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

Lesson 3.33.3 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can use a ratio table to find equivalent ratios — one step at a time, with support.

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 1

Group 1Supported practice

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

Learning target With my small group, I can use a ratio table to find equivalent ratios — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    Batches13Lemon juice (cups)2?Water (cups)5?× ?× ?
    Fill in the column for 3 batches.

    A lemonade recipe uses 2 cups of lemon juice for every 5 cups of water. How much lemon juice and water do you need for 3 batches?

    1. 1What scale factor takes 1 batch to 3 batches?
    2. 2Multiply the lemon juice by 3. How many cups?
    3. 3Multiply the water by 3. How many cups?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Nuts (cups)3?Raisins (cups)28× ?× ?
    This time you know the raisins.

    A trail mix uses 3 cups of nuts for every 2 cups of raisins. How many cups of nuts go with 8 cups of raisins?

    1. 1What number times 2 makes 8? That is the scale factor.
    2. 2Multiply the nuts by the same scale factor. How many cups?
    Final answer:
  3. 3Complete each step, then write the final answer.
    BagsApples________________

    One bag holds 6 apples. Complete the ratio table. How many apples are in 5 bags?

    Show your work

    Hint The scale factor from 1 bag to 5 bags is 5.

    Final answer:
  4. 4Complete each step, then write the final answer.
    TomatoesOnions________________

    A food truck uses 4 tomatoes for every 3 onions in its salsa. How many tomatoes go with 12 onions?

    Show your work

    Hint Find what number times 3 makes 12. Use it on the tomatoes too.

    Final answer:
  5. 5Complete each step, then write the final answer.
    Blue paint (cans)White paint (cans)________________

    A paint color uses 2 cans of blue paint for every 7 cans of white paint. Ella uses 10 cans of blue paint. How many cans of white paint does she need?

    Show your work

    Hint Find the scale factor from 2 cans of blue to 10 cans of blue.

    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.
    Rice (cups)Water (cups)________________

    A ratio table starts with 3 cups of rice for every 4 cups of water. Raj adds 2 to each number and writes 5:6. Which row really belongs in the table?

    1. A9:12
    2. B5:6
    3. C6:7
    4. D4:5

    Hint A new row multiplies both numbers by the same scale factor.

    Show your work

Explain your thinkingRaj added 2 to both numbers in 3:4. Why does multiplying keep the same recipe, but adding changes it?

Sentence starter To make a new row, I multiply ___ by ___. · Adding the same number is wrong because ___.

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