How to teach ratios, rates and scale
Year 7 to Year 10 (ages 12 to 16)
A ratio compares two or more quantities of the same kind, such as 3 red to 2 blue counters. Simplifying a ratio, sharing an amount in a given ratio, and using rates and map scales are the core skills built on this idea across secondary school.
How to teach it
- Teach simplifying a ratio the same way as simplifying a fraction: divide both parts by their highest common factor.
- Model sharing an amount in a ratio step by step: total the parts, find the value of one part, then multiply out.
- Introduce rate as a ratio between two DIFFERENT kinds of quantity (distance and time, cost and quantity), always carrying units.
- Use map scales (e.g. 1 cm represents 5 km) as a real-world ratio application, converting map distance to real distance.
- Keep early examples to nice, whole-number-friendly ratios before introducing awkward numbers.
Worked example
Share $60 in the ratio 2 : 3 Total parts = 2 + 3 = 5 Value of 1 part = $60 / 5 = $12 2 parts = $24, 3 parts = $36
Common mistakes
- Dividing by a common factor that is not the HIGHEST common factor, leaving the ratio not fully simplified.
- Sharing the amount by the number of PARTS in only one share, instead of the total number of parts.
- Confusing a ratio (same kind of quantity) with a rate (different kinds, with units).
- Multiplying instead of dividing the map distance by the scale factor when converting to real distance.
Frequently asked questions
How do you simplify a ratio?
Divide both parts of the ratio by their highest common factor (HCF). For example 20 : 30 has HCF 10, so it simplifies to 2 : 3, the same relationship in its smallest whole numbers.
How do you share an amount in a given ratio?
Add the parts of the ratio to find the total number of parts, divide the amount by that total to find the value of one part, then multiply by each ratio number. Sharing $60 in the ratio 2:3 (5 parts total) gives $12 per part, so $24 and $36.
What is the difference between a ratio and a rate?
A ratio compares two quantities of the SAME kind (e.g. 3 red marbles to 2 blue marbles). A rate compares two quantities of DIFFERENT kinds (e.g. 60 kilometres per hour), so a rate always carries units.
What year are ratios, rates and scale taught?
In the Australian Curriculum, ratios are introduced at Year 7 (AC9M7N08, AC9M7M06), rates at Year 8 (AC9M8M05, AC9M8M07), and modelling proportion and scaling problems continues through Year 9 and Year 10 (AC9M9M05, AC9M10M05).
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.