The first four slides of Scatterplot_Day 1 are covered during the Opening. I will continue on Slide 5 as we begin today's Direct Instruction. First, I show students the different types of correlation. I emphasize that with positive correlation, as one variable increases so does the value of the other. In a negative correlation, as one variable increases the other decreases. A scatterplot with no correlation shows no relationship between the variables.
Once I introduce the different types of correlation, I want to give my students some examples of each so that they can anchor their understanding of these definitions in context. Most of my students are much more likely to remember examples, than definitions. In this case, the examples are verbal descriptions where correlation between two variables may or may not exist.
I ask students to grab a whiteboard to record their answer. I explain that I want them to look at each example when I uncover it and write down either positive, negative or no correlation, based on their interpretation of the scenario. In order to make this quick and efficient, I have the student on the left of each partnership tell the student on the right what they wrote down for their correlation. The student on the right can either agree (no further conversation needed) or disagree and explain why. Then, when I present the next example the person on the right begins the same process.
By this time, my student volunteer has entered in all of the data and we can look at it as a class once we are done looking at the examples. We will do this as the first step of today's explanation.
In this portion of the lesson, students will have the opportunity to visualize the data using a scatter plot. I have students turn to the graphing side of their whiteboard. The first step is for students to examine the data and set up an appropriate scale on both axes. Before students begin plotting points I ask them to turn and talk with their partner about what type of correlation they expect to see in the data. (In my experience, most students will typically predict a positive correlation) Then students can plot each point for the students in our class. As students plot the point they are usually surprised by the lack of correlation in the data. I have done this lesson over several years and each time it usually turns out that the data has either no correlation or a slight negative correlation.
This portion of the lesson will serve as an opportunity to do some skill building. While we will be using technology for a good portion of the linear regression calculations, we also want students to know how to calculate a line of best fit by hand. That said, I want to use this practice time for students to make connections between finding the equation of a line between two points both graphically and algebraically. While this is a skill that should be secure for most students, this will be a good opportunity to circulate around the room to diagnose student understanding. If any students are struggling, pull a small group to go through each question individually and break the skill down into smaller component parts (find slope, plug into y=mx+b, find y-intercept).
This closing activity will give students an opportunity to write about mathematics. Have students choose 1 type of correlation that they learned about today (positive, negative, zero, or none) and write a scenario that would be modeled by that type of correlation. After students write their scenario they should also explain why the scenario demonstrates that type of correlation. If time permits, have students share with their partner and then try to find one of each type of correlation that can be shared out with the class.