What students learn in AC9M8A01
This unit helps students build a clear, usable understanding of Create, expand, factorise, rearrange and simplify linear expressions, applying the.... 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: create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- rearranging and simplifying linear expressions involving variables with integer coefficients and constants; using manipulatives such as algebra tiles to support calculations; for example, using manipulatives to demonstrate that 2x+4\;=\;2(x+2),\;3(a-b)=3a -3b, or 5(m+2n)+3m-4n\;=\;5m+10n+3m-4n\;=\;8m+6n demonstrating the relationship between factorising and expanding linear expressions using manipulatives, such as algebra tiles or area models, and describing with mathematical language
- 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: create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties
- E1: rearranging and simplifying linear expressions involving variables with integer coefficients and constants; using manipulatives such as algebra tiles to support calculations; for example, using manipulatives to demonstrate that 2x+4\;=\;2(x+2),\;3(a-b)=3a -3b, or 5(m+2n)+3m-4n\;=\;5m+10n+3m-4n\;=\;8m+6n
- E2: demonstrating the relationship between factorising and expanding linear expressions using manipulatives, such as algebra tiles or area models, and describing with mathematical language
- E3: using the distributive, associative, commutative, identity and inverse properties to expand and factorise algebraic expressions using strategies such as the area model
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
AC9M8A01 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 | AC9M8A01 — create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties |
| Victoria | Victorian Curriculum F-10 | Year 8 Maths: closest match in Algebra. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 4 Maths: closest content focus for Create, expand, factorise, rearrange and simplify linear expressions, applying the... and related outcomes. |
| United States | Common Core / NGSS | Grade 8 Common Core Mathematics/ELA closest topic match for Create, expand, factorise, rearrange and simplify linear expressions, applying the.... |
| England / UK | National Curriculum | Key Stage 3 / Year 8: closest programme-of-study match for Create, expand, factorise, rearrange and simplify linear expressions, applying the.... |
| 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 Create, expand, factorise, rearrange and simplify linear expressions, applying the.... |
| India | NCERT / CBSE | Class 8 closest NCERT/CBSE topic match for Create, expand, factorise, rearrange and simplify linear expressions, applying the.... |