What students learn in AC9M7M06
This unit helps students build a clear, usable understanding of Mathematical modelling to solve practical problems involving ratios; formulate problems.... 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 practical problems involving ratios; formulate problems, interpret and communicate solutions in terms of the situation, justifying choices made about the representation.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- using fractions to model and solve ratio problems involving comparison of quantities, and considering part-part and part-whole relations modelling and solving practical problems involving ratios of length, capacity or mass, such as in construction, design, food or textile production; for example, mixing concrete, the golden ratio in design, mixing a salad dressing
- 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 practical problems involving ratios; formulate problems, interpret and communicate solutions in terms of the situation, justifying choices made about the representation
- E1: using fractions to model and solve ratio problems involving comparison of quantities, and considering part-part and part-whole relations
- E2: modelling and solving practical problems involving ratios of length, capacity or mass, such as in construction, design, food or textile production; for example, mixing concrete, the golden ratio in design, mixing a salad dressing
- E3: modelling the situation using manipulatives, diagrams and/or mathematical discussion; for example, mixing primary colours in a variety of ratios to investigate how new colours are created and the strength of those colours
- E4: investigating commercialised substances founded on First Nations Australians’ knowledges of substances including pharmaceuticals and toxins, understanding how ratios are used in their development (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
AC9M7M06 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 | AC9M7M06 — use mathematical modelling to solve practical problems involving ratios; formulate problems, interpret and communicate solutions in terms of the situation, justifying choices made about the representation |
| Victoria | Victorian Curriculum F-10 | Year 7 Maths: closest match in Measurement. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 4 Maths: closest content focus for Mathematical modelling to solve practical problems involving ratios; formulate problems... and related outcomes. |
| United States | Common Core / NGSS | Grade 7 Common Core Mathematics/ELA closest topic match for Mathematical modelling to solve practical problems involving ratios; formulate problems.... |
| England / UK | National Curriculum | Key Stage 3 / Year 7: closest programme-of-study match for Mathematical modelling to solve practical problems involving ratios; formulate problems.... |
| 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 Mathematical modelling to solve practical problems involving ratios; formulate problems.... |
| India | NCERT / CBSE | Class 7 closest NCERT/CBSE topic match for Mathematical modelling to solve practical problems involving ratios; formulate problems.... |