AC9M7N09 • Year 7 Maths • Number • Learn
use mathematical modelling to solve practical problems, involving rational numbers and percentages, including financial contexts; formulate problems, choosing representations and efficient calculation strategies, using digital tools as appropriate; interpret and communicate solutions in terms of the situation, justifying choices made about the representation.
We are learning to use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; choose representations, efficient strategies and digital tools; interpret and communicate justified solutions.
A mathematical model represents the quantities, relationships and constraints relevant to a practical problem. Financial models must include the correct percentage base as well as fixed fees, thresholds and timing.
A complete comparison calculates final costs under the same assumptions. For a $480 item, 15% off costs $408, while $90 off plus a $25 fee costs $415.
Sensitivity analysis varies an input to test whether a recommendation changes. A break-even point occurs when two modelled costs are equal, and conclusions should state assumptions and limits rather than claim universal validity.
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: Plan A costs $408 and is $7 cheaper.
Check: Recalculate each offer including every fee.
Example 2
Final answer: The offers break even at $240.
Check: Both offers cost $192 when p=$240.
Example 3
Problem: Plan A gives 25% off a $240 item plus a $12 fee. Plan B gives 18% off with no fee. Which is cheaper, by how much, and what assumptions are you making?
Final answer: Plan A costs $240×0.75+$12 = $192. Plan B costs $240×0.82 = $196.80. Plan A is cheaper by $4.80, assuming the discounts apply to the same original price and there are no other fees.
Check: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Example 4
Problem: A store offers 25% off then charges 10% tax on the discounted price. Find the final cost of $240 and compare with subtracting 15% once.
Final answer: Sequential cost is 240×0.75×1.10=$198; 15% off gives $204, so sequential is $6 cheaper.
Check: Successive percentages use changing bases.
Common mistake: Discount percentages added to dollar fees.
Correction: Calculate each type with its correct base and unit.
Common mistake: Cheapest-looking headline chosen.
Correction: Include all conditions and costs.
Common mistake: Spreadsheet output lacks formula explanation.
Correction: Show the mathematical relationship.
Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.
1. Find 15% of $200.
Answer: $30.
Hint: Convert 15% to 0.15.
Why: The percentage amount is 0.15×200.
2. A $90 item has $12 postage. Find total cost.
Answer: $102.
Hint: Add item price and postage.
Why: A model includes all relevant charges.
3. State one assumption needed when comparing two phone plans.
Answer: For example, assume the same usage and comparison period.
Hint: Identify what must be equal across plans.
Why: A defensible mathematical model states a constraint or assumption that keeps the phone-plan comparison fair.
4. A $320 bike is discounted 12.5%. Find its sale price.
Answer: 12.5% is 1/8; discount $40, sale price $280.
Hint: Find one eighth of 320.
Why: Subtract the discount from the original price.
5. Compare 10% off $500 with $65 off plus a $20 fee.
Answer: 10% off costs $450; the second costs $455, so 10% off is $5 cheaper.
Hint: Model each final price separately.
Why: Complete costs include the fee.
6. A budget is $600 with a 5% contingency. Find the planned total.
Answer: $600×1.05=$630.
Hint: Add 5% of 600.
Why: A contingency increases the base amount.
7. Why can a spreadsheet help compare changing prices?
Answer: It can apply transparent formulas repeatedly and reveal where the cheaper option changes.
Hint: State the formula and varied input.
Why: Digital tools support sensitivity analysis after formulas are defined.
8. Plan A costs $18+$0.08 per message; Plan B costs $10+$0.12 per message. Find the break-even usage.
Answer: 18+0.08m=10+0.12m, so 8=0.04m and m=200 messages.
Hint: Set the two complete cost formulas equal.
Why: Equal costs define the break-even point.
9. A store offers 25% off then charges 10% tax on the discounted price. Find the final cost of $240 and compare with subtracting 15% once.
Answer: Sequential cost is 240×0.75×1.10=$198; 15% off gives $204, so sequential is $6 cheaper.
Hint: Apply each multiplier in order.
Why: Successive percentages use changing bases.
10. Plan A gives 25% off a $240 item plus a $12 fee. Plan B gives 18% off with no fee. Which is cheaper, by how much, and what assumptions are you making?
Answer: Plan A costs $240×0.75+$12 = $192. Plan B costs $240×0.82 = $196.80. Plan A is cheaper by $4.80, assuming the discounts apply to the same original price and there are no other fees.
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: use mathematical modelling to solve practical problems, involving rational numbers and percentages, including financial contexts; formulate problems, choosing representations and efficient calculation strategies, using digital tools as appropriate; interpret and communicate solutions in terms of the situation, justifying choices made about the representation.
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:
Math Antics — Connect a percentage with an amount out of one hundred before modelling a financial situation.
As you watch: How are a percentage, a decimal and a fraction related?
Load video player Loads YouTube in this lesson. See the video notice below.
Try it: A $60 item is reduced by 25%. Model the saving and final price, and explain your method.
Video unavailable, inaccurate or unsuitable for this year? Report a video problem to SkillrHub by email. You can continue with the written lesson and practice resources.
Videos are curated from trusted independent educational creators and played through YouTube. Rights remain with their respective owners. Inclusion does not imply that a creator or YouTube endorses SkillrHub.
YouTube’s terms and privacy policy apply to its player. Advertising, recommendations and external links may appear, and videos may change or become unavailable. SkillrHub’s written lessons and practice resources remain available separately.
To report a content, suitability or rights concern, email skillrhublearning@gmail.com with the lesson code and video link. Please do not include personal student information.
Mapped skill: use mathematical modelling to solve practical problems, involving rational numbers and percentages, including financial contexts; formulate problems, choosing representations and efficient calculation strategies, using digital tools as appropriate; interpret and communicate solutions in terms of the situation, justifying choices made about the representation
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 | AC9M7N09 · Year 7 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M7N09 · Level 7 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA4-FRC-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.
Help improve SkillrHub
Ask about this lesson, suggest an improvement or report an error. Facebook opens only when you choose an option below.
Topic reference: AC9M7N09 — Modelling Rational and Percentage Problems
Privacy: Please don’t share personal student or school information. Younger students should ask a parent, guardian or teacher to post on their behalf.