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Fire: Modeling Probability
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Abstract

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:

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

Teacher Preparation

Students will need:

  • Access to a browser
  • Copies of the Worksheet

Key Terms

averageIt 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
probabilityThe 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

  1. 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?

  2. 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.

  3. 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.

  4. 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.

  5. Independent Practice

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

  6. 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.

Suggested Follow-Up

Students can explore probability further in the Playing with Probability Lesson.

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