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Content Area: Math
Index: 4.4C Grade 12 CPI 1
Standard: 4.4 - Data Analysis, Probability, and Discrete Mathematics
Strand: C - Mathematics--Systematic Listing and Counting
Cumulative Progress Indicator: 1 - The student will calculate combinations with replacement (e.g., the number of possible ways of tossing a coin 5 times and getting 3 heads) and without replacement (e.g., number of possible delegations of 3 out of 23 students).
Grade: 12
Sample Activities:
· Students determine the number of ways a committee of three members could be selected from the class, and the number of ways three people with specified roles could be selected. They generalize this activity to finding a formula for the number of ways an n person committee can be selected from a class of m people, and the number of ways n people with specified roles can be selected from a class of m people.
· Students find the number of ways of lining up thirty students in a class, and compare that to other large numbers; for example, they might compare it to the number of raindrops (volume = .1 cc) it would take to fill a sphere the size of the earth (radius = 6507 KM).
· Students determine the number of ways of dividing 52 cards among four players, as in the game of bridge, and compare the number of ways of obtaining a flush (five cards of the same suit) and a full house (three cards of one denomination and two cards of another) in the game of poker.
· Students play Nim (and similar games) and discuss winning strategies using binary representations of numbers.
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