Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.3a

Lesson 3.4Determine Equivalent Ratios Using Graphs

Set B · Version ASecond form · supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can graph the values from a ratio table as points on the coordinate plane.

Why This Matters 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?

RememberDetermine Equivalent Ratios Using Graphs

Graphing Equivalent Ratios 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).

  1. Form ordered pairs (x, y) from columns or rows in a ratio table.
  2. Plot the points on the coordinate plane.
  3. Proportional Relationship: Points form a straight line passing through the origin (0, 0)

Words: Coordinate plane (Plano cartesiano)Ordered pair (Par ordenado)Linear pattern (Patrón lineal)Proportional (Proporcional)Origin (Origen)

  1. 1Circle the letter of the best answer. Show how you know.

    A ratio table for 2:5 starts with 2:5, 4:10. What is the third row?

    1. A5:10
    2. B6:12
    3. C6:15
    4. D8:15
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Which row does NOT belong in a ratio table for 4:5?

    1. A6:10
    2. B8:10
    3. C12:15
    4. D16:20
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    A ratio table shows 3:7, 6:14, and 9:21. What is the next row?

    1. A10:24
    2. B12:24
    3. C12:28
    4. D15:28
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    A recipe uses 3 eggs for every 5 cups of flour. How many eggs are needed for 15 cups of flour?

    1. A6
    2. B9
    3. C10
    4. D12
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A food truck tracks how many tacos it sells and how much salsa it uses. After recording data for a week, the owner plots the points on a graph and notices they form a straight line. This helps the owner predict exactly how much salsa to prepare for any number of tacos. The graph shows 1 taco uses 2 oz of salsa. How much salsa for 15 tacos?

    1. A7.5 oz
    2. B17 oz
    3. C20 oz
    4. D30 oz
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    A food truck tracks how many tacos it sells and how much salsa it uses. After recording data for a week, the owner plots the points on a graph and notices they form a straight line. This helps the owner predict exactly how much salsa to prepare for any number of tacos. Why do the points form a straight line through (0, 0)?

    1. ABecause the quantities are proportional — the same ratio holds for every pair
    2. BBecause the owner sold the same number of tacos every day
    3. CBecause all graphs of data are straight
    4. DBecause salsa is measured in ounces
    Show your work

Explain your thinkingWhat pattern do the plotted points make? How does the graph show the ratio of 1 sundae to 2 ounces of sauce?

Sentence starter Every time the sundaes go up by ___, the ounces go up by ___, so the points line up in a ___ starting from ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.3a

Lesson 3.4Determine Equivalent Ratios Using Graphs

Set B · Version BSecond form · core practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can graph the values from a ratio table as points on the coordinate plane.

Why This Matters 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?

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each cups-to-scoops table row to the ordered pair you would plot (rule: y = 2x).

    1. 2 cups → 4 scoops
    2. 3 cups → 6 scoops
    3. 5 cups → 10 scoops
    4. 6 cups → 12 scoops
    • A(2, 4)
    • B(3, 6)
    • C(5, 10)
    • D(6, 12)
  2. 2Write the name of the correct group on each line.

    The smoothie line follows the rule y = 2x (2 scoops per cup). Sort each ordered pair: is it ON the line or OFF the line?

    Groups: ON the line (y = 2x) OFF the line
    • (1, 2)
    • (4, 8)
    • (5, 10)
    • (2, 3)
    • (3, 5)
    • (1, 4)
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A food truck tracks how many tacos it sells and how much salsa it uses. After recording data for a week, the owner plots the points on a graph and notices they form a straight line. This helps the owner predict exactly how much salsa to prepare for any number of tacos. Which point would NOT be on this line?

    1. A(4, 8)
    2. B(5, 12)
    3. C(6, 12)
    4. D(10, 20)
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    Recipe: 1 cup berries to 2 scoops yogurt. With cups on x and scoops on y, which pair shows 3 cups?

    1. A(3, 6)
    2. B(3, 5)
    3. C(3, 3)
    4. D(6, 3)
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    On the smoothie graph, every point follows the rule scoops = 2 × cups. Which equation describes the pattern between x (cups) and y (scoops)?

    1. Ay = 2x
    2. By = x + 2
    3. Cy = x ÷ 2
    4. Dx = 2y
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Level 2 Extension — The Swapped Smoothie Point

    1. 1Read the tableCups of blueberries: 2 | Scoops of yogurt: 4 (rule: 2 scoops per cup)
    2. 2Name the axesCups go on the x-axis, scoops go on the y-axis
    3. 3Write the ordered pair(4, 2)
    4. 4Plot the pointGo right 4, up 2 on the grid

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingWhat pattern do the plotted points make? How does the graph show the ratio of 1 sundae to 2 ounces of sauce?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help