gr8_games

//It is expected that students will:// D2 solve problems involving the probability of independent events [C, CN, PS, T] || "You are going to a carnival with your friends, at which there are numerous games of chance. You don't want to walk away empty handed, and so want to find out which games will give you the best chance of winning."
 * **Prescribed Learning Outcomes**
 * **Planning for Assessment** || **Assessment Strategies** ||
 * Present students with the following context for the unit:

Demonstrate each of the following games and then allow students some time to play them:
 * Two of a Kind: The player flips two coins in order. If both coins are heads or both are tails, the player wins. Otherwise, if the coins are different, the player loses.
 * High and Low: The player rolls two dice in order. If either a 'one' or a 'six' is displayed on either dice, the player loses. Otherwise, the player wins.
 * Greedy Royalty: The player draws one card from a standard deck, replaces it, and draws another card. If either of the two cards are a face card (J, Q, or K) then the player loses. Otherwise the player wins. || As students are playing ask the following questions to assess prior knowledge of probability:
 * "Which of these games give you the best chance of winning? Why?"
 * "How are these games similar? How are they different?" ||
 * Have students compile a table demonstrating the number of different ways that two dice can be rolled to produce each sum from 2 - 12. Have students create a bar graph to represent this information.

Discuss how the number of different ways of rolling each sum relates to the relative probability of each roll. Ask students to explain how a circle graph might be considered an appropriate method of representing the information.

Demonstrate how to draw a probability tree or table for "Two of a Kind"

Divide the class into small groups and have the groups construct a probability tree or table for "High and Low"

Have each group use their probability tree or table to determine the probability of various outcomes (for example, the probability of rolling two even numbers)

Using their probability tree, each group will construct a table showing the probability of a certain first roll, the probability of a certain second roll, and the probability of the compound event, for several different combinations of independent events. Some examples are:
 * The probability of first rolling an even number, and then a number less than 5
 * The probability of first rolling a six, and then anything but a six.

Students are asked to find a pattern in the results. || Assess students' abilities to compare different ways of representing a given set of data and to identify the strengths and weaknesses of each.

Circulate to assess each group's use of the tree to determine probabilities.

Collect the probability trees and assess students' abilities to:
 * determine the probability of two independent events
 * generalize a rule for determining the probability of independent events ||
 * Perform a probability experiment to verify the rule determined previously:

Have students play "High and Low" and/or "Two of a Kind" to experimentally determine the probability of winning the game.

Using the probability tree or table, and the rule generalized in class, determine the theoretical probability of winning each game.

Compile class results in a spreadsheet and calculate a whole-class average for the experimental probability of winning.

Compare the experimental with the theoretical to verify the validity of the rule.

Having verified the rule, students apply it to each of the three games to calculate the probability of winning each. They present their calculations and reasoning in a small "carnival strategy guide" which explains which games should be played and avoided, with mathematical justification for their suggestions. || Assess students' ability to verify a determined probability through experimentation

Collect students' work and asses their abilities to: Repeat the questions posed at the beginning of the unit in order to comparatively assess student progress:
 * apply a rule for determining the probability of independent events
 * solve a problem that involves determining the probability of independent events
 * "Which of these games give you the best chance of winning? Why?"
 * "How are these games similar? How are they different?" ||