of compound events in a uniform probability model (the main topic of the next section).
WHAT: Students are given the rules for a simplified game of Craps and asked questions that draw on computation of theoretical probabilities. They are asked to play 20 games, keeping track of wins and losses, and to determine a player’s chance of winning in two situations: the first roll is 6; the first roll is 4.
WHY: Only grade 7 knowledge is needed to accomplish the tasks in Oh, Craps: sample spaces can be described by tables; and theoretical probabilities can be calculated by counting the number of equally likely successes in a sample space and compared with experimental outcomes. An implicit assumption (which might be made explicit (MP.6)) is that the dice are fair.
This lesson can be used to give a preview of some important ideas in this unit: using “and,” “or,” and “not” to describe events as intersections, unions, and complements of subsets in the sample space (S-CP.A.1); the probability of equally likely independent events occurring simultaneously is the product of the probability of each (S-CP.A.2); and recognizing situations that involve conditional probability (S-CP.A.5).
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WHAT: In this task, students determine the likelihood of getting a two-Starburst package with Starbursts of given colors, given information about the frequencies of different colors (7.SP.A.1, 7.SP.C.7, 7.SP.C.8).
WHY: This task provides a review of probability as relative frequency. The task is intended to be open-ended so that students can ask questions and investigate the probability of getting various Starburst colors.