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Stick or Switch?

Grade Levels

10th Grade, 11th Grade, 12th Grade, 6th Grade, 7th Grade, 8th Grade, 9th Grade

Course, Subject

Related Academic Standards
  • Big Ideas
    Bivariate data can be modeled with mathematical functions that approximate the data well and help us make predictions based on the data.
    Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
    Numerical quantities and calculations can be estimated by using numbers that are close to the actual values, but easier to compute.
    Some questions can be answered by collecting, representing, and analyzing data, and the question to be answered determines the data to be collected, how best to collect it, and how best to represent it.
    The likelihood of an event occurring can be described numerically and used to make predictions.
  • Concepts
    Compound probabilities: addition and multiplication rules
    Data displays: Histograms, circle graphs, stem and leaf plots, line graphs
    Elementary Probability
    Multiplication and division: fractions and decimals
    Prediction and Inference
    Ratio and Rates
    Theoretical probability
  • Competencies
    Determine the sample space for one-stage experiments and determine, when possible, the theoretical probabilities for events defined in the sample space.
    Distinguish between independent and dependent events in order to calculate compound probabilities within real world situations.
    Extend understanding of probability to make comparisons of empirical probability and theoretical probability for the experiment.
    Use elementary probability and proportions to make appropriate predictions.


This lesson plan presents a classic game-show scenario. A student picks one of three doors in the hopes of winning the prize. The host, who knows the door behind which the prize is hidden, opens one of the two remaining doors. When no prize is revealed, the host asks if the student wishes to "stick or switch." Which choice gives you the best chance to win? The approach in this activity runs from guesses to experiments to computer simulations to theoretical models. This lesson was adapted from an article written by J. Michael Shaughnessy and Thomas Dick, which appeared in the April 1991 issue of the Mathematics Teacher.


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Stick or Switch?

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Illuminations is a project designed by the National Council of Teachers of Mathematics (NCTM) and supported by the Verizon Foundation.  Illuminations works to serve you by increasing access to quality standards-based resources for teaching and learning mathematics, including interactive tools for students and instructional support for teachers.

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