Grade 8: Statistics & Bivariate Data

Objective

Students will construct and interpret scatter plots for bivariate data, describing patterns such as clustering, outliers, and positive, negative, or no apparent association between two quantities (Utah Standard 8.SP.1).

Materials

• Resource packet: Section 6.1a Class Activity: Read and Interpret a Scatter Plot
• The "field goals attempted vs. field goals made" scatter plot example (from the Mathematical Practice Standards section of the resource)
• Pencil and paper (graph paper if available)
• Chalkboard/whiteboard to record vocabulary

Warm-up (~5 min)

1. Write these vocabulary words on the board from the resource's Academic Vocabulary list: bivariate data, scatter plot, association, positive association, negative association, cluster, outlier.
2. Read aloud the tomato story from the resource: Emina loves garden tomatoes but her friend Renzo dislikes grocery-store tomatoes, and Emina wonders if there's an association between liking tomatoes and having a garden at home.
3. Ask students, in pairs, to guess (30 seconds each): "Do you think there's a connection between growing your own vegetables and liking how they taste? Why?" Take 2–3 quick verbal answers. No wrong answers—this is just to activate thinking about "association" between two things.

Main Activity (~25 min)

1. Distribute or display 6.1a Class Activity: Read and Interpret a Scatter Plot from the resource.
2. Have students work individually or in pairs to complete the activity, examining the scatter plot(s) provided in the packet.
3. As they work, remind them to look for and label these features (write on board as a checklist):
4. Clustering – do points group together in certain areas?
5. Outliers – are there any points that don't fit the pattern?
6. Positive association – do y-values tend to increase as x-values increase?
7. Negative association – do y-values tend to decrease as x-values increase?
8. Linear vs. non-linear association – does the pattern roughly follow a straight line, a curve, or no pattern at all?
9. Midway through, pause the class and use the resource's field goals attempted vs. field goals made example: display or read the prompt, "Using the scatter plot, determine if there is a relationship between field goals attempted and field goals made. Describe any trends or patterns you observe in the data." Have 2–3 students share their reasoning aloud and have classmates agree/disagree with the reasoning (supports "critique the reasoning of others").
10. Students finish the rest of the 6.1a Class Activity independently, writing a sentence or two describing the pattern of association they see in each scatter plot in the packet.

Wrap-up / Exit Ticket (~10 min)

Have students answer the following on a half-sheet of paper to turn in:

1. In your own words, define positive association and negative association.
2. Looking back at the scatter plot(s) from today's activity, describe one cluster or outlier you noticed.
3. Using the field goals attempted/field goals made scatter plot, state whether there is a relationship between the two variables and describe the trend.

If Time Remains

Introduce the resource's Anchor Problem: Tongue Twisters (6.0) as a preview of upcoming bivariate data collection. Explain the setup: students say a tongue twister (e.g., "Peter Piper picked a peck of pickled peppers") in a chain—first just one student says it, then two students say it together, then three, and so on—while the class records the total elapsed time at each trial. Discuss as a class: "What two quantities are we measuring here, and do you think there will be an association between them?" (No need to actually run the full trial—just discuss the setup and prediction if time is short.)