Illuminations: On Fire

# On Fire

## Investigating Fire Environments

 Students consider the meaning of the term variable, both in a mathematical and an everyday sense, by considering a text‑based "equation." Data regarding flame length, vegetation and fire speed will be organized in a table, and students will investigate correlations between variables using scatterplots and lines of best fit.

### Learning Objectives

 By the end of this lesson, students will be able to: Recognize the impact that variables have on results. Draw conclusions based on numerical information organized in a table. Make predictions using a graph of data and a line of best fit.

### Materials

 Computer and Internet connection Wildfire Equation Handout Fire Behavior Activity Sheet

### Questions for Students

 How did organizing the data in a table help you see and understand the relationships among fire speed, flame length, and burn rate? How did translating this data to a scatterplot show relationships? Describe the differences between these two representations. [A scatterplot shows a visual representation of the numbers that appear in a table. Scatterplots often show patterns that are more difficult to detect using a table of data.] For what purposes would you consider using a scatterplot to show data? Are there times that using a scatterplot would be useful in providing a convincing argument to your parents or a friend? [As shown in this lesson, a scatterplot will often make patterns obvious.]

### Assessment Options

 Ask students to write a reflection that compares the benefits of analyzing data in a table as opposed to analyzing data with a scatterplot. Collect the student activity sheets and evaluate their scatterplots that compare fire speed to burn rate. In addition, require students to submit the equation of the line of best fit for this data. Have students ask their classmates for two pieces of information—for instance, shoe size and height; age of mother and number of siblings; or, number of hours playing video games per week and number of hours doing homework per week. Then, have students organize the data in a table, represent it in a scatterplot, and find the equation for an estimated line of best fit. (Note that a line of best fit will fit some sets of data better than others. A discussion about when it is and is not appropriate to draw a line of best fit could occur.)

### Extensions

 Have students use the On Fire applet. For each probability, have them run five trials and determine the average of the five trials. Then, have them plot probability along the vertical axis and average percent of the forest that burned on the vertical axis. Is there a correlation? Is it linear? Can the correlation be represented by a line of best fit? Have students use information from the chart in the Defensible Space handout to create a scatterplot that compares steepness of slope to the recommended distance for defensible space. (This handout is the basis for the next lesson, How Steep Can You Be?) Students will need to determine how to deal with the slope; specifically, because a range is given in the chart, such as 0 to 20%, students will need to decide if they should use one of the extreme values (0 or 20) or the average value (10). Then have students determine if there is a correlation between these variables and, if there is, write an equation that relates them.

### Teacher Reflection

 What relationships did students articulate and use when transferring information from the table to the graph? What level of expertise did students demonstrate in preparing and using scatterplots? What additional experiences do they need with this type of graphical representation? Did students have a clear idea of what pieces to include in the graph, such as labels on the axes, a title, and so forth? What additional knowledge and skills do they need that might be presented in a mini-lesson on creating graphs?

### NCTM Standards and Expectations

 Algebra 6-8Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. Develop an initial conceptual understanding of different uses of variables. Model and solve contextualized problems using various representations, such as graphs, tables, and equations. Use graphs to analyze the nature of changes in quantities in linear relationships.

1 period

### Activities

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