What students learn in AC9M7A06
This unit helps students build a clear, usable understanding of Manipulate formulas involving several variables using digital tools, and describe.... 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: manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- experimenting with different sets of tables of values from formulas; for example, using volume of a rectangular prism = length × width × height, and specifying a fixed width and equal length and varying the height using spreadsheets and the formula function to recognise the effect of changing parameters on the entries in cells
- 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: manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables
- E1: experimenting with different sets of tables of values from formulas; for example, using volume of a rectangular prism = length × width × height, and specifying a fixed width and equal length and varying the height
- E2: using spreadsheets and the formula function to recognise the effect of changing parameters on the entries in cells
- E3: analysing distance travelled for different combinations of average speed and time of travel using a table of values and the distance formula
- E4: exploring how deep learning models used for training artificial intelligence agents can involve the manipulation of mathematical functions with multiple variables; for example, conducting a sensitivity analysis to understand the artificial intelligence model's behaviour
- E5: understanding that the relationship between variables in an artificial intelligence model assists with explainability and interpretability; for example, manipulating and analysing formulas allows researchers to gain insights into how and why a model makes certain predictions
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
AC9M7A06 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 | AC9M7A06 — manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables |
| Victoria | Victorian Curriculum F-10 | Year 7 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 Manipulate formulas involving several variables using digital tools, and describe... and related outcomes. |
| United States | Common Core / NGSS | Grade 7 Common Core Mathematics/ELA closest topic match for Manipulate formulas involving several variables using digital tools, and describe.... |
| England / UK | National Curriculum | Key Stage 3 / Year 7: closest programme-of-study match for Manipulate formulas involving several variables using digital tools, and describe.... |
| Canada | Provincial and territory curricula | Grade 7 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 Manipulate formulas involving several variables using digital tools, and describe.... |
| India | NCERT / CBSE | Class 7 closest NCERT/CBSE topic match for Manipulate formulas involving several variables using digital tools, and describe.... |