What students learn in AC9M9A05
This unit helps students build a clear, usable understanding of Mathematical modelling to solve applied problems involving change including financial.... 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 change including financial contexts; formulate problems, choosing to use either linear or quadratic functions; interpret solutions in terms of the situation; evaluate the model and report methods and findings.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- modelling practical contexts using linear functions such as cooking times that include resting or cooling times, or water leakage from water tanks, using tables and graphs or digital tools and algebraically modelling measurement situations and determining the perimeter and areas of rectangles where the length, l, of the rectangle is a linear function of its width, w; for example, l=w,\;l=w+5,\;l=3w,\;l=2w+7
- 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 change including financial contexts; formulate problems, choosing to use either linear or quadratic functions; interpret solutions in terms of the situation; evaluate the model and report methods and findings
- E1: modelling practical contexts using linear functions such as cooking times that include resting or cooling times, or water leakage from water tanks, using tables and graphs or digital tools and algebraically
- E2: modelling measurement situations and determining the perimeter and areas of rectangles where the length, l, of the rectangle is a linear function of its width, w; for example, l=w,\;l=w+5,\;l=3w,\;l=2w+7
- E3: modelling practical contexts using simple quadratic functions, tables and graphs (hand drawn or using digital tools) and algebraically, interpreting features of the graphs such as the turning point and intercepts in context; for example, area, paths of projectiles, parabolic mirrors, satellite dishes
- E4: modelling and solving problems involving financial contexts using linear functions; for example, combinations of purchases of different items when they have a set amount of money to spend, profit/loss situations and trade quotes involving call out fees
- E5: modelling situations involving change; for example, change in daily temperature during the ski season, fluctuation of speed above and below the speed limit, acceleration and deceleration of a car coming to and moving off from a set of traffic lights
- E6: modelling the hunting techniques of First Nations Australians using quadratic functions and exploring the effect of increasing the number of hunters to catch more prey (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
AC9M9A05 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 | AC9M9A05 — use mathematical modelling to solve applied problems involving change including financial contexts; formulate problems, choosing to use either linear or quadratic functions; interpret solutions in terms of the situation; evaluate the model and report methods and findings |
| Victoria | Victorian Curriculum F-10 | Year 9 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 change including financial... and related outcomes. |
| United States | Common Core / NGSS | Grade 9 Common Core Mathematics/ELA closest topic match for Mathematical modelling to solve applied problems involving change including financial.... |
| England / UK | National Curriculum | Key Stage 3 / Year 9: closest programme-of-study match for Mathematical modelling to solve applied problems involving change including financial.... |
| Canada | Provincial and territory curricula | Grade 9 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 change including financial.... |
| India | NCERT / CBSE | Class 9 closest NCERT/CBSE topic match for Mathematical modelling to solve applied problems involving change including financial.... |