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

Lesson 3.8Solve Problems with Unit Rates

Set B · Version ASecond form · supported practice

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

Learning target I can solve real-world problems by using unit rates to compare options.

Why This Matters You're the new supply manager for the arcade! You need to order tokens, prizes, and snacks from different suppliers. Each supplier offers a different package deal. Your job is to find the unit rate for each deal and figure out which supplier gives you the best value for every item you need to order. Fun Supply Co. sells 500 tokens for $60. Arcade Depot sells 350 tokens for $38.50. Which supplier gives the better value for tokens?

RememberSolve Problems with Unit Rates

Solving Problems with Unit Rates. Formula: Unit Price = Cost ÷ Quantity | Total Cost = Unit Price × Quantity A unit rate is the cost for just 1 item, like the price per token. When packages have different sizes, the unit rate lets you compare them fairly.

  1. Find the unit rate by dividing total cost by quantity.
  2. Compare unit rates to determine the best deal.
  3. Multiply unit rate by desired quantity to calculate total cost

Words: Unit Rate (Tasa unitaria)Better Buy (Mejor compra)Comparison (Comparación)Per Unit (Por unidad)Rate (Tasa)

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

    About how many pounds is 10 kilograms? (1 kg ≈ 2.2 lb)

    1. Aabout 2.2 pounds
    2. Babout 4.5 pounds
    3. Cabout 12.2 pounds
    4. Dabout 22 pounds
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    About how many centimetres are in 4 inches? (1 in ≈ 2.54 cm)

    1. Aabout 1.6 cm
    2. Babout 6.5 cm
    3. Cabout 10.2 cm
    4. Dabout 25.4 cm
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    A race is 5 kilometres long. About how many miles is that? (1 mi ≈ 1.6 km)

    1. Aabout 1.6 miles
    2. Babout 3.1 miles
    3. Cabout 5 miles
    4. Dabout 8 miles
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    You change 10 pounds into kilograms using 1 kg ≈ 2.2 lb. Should the number of kilograms be greater or less than 10?

    1. AGreater than 10, because a kilogram is lighter
    2. BExactly 10
    3. CYou cannot tell
    4. DLess than 10, because a kilogram is heavier than a pound
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    The arcade needs 600 prize tickets printed. Printer A prints 150 tickets in 5 minutes. Printer B prints 200 tickets in 8 minutes. The manager wants to use the faster printer. What is Printer A's unit rate?

    1. A5 tickets per minute
    2. B25 tickets per minute
    3. C30 tickets per minute
    4. D150 tickets per minute
    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?
  6. 6Circle the letter of the best answer. Show how you know.

    The arcade needs 600 prize tickets printed. Printer A prints 150 tickets in 5 minutes. Printer B prints 200 tickets in 8 minutes. The manager wants to use the faster printer. What is Printer B's unit rate?

    1. A8 tickets per minute
    2. B25 tickets per minute
    3. C30 tickets per minute
    4. D200 tickets per minute
    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 do you use unit rates to determine the better buy?

Sentence starter I find the better buy by comparing the ___ for each option. The option with the ___ unit rate is the better buy because ___.

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 3.8Solve Problems with Unit Rates

Set B · Version BSecond form · core practice

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

Learning target I can solve real-world problems by using unit rates to compare options.

Why This Matters You're the new supply manager for the arcade! You need to order tokens, prizes, and snacks from different suppliers. Each supplier offers a different package deal. Your job is to find the unit rate for each deal and figure out which supplier gives you the best value for every item you need to order. Fun Supply Co. sells 500 tokens for $60. Arcade Depot sells 350 tokens for $38.50. Which supplier gives the better value for tokens?

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    For each prize item, find the unit rate of both deals and sort each card into Better Buy or Worse Buy.

    Groups: Better Buy (lower unit rate) Worse Buy (higher unit rate)
    • Snack packs: 4 for $5.00 ($1.25 each)
    • Snack packs: 6 for $9.00 ($1.50 each)
    • Stickers: 25 for $8.75 ($0.35 each)
    • Stickers: 10 for $4.00 ($0.40 each)
    • Tokens: 250 for $20.00 ($0.08 each)
    • Tokens: 100 for $9.00 ($0.09 each)
  2. 2Write the letter of the matching item on each line.

    Match each prize deal to its unit price (price ÷ quantity).

    1. Glow bracelets: 5 for $4.50
    2. Bouncy balls: 8 for $6.00
    3. Mini erasers: 3 for $2.40
    4. Temporary tattoos: 10 for $3.50
    • A$0.90 each
    • B$0.75 each
    • C$0.80 each
    • D$0.35 each
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    The arcade needs 600 prize tickets printed. Printer A prints 150 tickets in 5 minutes. Printer B prints 200 tickets in 8 minutes. The manager wants to use the faster printer. Which printer is faster, and how long for 600 tickets?

    1. APrinter A, 20 minutes
    2. BPrinter B, 20 minutes
    3. CPrinter B, 24 minutes
    4. DPrinter A, 24 minutes
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    The snack bar compares two popcorn deals: 12 oz for $3.00 or 20 oz for $4.00. Which is the better buy?

    1. A12 oz for $3.00 — $0.25 per oz
    2. BThey cost the same per ounce
    3. CNot enough information
    4. D20 oz for $4.00 — $0.20 per oz
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    The delivery van brings arcade supplies 150 miles in 3 hours. What is the unit rate in miles per hour?

    1. A30 miles per hour
    2. B45 miles per hour
    3. C50 miles per hour
    4. D153 miles per hour
    per 1
  4. 6Circle the letter of the best answer. Show how you know.

    The ticket counter sells redemption tickets two ways: 8 tickets for $2.00 or 15 tickets for $3.00. Which costs less per ticket?

    1. A8 tickets for $2.00 — $0.25 each
    2. BThey cost the same per ticket
    3. CCannot determine
    4. D15 tickets for $3.00 — $0.20 each
    Show your work

Explain your thinkingHow do you use unit rates to determine the better buy?

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