AC9M7A06 • Year 7 Maths • Algebra • Learn
manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables.
We are learning to manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables.
A formula with several variables describes how an output depends on multiple inputs. A digital table or spreadsheet makes systematic variation visible.
To attribute an effect, hold all but one input constant; when several inputs change, combine their scale factors and expose the spreadsheet formula used.
Use controlled tables to test proportionality and sensitivity in area, volume, distance and cost models. Verify results by recalculating one row independently.
Use these models to connect the mathematical idea to values, diagrams, coordinates, graphs or structure before moving to symbolic calculation.
Follow each example from representation and setup through calculation/reasoning, interpretation and an independent check.
Example 1
Final answer: The areas are 10, 20, 30 and 40 square units for l=2,4,6,8.
Check: A/l=5 in every row, matching the displayed variation table.
Example 2
Final answer: Areas are 6, 24 and 54 square units.
Check: Doubling both dimensions from row 1 to 2 quadruples 6 to 24.
Example 3
Problem: For A=lw, keep w=4 cm and let l take values 2,4,6,8 cm. Create the value table, describe the pattern, then predict what happens if both l and w are doubled.
Final answer: Areas are 8,16,24,32 cm², so A increases by 8 cm² whenever l increases by 2 cm. Doubling both l and w multiplies area by 4.
Check: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Example 4
Problem: A spreadsheet uses V=lwh. Starting from l=2, w=3 and h=4, calculate the volume when only l doubles, when only w triples, and when l doubles, w triples and h halves. Describe each scale factor.
Final answer: The starting volume is 2×3×4=24 cubic units; doubling l gives 48, tripling w gives 72, and changing l by 2, w by 3 and h by ½ gives 72, so the respective volume factors are 2, 3 and 3.
Check: The complete model for “A spreadsheet uses V=lwh. Starting from l=2, w=3 and h=4, calculate the volume when only l doubles, when only w triples, and when l doubles, w triples and h halves. Describe each scale factor.” shows The starting volume is 2×3×4=24 cubic units; doubling l gives 48, tripling w gives 72, and changing l by 2, w by 3 and h by ½ gives 72, so the respective volume factors are 2, 3 and 3.
Common mistake: Several inputs varied together without plan.
Correction: Isolate effects before combining them.
Common mistake: Spreadsheet values accepted without formula audit.
Correction: Check references and units.
Common mistake: Additive language used for multiplicative effect.
Correction: Say doubles, triples or scales by a factor.
Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.
1. For A=lw, find A when l=7 and w=3.
Answer: 21 square units.
Hint: Substitute both values and multiply.
Why: Using the method “Substitute both values and multiply.” gives 21 square units.
2. In d=rt, what happens to d when t doubles and r stays fixed?
Answer: d doubles.
Hint: Hold r constant and compare scale factors.
Why: Using the method “Hold r constant and compare scale factors.” gives d doubles.
3. Write a spreadsheet formula multiplying cells B2 and C2.
Answer: =B2*C2.
Hint: Begin a spreadsheet formula with =.
Why: Using the method “Begin a spreadsheet formula with =.” gives =B2*C2.
4. For P=2l+2w with w=5, compare l=4 and l=8.
Answer: P changes from 18 to 26.
Hint: Calculate both cases rather than assuming doubling.
Why: Using the method “Calculate both cases rather than assuming doubling.” gives P changes from 18 to 26.
5. For V=lwh, double h only. What happens to V?
Answer: V doubles.
Hint: Hold l and w fixed.
Why: Using the method “Hold l and w fixed.” gives V doubles.
6. A student changes l and w together and credits l alone for the area change. Evaluate.
Answer: The claim is invalid because both l and w changed, so their effects are confounded; vary l while holding w fixed to isolate the effect of l.
Hint: Change only one input to attribute an effect.
Why: A controlled variable is held fixed so systematic variation can isolate the effect of the input being changed.
7. For C=3n+10, list C for n=0,5,10.
Answer: 10, 25, 40.
Hint: Apply the formula to each input.
Why: Using the method “Apply the formula to each input.” gives 10, 25, 40.
8. In V=lwh, l doubles, w triples and h halves. Find the volume factor.
Answer: The volume scale factor is 2×3×½=3, so the new volume is three times the original even though one dimension was halved.
Hint: Multiply 2×3×1/2.
Why: The complete model for “In V=lwh, l doubles, w triples and h halves. Find the volume factor.” shows The volume scale factor is 2×3×½=3, so the new volume is three times the original even though one dimension was halved.
9. A spreadsheet uses V=lwh. Starting from l=2, w=3 and h=4, calculate the volume when only l doubles, when only w triples, and when l doubles, w triples and h halves. Describe each scale factor.
Answer: The starting volume is 2×3×4=24 cubic units; doubling l gives 48, tripling w gives 72, and changing l by 2, w by 3 and h by ½ gives 72, so the respective volume factors are 2, 3 and 3.
Hint: Calculate the starting row, change the named inputs only, then compare each output with 24.
Why: The complete model for “A spreadsheet uses V=lwh. Starting from l=2, w=3 and h=4, calculate the volume when only l doubles, when only w triples, and when l doubles, w triples and h halves. Describe each scale factor.” shows The starting volume is 2×3×4=24 cubic units; doubling l gives 48, tripling w gives 72, and changing l by 2, w by 3 and h by ½ gives 72, so the respective volume factors are 2, 3 and 3.
10. For A=lw, keep w=4 cm and let l take values 2,4,6,8 cm. Create the value table, describe the pattern, then predict what happens if both l and w are doubled.
Answer: Areas are 8,16,24,32 cm², so A increases by 8 cm² whenever l increases by 2 cm. Doubling both l and w multiplies area by 4.
Hint: Represent the information first, then calculate, interpret and independently check the result.
Why: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Content description: manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables.
The Australian Curriculum code above is exact. Victorian Year 7, NSW Stage 4, US Grade 7, England Key Stage 3, New Zealand Level 4 and comparable international curricula contain broadly related learning, but code-to-code equivalence varies by jurisdiction.
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
Khan Academy — Substitute values into a formula with two variables before investigating how changing an input changes the result.
As you watch: Why is it helpful to change one variable at a time?
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Try it: Use A = l × w in a spreadsheet with w = 3 and l from 1 to 5; describe the outputs, then repeat with w = 6.
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Mapped skill: manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M7A06 · Year 7 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M7A06 · Level 7 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA4-ALG-C-01 · Stage 4 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 7 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 7 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 8, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 7 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
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Topic reference: AC9M7A06 — Systematic Variation in Multi-variable Formulas
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