What students learn in AC9M8A04
This unit helps students build a clear, usable understanding of Experiment with linear functions and relations using digital tools, making.... 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: experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- using graphing software to investigate the effect of systematically varying parameters of linear functions on the corresponding graphs, making and testing conjectures; for example, making a conjecture that if the co-efficient of x is negative, then the line will slope down from left to right using graphing software to systematically contrast the graphs of y\;=\;2x, -y\;=\;2x, y\;=\;-2x and -y\;=\;-2x with those of y 2x, -y>2x, y>-2x and -y>-2x, making and testing conjectures about sign and direction of the inequality
- 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: experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns
- E1: using graphing software to investigate the effect of systematically varying parameters of linear functions on the corresponding graphs, making and testing conjectures; for example, making a conjecture that if the co-efficient of x is negative, then the line will slope down from left to right
- E2: using graphing software to systematically contrast the graphs of y\;=\;2x, -y\;=\;2x, y\;=\;-2x and -y\;=\;-2x with those of y 2x, -y>2x, y>-2x and -y>-2x, making and testing conjectures about sign and direction of the inequality
- E3: using digital tools to investigate integer solutions to equations such as 2x+3y\;=\;48
- E4: exploring how linear functions are used in linear regression models as a statistical technique in machine learning of artificial intelligence agents; for example, linear functions are used to model the relationship between input variables and a target variable, to predict stock or house prices in the financial and real-estate sectors
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
AC9M8A04 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 | AC9M8A04 — experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns |
| 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 Experiment with linear functions and relations using digital tools, making... and related outcomes. |
| United States | Common Core / NGSS | Grade 8 Common Core Mathematics/ELA closest topic match for Experiment with linear functions and relations using digital tools, making.... |
| England / UK | National Curriculum | Key Stage 3 / Year 8: closest programme-of-study match for Experiment with linear functions and relations using digital tools, making.... |
| 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 Experiment with linear functions and relations using digital tools, making.... |
| India | NCERT / CBSE | Class 8 closest NCERT/CBSE topic match for Experiment with linear functions and relations using digital tools, making.... |