What students learn in AC9M7A04
This unit helps students build a clear, usable understanding of Relationships between variables represented in graphs of functions from authentic.... The goal is not to memorise one answer pattern. Students should be able to explain the idea, recognise it in a new example and apply it in a short practice or worksheet task.
- Start with the main idea: describe relationships between variables represented in graphs of functions from authentic data.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- using graphs to analyse a building’s electricity or gas usage over a period of time, the value of shares on a stock market, or the temperature during a day, interpreting and discussing the relationships they represent using travel graphs to compare the distance travelled to and from school, interpreting and discussing features of travel graphs such as the slope of lines and the meaning of horizontal line segments
- Finish with mixed questions so students must choose the correct strategy rather than copy the last example.
Curriculum coverage and elaborations
The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning but may not appear in the initial eight-question activity.
- Content description: describe relationships between variables represented in graphs of functions from authentic data
- E1: using graphs to analyse a building’s electricity or gas usage over a period of time, the value of shares on a stock market, or the temperature during a day, interpreting and discussing the relationships they represent
- E2: using travel graphs to compare the distance travelled to and from school, interpreting and discussing features of travel graphs such as the slope of lines and the meaning of horizontal line segments
- E3: telling the story behind what is being represented in graphs of functions; for example, graphs representing pouring rates or distance versus time
- E4: exploring how functions are used in machine learning to model relationships; for example, in linear regression models, a linear function is used to map input features to predictions
- E5: using graphs of evaporation rates to explore and discuss First Nations Australians’ methods of water resource management (teaching context)
How to use this unit
Read the topic guide, use the teacher slide for instruction, then complete the Worksheet, Practice and Test. These three activities use the same eight-question unit bank.
Teacher resource
AC9M7A04 teacher slide
Use this one-page PDF to introduce the key idea, vocabulary and teaching sequence before students begin the activities.
Open teacher slide (PDF)Common mistakes to watch for
- Rushing to a rule before checking the concrete model, drawing or number sentence.
- Using the correct answer once but not being able to explain why it works.
- Mixing up similar vocabulary such as more/less, before/after, longer/shorter or equal groups/sharing.
International curriculum mapping
This table gives closest-topic mapping for search and planning. The Australian Curriculum code is exact; overseas entries are broad equivalents because each jurisdiction structures outcomes differently.
| Region | Curriculum | Closest mapping |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M7A04 — describe relationships between variables represented in graphs of functions from authentic data |
| Victoria | Victorian Curriculum F-10 | Year 7 Maths: closest match in Algebra. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 4 Maths: closest content focus for Relationships between variables represented in graphs of functions from authentic... and related outcomes. |
| United States | Common Core / NGSS | Grade 7 Common Core Mathematics/ELA closest topic match for Relationships between variables represented in graphs of functions from authentic.... |
| England / UK | National Curriculum | Key Stage 3 / Year 7: closest programme-of-study match for Relationships between variables represented in graphs of functions from authentic.... |
| Canada | Provincial and territory curricula | Grade 7 closest topic match. Canada varies by province, so use this as a broad Ontario/BC-style learning outcome reference. |
| New Zealand | New Zealand Curriculum | Level 4 Maths: closest achievement-objective topic for Relationships between variables represented in graphs of functions from authentic.... |
| India | NCERT / CBSE | Class 7 closest NCERT/CBSE topic match for Relationships between variables represented in graphs of functions from authentic.... |