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

Lesson 3.9Equivalent Ratios

Set B · Version ASecond form · supported practice

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

Learning target I can find and check equivalent ratios using multiplication and division.

Why This Matters Chef Montoya is preparing her famous tomato soup for a school banquet. Her original recipe serves 8 people, but tonight she needs to serve 32 guests. She needs your help to scale the recipe without changing the flavor!

RememberEquivalent Ratios

Proportions & Equivalent Ratios. Formula: a/b = c/d Equivalent ratios are ratios that mean the same thing. You make one by multiplying or dividing BOTH numbers by the same amount.

  1. Two ratios are equivalent if their simplified forms or cross products are equal.
  2. Find the scale factor between corresponding terms.
  3. Multiply or divide to solve for the missing term in the proportion

Words: Equivalent Ratios (Razones equivalentes)Ratio (Razón)Rate (Tasa)Proportion (Proporción)Simplify (Simplificar)

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

    A printer prints 30 pages every minute. How many pages does it print in 4 minutes?

    1. A7.5 pages
    2. B30 pages
    3. C34 pages
    4. D120 pages
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    A faucet fills 3 gallons every 2 minutes. How long does it take to fill 18 gallons?

    1. A6 minutes
    2. B9 minutes
    3. C12 minutes
    4. D36 minutes
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    A recipe uses 3 cups of flour for 12 muffins. How much flour is needed for 20 muffins?

    1. A2.4 cups
    2. B4 cups
    3. C5 cups
    4. D6 cups
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    Store A sells 5 notebooks for $6.25. Store B sells 8 notebooks for $9.60. Which store has the lower price per notebook?

    1. AStore A
    2. BThey are equal
    3. CYou cannot tell
    4. DStore B
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A local smoothie shop sells a Berry Blast smoothie. The recipe calls for 2 cups of strawberries for every 3 cups of yogurt. Today they need to make 15 cups of yogurt worth of smoothies for a catering order. What is the scale factor from 3 cups of yogurt to 15 cups?

    1. A3
    2. B5
    3. C12
    4. D45
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    A local smoothie shop sells a Berry Blast smoothie. The recipe calls for 2 cups of strawberries for every 3 cups of yogurt. Today they need to make 15 cups of yogurt worth of smoothies for a catering order. How many cups of strawberries are needed?

    1. A5
    2. B10
    3. C12
    4. D15
    Show your work

Explain your thinkingHow did you find the missing values in Chef Montoya's table? How can you PROVE two of your rows are equivalent ratios?

Sentence starter I multiplied ___ and ___ by the same number, ___, so the ratio ___ is equivalent to 3:2.

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.3

Lesson 3.9Equivalent Ratios

Set B · Version BSecond form · core practice

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

Learning target I can find and check equivalent ratios using multiplication and division.

Why This Matters Chef Montoya is preparing her famous tomato soup for a school banquet. Her original recipe serves 8 people, but tonight she needs to serve 32 guests. She needs your help to scale the recipe without changing the flavor!

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

    Match each recipe ratio to a batch that tastes exactly the same.

    1. 2:3
    2. 3:5
    3. 4:7
    4. 5:6
    • A8:12
    • B9:15
    • C12:21
    • D10:12
  2. 2Write the name of the correct group on each line.

    The recipe ratio is 2 cups flour to 5 cups milk (2:5). Sort each batch: does it taste the same (equivalent) or not?

    Groups: Equivalent to 2:5 NOT Equivalent to 2:5
    • 4:10
    • 6:15
    • 8:20
    • 4:9
    • 2:7
    • 5:2
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A local smoothie shop sells a Berry Blast smoothie. The recipe calls for 2 cups of strawberries for every 3 cups of yogurt. Today they need to make 15 cups of yogurt worth of smoothies for a catering order. Why must both ingredients be multiplied by the same factor?

    1. ABecause 2 and 3 are both small numbers
    2. BBecause addition would be harder
    3. CSo the total is a whole number
    4. DSo the ratio stays 2:3 and the smoothie tastes the same
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    Chef Montoya's dressing uses 3 spoons of oil to 4 spoons of vinegar (3:4). Which recipe card shows an EQUIVALENT ratio?

    1. A3:8
    2. B4:3
    3. C6:7
    4. D9:12
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    The lemonade station mixes 5 cups of lemon juice to 2 cups of sugar (5:2). Which batch keeps the SAME taste?

    1. A5:4
    2. B7:4
    3. C10:6
    4. D15:6
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Level 2 Extension — The Scaled-Up Pancake Batter

    1. 1Set up the ratio3 cups flour : 8 cups water = ? : 24 cups water
    2. 2Find the multiplier24 ÷ 8 = 3
    3. 3Apply to the flour3 + 3 = 6
    4. 4Answer6 cups flour : 24 cups water

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

    Correct work
    Correct answer:

Explain your thinkingHow did you find the missing values in Chef Montoya's table? How can you PROVE two of your rows are equivalent ratios?

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