Exploring Scattergraphs

Overview

This 60-minute lesson introduces Year 11 students to scattergraphs, focusing on interpreting relationships between two variables using scatterplots. The lesson aligns closely with the New Zealand Curriculum Refresh for Mathematics & Statistics, emphasizing statistical investigation, data visualisation, and informal inference about relationships in multivariate data.

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Learning Objectives

By the end of the lesson, students will be able to:

• Construct and interpret scattergraphs from given or collected bivariate data.
• Identify features such as clusters, gaps, outliers, and general trends.
• Draw and use a line of best fit informally to make predictions.
• Communicate findings with reference to the variables and context.
• Understand limitations of scattergraphs and reflect on data quality.

NZ Curriculum References

• Statistics strand (Year 11) – Investigate multivariate datasets using summary and relationship situations through posing investigative questions, planning data collection, visualisation, analysis including lines of best fit, and drawing informal inferences.
• Statistical literacy – Critically evaluating data visualisations to assess correctness and possible misrepresentations.
• Development of key competencies: Thinking (to identify patterns and relationships), Using language, symbols, and texts (interpreting graphs), and Relating to others (collaborating and discussing findings).

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Lesson Sequence (60 minutes)

1. Getting Started (10 mins)

• Hook / Starter: Show an engaging real-life scattergraph (e.g., relationship between hours studied and test scores). Ask students to note what they observe.
• Discussion: Introduce key terminology: scattergraph, variables (explanatory and response), clusters, gaps, outliers, and line of best fit.
• Learning Intentions: Share the objectives focusing on interpreting relationships in bivariate data using scattergraphs.

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2. Working (40 mins)

a) Constructing Scattergraphs (15 mins)

• Activity: Provide each student with a simple bivariate dataset relating two numeric variables relevant to their lives (e.g., shoe size and height, or screen time and hours of sleep).
• Using graph paper or digital tools (like GeoGebra or a graphing app), guide students to plot points carefully and label axes with correct variable names and units.
• Highlight the importance of scale and accuracy.

b) Analysing Scattergraphs (15 mins)

• In pairs, students examine pre-made scattergraphs with different patterns (positive, negative, no correlation).
• Tasks include identifying clusters, outliers, and describing the general trend (increasing, decreasing, or no relationship).
• Teacher models drawing an informal "line of best fit" by eye and using it to predict values.

c) Informal Inference and Reflection (10 mins)

• Class discussion: What can scattergraphs tell us about real-world relationships? What are the limitations?
• Highlight that correlation does not imply causation. Consider potential misleading interpretations and errors in data.
• Connect to the Statistical Enquiry Cycle: how posing questions and collecting good data impacts findings.

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3. Connecting and Reflecting (10 mins)

• Mini-Assessment: Students individually answer an investigative question based on a scattergraph (e.g., “Describe the relationship shown and make an informal prediction for a given point”).
• Share answers and discuss different interpretations.
• Encourage students to self-assess their understanding and note any further questions.
• Preview next steps: More formal methods of lines of best fit and statistical measures (e.g., correlation coefficient).

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Assessment & Feedback

• Observe pairs during graph analysis for use of appropriate vocabulary and reasoning.
• Evaluate mini-assessment responses for clear communication referencing the data and context.
• Provide constructive oral feedback encouraging deeper thinking about data quality and variability.

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Resources & Materials

• Sample datasets related to student interests.
• Graph paper and rulers or digital graphing tools (recommended).
• Pre-made scattergraph examples with varied relationships.
• Teacher’s visualiser or whiteboard for demonstration.

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Additional Teaching Tips & Innovations

• Use Digital Tools: Leverage online graphing software or spreadsheets to allow easy plotting and manipulation, helping visual learners.
• Contextualised Data: Use data linked to current student contexts or cross-curricular themes (e.g., science, health).
• Interactive Group Work: Foster group discussions where students question and compare each other’s interpretations to build robust understanding and critical thinking.
• Ethical Considerations: Briefly touch on how data collection methods and sample selection can impact scattergraphs and conclusions drawn, linking to data as taonga (treasure) respecting tikanga.

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This lesson plan embodies the spirit of Te Mātaiaho by promoting mathematical thinking, reasoning, and communication through engaging, relevant statistical investigation, and aligns tightly with Year 11 expectations in the New Zealand Curriculum Refresh .