What students learn in AC9M9A06
This unit helps students build a clear, usable understanding of Experiment with the effects of the variation of parameters on.... 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 the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- investigating transformations of the graph of y=x to the graph of y=ax+b by systematic variation of a and b and interpretating the effects of these transformations using digital tools; for example, y=x\rightarrow y=2x (vertical enlargement as a>1) \rightarrow y=2x-1 (vertical translation) and y=x\rightarrow y=\frac12x (vertical compression as a<1) \rightarrow y=-\frac12x (reflection in the horizontal axis) \rightarrow y=-\frac12x+3 (vertical translation) investigating transformations of the parabola y=x^2 in the Cartesian plane using digital tools to determine the relationship between graphical and algebraic representations of quadratic functions, including the completed square form; for example, y=x^2\rightarrow y=\frac13x^2 (vertical compression as a 1) \rightarrow y=-2x^2 (reflection in the horizontal axis) \rightarrow y=-2(x+6)^2 (horizontal translation) \rightarrow y=-2(x+6)^2+10 (vertical translation)
- 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 the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns
- E1: investigating transformations of the graph of y=x to the graph of y=ax+b by systematic variation of a and b and interpretating the effects of these transformations using digital tools; for example, y=x\rightarrow y=2x (vertical enlargement as a>1) \rightarrow y=2x-1 (vertical translation) and y=x\rightarrow y=\frac12x (vertical compression as a<1) \rightarrow y=-\frac12x (reflection in the horizontal axis) \rightarrow y=-\frac12x+3 (vertical translation)
- E2: investigating transformations of the parabola y=x^2 in the Cartesian plane using digital tools to determine the relationship between graphical and algebraic representations of quadratic functions, including the completed square form; for example, y=x^2\rightarrow y=\frac13x^2 (vertical compression as a 1) \rightarrow y=-2x^2 (reflection in the horizontal axis) \rightarrow y=-2(x+6)^2 (horizontal translation) \rightarrow y=-2(x+6)^2+10 (vertical translation)
- E3: experimenting with digital tools by applying transformations to the graphs of functions, such as reciprocal y=\frac1x, square root y=\sqrt x, cube y=x^3 and exponential functions, y=2^x, y=(\frac12)^x, identifying patterns
- E4: investigating how experimenting with the effects of the variation of parameters of related functions can provide artificial intelligence researchers insights into the predictive behaviour of artificial intelligence models
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
AC9M9A06 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 | AC9M9A06 — experiment with the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns |
| Victoria | Victorian Curriculum F-10 | Year 9 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 Experiment with the effects of the variation of parameters on... and related outcomes. |
| United States | Common Core / NGSS | Grade 9 Common Core Mathematics/ELA closest topic match for Experiment with the effects of the variation of parameters on.... |
| England / UK | National Curriculum | Key Stage 3 / Year 9: closest programme-of-study match for Experiment with the effects of the variation of parameters on.... |
| Canada | Provincial and territory curricula | Grade 9 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 Experiment with the effects of the variation of parameters on.... |
| India | NCERT / CBSE | Class 9 closest NCERT/CBSE topic match for Experiment with the effects of the variation of parameters on.... |