Scatter Plots and Correlation

Scatter plots make abstract relationships visible, turning raw numbers into patterns students can see and discuss. Active learning works especially well here because students need repeated practice translating between data points and descriptions of association, which builds their statistical intuition.

• 9th Grade
• Mathematics
• 3 activities
• 15 min–35 min

Learning Objectives

1. Create scatter plots to visually represent the relationship between two quantitative variables from a given dataset.
2. Analyze the pattern of points on a scatter plot to describe the direction and strength of the relationship between variables.
3. Differentiate between positive, negative, and no correlation based on the visual distribution of points on a scatter plot.
4. Explain why a strong correlation between two variables does not necessarily imply a causal relationship, using a concrete example.

Inquiry Circle

⏱ 35 min·Small Groups

Inquiry Circle: Create and Interpret a Real-Data Scatter Plot

Provide groups with a dataset of two quantitative variables such as hours of sleep versus average GPA or temperature versus energy use across US cities. Groups create the scatter plot, describe the form, direction, and strength of the association in complete sentences, and identify any points that appear to be outliers with a written justification.

Prepare & details

Analyze what the pattern of points on a scatter plot reveals about the relationship between variables.

Facilitation Tip: During Collaborative Investigation, circulate and ask each group, ‘What does the overall trend suggest about how these two variables might be related?’ to keep conversation focused on pattern recognition.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Think-Pair-Share

⏱ 15 min·Pairs

Think-Pair-Share: Describe What You See

Show a scatter plot without labels or context. Students individually write a description of the pattern using specific vocabulary (positive or negative, strong or weak, linear or nonlinear), then compare descriptions with a partner and reconcile any differences in language or interpretation before sharing with the class.

Prepare & details

Differentiate between positive, negative, and no correlation.

Facilitation Tip: During Think-Pair-Share, assign roles explicitly: one student describes the plot, one gives the correlation type, and one connects the visual to a real-world interpretation.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Gallery Walk

⏱ 25 min·Small Groups

Gallery Walk: Matching Correlation to Scatter Plot

Post scatter plots at stations alongside cards showing r values such as -0.9, -0.4, 0.1, 0.7, and 0.95. Students rotate to each station and match the plot to the most appropriate r value, writing one sentence explaining the visual feature that most influenced their choice.

Prepare & details

Explain why correlation does not imply causation.

Facilitation Tip: During Gallery Walk, post the correlation coefficients next to each scatter plot so students practice matching r values to visual patterns immediately after observing them.

Setup: Wall space or tables arranged around room perimeter

Materials: Large paper/poster boards, Markers, Sticky notes for feedback

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Teaching This Topic

Teach correlation with both real datasets and counterexamples to prevent oversimplification. Avoid rushing to the formula for r; instead, let students estimate strength and direction visually first. Research shows that students grasp correlation better when they distinguish between linear and non-linear patterns early, so include at least one U-shaped plot in every set of examples.

What to Expect

Students will confidently create scatter plots from real data, describe correlation types using clear language, and connect visual patterns to correlation coefficients. They will also recognize that correlation does not imply causation and explain why with evidence.

Watch Out for These Misconceptions

Common Misconception

During Collaborative Investigation, watch for students assuming that r = 0 means there is no relationship at all.

What to Teach Instead

During Collaborative Investigation, have students plot a U-shaped dataset (e.g., temperature vs. ice cream sales in winter vs. summer) and calculate r to see it’s near 0 despite a clear pattern.

Common Misconception

During Gallery Walk, watch for students thinking a steeper slope means a stronger correlation.

What to Teach Instead

During Gallery Walk, place two scatter plots side by side with the same r but different slopes (e.g., using different axis scales) and ask students to compare the patterns and r values directly.

Common Misconception

During Think-Pair-Share, watch for students interpreting positive correlation as requiring both variables to have large values simultaneously.

What to Teach Instead

During Think-Pair-Share, give students a dataset where both variables are small but increase together (e.g., number of pencils vs. number of erasers in a classroom) and ask them to describe the direction of change rather than the size of values.

Assessment Ideas

Exit Ticket

After Collaborative Investigation, give students a small dataset (e.g., hours of TV watched vs. homework completion time for 6 students). Ask them to plot the data, describe the correlation type and strength, and write one sentence explaining why this correlation does not prove that TV watching causes less homework time.

Discussion Prompt

During Gallery Walk, present students with a scatter plot showing strong positive correlation between ice cream sales and drowning incidents. Ask: ‘What is the relationship shown in this plot? Is it reasonable to conclude that eating ice cream causes drowning? What other factor might explain both of these trends?’

Quick Check

After Think-Pair-Share, show students three scatter plots (positive, negative, none) on the board and ask them to label each with the correct correlation type and justify their choice based on the pattern of points.

Extensions & Scaffolding

• Challenge: Ask students to collect their own paired data (e.g., hours of sleep vs. mood rating) and create a scatter plot with a short written analysis of correlation and causation.
• Scaffolding: Provide partially completed scatter plots with labeled axes and some points plotted, so students focus on completing the pattern and describing it.
• Deeper exploration: Introduce the concept of a lurking variable using a dataset like ‘teacher salary vs. student test scores’ to discuss real-world implications of correlation.

Key Vocabulary

Scatter Plot	A graph that displays the relationship between two quantitative variables. Each point on the plot represents a pair of values for the two variables.
Correlation	A statistical measure that describes the extent to which two variables change together. It indicates the direction and strength of a linear relationship.
Positive Correlation	A relationship where as one variable increases, the other variable also tends to increase. Points on the scatter plot generally rise from left to right.
Negative Correlation	A relationship where as one variable increases, the other variable tends to decrease. Points on the scatter plot generally fall from left to right.
No Correlation	A relationship where there is no discernible pattern between the two variables. Points on the scatter plot appear randomly scattered.