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

Lesson 3.93.9 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find and check equivalent ratios using multiplication and division, 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
Equivalent RatiosSpanish: Razones equivalentes Ratios that compare quantities in the same relationship. 2:3 = 4:6 because both parts were multiplied by 2.
RatioSpanish: Razón A way to compare two amounts, like 3 to 2. 3 red apples : 5 green apples
RateSpanish: Tasa A ratio comparing two amounts with different units, like miles per hour. 60 miles per 1 hour
ProportionSpanish: Proporción A math sentence saying two ratios are equal. 2/3 = 4/6
SimplifySpanish: Simplificar To write a ratio with smaller numbers that still compares the same way. 6:8 and 3:4 are the same ratio. 12:18 → divide both by 6 → 2:3
Ratio tableSpanish: Tabla de razones A table of equal ratios that shows a pattern. Cups of juice: 2, 4, 6 | Cups of water: 3, 6, 9

How it worksWorked example

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

Chef Montoya's dressing uses 6 cups of oil for 4 cups of vinegar. Chef Lee's uses 9 cups of oil for 6 cups of vinegar. Do the two dressings have equivalent ratios?

  1. Write Chef Montoya's 6:4 in the first column.
  2. Divide both numbers by 2: 6 ÷ 2 = 3; 4 ÷ 2 = 2
  3. Multiply both numbers of 3:2 by 3: 3 × 3 = 9; 2 × 3 = 6
  4. Compare with Chef Lee's 9:6: 9:6 and 9:6
  5. Yes. 6:4 scales to 3:2 and then to 9:6, so the ratios are equivalent.

Now you trySame steps, your turn

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

A ratio is 2:5. Use a scale factor of 3 to make an equivalent ratio.

Answer:

Say it and write itSentence starters

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

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

Word bank Equivalent RatiosRatioRateProportionSimplifyRatio tablemultiplysame numberequivalentscaletomatoesbroth

Watch outA common mistake

A common mistake in Equivalent Ratios is ADDING the scale factor to one part instead of MULTIPLYING both parts by it. For example, scaling 2:5 by a factor of 4 should give 8:20 (2×4 and 5×4) — not 6:9 (2+4 and 5+4). Adding changes the taste of the recipe (and the value of the ratio); only multiplying or dividing both numbers by the same amount keeps it equivalent.

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

Lesson 3.93.9 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can find and check equivalent ratios using multiplication and division, 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.
    Oats (cups)8?12Nuts (cups)6??÷ 2÷ 2× ?× ?
    Scale Mix A to 12 cups of oats. Compare the nuts.

    Mix A uses 8 cups of oats for 6 cups of nuts. Mix B uses 12 cups of oats for 9 cups of nuts. Do the two mixes have equivalent ratios?

    1. 1Divide both by 2. How many cups of nuts go with 4 cups of oats?
    2. 2Find the scale factor from 4 to 12 cups of oats.
    3. 3Multiply 3 cups of nuts by 3. How many cups of nuts?
    4. 4Mix B uses 12 cups of oats and 9 of nuts. Equivalent? Type yes or no.
    Final answer:
  2. 2Complete each step, then write the final answer.
    First amount6?9Second amount10??÷ 2÷ 2× ?× ?

    The ratio 6:10 is equivalent to 9 : ?. Find the missing number.

    1. 1Divide 6 and 10 by 2. What is 10 ÷ 2?
    2. 2What times 3 makes 9?
    3. 3Multiply 5 by 3. What is the missing number?
    4. 4Why did we use the middle column?
    Final answer:
  3. 3Complete each step, then write the final answer.
    First amountSecond amount________________________

    Is 20:8 equivalent to 25:10? Type yes or no.

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

    Is 12:16 equivalent to 15:21? Type yes or no.

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    Berries (cups)Yogurt (cups)________________________

    A smoothie uses 6 cups of berries for 8 cups of yogurt. Lin uses 15 cups of berries. How many cups of yogurt keep the same ratio?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.
    First amountSecond amount________________________

    Lia says 9:12 and 12:15 are equivalent, because both numbers went up by 3. Find the number that makes 12 : ? equivalent to 9:12.

    Show your work
    Final answer:

Explain your thinkingNo whole number turns 6 into 9. How can you still check whether 6:10 and 9:15 are equivalent?

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