六至八年级Number计划中
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
本主题的课程尚未编写。下面的提纲是课程地图的一部分，尚未经过审校。
前置知识
5 项必需的前置知识（一直追溯到底）
你将学会
- 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.
定义
- 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.
定理
- 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.
常见误解
- 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.
通向
可选发现
- Probability When outcomes are equally likely, a probability is the ratio of favourable outcomes to all outcomes.