What students learn in AC9M10A04
This unit helps students build a clear, usable understanding of Mathematical modelling to solve applied problems involving growth and decay.... 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: use mathematical modelling to solve applied problems involving growth and decay, including financial contexts; formulate problems, choosing to apply linear, quadratic or exponential models; interpret solutions in terms of the situation; evaluate and modify models as necessary and report assumptions, methods and findings.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- modelling situations and choosing between linear, quadratic and exponential models by representing relationships in a table of values and recognising that linear functions have constant first differences, quadratic functions have constant second differences and exponential functions have a constant ratio between consecutive values of the dependent variable modelling situations involving exponential growth and decay, and contrasting this with linear growth or decay; for example, situations involving constant percentage change and constant ratio; determining doubling time and half-life and approximate intervals for which the values of the model lie within a given range
- 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: use mathematical modelling to solve applied problems involving growth and decay, including financial contexts; formulate problems, choosing to apply linear, quadratic or exponential models; interpret solutions in terms of the situation; evaluate and modify models as necessary and report assumptions, methods and findings
- E1: modelling situations and choosing between linear, quadratic and exponential models by representing relationships in a table of values and recognising that linear functions have constant first differences, quadratic functions have constant second differences and exponential functions have a constant ratio between consecutive values of the dependent variable
- E2: modelling situations involving exponential growth and decay, and contrasting this with linear growth or decay; for example, situations involving constant percentage change and constant ratio; determining doubling time and half-life and approximate intervals for which the values of the model lie within a given range
- E3: modelling situations that involve working with authentic information, data and interest rates to calculate compound interest and solve related problems
- E4: modelling and investigating how exponential equations are used in carbon dating to estimate the age of First Nations Australians’ artefacts or material culture (teaching context)
- E5: modelling and formulating situations involving population growths of native animals on Country/Place with varying reproductive behaviour, using exponential equations and critiquing their applicability to real-world situations
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
AC9M10A04 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 | AC9M10A04 — use mathematical modelling to solve applied problems involving growth and decay, including financial contexts; formulate problems, choosing to apply linear, quadratic or exponential models; interpret solutions in terms of the situation; evaluate and modify models as necessary and report assumptions, methods and findings |
| 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 Mathematical modelling to solve applied problems involving growth and decay... and related outcomes. |
| United States | Common Core / NGSS | Grade 10 Common Core Mathematics/ELA closest topic match for Mathematical modelling to solve applied problems involving growth and decay.... |
| England / UK | National Curriculum | Key Stage 4 / Year 10: closest programme-of-study match for Mathematical modelling to solve applied problems involving growth and decay.... |
| 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 Mathematical modelling to solve applied problems involving growth and decay.... |
| India | NCERT / CBSE | Class 10 closest NCERT/CBSE topic match for Mathematical modelling to solve applied problems involving growth and decay.... |