What students learn in AC9M7N08
This unit helps students build a clear, usable understanding of Recognise, represent and solve problems involving ratios. 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, represent and solve problems involving ratios.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- using diagrams, physical or virtual materials to represent ratios, recognising that ratios express the quantitative relationship between 2 or more groups; for example, using counters or coloured beads to show the ratios 1:4 and 1:1:2 using fractions to solve ratio problems involving comparison of quantities and considering part-part and part-whole relations; for example, dividing a set into the ratio 1:2 by determining the number of parts as 3
- 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, represent and solve problems involving ratios
- E1: using diagrams, physical or virtual materials to represent ratios, recognising that ratios express the quantitative relationship between 2 or more groups; for example, using counters or coloured beads to show the ratios 1:4 and 1:1:2
- E2: using fractions to solve ratio problems involving comparison of quantities and considering part-part and part-whole relations; for example, dividing a set into the ratio 1:2 by determining the number of parts as 3
- E3: sharing quantities in a given ratio; for example, sharing an amount of money in a given ratio, such as sharing \$20 in the ratio 2:3
- E4: applying ratios to realistic and meaningful contexts; for example, mixing 500 millilitres of a liquid with a concentration of 1:4 means \frac15 concentrate and \frac45 water so, 0.2 of 500 millilitres is concentrate and 0.8 of 500 millilitres is water; interpreting results in 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
AC9M7N08 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 | AC9M7N08 — recognise, represent and solve problems involving ratios |
| Victoria | Victorian Curriculum F-10 | Year 7 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 Recognise, represent and solve problems involving ratios and related outcomes. |
| United States | Common Core / NGSS | Grade 7 Common Core Mathematics/ELA closest topic match for Recognise, represent and solve problems involving ratios. |
| England / UK | National Curriculum | Key Stage 3 / Year 7: closest programme-of-study match for Recognise, represent and solve problems involving ratios. |
| 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 Recognise, represent and solve problems involving ratios. |
| India | NCERT / CBSE | Class 7 closest NCERT/CBSE topic match for Recognise, represent and solve problems involving ratios. |