Scatter Graph Relationships

Overview

In this 45-minute lesson, students plot paired numerical data on scatter graphs and interpret the relationship between the variables. They build on prior learning about axes, scales and reading graphs, then use mathematical evidence to describe positive, negative or no association, identify clusters and distinguish association from causation.

Learning intentions

• WALT plot paired numerical data accurately on a scatter graph.
• WALT describe positive, negative and no association.
• WALT identify clusters and use data to support a statement.
• WALT explain why an association does not necessarily prove causation.

Success criteria

• I can label axes, choose suitable scales and plot paired data correctly.
• I can describe the overall association shown by a scatter graph.
• I can identify a cluster or unusual point and refer to evidence from the graph.
• I can explain that two variables being linked does not prove that one caused the other.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking and challenge through non-routine data questions.
• Mathematics and Statistics — Mathsteasers / Alignment: applying graphing and data knowledge to relevant mathematical challenges.
• Mathematics and Statistics — Additional resources for advanced learners: reasoning, explanation and justification using data.
• Mathematical and Statistical Thinking: communicating findings, noticing patterns, questioning conclusions and recognising the limits of data.

Lesson structure (45 minutes)

1. 0–5 min · Hook and prediction. Teacher displays the question, “Do taller people always have larger feet?” using the opening question and paired-data image, and invites students to predict what a graph might show. Students think independently, discuss with a partner and share reasons, using “I predict… because…”.

2. 5–12 min · Explicit teaching. Teacher uses the graphing and association slides to model plotting paired data, explaining that the first value in each pair goes on the horizontal axis and the second on the vertical axis. Model a suitable scale, labelled axes and accurate plotting, then introduce the terms positive association, negative association, no association and cluster. Students help identify the direction of the modelled pattern and explain how the plotted points provide evidence.

3. 12–27 min · Paired graphing investigation. Teacher distributes the paired-data scatter graph investigation to pairs and reminds students to use a ruler and check each point against the table. Students plot two small data sets, such as weekly exercise time and resting pulse rate, and hours of sunshine and ice-block sales. They label both axes, add an appropriate title and write one sentence describing each relationship.

4. 27–35 min · Reasoning and causation. Teacher returns to the comparison and causation discussion slides and presents statements such as, “There is an association between sunshine and ice-block sales, so sunshine causes every person to buy an ice block.” Students decide whether each statement is justified, then improve it by using cautious language such as “The data suggests…” or “These variables may be related…”. Discuss other possible factors, including temperature, weekends, holidays or location.

5. 35–41 min · Cluster talk and peer check. Teacher asks pairs to compare graphs and locate a cluster, gap or point that does not fit the general pattern. Students use the checklist on the paired-data scatter graph investigation to peer-check plotting accuracy, axis labels, scale, association statement and causation explanation. Each pair shares one claim and points to the graph evidence supporting it.

6. 41–45 min · Plenary and exit response. Teacher shows the final challenge and reflection slide and asks, “A graph shows that students who read more often tend to have larger vocabularies. Does reading more definitely cause the larger vocabulary?” Students complete the final response on the worksheet: describe the association, identify one possible additional factor and explain why association is not proof of causation. Invite two or three responses before collecting the work.

Resources

• the Scatter Graph Relationships slide deck
• the paired-data scatter graph investigation
• Rulers and sharpened pencils
• Graph paper or exercise books
• Data display or whiteboard
• Projector or interactive whiteboard
• Highlighters for marking clusters and unusual points

Assessment

• Observe whether students place ordered pairs correctly, use scales consistently and label both axes.
• During partner discussion, listen for accurate use of positive, negative, no association and cluster; prompt students to refer to plotted evidence rather than impressions.
• Collect the worksheet and check the final explanation distinguishes association from causation and suggests a possible additional variable.

Differentiation

• Support students by providing a partially labelled graph, a suggested scale and a plotting demonstration kept visible on the board. Seat students strategically and pair a confident reader with a learner who needs language support.
• Provide sentence starters: “The graph shows a ___ association because…”, “Most points are clustered around…”, and “This does not prove causation because…”.
• For EAL learners, combine the terms positive, negative, no association and cluster with simple visual examples and allow oral rehearsal before writing.
• Challenge early finishers to suggest a third variable that could affect each relationship, or to design a new paired-data question where an apparent association might be misleading.