Investigate Data Relationships

Overview

Students investigate a real-world bivariate dataset comparing height and arm span. They plot and interpret a scatter graph, using statistical language to describe direction, form, strength and outliers, then consider why association does not necessarily mean causation.

Learning intentions

• WALT identify and classify two variables in a bivariate dataset.
• WALT construct and label an accurate scatter graph.
• WALT describe an association using evidence from the graph.
• WALT distinguish between association and causation when interpreting data.

Success criteria

• I can identify the explanatory and response variables and choose sensible scales.
• I can plot points accurately, add a title, and label both axes with units.
• I can describe the direction, form and strength of an association.
• I can identify a possible outlier and explain why association does not prove causation.

Curriculum links

• Mathematics and Statistics — statistical thinking, reasoning and communication through investigation of data.
• Mathematics and Statistics — interpreting and communicating findings in context using evidence.
• Mathsteasers — higher-order thinking questions that challenge learners and deepen understanding.
• Mathsteasers / Alignment — relevant challenge connected to statistical learning and textbook content.

Lesson structure (50 minutes)

1. 0–5 min · Hook: association or coincidence. Teacher displays two contrasting scatter plots using the opening comparison slides and asks, “What might these graphs tell us—and what can’t they tell us?” Students silently notice patterns, then discuss with a partner using the words association, variable and evidence. Invite two or three responses without confirming conclusions yet.

2. 5–12 min · Build shared language. Teacher introduces bivariate data and models how to identify the explanatory variable and response variable, choose axes and scales, and describe direction, form and strength. Use the vocabulary and worked-example slides and briefly classify examples with the scatter plot correlation cards. Students match descriptions such as positive, negative, weak, strong, linear and non-linear to the displayed graphs, explaining their choices.

3. 12–17 min · Model plotting and questioning. Teacher models plotting a small height-and-arm-span dataset, including a clear title, labelled axes, units and sensible intervals; deliberately discusses whether an unusual point is an outlier. Students check the model against the plotting checklist on the scatter graph investigation worksheet and identify one feature that would make a graph difficult to interpret.

4. 17–34 min · Pair investigation. Teacher forms pairs or groups of three, distributes the scatter graph investigation worksheet, and directs students to plot the provided height and arm-span data. Circulate and ask: “Which variable belongs on each axis?”, “How did you choose your scale?”, and “What evidence supports your description?” Students record paired values, plot and label the graph, then answer questions about direction, form, strength, clusters and possible outliers. Students should use a ruler where appropriate and check one another’s points.

5. 34–44 min · Interpret and communicate. Teacher displays the discussion prompts using the investigation discussion slides and selects several pairs to share conclusions. Students give a concise evidence-based statement, for example: “There is a strong positive, approximately linear association because most points rise from left to right and lie fairly close to a straight trend.” Classmates ask whether the evidence supports the claim and suggest alternative explanations, including age, measurement variation or the sample used.

6. 44–50 min · Association versus causation and exit check. Teacher uses the causation and plenary slides to present the statement, “People with larger hands are better at mathematics,” and asks students to critique it. Students complete the final worksheet prompt: “The data show an association between height and arm span. Explain why this does not prove that height causes arm span to increase.” Collect worksheets or sample several responses as the exit assessment.

Resources

• the complete scatter graph teaching deck
• the scatter graph investigation worksheet
• the scatter plot correlation cards
• Rulers and pencils
• Calculators, if needed for checking measurements
• Board or projector
• Prepared bivariate height-and-arm-span dataset
• Coloured pens for highlighting an outlier or trend

Assessment

• During the card sort and modelling, listen for accurate use of variable, positive/negative, linear/non-linear and strength.
• Check graphs during pair work for correct axis choice, scales, plotting, labels, title and units; question students rather than correcting immediately.
• Use the final causation response to assess whether students can interpret in context and avoid claiming that association proves cause and effect.

Differentiation

• Provide a partially completed axis and a scale suggestion on selected copies of the scaffolded scatter graph investigation worksheet for students who need support.
• Pair students strategically and provide sentence starters: “The association is ___ because…”, “The possible outlier is…”, and “This does not prove causation because…”.
• Allow students with fine-motor or visual needs to use enlarged graph paper, a ruler guide, or a digital graphing tool; read instructions aloud and check understanding of key terms.
• Extend confident students by asking whether the sample is representative, how a different sample might change the association, and whether a line of best fit would be appropriate.