Tell students that the lessons in this unit will help them to answer the following question:
If you live in an area where wildfires occur, what can you do to protect your family and property? That is, how can you reduce the probability of a fire spreading to your home?
Explain that this lesson, in particular, will allow them to understand the factors that cause a wildfire to spread, and they will run a simulation to understand the devastation that a wildfire can cause.
If a wildfire has occurred recently in your area, you may want to reference it during the introduction to this lesson. You may also want to show a picture of a forest fire, such as the one that is shown on the Wildfire Overhead.
Other photos of widlfires are available from the following web sites:
Explain that forest fires begin for many reasons, including natural causes (lightning strikes) and human interactions (careless campfires, dropped cigarettes). Then, ask students to generate a list of factors that might cause a forest fire to spread. You might want to pose the following question:
Once a forest fire begins, what factors influence whether it remains small and contained, or whether it will rage out of control?
Students may suggest the following reasons:
- Density of Trees – if the trees are spread out, there is less chance of the fire "jumping" from one tree to another
- Recent Weather – dry, warm weather may have caused the trees to dry out, making them more susceptible to fire
- Steepness of Ground – fire travels faster up a steep slope than over flat ground or down a hill
- Amount of Wind – strong winds can push the fire
- Rain and Snow – a small fire might be squelched by wet conditions
After this discussion, distribute the Heating Up activity sheet. Have students compare their list of factors with the information in the diagram. Then have students create a chart that lists the four components of the fire environment, and for each component, have them list at least three factors. Students can enter this information into the chart on the activity sheet, or they can use the
Heating Up Chart Maker.
Explain to students that organizing data in a table makes it is easy to see relationships among the various parts.
When students have completed their charts, conduct a class discussion in which students describe the following:
- An area in which a wildfire is likely to spread very quickly [windy, steep slopes, dry and dead trees for fuel]
- An area in which a wildfire is likely to spread slowly [wet ground, rainy, flat terrain, healthy trees]
Once students understand the factors that contribute to the probability of a fire spreading, explain that they will model the spread of a forest fire with coin tosses. To show students how the simulation will work, display a 5 × 5 grid on the blackboard or overhead projector. Explain that the grid represents a forest, and each square represents a portion of the forest; a fire has started in the middle square (color it red), and the simulation will determine how the fire spreads.
One by one, flip a coin for each of the four squares adjacent to the middle square. If the coin lands heads, the square catches on fire; if it lands tails, the square does not catch on fire. Squares that catch on fire should be colored red. Squares that do not catch on fire should be marked to indicate that they have been tested; however, a square that does not catch on fire now may catch fire later if another adjacent square catches fire. (You may therefore wish to only mark along the side adjacent to the on-fire square, to show that a square could catch fire from a different direction.) When it is no longer possible for a square to catch fire from any direction, color it green. Repeat this process for any square adjacent to an on-fire square. Continue the demonstration until students have a thorough understanding of how the simulation is conducted.
Then, divide students into pairs, and randomly assign each pair a letter, A, B, or C. Explain that each pair will flip two coins to determine if the fire spreads. Students in Group A will simulate a fire where the probability of spreading is low, Group B will simulate a fire with a slightly higher probability, and Group C will simulate a fire with the highest probability of spreading.
Students may believe that the percent of the forest that will burn is directly proportional to the probability of the fire spreading. That is, students may think that if the probability of spreading is 30%, then 30% of the forest will go up in flames. The following question should be asked prior to students performing the simulation; then, it should be asked again after the simulation is completed:
How do you think the probability of the fire spreading and the amount of forest that will burn are related? That is, if the probability of the fire spreading to an adjacent tree is 25%, what percent of the forest do you think will burn? What percent will burn if the probability is 75%? Make a conjecture.
As students conduct the simulation, adjacent squares catch fire if:
- Group A: Both coins land heads
- Group B: The coins are different
- Group C: Either coin lands heads
Distribute the Wildfire Simulation student sheet, and allow students time to complete the simulation and answer the questions. (Note that this activity is simplistic in its execution, but it may take a long time to complete because of repeated coin flips. To shorten the activity, you may wish to have students use a 3 × 3 or 4 × 4 grid instead.) Then review the results with the class. Have students within the same groups (A, B, and C) compare their results.
- What is the probability of catching fire for each group? [When two coins are tossed, there are four possible outcomes: HH, HT, TH, and TT. For A, only the first outcome causes the fire to spread, so the probability for A is 1/4. For B, two possibilities cause the fire to spread, so the probability is 1/2. For C, the probability is 3/4.]
- In general, did more squares catch fire for group A, B, or C? [The numbers will vary, but on average, the number of squares that catch fire will be fewest for A and greatest for C, with B somewhere in the middle.]
- What was the average number of squares that caught fire for each group? [For A, the average will be 1-3; for B, the average will be 11-14; and for C, the average will be 20-25.]
After discussing these questions, allow students to further investigate this scenario with the Illuminations Fire Tool.
Students can use the Fire Tool to investigate the percent of the forest that burns for various probabilities. They can enter probabilities of 0.25, 0.5, and 0.75 to replicate the experiment that was done with coins, or they can try other probabilities. Note that the Fire Tool uses an example with far more trees than would be reasonable if the experiment were done with coins.
At the end of the lesson, you may wish to have students reconsider the question about the relationship between the probability of the fire spreading and the percent of the forest that burned. Student opinions will likely have changed after conducting the simulations in this lesson.
