Lesson 11

This activity is a review of scatter plots and how to interpret information from a scatter plot.

Keep students in same groups. Tell students that they will look at an image, and their job is to think of at least one thing they notice and at least one thing they wonder. Display the image for all to see. Ask students to give a signal when they have noticed or wondered about something. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice with their group, followed by a whole-class discussion.

Invite students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the image. After each response, ask the class if they agree or disagree and to explain alternative ways of thinking, referring back to the images each time.

Discuss what each point in the scatter plot represents. Ask students to describe general patterns visible in the plot. Ask, “Is there a pattern of association?” (Yes, it is not linear, but it is possible to say that there is more rain in the winter and less rain in the summer.)

The task statement provides data students can analyze for the remainder of this lesson. It gives the average high temperature in September at different cities across North America. This is only one possible choice for data to analyze. If appropriate, students can instead collect their own data and then continue using it. If so, then the instructions are the same just with the students’ data.

Students in same groups of 3–4.

Make sure students understand the information listed in the table. Invite students to share their responses to the last question, then move on to the next activity.

In this activity, students use the data from the previous activity and draw a scatter plot and a line that fits the data. The given data show a clear linear association, so it is appropriate to model the data with a line. Students can use a piece of dried linguine pasta or some other rigid, slim, long object (for example, wooden skewer) to eyeball the line that best fits the data. (The line of best fit has a variance of \(R^2=0.94\).) Even though different answers will have slightly different slopes and intercepts, they will be close to each other.

Students in same groups of 3–4. Provide access to pieces of dried linguine pasta.

If a student is stuck on making the scale on the graph, remind them to look at the range from the previous problem.

At the start of the discussion, make sure students agree that there seems to be a negative association that looks like a line would fit the data nicely before moving on.

Invite several groups to share the equations they came up with and how they found them. They will likely have slightly different slopes and intercepts. Ask students to explain where those differences come from. (Not everyone chose the same points to guide the trendline they drew for the data.) The differences should be small and the different models give more or less the same information. In the next activity, students will be using the model (equation and graph) to make predictions.