Grade 7 · Unit 1 · Lesson 3

The Unit Rate

The number every row divides to is the unit rate, how much for one. Its formal name is the constant of proportionality: constant means it never changes, so it is the number the relationship always multiplies by. Find it from a table or from words, check which pairs fit it, and use it to compare two relationships.

About 25 minutes Two names, one number

ElleMath-speak

I say it the way your test says it.

FinnPlain English

And I say it the way you would say it to a friend. Same idea, two ways.

Finn

Remember the number every row divided to? Today it gets a name. Two names, actually.

The big idea

Finn says

A proportional relationship always multiplies by the same number, the unit rate.

A proportional relationship always multiplies by the same number, the unit rate. That number has two names. Unit rate means how much for one. Constant of proportionality means the same thing with a formal name: constant means it never changes. Find it from a table by dividing an output by its input, or from words by asking how much for one. To check whether a pair fits, multiply the input by the constant and see if you get the output. To compare two relationships with the same kind of units, find each unit rate: the bigger unit rate gives more for the same input.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2Two names for one numberIn Lesson 2 you divided every row of a table and looked for the same number. 3Which pairs fit?The landscaper's fee is proportional: $35 for every hour, always multiplying by 35. 4Comparing two relationshipsThe standard also asks you to compare two proportional relationships: decide which is more, and say why. 5Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the two names, the four places to find the number, the landscaper pairs, and Mia versus Jordan. Plus a worksheet with an answer key and a short lesson plan for the parent or tutor.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Previous lesson: What Makes It ProportionalChecking tables and graphs for the same multiplier. Next lesson: Proportional GraphsA straight line through zero. Back to the Math 7 mapEvery 7th grade lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.

NC Grade 7 standards in this lesson: NC.7.RP.2.