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

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.

- 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.

*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.

- access to a browser.
- access to pencil and graph paper.
- access to dice.

**Focus and Review**
Review the difference between experimental and theoretical probability.
**Objectives**
Students will be able to model possible outcomes of the controlled burning of a forest both by
hand and by using computer applets.
**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.

**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.

**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

**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.