This worksheet applies ratios and rates to real-world modelling problems — map scales, currency conversion, phone plans and mixing — requiring students to formulate, solve and interpret each problem in context. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- A map or plan scale (e.g. 1:25,000) is a ratio between the drawing and the real-world size.
- A currency exchange rate is a rate — it converts an amount in one currency to another.
- Phone/data plans often combine a fixed fee with a rate per unit (per minute, per mb) — a linear model, just like Year 8's linear modelling.
- Mixing and dilution problems (concentrate:water) use ratios to find how much of each ingredient is needed.
- Combining two rates in sequence (e.g. converting aud→usd→cad) gives an equivalent single combined rate.
What your child will practise:
- Applying a scale ratio to convert between a drawing/model and real-world measurements.
- Applying a currency exchange rate to convert between currencies.
- Formulating a phone/data plan's cost as fixed fee + rate × usage, then compare plans.
- Using a mixing ratio to find the amount of each ingredient needed for a given total or rate of production.
- Combining two sequential rates to find a single equivalent rate.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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