What students learn in AC9M8A02
This unit helps students build a clear, usable understanding of Graph linear relations on the Cartesian plane using digital tools.... 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: graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- recognising that in a table of values, if the first difference between consecutive values of the dependent variable is constant, then it is a linear relation graphing linear functions and relations of the form x\;=\;a,\;y\;=\;a,\;x\;\leq\;a,\;x\;>\;a,\;y\leq\;a,\;y>\;a on the Cartesian plane for known values of a
- 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: graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution
- E1: recognising that in a table of values, if the first difference between consecutive values of the dependent variable is constant, then it is a linear relation
- E2: graphing linear functions and relations of the form x\;=\;a,\;y\;=\;a,\;x\;\leq\;a,\;x\;>\;a,\;y\leq\;a,\;y>\;a on the Cartesian plane for known values of a
- E3: completing a table of values, plotting the resulting points on the Cartesian plane and determining whether the relationship is linear
- E4: graphing the linear relationship ax+b\;=\;c for given values of a, b and c and identifying from the graph where ax+b\; \;c
- E5: solving linear equations of the form ax+b\;=\;c and one-variable inequalities of the form ax+b\; \;c where a>0 using inverse operations and digital tools, and checking solutions by substitution
- E6: solving linear equations such as 3x+7\;=\;6x-9, representing these graphically, and verifying solutions by substitution
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
AC9M8A02 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 | AC9M8A02 — graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution |
| 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 Graph linear relations on the Cartesian plane using digital tools... and related outcomes. |
| United States | Common Core / NGSS | Grade 8 Common Core Mathematics/ELA closest topic match for Graph linear relations on the Cartesian plane using digital tools.... |
| England / UK | National Curriculum | Key Stage 3 / Year 8: closest programme-of-study match for Graph linear relations on the Cartesian plane using digital tools.... |
| 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 Graph linear relations on the Cartesian plane using digital tools.... |
| India | NCERT / CBSE | Class 8 closest NCERT/CBSE topic match for Graph linear relations on the Cartesian plane using digital tools.... |