What students learn in AC9M10A05
This unit helps students build a clear, usable understanding of Experiment with functions and relations using digital tools, making and.... 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 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.
- applying the graphing zoom functionality of digital tools and systematically refining intervals to identify approximate location of points of intersection of the graphs of 2 functions, such as x^2=2^x applying a bisection algorithm to determine the approximate location of the horizontal axis intercepts of the graph of a quadratic function such as f(x)=2x^2-3x-7
- 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 functions and relations using digital tools, making and testing conjectures and generalising emerging patterns
- E1: applying the graphing zoom functionality of digital tools and systematically refining intervals to identify approximate location of points of intersection of the graphs of 2 functions, such as x^2=2^x
- E2: applying a bisection algorithm to determine the approximate location of the horizontal axis intercepts of the graph of a quadratic function such as f(x)=2x^2-3x-7
- E3: applying transformations to the graph of x^2+y^2=1
- E4: identifying the coordinates of any points of intersection of the graph of a linear function with the graph of a quadratic function or a circle
- E5: identifying intervals on the real number line over which a given quadratic function is positive or negative
- E6: using a table of values to determine when an exponential growth or decay function exceeds or falls below a given value, such as monitoring the trend in value of a share price in a context of exponential growth or decay
- E7: investigating how functions and relations serve as the mathematical underpinnings of machine learning, allowing data to be transformed, models to be defined and optimisation to occur
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
AC9M10A05 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 | AC9M10A05 — experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns |
| 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 Experiment with functions and relations using digital tools, making and... and related outcomes. |
| United States | Common Core / NGSS | Grade 10 Common Core Mathematics/ELA closest topic match for Experiment with functions and relations using digital tools, making and.... |
| England / UK | National Curriculum | Key Stage 4 / Year 10: closest programme-of-study match for Experiment with functions and relations using digital tools, making and.... |
| 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 Experiment with functions and relations using digital tools, making and.... |
| India | NCERT / CBSE | Class 10 closest NCERT/CBSE topic match for Experiment with functions and relations using digital tools, making and.... |