Lesson 3.8Solve Problems with Unit Rates
Start hereWords, worked example, and sentence starters
Learning target I can solve real-world problems by using unit rates to compare options.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| 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. I want the cost for 1 token.
- I divide the price by the tokens: $60 ÷ 500 = $0.12.
- So this deal is $0.12 per token. That is the unit rate.
- Now I can compare it fairly to a deal with a different number of tokens.
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. What do we divide?
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.
Lesson 3.8Solve Problems with Unit Rates
Version ASupported practice
Learning target I can solve real-world problems by using unit rates to compare options.
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1Complete the table. Show how you found each value.
Find the unit rate for each deal to determine which is cheaper.
Item Deal Unit Rate Erasers Pack A 12 for $3.60 $0.30 each Erasers Pack B 8 for $2.80 Erasers Pack C 20 for $5.00 Hint Pack A's finished row shows the move: 12 for $3.60 became $3.60 ÷ 12 = $0.30 each.
Show your work
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2Circle the letter of the best answer. Show how you know.
Which is the better buy: 6 bouncy balls for $4.50 or 10 bouncy balls for $8.00?
- A10 for $8.00 — $0.80 each
- BThey cost the same per ball
- CNot enough information
- D6 for $4.50 — $0.75 each
Hint You can't compare $4.50 and $8.00 straight across — the packs hold different numbers of balls.
Show your work -
3Circle the letter of the best answer. Show how you know.
A faucet drips 15 ounces of water in 5 minutes. What is the unit rate?
- A0.33 ounces per minute
- B3 ounces per minute
- C5 ounces per minute
- D15 ounces per minute
Hint The unit rate here is ounces per ONE minute — 15 ounces spread across 5 minutes.
per 1 - 1LabelWrite what each column is.
- 2Find per 1Divide to get one.
- 3ScaleMultiply up to what is asked.
- 4CheckDoes the size make sense?
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4Circle the letter of the best answer. Show how you know.
A printer prints 42 pages in 6 minutes. How many pages does it print in 15 minutes at the same rate?
- A70 pages
- B90 pages
- C105 pages
- D120 pages
Hint This takes two steps: first find pages per ONE minute, then scale up to 15 minutes.
Show your work -
5Circle the letter of the best answer. Show how you know.
Store A sells 5 notebooks for $8. Store B sells 3 notebooks for $5.25. Which has the lower price per notebook?
- AStore B ($1.75 each)
- BStore A ($1.60 each)
- CSame price
- DCannot determine
Hint Each store sells a different number of notebooks, so compare the price of ONE notebook at each store.
Show your work
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6Find the mistake. Explain it, then show the correct work.
Spot the Common Mistake
- 1ReadWhich gum deal is the better buy: 4 packs for $2.00 or 10 packs for $4.50?
- 2AttemptA student says: "$2.00 is less than $4.50, so 4 packs for $2.00 is the better buy."
- 3CheckThe student compared the total prices instead of the cost for one pack.
Which step has the mistake? Explain what went wrong, then show the correct work.
Hint The packages hold different numbers of packs, so a smaller total price does not automatically win.
Correct workCorrect answer:
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 ___.
Lesson 3.8Solve Problems with Unit Rates
Version BCore practice
Learning target I can solve real-world problems by using unit rates to compare options.
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1Complete the table. Show how you found each value.
Find the unit rate for each deal and identify the better buy.
Option Deal Unit Rate Store A Batteries 8 for $6.00 Store B Batteries 12 for $8.40 Store A Candy 15 for $6.75 Store B Candy 20 for $8.00 Show your work -
2Write the name of the correct group on each line.
Three friends each walked different distances in different times. Sort them from fastest to slowest.
- Aiden: 6 miles in 2 hours
- Bella: 10 miles in 4 hours
- Carlos: 4 miles in 2 hours
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3Circle the letter of the best answer. Show how you know.
A machine dispenses 24 tokens in 3 minutes. At this rate, how many tokens does it dispense in 10 minutes?
- A60 tokens
- B72 tokens
- C80 tokens
- D240 tokens
Show your work -
4Circle the letter of the best answer. Show how you know.
A factory produces 360 widgets in 8 hours. At the same rate, how many widgets are produced in a 12-hour shift?
- A360 widgets
- B480 widgets
- C540 widgets
- D720 widgets
Show your work
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5Find the mistake. Explain it, then show the correct work.
Spot the Common Mistake
- 1ReadA vending machine dispenses 24 tokens in 3 minutes. How many tokens per minute is that?
- 2AttemptA student writes: 3 ÷ 24 = 0.125, so the machine dispenses 0.125 tokens per minute.
- 3CheckThe student divided minutes by tokens, which gives minutes per token, not tokens per minute.
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer:
Explain your thinkingHow do you use unit rates to determine the better buy?
Lesson 3.8Solve Problems with Unit Rates
ChallengeExtension
Learning target I can solve real-world problems by using unit rates to compare options.
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1Complete the table. Show how you found each value.
Two delivery drones fly at different rates. Drone A travels 9 miles in 12 minutes. Drone B travels 7 miles in 10 minutes. Complete the table and determine which drone delivers faster.
Drone Distance Time Miles per Minute Faster? Drone A 9 miles 12 min Drone B 7 miles 10 min Show your work
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2Find the mistake. Explain it, then show the correct work.
Find the Unit Rate Error
- 1Which is the better buy: 5 lb for $8.75 or 3 lb for $5.10?Compare two deals
- 2Find unit rate for Deal 15 ÷ $8.75 = 0.57 lb per dollar
- 3Find unit rate for Deal 23 ÷ $5.10 = 0.59 lb per dollar
- 4Compare0.59 > 0.57, so Deal 2 is the better buy
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer: -
3Answer in complete sentences.
Two arcade supply companies offer token deals. Company X: 300 tokens for $36. Company Y: 500 tokens for $55. The arcade needs 1,000 tokens. Find the unit rate for each company, determine which is cheaper per token, and calculate the total cost of buying 1,000 tokens from the better deal.
Write your answer