Chapter 9: Activities and Lessons

Activity Name Activity Description
Crazy Choices Game Students represent simple chance games as theoretical probabilities by entering data on 'winning' and total outcomes. Students can then simulate a number of trial runs to generate experimental data and probabilities for comparison with theoretical values.
Spinner Students can adjust the number of sectors on a game spinner drawn by the applet, and then compare expected probabilities, calculated from percentage of spinner area, against experimental probabilities, calculated as a percentage of trial 'spins' initiated by the student.
Adjustable Spinner Students can adjust the number of sectors as well as the percentage covered by each sector to create a game spinner drawn by the applet. Students can then compare expected probabilities, calculated from percentage of spinner area, against experimental probabilities, calculated as a percentage of trial 'spins' initiated by the student.
Simple Monty Hall In the style of the TV program "Let's Make a Deal", students choose one of three doors, and then choose to 'stay' or 'switch' after a second door is revealed as a 'losing' choice. The applet compiles empirical probabilities on the value of the 'stay' or 'switch' choice.
Generalized Monty Hall Students select conditions for a series of "Let's Make a Deal" trials. The applet provides empirical data for 'number of wins' for a given set of trial simulations.
Advanced Monty Hall Students select conditions for a "Let's Make a Deal"-style game, and can play individual trials of the game. The applet compiles empirical probabilities on the 'stay' or 'switch' choice given the number of doors in the particular game.
Two Colors Applet The applet provides a conditional probability experiment whereby three boxes are pre-arranged to contain three possible combinations of colored marbles: two green, two red, and one red/one green. Students can run individual and multiple trials of drawing single marbles from a randomly chosen box. The applet accumulates trial results, providing empirical data for discussion of conditional probability.
Venn Diagrams Students learn about classifying numbers into various categories through answering questions about Venn Diagrams.
Marbles Students learn about sampling with and without replacement by modeling drawing marbles from a bag. Parameters: Number and color of marbles in the bag, replacement rule.
Dice Table Students input a set of 'winning' conditions for multiple players in a dice rolling game. The applet charts the possible outcomes on a two dimensional chart. Students then determine the probability of winning for a given player as a ratio, reduced fraction, converted decimal and percent chance.
Racing Game with One Die Two players each roll a die, and the lucky player moves one step to the finish. Parameters: what rolls win and how many steps to the finish line.
Racing Game with Two Dice One to eleven players roll two dice, the lucky player moves one step to the finish, or everybody moves one step and the lucky player moves two steps to the finish. Parameters: the number of players, number of trials and length of the race.
Fire!! The applet provides a simulation of how a fire spreads through a stand of trees. Students input the probability that a tree will catch fire given proximity to a burning tree. The applet graphically displays the burning of the forest and calculates a percentage destroyed.
Directable Fire!! The applet provides a simulation of how a fire spreads through a stand of trees. Students can vary the size of the grid of trees, and can input a set of probabilities that a tree will catch fire given proximity in a particular direction to a burning tree. The applet graphically displays the burning of the forest and calculates a percentage destroyed .
A Better Fire!! Students run a simulation of how a fire will spread through a stand of trees, learning about probability and chaos. Parameters: Forest density, wind direction, size of forest.
Rabbits & Wolves Students experiment with a simple ecosystem consisting of grass, rabbits and wolves, learning about probabilities, chaos and simulation.
The Chaos Game Students input initial conditions and probabilities to create geometric fractal patterns according to a chance-based set of rules.
Stock Exchange Students input winning probabilities and payoffs for two 'players', and can simulate a number of random payoff games.

Lesson Name Lesson Description
Ideas that Lead to Probability Students examine everyday experiences to learn the concepts of "fair" and "random".
Unexpected Answers Considers probability problems with unexpected and surprising answers.
Conditional Probability and Probability of Simultaneous Events Introduces conditional probability and the probability of simultaneous events.
Replacement and Probability Extends the notion of conditional probability by discussing the effects of replacement on drawing multiple objects.
Fractals and the Chaos Game Outlines the approach to playing the chaos game and how it relates to simulating geometric fractals.
Chaos Students learn about the relationship between probability and the concept of chaos by experimenting with simulations.
Expected Value Introduces the concepts of payoff and expected value.
From Probability to Combinatorics and Number Theory Looks at data structures and their applications to probability theory.
Introduction to the Concept of Probability Continues the introduction of concepts about probability.