Ratio, rates and similarity.
Connect constant rates, map scales, similar figures and enlargements, and check when proportional models are reasonable.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Direct proportion
Recognise a constant multiplicative relationship and use a proportional rule to predict a value.
- 02
Rates and unit conversions
Convert units before comparing rates, and use the relationship between speed, distance and time.
- 03
Scale drawings/maps
Interpret map scales as ratios of matching units and use them in both directions.
- 04
Corresponding lengths in similar figures
Match vertices and sides by angle information before writing equal ratios.
- 05
Finding missing lengths by similarity
Solve missing-length problems with matched ratios and check the direction of scaling.
- 06
Enlargement and scale factors
Describe enlargements using a centre and a scale factor, and calculate image coordinates.
- 07
Practical proportional models and limitations
Build a proportional model, state the assumptions, and recognise when a fixed charge or other constraint makes it unsuitable.
Topic review
Revisit the key ideas, then choose a practice paper.