# Lesson Study: Lines of Best Fit

I had the privilege of working with Integrated 1 teachers last week on statistics. We voiced our concern that students are often given the line of best fit for a data set rather than exploring how to create it themselves. We also wondered why their stats chapter was not right after exploring equations in slope-intercept form, as that how we wanted students to write the equation for the line they created.

Our goals for creating the lesson were as follows: 1) Students would review writing a linear equation in slope-intercept form from a graph, 2) Students would create lines of best fit for data plots on a graph, and 3) Students would write the equation for the line of best fit in slope-intercept form.

After searching several open resource sites, we settled on using some graphs from an earlier exploration to review writing equations of lines (please see the attached worksheet). We felt that these graphs would be easier for students to be able to read, and allowed students to determine the slope either by counting or by using their slope formula when given two points. We didn’t want the lesson to get stuck in this review section, so the cleaner the graphs were, the better. We strategically chose two with positive slopes, two with negative slopes, some with fraction values and one with a y-intercept of 0 so that we could frontload the necessary skills before moving to the new concept of creating lines of best fit.

The second component of the lesson was the Desmos activity, Fit Fights (see link below). We wanted to use the activity to build understanding for how lines of best fit are created. We used the following questions to drive the discussions:

• What do you notice?
• What do you think the gray lines represent?
• Do the data points make a line if we connect them? Is this a linear function? Why or why not?
• Do the data points gravitate towards making a line? Would it be a positive or negative (or zero or undefined for the graphs they created) slope?
• If we drew a line to ‘best fit’ our data points, where might it go?
• How can you tell if your line is a good fit for the data points?

The third component of the lesson was to relate the lines of best fit students created to writing equations of linear functions in slope-intercept form. We took snap shots of the lines of best fit from the Desmos activity, strategically choosing lines that had at least two whole number coordinates. We purposefully related the warm up to the lines of best fit, using similar language and questioning.

### Our Take-Aways

• Our students are successful in determining the slope by counting rise/run, but need to continue to work on using the slope formula when given two points.
• The Desmos activity only had negative slope lines of best fit. Consider having students create data points that could have lines of best fit that have other correlations so they don’t overgeneralize and think it will always be a negative correlation.
• Students struggle when the axis are scaled differently. Need to build in some warm-ups that continue to explore differently scaled axes.
• We need to be clear in our questioning. Using questions such as, “Are we good? Do you get it?, etc.” does not give us formative information to move forward.

Below are some of the students’ work and what they felt they had learned. Overall, students were more engaged with this lesson than they have been in the past when learning this concept. We definitely want to use this lesson again, and hope you find it helpful as well!

Lesson Study Worksheet (Shout out to Fontana High School!): Stats Lesson Study Worksheet