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

Lesson 3.93.9 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can find and check equivalent ratios using multiplication and division — 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
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 soup serves 8 people. It uses 3 cups of tomatoes for every 2 cups of broth. She needs to serve 32 people. How many cups of tomatoes and broth does she need?

  1. Write the recipe in the first column: 8 : 3 : 2
  2. Find the scale factor: 32 ÷ 8 = 4
  3. Multiply the tomatoes by 4: 3 × 4 = 12
  4. Multiply the broth by 4: 2 × 4 = 8
  5. She needs 12 cups of tomatoes and 8 cups of broth. 3:2 and 12:8 are equivalent ratios.

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 1

Group 1Supported practice

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

Learning target With my small group, I can find and check equivalent ratios using multiplication and division — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    Bags520Nuts (cups)2?Raisins (cups)3?× ?× ?
    Use the same scale factor in every column.

    A trail mix recipe makes 5 bags. It uses 2 cups of nuts for every 3 cups of raisins. You want to make 20 bags. How many cups of nuts and raisins do you need?

    1. 1The recipe makes 5 bags. How many cups of nuts go in the first column?
    2. 2Find the scale factor: 20 ÷ 5.
    3. 3Multiply the nuts by 4. How many cups of nuts?
    4. 4Multiply the raisins by 4. How many cups of raisins?
    Final answer:
  2. 2Complete each step, then write the final answer.
    First amount15?Second amount20?÷ 5÷ 5
    Divide both numbers by 5.

    A ratio is 15:20. Divide both numbers by 5. What is the equivalent ratio?

    1. 1Divide the first number by 5: 15 ÷ 5.
    2. 2Divide the second number by 5: 20 ÷ 5.
    3. 3Write the equivalent ratio.
    Final answer:
  3. 3Complete each step, then write the final answer.
    First amountSecond amount________________

    A ratio is 3:5. Multiply both numbers by 2. The new ratio is 6 : ?. What is the missing number?

    Show your work

    Hint Multiply the second number by 2, the same as the first.

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

    Chef Montoya uses 5 onions for every 2 peppers. Today she uses 35 onions. How many peppers does she need?

    Show your work

    Hint Find the scale factor from 5 to 35. Use it on the peppers too.

    Final answer:
  5. 5Complete each step, then write the final answer.
    BoysGirls________________

    A class has 3 boys for every 4 girls. There are 16 girls. How many boys are in the class?

    Show your work

    Hint What times 4 makes 16? Multiply the boys by the same number.

    Final answer:
  6. 6Complete each step, then write the final answer.
    First amountSecond amount________________

    Jay adds 2 to each number in 2:3 and gets 4:5. He says they are equivalent. Find the correct ratio 4 : ?. What is the missing number?

    Show your work

    Hint To go from 2 to 4, you multiply by 2. Do the same to the 3.

    Final answer:

Explain your thinkingJay added 2 to both numbers. Why must you multiply both numbers by the same number instead?

Sentence starter Adding 2 does not work because ___. · 2:3 and 4:6 are equivalent because ___.

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