Directable Fire!!

What is Directable Fire!!?

This activity allows the user to see the results of a fire if a forest is densely planted in a rectangular grid when directional probabilities are set.

The probability that a tree will burn is set, and the fire is started. For each tree the same probability "die" is thrown to see if that tree will burn or not, given that its neighbor is on fire.

The behavior of this activity is chaotic, since we cannot predict in advance whether a particular tree is burned or not, and since small changes in the set probability and the location of the initial burning can radically alter the final state of the forest. However, general patterns in the burning of the trees can be seen for particular probabilities.

This fire is somewhat unrealistic since in most fires, if a tree has a close neighbor on fire it will catch fire, too, unless the wind changes. Directional probabilities can be entered to simulate directional winds.

How Do I Use This Activity?

This activity allows the user to see the results of a fire if a forest is densely planted in a rectangular grid when directional probabilities are set.

Controls and Output

  • The Configure Probabilities button on the top-left corner of the applet pops up a box that allows you to choose what probability the fire will spread in each of eight directions.
  • The resize to menu on the top center of the applet allows you to choose the size of the forest.
  • The burn speed scroll bar allows you to choose the speed at which the fire will burn.
  • The Tree Display is where you will need to click to select were the fire will start. Note: You can start the fire in as many places as you want by clicking on another tree. You can also deselect any tree by clicking on it a second time.
  • To start the fire click the Start the fire button in the lower left corner of the applet. To step thru the fire step by step click the step thru fire button in the bottom center of the applet.
  • The Re-grow Forest button revitalizes the forest after it has been burned. You must re-grow the forest after every fire.

Description

This activity allows the user to see the results of a fire if a forest is densely planted in a rectangular grid when directional probabilities are set. This activity would work well in mixed ability groups of two for about thirty to forty-five minutes if you use the exploration questions and ten to fifteen minutes otherwise.

Place in Mathematics Curriculum

This activity can be used to:

  • demonstrate randomness
  • motivate the ideas of chaos
  • demonstrate the basic concepts of probability

Standards Addressed

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.

Grade 10

  • 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.

Number and Quantity

  • Quantities

    • Reason quantitatively and use units to solve problems.

Statistics and Probability

  • Conditional Probability and the Rules of Probability

    • Understand independence and conditional probability and use them to interpret data
    • Use the rules of probability to compute probabilities of compound events in a uniform probability model

  • 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

    • Calculate expected values and use them to solve problems
    • Use probability to evaluate outcomes of decisions

Grades 6-8

  • Algebra

    • Use mathematical models to represent and understand quantitative relationships

  • Data Analysis and Probability

    • Develop and evaluate inferences and predictions that are based on data
    • Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

Grades 9-12

  • Algebra

    • Use mathematical models to represent and understand quantitative relationships

  • Data Analysis and Probability

    • Develop and evaluate inferences and predictions that are based on data

Grade 6

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

    • COMPETENCY GOAL 1: The learner will understand and compute with rational numbers.
    • COMPETENCY GOAL 4: The learner will understand and determine probabilities.

Grade 7

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

    • COMPETENCY GOAL 1: The learner will understand and compute with rational numbers.

Advanced Functions and Modeling

  • Data Analysis and Probability

    • Competency Goal 1: The learner will analyze data and apply probability concepts to solve problems.

Integrated Mathematics

  • Data Analysis and Probability

    • Competency Goal 3: The learner will analyze data and apply probability concepts to solve problems.

AP Statistics

  • Data Analysis and Probability

    • Competency Goal 3: The learner will collect and analyze data to solve problems.

  • Number and Operations

    • Competency Goal 1: The learner will analyze univariate data to solve problems.

Elementary Algebra

  • Elementary Algebra

    • Standard EA-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

7th Grade

  • Computation and Estimation

    • 7.6 The student will use proportions to solve practical problems, which may include scale drawings, that contain rational numbers (whole numbers, fractions, and decimals) and percents.

5th Grade

  • Probability and Statistics

    • 5.17a The student will solve problems involving the probability of a single event by using tree diagrams or by constructing a sample space representing all possible results

Be Prepared to

  • give implicit directions on what they are to do. For example, "Today we are going to run a set ofexperiments and answer the questions on the worksheet..."
  • answer the question "What decimal will make the trees burn 3/4(some fraction) of the time?"
  • discuss decimals, percents, and fractions