Neft Teacher · Learn It

Unit 3 · Standard 6.AT.3a

Determine Equivalent Ratios Using Graphs

Lesson 3-4 · Learn It — how the math works

Why we're learning this

The organizers of a soccer league ordered 6 of the bags shown to hold soccer balls. Each bag holds the same number of soccer balls. How many soccer balls will the bags hold?

✱ Math Workbench

Learn It

How do we graph a ratio table?

An ordered pair (x, y) tells where to plot a point: go right x, then up y. When you graph equal ratios, the points make a straight line through the origin (0, 0).

Picture itSee what the math looks like before you read about it

Chef Reyes keeps a table for sundae sauce: 1 sundae takes 2 ounces of chocolate sauce, 2 sundaes take 4 ounces, and 3 sundaes take 6 ounces. She starts plotting the (sundaes, ounces) pairs on a coordinate grid.
Where you see this in real lifeChef Reyes keeps a table for sundae sauce: 1 sundae takes 2 ounces of chocolate sauce, 2 sundaes take 4 ounces, and 3 sundaes take 6 ounces. She starts plotting the (sundaes, ounces) pairs on a coordinate grid.

Watch me solve itI do — read one step at a time

The problem looks like this
A coordinate grid with (1, 2), (2, 4), (3, 6) plotted, forming a straight line through the origin.−7−7−6−6−5−5−4−4−3−3−2−2−1−111223344556677 x y 0 (1, 2)(2, 4)(3, 6)The points line up straight through the origin.
  1. The recipe uses 2 ounces of sauce for every 1 sundae.
  2. I put sundaes on the x-axis and ounces of sauce on the y-axis.
  3. For 1 sundae I need 2 ounces, so I plot the (1, 2): right 1, up 2.
  4. For 2 sundaes I need 4 ounces, so I plot (2, 4): right 2, up 4.
  5. When I connect (1, 2), (2, 4), (3, 6), they form a straight line through the (0, 0).

Watch out — mistakes students make here

  • Does 6 = 2 × 4? Each y must be double its x.
  • Is 10 = 2 × 6? Keep y exactly double the x-value.
  • Those numbers do come from the table, but they are written x to y and left unsimplified. Divide y by x and reduce.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. A recipe uses 1 cup of sugar for every 3 cups of flour.
  2. For 1 cup of sugar, the is (1, 3): right 1, up 3.
  3. For 2 cups of sugar, what is the pair?
    Check this step
    It is (2, 6): right 2, up 6.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Check that your points line up straight through the .

Solve: Points from a are plotted at (1, 4), (2, 8), and (3, 12). What is the ratio of y to x for each point?

My answer

Stuck? Open one hint at a time.

Hint 1

The question asks y to x — the up-value compared to the across-value, in that order.

Hint 2

Divide y by x for each point. Equivalent ratios should give the same result all three times.

Hint 3

Take (2, 8): divide 8 ÷ 2. Check that (1, 4) and (3, 12) give the same value, then write it as y first, x second.

Check my answer
✅ Answer: 4:1
For each point: 4÷1 = 4, 8÷2 = 4, 12÷3 = 4. The ratio of y to x is always 4:1.

Turn & TalkSay it out loud with a partner

Each bag holds the same number of soccer balls, and the picture shows one bag with 6 balls. How can you use that one bag to find what 6 bags hold?

Try starting with:

  • I think ___ because ___.Pienso que ___ porque ___.
  • I agree / disagree with you because ___.Estoy / no estoy de acuerdo contigo porque ___.
Use these wordsGraph Ratio TablesCoordinate planeOrdered pairLinear patternProportional