Graph compression force vs. deformation

4.B.1 Analyze and interpret graphical data (patterns) from tests of compression force vs. amount and type of deformation (effect) to provide evidence that supports an argument that all objects behave elastically up to a specific limit beyond which permanent damage occurs.

student graphs should include the following:

the x-axis labeled as the force applied to the object (in N)

the y-axis labeled as the amount of deformation in the object (in cm)

stretching out the intervals to maximize the use of the graph paper while still capturing the highest x value and highest y value

equal intervals identified on each axis

a straight line of best fit through the data that are represented with points drawn as open circles (anywhere the beam returned to its original shape after the weight was removed)

Since this may be the first time students have drawn a trend line in 8th grade, talk with your math teachers in 8th grade to determine when students will be encountering this idea in their math class. It is a CCMS target learning goal for 8th grade.

If students struggle with these graphing skills, coordinate with the grade-level math teacher to ask about additional contexts that students may be familiar with from math class that they can practice applying these skills to. These examples can be a useful reference for students. You may want to post these as anchor charts in your class to help students see how to transfer to their science class the ideas and skills they are developing in math.

Introduce the additional data that were collected. Say, Next I want us to talk about how we can develop a mathematical model of the relationship you see in your data. I have a set of data for us to look at together to help us think about how to do this.

Project slide D. Explain that the data on the slide were collected from three wood stirrers taped together. Emphasize that for every data point, the object returned to its original shape and position after the force was removed. Give students a minute to look at the graph and then ask them to share what patterns they notice.✱

Suggested prompt

Sample student response

What patterns do you notice in the data?

The data look a bit scattered.

What tends to happen to the amount of deformation as the amount of force applied to this object increases?

It tends to increase.

Where on the graph do we see evidence of having recorded more than one deformation measurement for a certain amount of force?

At 3 N.

At 7 N.

Describe what a trend line is and how to make one. Say, When you have multiple data points and some of them are for the same value you plotted for your independent variable, it can be helpful to plot all that data on a coordinate graph like we’ve done here. What we end up producing is sometimes called a scatter plot. Because we haven’t averaged any of our results yet, it can be useful to think about what the average trend in all of the data is. One way to do this is to create a trend line to show how close the data are to a linear relationship. Constructing a trend line can be done by holding up a ruler or straight edge over the graph and shifting its angle and position so that the slope and y-intercept of the line it would make is as close as possible to all the data points on the graph. This line may pass through some of the points, none of the points, or all of the points. The key is to try to fit the line as closely as possible to the average trend in the data.

Compare lines of best fit. Project slide E. Ask which line is a better fit to the average trend in the data. Students should say line C.

Say, This trend line is also sometimes called the “best fit line” or “line of best fit”. It helps us see that the data might be closer to a linear relationship than we suspected at first. If we collected and graphed additional data, this line also shows our best estimate of where we would expect that additional data to fall.

• Post a copy of Example Line of Best Fit on the Word Wall. Remember to cover this posting or remove it before your next class.
• Instruct students to use an extra sheet of paper to cover the data points on their graph that represent when the object showed evidence of permanent deformation (these data points will be a solid circle or an “x”). Students should be looking at only the data points that are represented with an open circle on the graph.

Construct trend lines for the data that students collected. Tell students, Sometimes data that don’t look that linear end up looking much more so after we draw a best fit line. Let’s see what that looks like for your data now. Show slide F. Give students a minute to construct on Deformation Results the best fit line for their own data using a ruler (or wood stirrer) and a pencil or pen. Emphasize that students should only be c…