Analyzing Residuals

I begin today's lesson by using a document camera to show student's work from a previous lesson. I plan to have students look at each response and determine if the student showed which is the line of best fit and how they mathematically supported their work. The original assignment is included in the resources (Scatterplot_Day 3_TOD).

I then do a Think-Pair-Share and allow the students to come up with a in your own words definition for describing how well a line fits the data in a scatter plot.  I expect my students to say something like "the closer all of the points are to the line the better the fit."  I will choose one or two examples of student work that support the student definitions and show them under the document camera again. This time, we will apply their new definition to assess the fit. 

If no students came up with this response then we could leave the question “hanging” until after the investigation. My goal is to pursue this lesson as a process of the students refining their own definition of fit, guiding them towards the conventional definition. 

For most of today's lesson, my students will complete a Webquest Investigation. During the investigation, they use a series of applets. The applets allow students strengthen their understanding of best fit lines, as they consider how the residual value is ultimately minimized when the line of best fit is found. Each presents the concept of residuals from a different perspective.  During the investigation, students will construct their own understanding of the concept of residuals, progressively building their own in your own words definition of the concept.  

Webquest Investigation Resources:

1. Video Tutorial: https://www.youtube.com/watch?v=urAp0DibYlY (Accessed May 10, 2014)
2. Applet 1: Effects of outliers on a line of best fit (Accessed May 10, 2014)
3. Applet 2: Movement of best fit line (Accessed May 10, 2014)
4. Applet 3: Mr. B’s residual applet (Accessed May 10, 2014)
5. Applet 4: NCTM Illuminations Residual (Accessed May 10, 2014)

Both as a reflection and feedback tool, I ask students to choose one of the applets that they looked at today that they felt helped them understand the idea of residuals the best.  This reflective piece has a meta-cognitive component for the students but will also help to adjust this lesson for future years to give students access to the best possible resources for their learning.