Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.2

Lesson 3.2Understand Rates and Unit Rates

Set B · Version ASecond form · supported practice

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

Learning target I can describe a rate using its two different units and use a model to find a travel time, and I can find a unit rate to compare prices and decide the better buy.

Why This Matters You're comparing ticket prices at different game booths in the arcade. Booth A charges $3 for 5 games, and Booth B charges $5 for 8 games. Which booth gives you a better deal? To find out, you need to figure out the cost per game — that's the unit rate!

RememberUnderstand Rates and Unit Rates

Rates & Unit Rates. Formula: Unit Rate = (Total Quantity) ÷ (Number of Units) A rate compares two amounts with different units. A unit rate tells you the amount for just 1 of something, like the cost for 1 game.

  1. Rate: A ratio comparing two quantities with different units (e.g. $12 for 3 lbs).
  2. Unit Rate: A rate simplified to a denominator of 1 unit ($4 per 1 lb).
  3. Divide numerator by denominator to compute the per-one amount

Words: Rates and Unit Rates (Tasas y tasas unitarias)Rate (Tasa)Unit Rate (Tasa unitaria)Per (Por)Ratio (Razón)

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    What does the ratio 3:1 mean in words?

    1. AThe first amount is 3 more than the second
    2. BThere are 4 things altogether
    3. CFor every 3 of the first amount there is 1 of the second
    4. DThe two amounts are equal
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    A bag holds 4 red marbles and 6 blue marbles. Write the ratio of red marbles to blue marbles in simplest form.

    1. A2:3
    2. B3:2
    3. C4:10
    4. D10
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    A bowl holds 4 apples and 6 oranges. What is the ratio of apples to the TOTAL pieces of fruit?

    1. A4:10
    2. B4:6
    3. C6:10
    4. D10:4
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    Which pair of amounts does the ratio 2:5 compare?

    1. ATwo different quantities
    2. BA number and its opposite
    3. CA total and its parts added
    4. DThe same quantity twice
    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    The arcade snack bar sells popcorn in two sizes: a small bag with 3 cups for $2.25 and a large bag with 8 cups for $5.60. You want the most popcorn for your money. What is the unit rate for the small bag?

    1. A$0.70 per cup
    2. B$0.75 per cup
    3. C$1.33 per cup
    4. D$2.25 per cup
    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. 6Circle the letter of the best answer. Show how you know.

    The arcade snack bar sells popcorn in two sizes: a small bag with 3 cups for $2.25 and a large bag with 8 cups for $5.60. You want the most popcorn for your money. What is the unit rate for the large bag?

    1. A$0.70 per cup
    2. B$0.75 per cup
    3. C$1.43 per cup
    4. D$5.60 per cup
    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?

Explain your thinkingHow does finding the unit rate help you compare the booths?

Sentence starter The best deal is Booth ___ because its unit rate of ___ per game is the ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.2

Lesson 3.2Understand Rates and Unit Rates

Set B · Version BSecond form · core practice

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

Learning target I can describe a rate using its two different units and use a model to find a travel time, and I can find a unit rate to compare prices and decide the better buy.

Why This Matters You're comparing ticket prices at different game booths in the arcade. Booth A charges $3 for 5 games, and Booth B charges $5 for 8 games. Which booth gives you a better deal? To find out, you need to figure out the cost per game — that's the unit rate!

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each arcade deal to its unit rate (coins per play).

    1. 80 coins for 4 plays
    2. 63 coins for 7 plays
    3. 48 coins for 6 plays
    4. 55 coins for 5 plays
    • A20 coins per play
    • B9 coins per play
    • C8 coins per play
    • D11 coins per play
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    The arcade snack bar sells popcorn in two sizes: a small bag with 3 cups for $2.25 and a large bag with 8 cups for $5.60. You want the most popcorn for your money. Which size is the better deal, and why?

    1. AThe small bag, because $2.25 is less than $5.60
    2. BThe small bag, because it has fewer cups
    3. CThe large bag, because $0.70 per cup is less than $0.75 per cup
    4. DThey are the same deal
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    The Star Blaster cabinet scored 90 points in 3 games. What is the unit rate in points per game?

    1. A3 points per game
    2. B30 points per game
    3. C93 points per game
    4. D270 points per game
    per 1
  3. 4Circle the letter of the best answer. Show how you know.

    Nova: 78 points in 6 min. Pulse: 75 points in 5 min. Which scores faster (more points per minute)?

    1. APulse, at 15 points per minute
    2. BNova, at 13 points per minute
    3. CThey score at the same rate
    4. DThere is not enough information
    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    Machine A: 150 coins for 5 plays. Machine B: 168 coins for 8 plays. Which is the better value (fewer coins per play)?

    1. AMachine A, at 30 coins per play
    2. BMachine B, at 21 coins per play
    3. CThey are the same value
    4. DMachine A, because it costs fewer coins total
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Level 2 Extension — Inverted Unit Rate: Points per Minute

    1. 1Find the scoring rate in points per minute: 96 points in 6 minutes96 points in 6 minutes
    2. 2Set up the division6 ÷ 96 = 0.0625
    3. 3Write the unit rateThe unit rate is 0.0625 points per minute

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingHow does finding the unit rate help you compare the booths?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help