Grade 7 · Unit 1 · Lesson 2

What Makes It Proportional

Proportional comes from portion, a share. In a proportional relationship every part keeps the same share, so the relationship always multiplies by the same number. The test with a table: divide each output by its input. Same number every row means proportional. A fee that is there at zero breaks it.

About 25 minutes Same number every row

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

Some things grow in a steady way and some do not. Today you get a test to tell them apart.

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. Proportional comes from portion, a share: every part keeps the same share. To test a table, divide each output by its input. If every row gives the same number, the relationship is proportional, and that number is what it multiplies by. If the number changes, it is not, and usually a fee or a starting charge is the reason: a proportional relationship always gives nothing for nothing, so zero in means zero out. Two equal ratios make a proportion.

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 2Portion, share, proportionalThe word proportional comes from portion , a share. 3Test some tables yourselfTry the test yourself. 4A proportion, and a peek at the graphWhen two ratios are equal, the pair of them has a name: a proportion . 5Sort the storiesRead each story or table. Ask: does it always multiply by the same number? Does nothing cost nothing? 6Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the table test, lemonade and bowling worked side by side, what a proportion is, and the zero-for-zero check. 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: Rates with FractionsFinding a unit rate when the amounts are fractions. Next lesson: The Unit RateThe unit rate is the constant of proportionality. 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.