Grade 7 · Unit 1 · Lesson 4

Proportional Graphs

Plot a proportional table and the points make a straight line through the origin, the point (0, 0). That is the graph test, and both parts matter: bowling is straight but misses the origin, and a bending curve goes through the origin but is not straight. A bigger unit rate makes the line steeper. Connect the dots only when both amounts can be split.

About 25 minutes Straight, and through (0, 0)

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

Same idea, new picture. Today we draw it.

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 a graph, that looks like a straight line through the origin, the point (0, 0) where both amounts are zero. Both parts of the test matter: a line that misses the origin has a fee hiding in it, and a graph that bends does not multiply by the same number. The unit rate shows up as steepness: a bigger unit rate makes a steeper line, because every 1 across gives more up. Connect the points only when both amounts can be split into smaller parts.

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 2Plot the lemonadeIn Lesson 2 you tested the lemonade table by dividing. 3Two ways to failTwo ways a graph can fail the test. 4Pick the proportional graphThree graphs. Only one passes both tests. Match each description to its graph, then read why. 5The unit rate tips the lineNow connect the picture to the number. 6Dots, or a line?One more question: dots, or a line? 7Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the graph test, the two ways to fail, steeper means a bigger unit rate, and dots or a line. Plus a worksheet with grids to plot on, 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: The Unit RateThe unit rate is the constant of proportionality. Next lesson: Writing y = rxTurning the unit rate into an equation. 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.