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

Lesson 3.33.1–3.3 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 3.1–3.3 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

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

WordWhat it meansExample
Understand RatiosSpanish: Comprender razones Use a ratio to compare two quantities by division. 3 red tiles to 5 blue tiles can be written 3:5 or 3/5.
RatioSpanish: Razón A way to compare two amounts, like 3 to 2. 3 cups flour to 2 cups sugar → 3:2
ComparisonSpanish: Comparación Looking at two or more amounts to see how they are related. 5 eggs vs. 3 eggs — which recipe uses more?
Part-to-partSpanish: Parte a parte A ratio comparing one part of a group to another part. 3 teal counters to 5 amber counters → 3:5
Part-to-wholeSpanish: Parte a todo A ratio comparing one part to the whole group. 3 teal counters out of 8 counters in all → 3:8
Colon notationSpanish: Notación con dos puntos Writing a ratio with two dots between the numbers, like 3:2. 3 to 2 can be written as 3:2

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 3.33.1–3.3 Catch-Up

Catch-UpSkill bridge

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

Learning target I can show I am caught up on Lessons 3.1–3.3 by using each lesson's big idea in mixed practice.

  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 3.1) A recipe uses 4 cups of milk and 1 cup of cream. What is the ratio of milk to cream?

    1. A1:4
    2. B4:1
    3. C4:5
    4. D5:1

    Hint Re-read the question: it asks for milk to cream, in that exact order.

    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    (Lesson 3.1) Chef Reyes uses 6 strawberries and 2 bananas in a smoothie. What is the part-to-whole ratio of bananas to total fruit?

    1. A2:8
    2. B2:6
    3. C6:2
    4. D8:2

    Hint Notice the word 'total' — this is a part-to-WHOLE ratio, not banana-to-strawberry.

    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    (Lesson 3.2) A booth charges $4.50 for 9 games. What is the unit rate?

    1. A$0.45 per game
    2. B$0.50 per game
    3. C$2.00 per game
    4. D$4.50 per game

    Hint You know the total cost ($4.50) and the total games (9). A unit rate tells the cost of just ONE game.
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  4. 4Circle the letter of the best answer. Show how you know.

    (Lesson 3.2) A car travels 180 miles using 6 gallons of gas. What is the unit rate in miles per gallon?

    1. A6 miles per gallon
    2. B30 miles per gallon
    3. C36 miles per gallon
    4. D180 miles per gallon

    Hint Notice the units in the question: miles PER gallon. That tells you miles go on top and gallons on the bottom.
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  5. 5Circle the letter of the best answer. Show how you know.

    (Lesson 3.3) 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

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