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

Lesson 3.3Determine Equivalent Ratios Using Tables

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can use a ratio table to find equivalent ratios.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Ratio TablesSpanish: Tablas de razones Tables that organize pairs of equivalent ratios. 2:3, 4:6, and 6:9 belong in the same ratio table.
Ratio tableSpanish: Tabla de razones A table of equal ratios that shows a pattern. 5, 10, 15 / 2, 4, 6
Equivalent ratioSpanish: Razón equivalente Two ratios that mean the same thing, like 1:2 and 2:4. 2:3 = 4:6 = 6:9
Scale factorSpanish: Factor de escala The number you multiply both parts of a ratio by to get an equal ratio. 2:3 × 2 → 4:6 (scale factor is 2)
PatternSpanish: Patrón A rule that numbers follow again and again. Each row adds 2 cups juice and 3 cups water
Additive patternSpanish: Patrón aditivo Building new rows of a ratio table by adding each column's own constant amount, so the two columns grow together. 2:3 → 4:6 → 6:9 (add 2 and 3 each time)

How it worksWorked examplefilling in a ratio table

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A fruit bowl uses 5 apples for every 2 oranges. Fill the table for 15 apples.

  1. Write the base ratio. 5 apples : 2 oranges
  2. Find the factor. 5 × ? = 15, so the factor is 3
  3. Multiply BOTH rows by the same factor. 5 × 3 = 15 2 × 3 = 6
  4. Never ADD to make equivalent ratios — adding changes the comparison.

Answer: 15 apples go with 6 oranges.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A recipe uses 7 cups water for every 3 scoops mix. How much mix for 21 cups of water?

  1. Write the base ratio. water : mix
  2. Find the factor. 7 × = 21
  3. Multiply BOTH rows by that factor. 3 × =
  4. Check: did you multiply, not add?
Answer:scoops of mix

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • I multiplied both terms by .
  • and are equivalent because .
  • Adding does not work because .
  • The factor is because × = .

Word bank equivalentratio tablefactormultiplydividebothsamescale upscale downfor everyrowpattern

Watch outA common mistake

A common mistake in Ratio Tables is scaling only ONE part of the ratio, or adding the scale factor to a part instead of multiplying by it — for example, turning 2:3 into 6:3 (multiplying only the first number by 3 and forgetting the second) or into 4:5 (adding the scale factor 2 to the second number instead of multiplying, since 3+2=5 but 3×2=6). Before you submit, multiply BOTH numbers by the same scale factor and check that your new ratio simplifies back to the original.

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

Lesson 3.3Determine Equivalent Ratios Using Tables

Version ASupported practice

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

Learning target I can use a ratio table to find equivalent ratios.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    A cookie recipe uses 2 cups of butter for every 5 cups of flour. Complete the ratio table.

    BatchesButter (cups)Flour (cups)
    125
    2
    3

    Hint Row 1 shows ONE batch: 2 cups butter and 5 cups flour. Every other row is copies of that batch.

    Show your work
Part 2Apply itreal-world problems
  1. 2Circle 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

    Hint Notice the flour jumped from 5 cups to 15 cups — the eggs must grow by the same factor.

    Show your work
  2. 3Circle 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

    Hint Every row in a 4:5 table must simplify back to exactly 4:5.

    Show your work
  3. 4Circle 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. B12:28
    3. C12:24
    4. D15:28

    Hint Look down each column: how does 3 → 6 → 9 change? How does 7 → 14 → 21 change?

    Show your work
  4. 5Circle 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. B6:15
    3. C6:12
    4. D8:15

    Hint Compare row 1 (2:5) with row 2 (4:10). What happened to each column?

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Catch Priya's Mistake

    1. 1Read the orderA trail mix recipe uses 2 cups of nuts for every 5 cups of raisins (2:5). Priya wants to make a bigger batch using a scale factor of 4.
    2. 2Pick a scale factorPriya's scale factor is 4. A scale factor should multiply BOTH parts of the ratio.
    3. 3Scale the nuts2 × 4 = 8 cups of nuts
    4. 4Scale the raisins5 + 4 = 9 cups of raisins

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

    Hint Look at Step 4. Priya turned 5 into 9, but is 8:9 the same ratio as 2:5?

    Correct work
    Correct answer:

Explain your thinkingHow did you find each new row in the pancake ratio table? If someone asked for 10 batches instead of 4, would counting up by adding 2 and 3 each row still be a fast way to find the answer?

Sentence starter I found the 4-batch row by multiplying ___ and ___ by ___, which is faster than adding ___ and ___ over and over ___ times.

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 3.3Determine Equivalent Ratios Using Tables

Version BCore practice

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

Learning target I can use a ratio table to find equivalent ratios.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Complete the ratio table for lemon juice to water in Chef Reyes's lemonade recipe (1 cup lemon juice for every 4 cups water).

    PitchersLemon Juice (cups)Water (cups)
    114
    2
    5
    10
    Show your work
  2. 2Write the name of the correct group on each line.

    Which rows belong in a ratio table for 3:4? Sort them into correct and incorrect.

    Groups: Belongs in 3:4 Table Does NOT Belong
    • 6:8
    • 9:12
    • 15:20
    • 6:10
    • 12:14
    • 9:16
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    In a ratio table, the ratio of sugar to butter is 3:2. If you use 12 cups of sugar, how many cups of butter do you need?

    1. A6
    2. B8
    3. C9
    4. D10
    per 1
  2. 4Circle the letter of the best answer. Show how you know.

    A ratio table shows 5:8, 10:16, 15:24. What scale factor was used from the first row to the third row?

    1. A2
    2. B3
    3. C5
    4. D8
    per 1
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Catch Marcus's Mistake

    1. 1Read the tableA ratio table starts with 3:8. Marcus needs to find the row where the first value is 12.
    2. 2Find the changeMarcus sees the first value went from 3 to 12, a difference of 9.
    3. 3Apply the changeMarcus adds 9 to the second value: 8 + 9 = 17
    4. 4Write the new rowMarcus's answer: 12:17

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

    Correct work
    Correct answer:

Explain your thinkingHow did you find each new row in the pancake ratio table? If someone asked for 10 batches instead of 4, would counting up by adding 2 and 3 each row still be a fast way to find the answer?

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 3.3Determine Equivalent Ratios Using Tables

ChallengeExtension

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

Learning target I can use a ratio table to find equivalent ratios.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Chef Reyes needs to scale a soup recipe. The original uses 7 cups of broth for every 4 cups of vegetables. Complete the table, then explain the pattern you see.

    BatchesBroth (cups)Vegetables (cups)
    174
    2
    5
    0.5
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find Devon's Mistake

    1. 1Read the problemA recipe uses 5 cups of oats for every 2 cups of honey. Complete the table for 3 batches.
    2. 2Find the scale factor3 batches → multiply by 3
    3. 3Scale the oats5 × 3 = 15 cups of oats
    4. 4Scale the honey2 + 3 = 5 cups of honey

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

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    A recipe uses 4 cups of flour for every 3 cups of sugar. A student filled in a ratio table: 4:3, 8:6, 12:9, 14:12. Find and fix the error in the last row. Explain what went wrong.

    Write your answer

Explain your thinkingHow did you find each new row in the pancake ratio table? If someone asked for 10 batches instead of 4, would counting up by adding 2 and 3 each row still be a fast way to find the answer?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help