What students learn in AC9M10A03
This unit helps students build a clear, usable understanding of The connection between algebraic and graphical representations of exponential relations.... 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: recognise the connection between algebraic and graphical representations of exponential relations and solve related exponential equations, using digital tools where appropriate.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- recognising that in a table of values, if the ratio between consecutive values of the dependent variable is constant, then it is an exponential relation investigating the links between algebraic and graphical representations of exponential functions using graphing software
- 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: recognise the connection between algebraic and graphical representations of exponential relations and solve related exponential equations, using digital tools where appropriate
- E1: recognising that in a table of values, if the ratio between consecutive values of the dependent variable is constant, then it is an exponential relation
- E2: investigating the links between algebraic and graphical representations of exponential functions using graphing software
- E3: using digital tools with symbolic manipulation functionality to systematically explore exponential relations
- E4: investigating First Nations Australian Ranger groups’ and other groups’ programs that attempt to eradicate feral animals for survival of native animals on Country/Place, exploring the competition between feral and native animals and their impact on natural resources by formulating exponential equations for population growth for each animal species (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
AC9M10A03 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 | AC9M10A03 — recognise the connection between algebraic and graphical representations of exponential relations and solve related exponential equations, using digital tools where appropriate |
| Victoria | Victorian Curriculum F-10 | Year 10 Maths: closest match in Algebra. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 5 Maths: closest content focus for The connection between algebraic and graphical representations of exponential relations... and related outcomes. |
| United States | Common Core / NGSS | Grade 10 Common Core Mathematics/ELA closest topic match for The connection between algebraic and graphical representations of exponential relations.... |
| England / UK | National Curriculum | Key Stage 4 / Year 10: closest programme-of-study match for The connection between algebraic and graphical representations of exponential relations.... |
| Canada | Provincial and territory curricula | Grade 10 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 5 Maths: closest achievement-objective topic for The connection between algebraic and graphical representations of exponential relations.... |
| India | NCERT / CBSE | Class 10 closest NCERT/CBSE topic match for The connection between algebraic and graphical representations of exponential relations.... |