What students learn in AC9M8N05
This unit helps students build a clear, usable understanding of Mathematical modelling to solve practical problems involving rational numbers and.... 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 rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- modelling situations involving weather and environmental contexts including temperature or sea depths by applying operations to positive and negative rational numbers; for example, involving average temperature increases and decreases modelling situations that involve percentage increases or decreases and explaining why it is an increase or decrease, such as mark-ups, discounts, Goods and Services Tax, changes in populations or recycling rates
- 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 rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model
- E1: modelling situations involving weather and environmental contexts including temperature or sea depths by applying operations to positive and negative rational numbers; for example, involving average temperature increases and decreases
- E2: modelling situations that involve percentage increases or decreases and explaining why it is an increase or decrease, such as mark-ups, discounts, Goods and Services Tax, changes in populations or recycling rates
- E3: modelling situations involving personal income tax, interpreting tax tables to determine income tax at various levels of income, including overall percentage of income allocated to tax
- E4: modelling situations involving percentage increase or decrease such as market trends, effects on population, or effects on the environment over extended time periods
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
AC9M8N05 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 | AC9M8N05 — use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model |
| Victoria | Victorian Curriculum F-10 | Year 8 Maths: closest match in Number. 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 rational numbers and... and related outcomes. |
| United States | Common Core / NGSS | Grade 8 Common Core Mathematics/ELA closest topic match for Mathematical modelling to solve practical problems involving rational numbers and.... |
| England / UK | National Curriculum | Key Stage 3 / Year 8: closest programme-of-study match for Mathematical modelling to solve practical problems involving rational numbers and.... |
| Canada | Provincial and territory curricula | Grade 8 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 rational numbers and.... |
| India | NCERT / CBSE | Class 8 closest NCERT/CBSE topic match for Mathematical modelling to solve practical problems involving rational numbers and.... |