• Assess students as they work through the practice set with you.
• Assess students as they work through their own graph using the data generated from the Rocket Lab.

Say, “Now that you have completed the data collection portion of the Rocket Lab, it is time to analyze that data. One of the most powerful tools in analyzing data is to create a graph. You will be creating a graph by hand (or by using Excel). The information gathered from the graph will allow you to draw conclusions about your experiment.”

Present the following information on graphs to the students through handouts, an overhead projector, or copying it a presentation board for students to copy. A copy of Graph Notes can be found in the Resources folder (S-7-6-2_Graph Notes.doc).

The Graph

• The independent variable is placed on the x-axis.
• The dependent variable is placed on the y-axis.
• Both axes should be labeled with the proper variable and units of measure.
• The graph should have an informative title that includes the independent and dependent variables.
• You will plot your average values for each trial.
• You will draw a line of best fit.
• The equation of a line will be generated.

At this time, have students calculate the average height reached by each canister for Pennies 2–7 on the Rocket Lab worksheet (S-7-6-1_Rocket Lab Worksheet-Student Version.doc, and S-7-6-1_Rocket Lab Worksheet-Teacher Version.doc). Recall that to find the average, students will add up the height reached for each trial (for a given penny amount) and divide by 3, as there are 3 trials.

Hand out a piece of graph paper and a ruler to each student (S-7-6-2_Graph Paper.doc). Have students create graphs for their data. Say, “First, turn your paper to the landscape orientation (longer side parallel to the ground). Using a ruler, draw a long line at the bottom of the page to represent the x-axis. Draw a long line on the left side of the paper to represent the y-axis. Label each axis according to the parameters listed on the Graph Notes. At this point, your graph should look like this:”

Continue, “The next step is to create a scale on both axes. Look at your data. What is the smallest value for both the x and y axes? What is the largest value for both the x and y axes? For the x-axis, start with 0 and move up to 10. This range allows you to plot your data and still leaves room to extrapolate on either end. We will learn more about extrapolating data later in this lesson. The y-axis can also start with zero and go at least 20 cm higher than your highest value. Keep in mind that you CANNOT just write down your experimental values as a scale. The numbers need to be scaled, literally. Let each box or line represent a value and move up and down by the same amount. This graph is an example:”

“Notice how the numbers are spaced evenly. On the y-axis, the values increase by a factor of 15 each time. The values on the x-axis increase by a factor of 1 each time. Do you notice how the numbers are spaced, so that they take up the entire graph and are not scrunched at either end?”

“The next step is to plot the data. In this case, we will create a scatter plot, which involves plotting the data as points. Using the data from Part 1 of your Rocket Lab Worksheet (S-7-6-1_Rocket Lab Worksheet-Student Version.doc), create x-y coordinates to represent your data points. Using your coordinates, plot the data on your graph. Do not connect the dots, as that indicates you are sure of every data point in between each point, which you are not.”

“Your next task is to draw a line of best fit. Usually, it is best to guess at a straight line that goes as near as possible to as many points as possible. Generally, it is a good idea to have as many points above the line as you do below the line. It is wise to ignore any data point that looks like an extreme outlier. The ORIGIN is not always included as a point!”

“Now that you have drawn the line of best fit, you need to find the equation of the line.”

If students are unfamiliar with the slope of a line, refer to the Slope PowerPoint presentation (S-7-6-2_Slope Introduction PowerPoint Presentation.ppt and S-7-6-2_Slope Introduction Presentation PDF.pdf). This will be very useful in analyzing your Rocket Lab data. Recall that the equation of a line is:

y = mx + b

m = slope

b = y-intercept

“The first step is to calculate slope (m). Slope can be described as the change in y over the change in x, or rise over run.”

“Pick two points from your graph that are the farthest apart. Write them as coordinates or look at the data on your worksheet (you already wrote all the points as coordinates there). Label the coordinates you will be using to calculate your slope as follows:”

Example:

“Plug the correct numbers into the equation to find the slope. Recall that slope is the change of y over the change of x, which can be written as:”

y₂ ― y_{1
_________}

x₂ ― x₁

“Using the example shown above, the change in y is (30–105) or -75, and the change in x is (7–2) or 5. You can leave the slope as a reduced fraction: -75/5 or write as a decimal -15. Now, insert that value in place of m in the line equation:”

y = –15x + b

“You just found the slope of the line or how steep the line is. Notice that the number for slope is negative. A negative number indicates a negative graph, or a line that moves downward from left to right. A positive number for slope would be represented by a positive graph, or a line moving upward from left to right.”

“The next step is to find the y-intercept or where the line would cross the y-axis.

To do this, use either one of the coordinates that you used to calculate slope. I will use (2, 105) as in the example. Plug the y-coordinate into the y spot in the line equation, plug the x-coordinate into the x spot in the line equation, and solve for b.”

y = mx + b

105 = (–15)2 + b

105 = –30 + b

135 = b

“According to my example, the line would cross the y-axis at 135. The complete equation of the line would now look like this:”

“The last part of the graph is the title. Generally, the title is written as the dependent variable (y-axis) vs. independent variable (x-axis). The title of my example graph would be as follows:”

At this time, have students use their Rocket Lab data to construct a graph. They may show all of their work on Part 2 of the Rocket Lab Worksheet and attach their graph separately.

Extension:

• Students who might need an opportunity for additional learning can review an introduction to slope of a line. Provide them with part or all of the Slope PowerPoint presentation (S-7-6-2_Slope Introduction PowerPoint Presentation.ppt).
• You can give students sample coordinates and have them practice finding the equation of a line before moving on to the Rocket Lab data.
• Students who might be going beyond the standards can create a graph using Excel after they have made graphs by hand. Excel will generate the equation of a line in much less time. For a full tutorial, go to:

http://phoenix.phys.clemson.edu/tutorials/excel/graph.html