The 8th graders have recently been spending time learning to work with scatterplots. We reviewed scatterplots and what they looked like. The students are very competent in graphing points on the scatterplots. They had seen lines of best fit before but were struggling with the purpose of these lines.
We started with a review of some definitions. We talked about how the line of best fit could help us make a prediction of what to expect from the data. We then practiced drawing lines of best fit and creating equations for those lines.
I found an activity in the MTB0S about celebrity age guessing and making lines of best fit. I started by explaining to my students that I used to work at Valleyfair (a family amusement park in Shakopee, Minnesota.) I told them about my distaste of the guy that stood by the scale and tried to guess peoples age or weight. Basically he was/is annoying because he is constantly talking! I told them that I wanted to see if any of them could be the better guessers of age than he was. We went through a powerpoint of celebrities and students guessed the celebrities ages. They LOVED this! They also got into the idea of competing to see who would be the better guesser.
Once they had made all of their guesses, they spent some time entering their data into a table on Desmos. I they taught them how to create a line of best fit in slope-intercept form using sliders for m and b. We then exported their pictures to a padlet page where we could look at all the lines of best fit together. This was about all the time that we had, so we didn’t get to voting on who was the best guesser, but they still enjoyed working with Desmos and guessing peoples ages. It also made it so that they all had different answers to the problems and couldn’t copy what their friends answered.
I moved on to an activity from Math=Love about Best Line of Best Fit. We started with a desmos file that had a scatterplot already created on it. I printed this off for my students and they wrote directly on the paper to create lines of best fit. There was a five minute individual work time followed by some table time where they worked. The students had to create the equation for their line of best fit and since I only had one computer, I entered everyone’s equation in. This was a little time consuming since once I wrote the equation in and they saw it on the screen they thought they could make it better. I gave them some more time at their table to perfect their line of best fit and adjusted the equation in Desmos according to their specifications.
I was the only adult in the classroom so we did not have an unbiased judge, but some of the students got into the competitive nature of this activity. We displayed two lines of best fit and then had a discussion as a class about which line was better and why. We got very picky about which line we preferred. I also threw in some lines that were poor choices to see how they responded. (They rocked these problems!)
Our scatterplot unit ended with using some of the worksheets that I got off of teachers pay teachers that guided the students through creating equations of lines of best fit. These were nice because the students had to graph the points and then had to draw the line of best fit before deciding on the slope. Once they created their line of best fit, they had to use the line to determine what the data would yield for an unknown quantity. Here’s a link to the product by Mathink.
Thought for next year… my students tend to believe that the line of best fit has to have at least one or two dots on the line. This does make it easier for when they have to pick points that are on the line of best fit they can easily calculate slope. This is a challenge though since lines of best fit do not always have a point from the data set that lands directly on them.