A Better Fire!!

What is A Better Fire!!?

This activity allows the user to see the results of a fire on a virtual forest by setting parameters such as forest density and wind speed.

A probability "die" is thrown to see if a tree should be planted for each square. Then the fire is set and allowed to burn -- if a tree has a neighbor on fire, it will catch on fire in the next time period. This is a realistic simulation of actual forest fires, with controls for wind speed and direction to add more realism. More sophisticated versions of this simple simulation have been used with much success to model fire behavior and plan forest planting strategies.

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.

How Do I Use This Activity?

This activity allows the user to see the results of a fire on a virtual forest by setting parameters such as forest density and wind speed.

Controls and Output

  • The Wind Control box on the left side of the applet has two portions in which you can manipulate - the Wind Direction Control and the Wind Speed Control.
  • The Wind Direction Control compass, part of the Wind Control box, allows you to specify the direction in which the wind is blowing if there is any wind. Simply click in a portion of the circle to change the direction of the wind. For example, to have the wind blow south, click in the bottom-middle section of the circle.
  • The Wind Speed Control panel, part of the Wind Control box, allows you to specify the intensity of the wind. It has three levels - light/calm winds (specified by the bar being green) which you can select by clicking on the lower 1/3 portion of the bar; medium winds (specified by the bar turning yellow) which you can select by clicking on the middle 1/3 of the bar; and strong winds (specified by the bar turning red) which you can specify by clicking on the upper 1/3 of the bar. Light/calm winds do not modify the fire. Medium winds hasten the fire in the direction that the wind is blowing, and strong winds not only hasten the fire in the direction the wind is blowing more quickly, but actually stops the fire from spreading in the direction against the wind.
  • The Forest Tree Density scrollbar, located to the right of the Wind Control box, allows you to specify the percentage of the next-generated forest that will be filled with trees. Sliding the bar all the way to the right will specify a forest 100% full of trees; sliding the bar all the way to the left will specify a forest 0% full of trees.
  • The Size Buttons, located beneath the text "Size For Next Generated Forest," will allow you to specify the size of the next-generated forest.
  • The Regrow Forest button will generate a forest based on the specifications you chose above.
  • The Information Banner, located below the Regrow Forest button, will give you important information about what is going on with the forest currently.
  • The Tree Burn output box will appear below the Information Banner after a fire has burned through the forest.

Description

This activity allows the user to see the results of a fire spreading through a forest. The user can oberserve how properties like wind speed, wind direction, and forest density affect how the fire spreads. This activity would work well in mixed ability groups of two to four for about fifteen to twenty minutes if you use the exploration questions and ten 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 3-5

  • Data Analysis and Probability

    • Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

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

  • Measurement

    • Apply appropriate techniques, tools, and formulas to determine measurements

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.

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.

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.

7th Grade

  • Probability and Statistics

    • 7.14 The student will investigate and describe the difference between the probability of an event found through simulation versus the theoretical probability of that same event.

Textbooks Aligned

Grade Six

  • How Likely Is It?

    • Investigation One: A First Look at Chance
    • Investigation Two: More Experiments with Chance
    • Investigation Three: Using Spinners to Predict Chance
    • Investigation Four: Theoretical Probabilities

Grade Seven

  • What Do You Expect?

    • Investigation One: Evaluating Games of Chance
    • Investigation Two: Analyzing Number-Cube Games
    • Investigation Three: Probability and Area

Book 1

  • Module 2 - Patterns and Designs

    • Section 2: Fractions

  • Module 4 - Mind Games

    • Section 1: Experimental Probability
    • Section 1: Theoretical Probability

  • Module 6 - Comparisons and Predictions

    • Section 6: Tree Diagrams

  • Module 8 - Our Environment

    • Section 4: Geometric Probability

Book 2

  • Module 1 - Making Choices

    • Section 3: Theoretical Probability

  • Module 3 - A Universal Language

    • Section 2: Tree Diagrams and Probability

  • Module 4 - The Art of Motion

    • Section 4: Multiplying Integers
    • Section 4: Dividing Integers

  • Module 5 - Recreation

    • Section 1: Stem-and-Leaf Plots
    • Section 1: Histograms
    • Section 2: Cross Products
    • Section 2: Scatter Plots
    • Section 2: Box Plots
    • Section 3: Percents
    • Section 4: Predicting using Percents

  • Module 6 - Flights of Fancy

    • Section 1: Geometric Probability

Book 3

  • Module 2 - At the Mall

    • Section 3: Theoretical Probability, Experimental Probability
    • Section 3: Tree Diagrams

  • Module 4 - Patterns and Discoveries

    • Section 6: Geometric Probability

  • Module 5 - Inventions

    • Sectoin 5: Counting Principles, Permutations, Combinations, Probability and Counting

6th

  • Module 6 - Comparisons and Predictions

    • Section 6: Percents and Circle Graphs

8th

  • Module 1 - Amazing Feats and Facts and Fiction

    • Section 5: Problem Solving and Mathematical Models

  • Module 2 - At the Mall

    • Section 4: Surveys, Proportions, and Percents

Book 1

  • What Does the Data Say?

    • Lesson 7: Are You Improving?
    • Lesson 8: How Close Can You Get?
    • Lesson 9: Stories and Graphs
    • Lesson 10: What Are the Chances?
    • Lesson 11: Changing the Chances
    • Lesson 12: Which Bag Is Which?

Book 2

  • Chance Encounters

    • Lesson 3: From Never to Always
    • Lesson 11: The Shape Toss Game

Book 3

  • Looking Behind the Numbers

    • Lesson 4: Top Teams
    • Lesson 5: Comparing Sizes
    • Lesson 9: On Tour
    • Lesson 10: Lunch Specials

Grade 8

  • Great Expectations

    • Variability
    • Chance
    • Sample Size
    • Probability
    • Combinations
    • Simulations

  • Insights into Data

    • Understanding Graphs
    • Gathering Data
    • Bias
    • Representation of Data
    • Correlations
    • Scatter Plots
    • Box Plots

Grade 5

  • Taking A Chance

    • Fairness
    • Estimating and Computing Chance
    • Tree Diagrams

Grade 6

  • Dealing With Data

    • Scatter Plots
    • Box Plots
    • Stem and Leaf Plot
    • Histograms
    • Mean, Median, Mode and Range

  • Tracking Graphs

    • Line Graphs
    • Interpreting Graphs
    • Looking at a Graph's global features

Grade 7

  • Decision Making

    • Graphs of Data
    • Constraints
    • Graphing Inequalities
    • Discrete Functions

  • Statistics and the Environment

    • Collecting Data
    • Mean, Median, Mode and Range
    • Maps
    • Graphs and Tables

Be Prepared to

  • give implicit directions on what they are to do. For example, "Today we are going to study the nature of forest fires. We are going to determine the effect of different conditions on the outcome of a forest fire. The conditions we are going to study are wind direction, wind speed, and forest density ..."
  • discuss density, speed, direction, ...