In this lesson, students will learn about modeling probability in the spread of a forest fire.

Objectives

Upon completion of this lesson, students will:

understand probability and chance

understand the results of probability in real life situations

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.

Grades 3-5

Data Analysis and Probability

Understand and apply basic concepts of probability

Grade 3

Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

COMPETENCY GOAL 4: The learner will understand and use data and simple probability concepts.

Grade 4

Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

COMPETENCY GOAL 4: The learner will understand and use graphs, probability, and data analysis.

3rd Grade

Data Analysis and Probability

The student will demonstrate through the mathematical processes an understanding of organizing, interpreting, analyzing and making predictions about data, the benefits of multiple representations of a data set, and the basic concepts of probability.

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.

4th Grade

Data Analysis & Probability

The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

5th Grade

Data Analysis & Probability

The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

Grade 5

Probability and Statistics

12. The student describes and predicts the results of a probability
experiment.

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

Arithmetic: Student must be able to:

Calculate averages

Convert from percents to decimals

Technological: Students must be able to:

perform basic mouse manipulations such as point, click and drag

use a browser for experimenting with the activities

It is better to avoid this sometimes vague term. It usually refers to the (arithmetic) mean, but it can also signify the median, the mode, the geometric mean, and weighted mean, among other things

probability

The measure of how likely it is for an event to occur. The probability of an event is always a number between zero and 100%. The meaning (interpretation) of probability is the subject of theories of probability. However, any rule for assigning probabilities to events has to satisfy the axioms of probability

Lesson Outline

Focus and Review

Show the students the
Fire!! applet. Set one of the trees on fire and watch how the fire spreads. Then pose the following question to
the students: Why didn't all of the trees burn?

Objective

Let the students know what it is they will be doing and learning today. Say something like this:

Today, class, we are going to use a computer to simulate burning down a forest. Please do not
turn on your computers until I ask you to.

Teacher Input

Explain that the likelihood that a tree will catch on fire is determined by the probability you
select. Change the probability from 1/6 to 5/6 to show students that a greater number of trees
will burn with a higher probability. Begin asking the students why this is so.

Guided Practice

Explain the controls of the applet to the students. Fill out the first column of the record sheet
as a class.

Review how to convert from percentages and fractions to decimals if necessary.

Review how to find an average if necessary.

Independent Practice

Have students use the applet to fill out the record sheet. Remind them to look for patterns as
they collect their data.

Closure

Discuss as a class the following questions:

What patterns did you notice in your data?

What does changing the probability actually do?

Is this a realistic model?

Alternate Outline

This lesson can be rearranged in the following way:

Have the students do their own simulation:

Pair students and give each pair a die and a piece of grid paper. Have them outline two 5
x 5 grids and draw an X in the center square.

Tell the students they will be doing a paper simulation similar to the simulation that you
showed on the computer. This time though they will only use a 5 x 5 grid to work (as
opposed to a 17 x 17 grid) and they should use a probability of 50%.

Demonstrate on the board or overhead how the paper simulation should work by drawing a 5 x
5 grid with an X in the center. You may wish to discuss how you could use the die to
simulate a 50% probability of burn.

Place a small dot in the square above the X denoting this is the square you are testing to
see if it catches or not. Roll the die to determine if it catches. If it does, mark it
through with an X and if it does not, erase the dot. Repeat the other squares beside the
X. Work through the entire example on the board making sure all students understand how
the simulation works.

Calculate the percent of the forest burned.

Be sure to point out that it is only the trees above, below, left and right of a burning
tree they should test.

When students are finished, list the results of each trial on the board.

Demonstrate how this is the same as the applet by having one student demonstrate the applet
for the rest of the class. If you run multiple experiments, you can have multiple students
demonstrate.

Use this to gather data as a class, then use the discussion questions to close the lesson.