- explain the central idea: Construct two-way tables and use counts and proportions to investigate possible relationships between categorical variables.
- 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 · AC9M10ST04
Two-Way Tables and Categorical Relationships
Two-way tables cross-classify two categorical variables. Compare conditional percentages within groups, not just raw counts, before claiming an association
Ready to project and teach
Learning goalsSay it simply
Key conceptTeach from the board
A two-way table shows counts for combinations of two categorical variables plus row/column totals. If group sizes differ, compare proportions/percentages using the appropriate group total as denominator.
Cell
Count satisfying both row and column categories.
Row percentage
cell ÷ row total ×100%.
Column percentage
cell ÷ column total ×100%.
Association clue
Conditional percentages differ meaningfully across groups; do not infer causation automatically.
Worked examplesWe do
Worked examples
AC9M10ST04 - Two-Way Tables and Categorical Relationships
Example 1
Cell Count satisfying both row and column categories.
Example 2
Row percentage cell ÷ row total ×100%.
Example 3
Column percentage cell ÷ column total ×100%.
Example 4
Association clue Conditional percentages differ meaningfully across groups; do not infer causation automatically.
Curriculum examplesCopied content
Australian Curriculum: AC9M10ST04 — Year 10 Statistics. Construct two-way tables and use counts and proportions to investigate possible relationships between categorical variables.
Victoria: VC2M10ST03 — 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 | AC9M10ST04 | VC2M10ST03 — 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 AC9M10ST04 | 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
AC9M10ST04: construct two-way tables and discuss possible relationship between categorical variables.
- E1: compare Likert responses across two respondent categories such as junior/senior. Examples 1,2,6.
- E2: record data and use percentages/proportions to identify patterns/associations. Examples 2–5.
- E3: conduct a school litter survey considering categorical relationships such as canteen specials/day or hot weather/litter type. Examples 7–8.
Questions and answersWith answers
- If 24/40 juniors agree, find percentage.
- 60%.
- If 45/75 seniors agree, compare with Q1.
- 45/75=60%; same.
- Which denominator answers “given senior”?
- Total number of seniors.
Practice and reviewReady for practice
- Comparing raw counts when group sizes differ.
- Using grand total instead of conditional row/column total.
- Forgetting totals or producing inconsistent totals.
- Changing category definitions after looking at results.
- Claiming a two-way association proves causation.
Curriculum alignmentStart here
- explain the central idea: Construct two-way tables and use counts and proportions to investigate possible relationships between categorical variables.
- 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 closest HSS-ID.B.5; UK GCSE two-way tables/conditional frequencies; NSW Stage 5 and Victorian Level 10 categorical statistics; comparable Canadian/NZ data strands.
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