Chapter 7: Lessons and Activities

Activity Name Activity Description
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 N 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.
Crazy Choices Game Three players play games of chance using dice, cards, spinners or coin tosses, to compare theoretical and experimental probabilities. Parameters: Type of game for each player, number of trials.
Spinner Students can create a game spinner with one to twelve sectors to look at experimental and theoretical probabilities. Parameters: Number of sectors, number of trials.
Adjustable Spinner Students can create a game spinner with variable sized sectors to look at experimental and theoretical probabilities. Parameters: Sizes of sectors, number of sectors, number of trials.
Two Colors Applet Students choose between three boxes and choose one marble from the box to look at conditional probabilities. Parameters: Number of trials.
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.
Simple Monty Hall Students choose one of three doors to experimentally determine the odds of winning the grand prize behind one of the doors, as in the TV program "Let's Make a Deal." Parameters: Staying or switching between the two remaining doors.
Generalized Monty Hall Students run a simulation to mimic the simple monty hall activity with multiple trials. Parameters: Number of doors, number of trials, staying or switching between the two remaining doors.
Advanced Monty Hall Students choose one of N doors to experimentally determine the odds of winning the grand prize behind one of the doors, as in the TV program "Let's Make a Deal." Parameters: Number of doors, number of trials, staying or switching between the two remaining doors.
Dice Table Students experiment with the outcome distribution for a roll of two dice by playing a dice throwing game. Parameters: Which player wins on which rolls.
Stock Exchange Students learn about expected value and payoff for an event that will occur with a known probability, by playing a game in which the payoff is earnings from stocks. Parameters: Probability of receiving cash, cash amounts, number of trials.
Fire!! Students run a simulation of how a fire will spread through a stand of trees, learning about probability and chaos. Parameters: Probability that a tree will burn.
Directable Fire!! Students run a simulation of how a fire will spread through a stand of trees, learning about probability and chaos. Parameters: Probability that a tree will set fire to each of its eight neighbors.
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 and Wolves Students experiment with a simple ecosystem consisting of grass, rabbits and wolves, learning about probabilities, chaos and simulation.
The Chaos Game Students play the Chaos Game by experimenting with probabilities, and they learn about an apparently random process with a not-so-random, geometric fractal result.
Buffon's Needle Students experiment with a simulation to get an approximation of Pi.

Lesson Name Lesson Description
Ideas that Lead to Probability introduction to concepts about probability
Introduction to the Concept of Probability continues the introduction of concepts about probability
Probability and Geometry considers the connections between geometry and probability
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
From Probability to Combinatorics and Number Theory looks at data structures and their applications to probability theory
Expected Value introduces payoffs and expected value
Unexpected Answers considers probability problems with unexpected and surprising answers