Students use probability to set a simulated forest on fire.

Objectives

Upon completion of this lesson, students will:

understand possible outcomes of a probability experiment

Standards Addressed:

Grade 10

Statistics and Probability

The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 6

Statistics and Probability

The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 7

Statistics and Probability

The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 8

Statistics and Probability

The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 9

Statistics and Probability

The student demonstrates a conceptual understanding of probability and counting techniques.

Seventh Grade

Statistics and Probability

Investigate chance processes and develop, use, and evaluate probability models.

Statistics and Probability

Conditional Probability and the Rules of Probability

Understand independence and conditional probability and use them to interpret data

Making Inferences and Justifying Conclusions

Understand and evaluate random processes underlying statistical experiments

Make inferences and justify conclusions from sample surveys, experiments, and observational studies

Using Probability to Make Decisions

Use probability to evaluate outcomes of decisions

Grades 3-5

Data Analysis and Probability

Develop and evaluate inferences and predictions that are based on data

Understand and apply basic concepts of probability

4th grade

Data Analysis and Probability

Standard 4-6: The student will demonstrate through the mathematical processes an understanding of the impact of data-collection methods, the appropriate graph for categorical or numerical data, and the analysis of possible outcomes for a simple event.

5th grade

Data Analysis and Probability

The student will demonstrate through the mathematical processes an understanding of investigation design, the effect of data-collection methods on a data set, the interpretation and application of the measures of central tendency, and the application of basic concepts of probability.

The student will demonstrate through the mathematical processes an understanding of investigation design, the effect of data-collection methods on a data set, the interpretation and application of the measures of central tendency, and the application of b

3rd Grade

Probability and Statistics

3.23 The student will investigate and describe the concept of probability as chance and list possible results of a given situation.

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

access to a browser

pencil and graph paper

dice

Key Terms

experimental probability

The chances of something happening, based on repeated testing and observing results. It is the ratio of the number of times an event occurred to the number of times tested. For example, to find the experimental probability of winning a game, one must play the game many times, then divide the number of games won by the total number of games played

theoretical probability

The chances of events happening as determined by calculating results that would occur under ideal circumstances. For example, the theoretical probability of rolling a 4 on a four-sided die is 1/4 or 25%, because there is one chance in four to roll a 4, and under ideal circumstances one out of every four rolls would be a 4. Contrast with experimental probability

Lesson Outline

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.)

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.

Point out that it was much quicker and easier to model forest burns on a computer rather than
by hand.