Instructor Guide 5A: Forming Connections

Overview

  • In this in-class activity, students use scatterplots to begin understanding the nature of the relationship between two variables and then quantify the strength of the linear relationship using the Pearson Correlation Coefficient.
  • Throughout the activity, students will explore the meaning and range of values of the correlation coefficient.
  • This activity connects back to quantitative variables in Data Collection and Organization, and prepares students for linear regression in Module 5.
  • S2, S4, C4, C6, 01, 02, 03, V1, V4 ← Link to EBTP descriptions 

Prerequisite assumptions

Students should be able to do each of the following after completing the What to Know assignment.

  • Read a scatterplot.
  • Describe the trend in a scatterplot.
  • Describe the relationship in a scatterplot as linear or nonlinear.
  • Recognize outliers in a scatterplot.
  • Use technology to locate the correlation coefficient .

Intended goals for this activity

After completing this activity, students should understand that the correlation coefficient describes the strength and direction of the linear relationship between quantitative variables.. They should be able to use the correlation coefficient to describe the strength in the linear relationship between variables.

Synchronous Delivery and Activity Flow

The sample activity delivery below assumes a face-to-face class meeting but can be adapted to a fully online or hybrid delivery by using break-out rooms for pairs and small groups.

Frame the activity (5 minutes)

  • Question 1 — Think-Pair-Share S2, C4, V1, V4, O3
    • Use this question to set the stage for exploring the connection between the trend/shape of a scatterplot and the quantitative measure of the strength of a linear relationship.
    • Answers to this early question should focus on the direction and overall shape of the scatterplot.
    • Before continuing, consider using the following prompts for a quick debrief:
      • “As the energy content increases, what is happening, in general, to the carbon footprint? Is it increasing, decreasing, or staying the same?” [Answer: Increasing]
      • “Are there any points that stand out from the rest?” [Answer: No]
      • “What is the general shape of the scatterplot? Do the points form a curve, line, circle?” [Answer: They seem to form a line.]
  • Briefly discuss the objectives for the activity before continuing.

Activity Flow (15 minutes)

  • Questions 2 – 7 Working in pairs or merge the pairs into groups of four V1, V4, O3, S2, C6
  • Question 2
    • Goal: begin to connect the shape/trend to the correlation coefficient, [latex]r=0.621[/latex] (provided in the What to Know assignment).
    • Brief whole-class discussion prompts S4
      • Did you identify a positive or negative trend in Question 1?
      • Is the value of [latex]r[/latex] a positive or negative number?
      • What was the general shape of the scatterplot?
      • How close (if students mention the shape was linear) did the points come to forming a perfect line?
      • Guide students to connect [latex]r=0.621[/latex] with a positive trend that represents a moderately strong linear relationship.
  • Questions 3 – 4 O1
    • Give students time to scan the data in the table and read the descriptions in the data dictionary.
    • Have student complete one table (located in Question 3) to fill in answers to both questions (3 and 4).
    • Ensure students matched each graph with the correct correlation in a brief whole-class discussion.
    • After Question 4, have students reflect on their answer to Question 2. Would their descriptions change now that they have guidelines?
  • Questions 5 – 6
    • When describing a “perfect” linear relationship, ensure students consider both positive and negative relationships.
    • Ensure students discuss increasing and decreasing relationships in groups, not just increasing.
  • Question 7
    • Consider warning groups ahead of time that they will be sharing their answers with the whole class. Assign a reporter (or allow a self-selection) as you see fit.
    • Have groups share their answers during the wrap-up of the activity.

Wrap-up/transition (5 minutes)

  • After most groups have answered Question 7, have a few groups share their graphs. Point out that there are several “correct” answers.
  • Use the sample graphs in Question 7 to discuss, for [latex]r=0[/latex] or [latex]r\approx0[/latex], the difference between “no relationship” and “non-linear relationship.”
  • Provide a summary of graphs displaying different strengths of [latex]r[/latex] from [latex]-1[/latex] to [latex]1[/latex]. O1
  • Have students refer back to the Objectives for the activity and identify ones they recognized completing. S2, C4, O2
  • Transition: the next activity is about exploring complex graphical displays used in the media.
  • Assign the homework or Practice and any What to Know pages for the Forming Connections activities you plan to complete in the next class meeting. C2