My best fit line

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Objective

SWBAT draw the best fit line on a scatter plot of bivariate data.

Big Idea

Using a virtual manipulative, students draw their best fit line on real world data, then check and make predictions.

Accessing Prior Knowledge

15 minutes

To access help my students access their prior knowledge, I begin today's lesson by presenting the information in Scatter plot APK. I ask my students to read the directions on the first slide carefully and to see what they can do (see my reflection on The beginning of a lesson for more). I stress to my students that they should describe the correlation in a full sentence. For example, "The more hours spent playing cards, the lower the predicted test grades."

When we discuss this opening problem I will call on students who struggled in the previous lesson. By this time, most of my students can see the positive or negative, weak or strong correlation in a scatter plot. In our conversation I will try to focus on identifying outlier data points and considering them carefully. I will say to me students, "Be careful, sometimes there is more to learn from the outlier than from the rest of the data. It is never a good idea to ignore data carelessly!"

Here are the answer to the problems: Answers to APK Powerpoint


Using a Best Fit Line Applet

10 minutes

In this Activity many of my students experience their first opportunity students to draw their own best fit line on a scatter plot. At this stage, I like to use technology. My students are much more willing to try new things on the computer, than with a pencil and ruler.

We will use a digital manipulative from the NCTM Illuminations website. I ask each student to open the following URL:

http://illuminations.nctm.org/Activity.aspx?id=4186 

At first, I want students to practice drawing best fit lines with the tool. Once they are all comfortable doing this, we'll discuss how to check to see how close their line is to the actual best fit line given by the computer. I demonstrate this process in my Drawing a Best Fit line virtually video. Here are the steps I'll have each student follow:

  1. Place 12 points on the graph that would show a desired correlation, positive or negative.
  2. Check the box that says ‘student guess’ and try to draw the ‘line of best fit’ dragging the two purple endpoints
  3. Now check the box that says ‘computer fit’ to check how you did

As students explore I will walk around observing students' work. I encourage them all to try it a few times, until they until they get good at it. For many students, repeated trials on a computer is quite familiar, like playing a new game on a phone or computer. Generally, my students start playing around with the icons below the graph on their own. After a while I will encourage all students to do so. I usually wait until some of the students already know how to use them. This creates a ready source of helpers. (We will use these tools in Fitting a Line to Data, our next activity). 

I like to ask my students to share their strategies for drawing a best fit line. Some of the expected comments are: 

  • The line usually does not touch a bunch of points, rather it passes through points on both sides
  • I tried to touch as many points as possible
  • Try and leave the same number of points on both sides of the line
  • Look for equal distances from certain points on either side, perpendicular to the line, and adjust the line accordingly

Fitting a Line to Data

25 minutes

I like for my students to work together in pairs for this activity. I only provide copy of the My best fit line activity handout per pair. I want the students to discuss their results with each other. At the same time, some students engage more with the task when they can manipulate the best fit line themselves. So, I let each student have their own computer if one is available. 

Before letting them get started, I stress the idea that each point on the scatter plot has meaning. I say, "Keep this in mind each time you plot a point." (In the past I've found the students begin to ignore outliers before they have plotted all the points.) As I monitor students at work, I may point to any random point on the graph and ask my students to explain the meaning of that point in the context of the problem. I might say something like, "Tell me the story of that point. What does it tell us about the relationship between these two variables." 

During this activity students are asked to make a prediction using their line of best fit. This is an important part of the activity because it emphasizes a very important purpose of best fit lines, which is to predict values that may not be on the scatter plot. As they work I try not to give students too much guidance. In my experience students make predictions quite freely, about many things. As we work today we will build on this openness.

 

Extension

Today some of my students worked very quickly, so I gave them the following problem to explore:

Collect data on the arm-span and height of 10 students in the class. Let the arm-span size be the x variable and the height be the y variable. Plot these points with the scatter plot manipulative and write about what you see. Create a best fit line. What does the pattern you see have to do with the relationship between two variables. 

The task worked well even though some were familiar with this relationship. They enjoyed using the technology to confirm their prior experiences. Others were interested in this result, because it was new to them.