Grade 7 · Unit 1 · Lesson 7

Converting Rates

In 6th grade you changed one unit at a time. A rate has two units, so now both change, still one at a time, and it is still multiplying by the same number. Zoomy the racing snail goes from miles per hour to feet per minute in two steps, with a sense check after each one.

About 25 minutes Bigger or smaller?

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

I can run about 25 feet in 3 seconds. How many feet is that per minute? By the end of today, you can figure that out.

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. Converting a rate keeps that idea: change one unit, then the other, and each change is a multiply or a divide by one conversion fact. Miles to feet multiplies by 5,280. Hours to minutes divides by 60. After every step, sense check: smaller units mean more of them, so the number gets bigger; a shorter time means less happens in it, so the number gets smaller. Conversion facts live in a box. You look them up, you do not memorize them.

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 2Zoomy the racing snailIn 6th grade you changed one unit at a time: 3 feet is 36 inches, because 1 foot is 12 inches. 3Two more ratesTwo more. 4Predict the directionBefore you compute, predict the direction. 5Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the two-step method, the sense checks, Zoomy worked out, and the conversion facts box. 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 a Point MeansReading any point, plus (0, 0) and (1, r). Next lesson: Unit Rate ProblemsSolving real problems with the unit rate. 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.3.