Proportional Reasoning Vocabulary
Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts
What a learner can do afterwards
- Distinguish between 'direct proportion' and 'inverse proportion' with real-world examples
- Use 'rate', 'speed', and 'density' correctly and explain what units they are measured in
- Calculate using compound measures — e.g. work out the speed of a car that travels 120 miles in 2 hours
The lesson
You already compare amounts with ratios. Now it's time to learn the exact words mathematicians use for how two amounts behave together. When two quantities are in direct proportion, they grow at the same rate. Double one, and the other doubles too.
Not every relationship works that way. In inverse proportion, one quantity goes up while the other goes down. If more workers join a job, it usually takes fewer days to finish.
Here's how to keep the vocabulary straight. A rate compares two different kinds of quantities, like miles and hours. A unit rate is the amount for just one unit, such as 60 miles per hour. Speed and density are compound units: speed is distance divided by time, density is mass divided by volume. A scale factor tells you how much a map or drawing has been enlarged or shrunk.
Direct proportion means two amounts grow together, inverse proportion means one grows as the other shrinks, and words like rate, unit rate, compound unit, and scale factor let you describe those relationships precisely.
Watch it
Where it sits
Learn first
Nothing; this is a starting point.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.