Students learn to play a dice game called Catz, Ratz, and Batz. Analysis of the game reveals a quadratic function that governs the maximum possible score on each turn. Students also consider questions of expected value corresponding to various choices in the game to determine what is the best option.
60 to 120 minutes
Catz, Ratz, and Batz. Created by Maureen Hiron and published by Playroom Entertainment in 2003.
|HS.F-IF.4||For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercepts, increasing/decreasing intervals, positive/negative values, maxima/minima, symmetries, end behavior, and periodicity.|
|HS.Modeling||Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Quantities and their relationships in physical, economic, public policy, social, and everyday situations can be modeled using mathematical and statistical methods. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data.|
|HS.S-CP.6||Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.|
|HS.S-MD.5||Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.|