- explain the central idea: Construct and interpret scatterplots, describing association by direction, strength and linearity without confusing correlation with causation.
- choose and apply an appropriate method without relying on keyword matching
- check results using units, substitution, estimation, a second representation or contextual reasonableness
- justify a conclusion and communicate limitations where the context requires them
Year 10 Mathematics · AC9M10ST03
Scatterplots and Bivariate Association
Describe association using direction, strength and form, then interpret it cautiously: a scatterplot can reveal a pattern but cannot by itself prove causation
Ready to project and teach
Learning goalsSay it simply
Key conceptTeach from the board
A scatterplot displays paired numerical data. Describe direction (positive/negative/none), strength (weak/moderate/strong) and form (linear/nonlinear). Then mention outliers/clusters and context.
Positive
As x increases, y tends to increase.
Negative
As x increases, y tends to decrease.
Strength
Tighter clustering around a simple trend = stronger association.
Prediction
Interpolation is generally safer than extrapolation; association ≠ causation.
Worked examplesWe do
Worked examples
AC9M10ST03 - Scatterplots and Bivariate Association
Example 1
Positive As x increases, y tends to increase.
Example 2
Negative As x increases, y tends to decrease.
Example 3
Strength Tighter clustering around a simple trend = stronger association.
Example 4
Prediction Interpolation is generally safer than extrapolation; association ≠ causation.
Curriculum examplesCopied content
Australian Curriculum: AC9M10ST03 — Year 10 Statistics. Construct and interpret scatterplots, describing association by direction, strength and linearity without confusing correlation with causation.
Victoria: VC2M10ST02 — Level 10 Statistics
NSW: Stage 5 Core — Data classification, visualisation and analysis; Path — Data analysis and statistical enquiry
Alignment explanation: The explicit teaching and worked examples address the Australian Curriculum concept directly. The Victorian mapping follows the current Version 2.0 descriptor structure; where Victoria combines or extends content, that difference is stated rather than hidden. NSW uses a Stage 5 Core–Paths structure, so this page maps to the relevant content group(s) and Working mathematically processes instead of inventing a Year 10 one-to-one code.
| Lesson component | Australian Curriculum | Victoria | NSW |
|---|---|---|---|
| Explicit concept teaching and worked examples | AC9M10ST03 | VC2M10ST02 — Level 10 Statistics | Stage 5 Core — Data classification, visualisation and analysis; Path — Data analysis and statistical enquiry |
| Guided and independent practice | Builds fluency and application for AC9M10ST03 | Practises the mapped Level 10/10A knowledge as applicable | Practises the mapped Stage 5 Core/Path content |
| Reasoning and assessment tasks | Applies reasoning/problem solving in the descriptor context | Supports Victorian reasoning and modelling expectations | Embeds Working mathematically: reasoning, problem solving and communication |
Australian Curriculum elaborations
AC9M10ST03: construct scatterplots and comment on association between 2 numerical variables in terms of strength, direction and linearity.
- E1: distinguish association from cause/effect in health, species diversity, climate contexts. Example 5.
- E2: make/justify/critique association claims in climate, migration, shopping/social media. Examples 1–7.
- E3: use line of good fit informally and discuss prediction reliability. Examples 6–7.
- E4: explore scatterplots/association in data science and machine learning. Example 8.
- E5: investigate AI forecasting based on correlation and limitations around causality/context/ethics. Example 9.
- E6: investigate paired variables relating to spear throwers used by First Peoples of Australia using scatterplots/comparison. Example 10.
Questions and answersWith answers
- Define positive association.
- y tends to increase as x increases.
- What does strong association mean visually?
- Points cluster closely around the trend.
- Can a curved pattern be associated?
- Yes; it may be strong but nonlinear.
Practice and reviewReady for practice
- Saying correlation proves causation.
- Describing only direction and omitting strength/form.
- Calling a nonlinear relationship “no association” because it is not straight.
- Extrapolating far beyond observed data.
- Deleting outliers automatically.
Curriculum alignmentStart here
- explain the central idea: Construct and interpret scatterplots, describing association by direction, strength and linearity without confusing correlation with causation.
- choose and apply an appropriate method without relying on keyword matching
- check results using units, substitution, estimation, a second representation or contextual reasonableness
- justify a conclusion and communicate limitations where the context requires them
- Australian Curriculum Version 9 — ACARA
- Victorian Curriculum Mathematics Version 2.0 — VCAA
- NSW Mathematics K–10 Syllabus (2022) — NSW Curriculum/NESA
Official wording is paraphrased on SkillrHub; use the linked curriculum sites as the source of record.
Other curriculum comparisons retained
US CCSS HSS-ID.B.6; UK GCSE scatter graphs/correlation; NSW Stage 5 and Victorian Level 10 bivariate statistics; comparable Canadian/NZ association analysis.
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