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

Lesson 3.83.8 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can solve real-world problems by using unit rates to compare options, explain how I can tell, and judge a case I have not seen before.

Start hereWords for this lesson

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

WordWhat it meansExample
Unit RateSpanish: Tasa unitaria A rate for just 1 of something, like cost for 1 item. $2.50 per pound means $2.50 for every 1 pound
Better BuySpanish: Mejor compra The choice that costs less for each item. $0.10 each vs $0.15 each — the $0.10 option is the better buy
ComparisonSpanish: Comparación Looking at two or more amounts to see how they are related. $3 per game < $4 per game
Per UnitSpanish: Por unidad For each single item. $0.50 per token means each token costs $0.50
RateSpanish: Tasa A ratio comparing two amounts with different units, like miles per hour. 120 miles in 3 hours is a rate (miles and hours are different units)
ProportionSpanish: Proporción A math sentence saying two ratios are equal. It helps find a missing number. 5/3 = x/12 → x = 20

How it worksWorked example

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

Fun Supply Co. sells 500 tokens for $60. Arcade Depot sells 350 tokens for $38.50. Each store sells tokens at its unit price. You need 700 tokens. How much do you save at Arcade Depot?

  1. Write both deals in the table.
  2. Scale each deal down to 1 token: $60 ÷ 500 = $0.12; $38.50 ÷ 350 = $0.11
  3. Multiply both deals by 700: $0.12 × 700 = $84; $0.11 × 700 = $77
  4. Subtract to find the savings: $84 − $77 = $7
  5. You save $7 by buying 700 tokens at Arcade Depot.

Now you trySame steps, your turn

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

Arcade Depot sells 350 tokens for $38.50. Fun Supply Co. sells 500 tokens for $60. Which store is the better buy?

Answer:

Say it and write itSentence starters

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

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

Word bank Unit RateBetter BuyComparisonPer UnitRateProportionunit ratelowerdividecostpercompare

Watch outA common mistake

A common mistake in Solve Problems with Unit Rates is comparing the total prices instead of the cost per item — the deal with the smaller total can still cost more per unit. Always reduce each option to its unit rate before you decide, then pick the lower one.

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

Lesson 3.83.8 Small Group · Group 2

Group 2Challenge 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, explain how I can tell, and judge a case I have not seen before.

  1. 1Complete each step, then write the final answer.
    Store A stickers3001600Store A cost ($)$24?$48Store B stickers4001600Store B cost ($)$28??÷ ?÷ ?× ?× ?
    Scale to 1 sticker, then to 600.

    Store A sells 300 stickers for $24. Store B sells 400 stickers for $28. You need 600 stickers. How much do you save at the better store?

    1. 1Find each store's cost for 1 sticker.
    2. 2What do you multiply 1 sticker by to reach 600?
    3. 3What do 600 stickers cost at Store B?
    4. 4600 stickers cost $48 at Store A. How much do you save at Store B?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Beads60190Cost ($)$8.40??÷ ?÷ ?× ?× ?
    Use 1 bead as a bridge.

    A bag of 60 beads costs $8.40. At the same unit price, what do 90 beads cost?

    1. 1What do you divide 60 by to reach 1 bead?
    2. 2Divide $8.40 by the same number. What is the cost for 1 bead?
    3. 3Multiply both numbers by 90. What do 90 beads cost?
    4. 4Why find the cost for 1 bead first?
    Final answer:
  3. 3Complete each step, then write the final answer.
    BottlesCost ($)________________

    A 15-pack of water bottles costs $4.50. What is the cost for 1 bottle?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    TokensCost ($)________________

    Tokens cost $0.12 each at Fun Supply Co. How many tokens can you buy for $30?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    Bag A poundsBag A cost ($)Bag B poundsBag B cost ($)________________

    You need 15 pounds of apples. Bag A has 3 pounds for $5.40. Bag B has 5 pounds for $8.50. How much do you save if you buy the better bags?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.
    Tray A peopleTray A cost ($)Tray B peopleTray B cost ($)________________

    Tray A costs $12 and feeds 4 people. Tray B costs $21 and feeds 6 people. Tom says Tray B is the better deal because it feeds more people. What is the lower cost per person?

    Show your work
    Final answer:

Explain your thinkingOne deal has a lower total price. Another deal has a lower unit price. Which one should you choose when you need a lot? Defend your choice.

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