Grades 6–8NumberPlanned
Ratios, rates and proportional reasoning
Ratios, unit rates, percentages and proportional relationships, using tables, double number lines and the constant of proportionality.
math.number.ratios-proportions
The lesson for this topic has not been written yet. The outline below is part of the curriculum map and has not been reviewed.
Builds on
Required prerequisites, all the way down: 5
You will learn to
- Solve ratio and rate problems using tables, double number lines and unit rates.
- Recognise proportional relationships y = kx in tables, graphs and situations, and identify the constant k.
- Compute percentages and percentage changes, and explain why a 10% rise followed by a 10% fall does not return to the start.
Definition
- A ratio a : b compares two quantities; it is equivalent to ka : kb for every k > 0.
- A unit rate is the amount of one quantity per one unit of another.
- Quantities x and y are proportional if y = kx for a fixed constant k.
Theorem
- The graph of a proportional relationship is a straight line through the origin.
- p% of x is (p/100) · x.
- Successive percentage changes multiply: a 10% increase and then a 10% decrease give an overall factor of 1.1 × 0.9 = 0.99.
Common misconceptions
- Using additive reasoning ('3 more') where multiplicative reasoning ('3 times as many') is needed.
- Thinking every linear relationship is proportional; y = 2x + 1 is not.
- Adding successive percentage changes.
Leads to
Optional discoveries
- Probability When outcomes are equally likely, a probability is the ratio of favourable outcomes to all outcomes.