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

Lesson 3.33.3 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can use a ratio table to find equivalent ratios, explain why the method works, and use it on a problem I have not seen before.

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 3.33.3 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can use a ratio table to find equivalent ratios, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    Flour (cups)826Water (cups)12??÷ ?÷ ?× ?× ?
    Divide first, then multiply.

    A recipe uses 8 cups of flour for every 12 cups of water. How many cups of water go with 6 cups of flour?

    1. 1What do we divide 8 by to get 2?
    2. 2Divide 12 by 4 too. How much water goes with 2 cups of flour?
    3. 3What scale factor takes 2 cups of flour to 6 cups?
    4. 4Multiply 3 cups of water by 3. How much water?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Bags of chips6?10Juice boxes15??÷ ?÷ ?× ?× ?

    A party plan uses 6 bags of chips for every 15 juice boxes. How many juice boxes go with 10 bags of chips?

    1. 1Divide both numbers by 3. What is the smaller ratio?
    2. 2Multiply both by 5. How many juice boxes go with 10 bags?
    3. 3Ben adds 4 to both numbers and gets 10:19. Why is that wrong?
    Final answer:
  3. 3Complete each step, then write the final answer.
    BoxesPens________________________

    A ratio table shows 12 pens for every 4 boxes. How many pens are in 7 boxes?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    StrawberriesBananas________________________

    A smoothie uses 15 strawberries for every 6 bananas. How many strawberries go with 8 bananas?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    BurritosCost________________________

    A food truck sells 9 burritos for $24. At that rate, how much do 6 burritos cost?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.
    Rice (cups)Beans (cups)________________________

    A table shows 10 cups of rice for every 4 cups of beans. Kim says 15 cups of rice need 9 cups of beans, because 10 + 5 = 15 and 4 + 5 = 9. How many cups of beans are right?

    Show your work
    Final answer:

Explain your thinkingWhen can you multiply right away in a ratio table, and when should you divide first? Use 15:6 and 8 bananas to explain.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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