What students learn in AC9M8M05
This unit helps students build a clear, usable understanding of And use rates to solve problems involving the comparison of.... 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 and use rates to solve problems involving the comparison of 2 related quantities of different units of measure.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- identifying examples of rates in the real world, including constant rates, rate of pay, cost per kilogram, recipes, simple interest and average rates applying rates to solve problems involving the conversion between different units of measure; for example, using a conversion rate to convert distances from miles into kilometres; using currency exchange rates to determine the price of items
- 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 and use rates to solve problems involving the comparison of 2 related quantities of different units of measure
- E1: identifying examples of rates in the real world, including constant rates, rate of pay, cost per kilogram, recipes, simple interest and average rates
- E2: applying rates to solve problems involving the conversion between different units of measure; for example, using a conversion rate to convert distances from miles into kilometres; using currency exchange rates to determine the price of items
- E3: applying rates to calculate solutions to problems in different contexts; for example, required run rates in cricket, dilution of concentrated chemicals and comparing the petrol consumption rates of different vehicles
- E4: using taxation tables to calculate an individual's annual income tax
- E5: investigating the application of rates in First Nation Australians’ land management practices, including the rate of fire spread under different environmental conditions such as fuel types, wind speed, temperature and relative humidity; the conservation of water by First Nations Australians by estimating rates of water evaporation based on surface area and climatic conditions (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
AC9M8M05 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 | AC9M8M05 — recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure |
| Victoria | Victorian Curriculum F-10 | Year 8 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 And use rates to solve problems involving the comparison of... and related outcomes. |
| United States | Common Core / NGSS | Grade 8 Common Core Mathematics/ELA closest topic match for And use rates to solve problems involving the comparison of.... |
| England / UK | National Curriculum | Key Stage 3 / Year 8: closest programme-of-study match for And use rates to solve problems involving the comparison of.... |
| 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 And use rates to solve problems involving the comparison of.... |
| India | NCERT / CBSE | Class 8 closest NCERT/CBSE topic match for And use rates to solve problems involving the comparison of.... |