Bivariate Data and Scatter Plots

Active learning builds students’ confidence with bivariate data by letting them move from abstract numbers to concrete visual patterns. When students collect their own measurements and plot points by hand, they immediately see how trends emerge and can test their own ideas about relationships between variables.

• 8th Grade
• Mathematics
• 4 activities
• 20 min–35 min

Learning Objectives

1. Construct a scatter plot accurately from a given set of bivariate data.
2. Analyze scatter plots to identify and describe patterns of association, including positive, negative, and no association.
3. Differentiate between linear and non-linear associations depicted in scatter plots.
4. Interpret the meaning of data points and trends within the context of the bivariate data presented.

Case Study Analysis

⏱ 30 min·Pairs

Pairs Plotting: Class Height vs. Shoe Size

Pairs measure each other's height and shoe size, record data in a table, then plot on shared graph paper. They label axes correctly and draw a trend line by consensus. Pairs present their plot and association type to the class.

Prepare & details

Explain how to construct a scatter plot from a given set of bivariate data.

Facilitation Tip: Before Pairs Plotting, ask each pair to predict the direction of association and write it down so they connect their initial intuition to the final plot.

Setup: Groups at tables with case materials

Materials: Case study packet (3-5 pages), Analysis framework worksheet, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Case Study Analysis

⏱ 35 min·Small Groups

Small Groups Analyze: Association Sorting

Provide four printed scatter plots with real data sets like temperature vs. ice cream sales. Groups classify each as positive, negative, no association, linear, or nonlinear, then justify with evidence from points. Groups gallery walk to compare classifications.

Prepare & details

Analyze the different types of associations (positive, negative, no association) shown in scatter plots.

Facilitation Tip: During Association Sorting, circulate and ask each group to justify their category choice with one sentence that uses the terms 'positive,' 'negative,' or 'none.'

Setup: Groups at tables with case materials

Materials: Case study packet (3-5 pages), Analysis framework worksheet, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Case Study Analysis

⏱ 25 min·Whole Class

Whole Class: Human Scatter Plot

Collect class data on sleep hours vs. test scores. Students position themselves on a floor grid as (x,y) points. The class steps back to observe and discuss the association pattern, then records it on the board.

Prepare & details

Differentiate between linear and non-linear associations in scatter plots.

Facilitation Tip: During the Human Scatter Plot, have students hold a card with their value so everyone can see both coordinates at once and patterns become visible from across the room.

Setup: Groups at tables with case materials

Materials: Case study packet (3-5 pages), Analysis framework worksheet, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Case Study Analysis

⏱ 20 min·Individual

Individual Challenge: Survey Scatter

Students survey five peers on minutes exercising weekly vs. push-ups possible. They construct a scatter plot individually, identify the association, and write one sentence interpreting it. Share via digital submission for class review.

Prepare & details

Explain how to construct a scatter plot from a given set of bivariate data.

Facilitation Tip: For Survey Scatter, remind students to include an outlier deliberately so later discussions about validity can reference real choices they made.

Setup: Groups at tables with case materials

Materials: Case study packet (3-5 pages), Analysis framework worksheet, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Teaching This Topic

Teachers should model plotting with real student data first, showing how to label axes with units and choose scales that fit the range. Avoid rushing to definitions; let students articulate patterns in their own words before introducing formal terms like 'linear' or 'correlation.' Research shows that students grasp scatter plots best when they start with messy real data and then refine their understanding through repeated exposure to varied examples.

What to Expect

Students will correctly construct scatter plots, identify association types by eye, and explain why scatter does not imply causation. They will also distinguish linear from nonlinear trends and recognize when data points fall outside expected patterns.

Watch Out for These Misconceptions

Common Misconception

During Pairs Plotting, watch for students who claim that taller height causes larger shoe size because the plot trends upward.

What to Teach Instead

Pause the class and ask each pair to brainstorm one other possible reason shoe size and height both increase with age, then share aloud to highlight that shared growth does not mean one causes the other.

Common Misconception

During Association Sorting, watch for students who place all curved patterns into the linear category.

What to Teach Instead

Hand each group a ruler and ask them to lay it across their curved plot; if points diverge from the ruler line, they must reclassify the association as nonlinear.

Common Misconception

During the Human Scatter Plot, watch for students who think no trend means the variables have no relation at all.

What to Teach Instead

Ask students to step back and observe whether the human points form any cluster or if they truly scatter randomly, prompting a quick vote by raised hands to make the idea visible to all.

Assessment Ideas

Exit Ticket

After Pairs Plotting, have each student write one sentence describing the association in their plotted data and one question they still have about their graph.

Quick Check

During Association Sorting, after groups place their plots into categories, ask each group to hold up their plot and call out the type of association while you tally responses on the board to check for consensus.

Discussion Prompt

After the Human Scatter Plot, show a pre-selected data point from Survey Scatter that lies far from the trend and ask, 'Is this point invalid, or does it tell us something important about the situation? Explain your reasoning in one sentence.'

Extensions & Scaffolding

• After Survey Scatter, challenge students to design a follow-up survey that might reveal a hidden nonlinear pattern.
• During Pairs Plotting, give struggling students a pre-drawn grid with labeled axes so they focus on plotting rather than setup.
• After the Human Scatter Plot, invite pairs to add a hypothetical point that would change the association from linear to nonlinear and explain their choice.

Key Vocabulary

Bivariate Data	Data that consists of two variables for each individual or event, allowing for the study of relationships between them.
Scatter Plot	A graph that uses dots to represent the values of two different variables, showing the relationship or association between them.
Association	The relationship between two variables in a scatter plot, which can be positive, negative, or nonexistent.
Linear Association	A relationship between two variables where the data points on a scatter plot tend to form a straight line.
Non-linear Association	A relationship between two variables where the data points on a scatter plot tend to follow a curved pattern.