Plotting Paired Data

Overview

Students build on prior knowledge of coordinates, scales and reading tables to create and interpret a scatter plot. Using a non-sensitive Aotearoa New Zealand context—daily screen time and hours of sleep—students investigate association without collecting personal data.

Learning intentions

• WALT identify explanatory and response variables in paired numerical data.
• WALT create an accurate scatter plot with a sensible scale, labelled axes and units.
• WALT describe the overall association using evidence from a graph.
• WALT explain that association does not prove causation.

Prior knowledge: Students should be able to read ordered pairs, use Cartesian axes, choose equal intervals on a number line, and calculate or compare numerical values.

Success criteria

• I can identify which variable may help explain the other and which variable is the response.
• I can plot each ordered pair accurately and label both axes with units.
• I can describe the direction, form and strength of an association using context.
• I can avoid claiming that one variable causes another without further evidence.

Curriculum links

• Explore data using a statistical enquiry process: explain the data source, present an appropriate visualisation and describe features in context.
• Interpret and communicate statistical information to support an informed judgement.
• Use mathematical concepts, representations and appropriate mathematical language.
• Develop the key competencies of thinking; using language, symbols and texts; and participating and contributing.

Lesson structure (60 minutes)

1. 0–5 min · Hook and prior knowledge. Open with the screen-time and sleep hook slide and ask, “What might we notice if people who use screens for longer tend to sleep for fewer hours?” Students silently predict, then identify what information would be needed; teacher stresses that no student shares personal data.

2. 5–15 min · Vocabulary and explicit modelling. Use the vocabulary and worked-example slides to define: paired data (two measurements belonging together), explanatory variable (the variable that may help explain or predict), response variable (the outcome measured), association (a pattern or relationship), positive association (both tend to increase), negative association (one tends to increase as the other decreases), and outlier (a value unlike the others). Teacher colour-codes explanatory data blue, response data green, the horizontal axis blue and vertical axis green, then models plotting (2, 8) and (5, 7). Students repeat the sentence frames: “The explanatory variable is ___ because ___.” “The response variable is ___.” “The graph shows a ___ association.”

3. 15–25 min · Guided practice. Display a small prepared data table from the worksheet: daily screen time in hours and sleep in hours. Teacher models choosing scales that include all values, use equal intervals and fill the graph space. Students complete the first three points on the scatter-plot practice worksheet, checking each ordered pair with a partner. Pause for a whole-class check: “Which value is read first?” and “Why must the axes include units?”

4. 25–42 min · Collaborative plotting and interpretation. In groups of four, students finish the scatter plot and interpretation questions on the scatter-plot practice worksheet. Assign roles: reader, plotter, checker and reporter. Students use a ruler and two colours, then discuss: direction, form, strength, clusters and any possible outlier. Each group prepares one evidence-based statement using: “Overall, there is a ___ association between ___ and ___; as ___ increases, ___ tends to ___.”

5. 42–52 min · Discussion: association and causation. Return to the association-versus-causation discussion slides. Groups decide whether each statement is supported: “More screen time causes less sleep”; “The data show a negative association”; “Other factors, such as homework, sport, stress or bedtime routines, may affect sleep.” Students justify one decision using the graph and explain why observational data cannot establish cause.

6. 52–60 min · Independent exit task and plenary. Students complete the final question on the independent exit task without help: identify the variables, plot two points on a mini-graph, and write one contextual description plus one limitation. Collect responses and ask two students to share a strong use of evidence.

Resources

• the complete scatter-plot teaching deck
• the scatter-plot practice worksheet
• Projector or interactive board
• Rulers, pencils and blue/green coloured pencils
• Prepared, anonymised screen-time and sleep data
• Graph paper or lined exercise books
• Visual word bank displayed beside the board

Assessment

• During modelling, ask students to show with fingers which variable belongs on each axis; scan for reversed variables and uneven scales.
• During group work, check one plotted point, axis labels, units and the accuracy of each group’s association statement.
• Exit task answer guidance: explanatory variable = screen time; response variable = sleep; points must match the ordered pairs; the likely pattern is a negative association; acceptable limitations include small or non-representative data, self-reporting, confounding variables and association not proving causation.

Differentiation

• Support ESOL learners with the colour-coded axes, icons, bilingual dictionaries or first-language discussion, a completed example and sentence frames. Pre-teach vocabulary orally and allow students to rehearse answers with a partner before writing.
• Provide a partially labelled graph, a scale-choice box and enlarged data tables for learners who need additional support. Read instructions aloud, give one instruction at a time and check understanding by asking students to demonstrate rather than repeat.
• Use a dyslexia-friendly worksheet: clear sans-serif font, minimum 12–14 point text, high contrast, generous spacing, short lines, uncluttered graphs and no unnecessary italics. Offer text-to-speech, audio instructions, coloured overlays and verbal responses where appropriate.
• For learners ready for challenge, ask them to compare two possible scales, identify a possible outlier or lurking variable, and explain how a follow-up investigation could improve the evidence without collecting sensitive personal information.

Extension

• Students write a short statistical conclusion for a non-specialist audience, including the graph evidence, a cautious association statement and two limitations.
• Students design a safe follow-up question using existing or fictional data and explain why it would not, by itself, prove causation.