Probability: Playing with Fire Lesson Plan

Abstract

Students use probability to determine how likely it is for each tree in a small forest to catch on fire.

Standards (NCTM 3-5)

Data Analysis and Probability

Develop and evaluate inferences and predictions that are based on data
• propose and justify conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions.
Understand and apply basic concepts of probability
• describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible;
• predict the probability of outcomes of simple experiments and test the predictions;
• understand that the measure of the likelihood of an event can be represented by a number from 0 to 1.
Student Prerequisites
• Technological:

Students must be able to:

• perform basic mouse manipulations such as point, click and drag.
• use a browser such as Netscape for experimenting with the activities.
Teacher Preparation

Students will need:
• access to pencil and graph paper.
Lesson Outline

1. Focus and Review
2. Review the difference between experimental and theoretical probability.

3. Objectives
4. Students will be able to model possible outcomes of the controlled burning of a forest both by hand and by using computer applets.

5. Teacher Input
• Inform students that foresters use probability when setting what are known as controlled burns. In order to do a controlled burn, foresters need to be able to model the forest burning. They do this by assigning a certain burn probability to each tree. The burn probability depends on a variety of climatic conditions.
1. Guided Practice
• Have the students draw four 5x5 squares on a sheet of graph paper.
• Tell the students to draw a triangle inside of each block in the 5x5 squares
• Explain to the students that the triangles represent trees.
• Also make sure the students understand that only trees directly on top of, beneath, to the left and to the right of an already burning tree can catch on fire.
• Tell the students that the trees in the first 5x5 square have a 1/6 probability of catching on fire after the center tree has been set on fire.
• Tell the students that the trees in the second 5x5 square have a 1/3 probability of catching on fire after the center tree has been set on fire.
• Tell the students that the trees in the third 5x5 square have a 1/2 probability of catching on fire after the center tree has been set on fire.
• Tell the students that the trees in the fourth 5x5 square have a 2/3 probability of catching on fire after the center tree has been set on fire.
• Have the students use dice to decide wether or not each tree touching the burning tree catches on fire. For example, if a tree has a 1/2 probability to catch on fire then it will burn on rolls of 1, 2, and 3 and not burn on rolls of 4, 5, and 6.
• Work through one model on the board as a class
• After you have completed the burn, show the students how to calculate the percent burn.
1. Independent Practice
• Have the students work through all four of their forests.
• Monitor the students.
• As they finish have them open up the Fire Applet and do several burns with the burn probabilities they modeled using dice, pencil, and paper.
• After all the students have had a chance to work through their models on paper, write all the percent burns on the board in columns under their corresponding burn probability.
• Ask the students why they think there is such a large variation in percent burns for certain probabilities and such a small variation for others.
• Have the students use the Fire Applet to try to figure out which probability is most unpredictable.
• Ask the students if any of them can think of a way to model a burn if when the wind is blowing in a certain direction. (Set higher probabilities in the direction the wind is blowing while setting lower probabilities in the opposite direction of the wind.)
• Have the students open the Directable Fire Applet.
• Tell the students to try experimenting with the applet to see how they might manipulate the burn probabilities to model the effects that wind might have on a burning forest.
• Monitor the students' progress and have a couple of the students share their model with the class
1. Closure
• Draw connections between the probability that each tree will catch on fire and the percent of trees burned
• Be sure to point out that a 1/2 probability a tree will catch on fire does not imply that 50% of the trees will burn.
• Also be sure to point out that it was much quicker and easier to model forest burns on a computer rather than by hand.