What students learn in AC9M10A02
This unit helps students build a clear, usable understanding of Solve linear inequalities and simultaneous linear equations in 2 variables.... 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: solve linear inequalities and simultaneous linear equations in 2 variables; interpret solutions graphically and communicate solutions in terms of the situation.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- investigating situations involving linear equations in context, such as multiple quotes for a job, or profit and loss; solving the equations graphically, giving solutions in everyday language, such as “break-even point” or “point to change providers” for the job describing the solution of simultaneous equations within the context of the situation
- 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: solve linear inequalities and simultaneous linear equations in 2 variables; interpret solutions graphically and communicate solutions in terms of the situation
- E1: investigating situations involving linear equations in context, such as multiple quotes for a job, or profit and loss; solving the equations graphically, giving solutions in everyday language, such as “break-even point” or “point to change providers” for the job
- E2: describing the solution of simultaneous equations within the context of the situation
- E3: graphing regions corresponding to inequalities in the Cartesian plane; for example, graphing 2x+3y<24 and verifying using a test point such as (0, 0)
- E4: identifying all the combinations of trips to the movies, each costing \$12, and ice-skating sessions, each costing \$21, as the integer solutions for an entertainment budget of up to \$150 for the school holidays; expressing algebraically as 12m+21s\leq150
- E5: testing when a circle of a specified radius has a corresponding area greater than a given value, or whether a point satisfies an inequality; for example, whether the point (3, 5) satisfies 2y<x^2
- E6: investigating the strategies inherent in First Nations Australian children’s instructive games; for example, Weme from the Warlpiri Peoples of central Australia, and their connection to strategies to solve simultaneous linear equations in 2 variables (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
AC9M10A02 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 | AC9M10A02 — solve linear inequalities and simultaneous linear equations in 2 variables; interpret solutions graphically and communicate solutions in terms of the situation |
| Victoria | Victorian Curriculum F-10 | Year 10 Maths: closest match in Algebra. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 5 Maths: closest content focus for Solve linear inequalities and simultaneous linear equations in 2 variables... and related outcomes. |
| United States | Common Core / NGSS | Grade 10 Common Core Mathematics/ELA closest topic match for Solve linear inequalities and simultaneous linear equations in 2 variables.... |
| England / UK | National Curriculum | Key Stage 4 / Year 10: closest programme-of-study match for Solve linear inequalities and simultaneous linear equations in 2 variables.... |
| Canada | Provincial and territory curricula | Grade 10 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 5 Maths: closest achievement-objective topic for Solve linear inequalities and simultaneous linear equations in 2 variables.... |
| India | NCERT / CBSE | Class 10 closest NCERT/CBSE topic match for Solve linear inequalities and simultaneous linear equations in 2 variables.... |