What students learn in AC9M7N04
This unit helps students build a clear, usable understanding of Find equivalent representations of rational numbers and represent rational numbers.... 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: find equivalent representations of rational numbers and represent rational numbers on a number line.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- investigating equivalence of fractions using common multiples and a fraction wall, diagrams or a number line to show that a fraction such as \frac23 is equivalent to \frac46 and \frac69 and therefore \frac23<\frac56 expressing a fraction in simplest form using common divisors
- 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: find equivalent representations of rational numbers and represent rational numbers on a number line
- E1: investigating equivalence of fractions using common multiples and a fraction wall, diagrams or a number line to show that a fraction such as \frac23 is equivalent to \frac46 and \frac69 and therefore \frac23<\frac56
- E2: expressing a fraction in simplest form using common divisors
- E3: applying and explaining the equivalence between fraction, decimal and percentage representations of rational numbers; for example, 16\%, 0.16, \frac{16}{100} and \frac4{25}, using manipulatives, number lines or diagrams
- E4: representing positive and negative fractions and mixed numerals on various intervals of the real number line, including intervals that are not symmetrical about zero
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
AC9M7N04 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 | AC9M7N04 — find equivalent representations of rational numbers and represent rational numbers on a number line |
| 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 Find equivalent representations of rational numbers and represent rational numbers... and related outcomes. |
| United States | Common Core / NGSS | Grade 7 Common Core Mathematics/ELA closest topic match for Find equivalent representations of rational numbers and represent rational numbers.... |
| England / UK | National Curriculum | Key Stage 3 / Year 7: closest programme-of-study match for Find equivalent representations of rational numbers and represent rational numbers.... |
| 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 Find equivalent representations of rational numbers and represent rational numbers.... |
| India | NCERT / CBSE | Class 7 closest NCERT/CBSE topic match for Find equivalent representations of rational numbers and represent rational numbers.... |