Simulations
Section 9.3
| 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. |
| 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 experimental probabilities on the value of the 'stay' or 'switch' choice. |
| 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 select conditions for a "Let's Make a Deal"-style game, and can play individual trials of the game. The applet compiles experimental probabilities on the 'stay' or 'switch' choice given the number of doors in the particular game. |
| Racing Game with One Die | Students set conditions for a virtual auto race based on the rolling of a die. Students can then use the applet to observe individual races or to accumulate experimental probability statistics from multiple races. |
| Racing Game with Two Dice | Students use an outcome table to set conditions for a virtual race based on the rolling of two dice. Students can then use the applet to observe individual races or to determine the results from a set of races. |
| Marbles | Students input conditions representing a sequence of trials whereby colored marbles are randomly drawn from a bag. The applet accumulates data on the outcomes of each trial simulation, providing theoretical and experimental probabilities for direct comparison. |
| Fire!! | The applet provides a simulation of how a fire spreads through a stand of trees. Students input the probability, in decimal or fraction form, 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. Discussion should focus on the relationship between multistage probability and chaos. |
| 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, in decimal or fraction form, 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 . Discussion should focus on the relationship between multistage probability and chaos. |
| 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. |
