Grade 7 · Unit 1 · Lesson 6

What a Point Means

Every point on the graph is a small story: the point (x, y) means in x input units, you get y output units. Two points are special. The origin, (0, 0), says zero in gives zero out. The point (1, r) says one in gives the unit rate out, so you can read r straight off the graph.

About 25 minutes In x, you get y

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

Every point on a graph is a tiny story. Let us read a few.

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. On the graph, every point is a small story: the point (x, y) means in x input units, you get y output units. The origin, (0, 0), means zero in gives zero out, and it is on every proportional graph because nothing of one amount means nothing of the other. The point (1, r) means one in gives the unit rate out, so go over to 1 and up to the line to read r. A point between the grid lines is still on the line if the amounts can be split. A point off the line is a pair the relationship does not make.

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 2Every point is a small storyEvery point on a proportional graph is a small story. 3Two special points, and two tricky onesTwo points on every proportional graph are special. 4Read another graphThe same reading works for any story. 5Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the sentence frame, the origin, (1, r), the between-the-lines point, and the off-the-line point, all on Jordan's graph. 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: Writing y = rxTurning the unit rate into an equation. Next lesson: Converting RatesChanging both units in a 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.2.