Lesson 3.5Comparing Rates with Benchmarks
Start hereWords, worked example, and sentence starters
Learning target I can compare ratios by finding unit rates or using equivalent ratios.
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 lb |
| Equivalent ratioSpanish: Razón equivalente | Two ratios that mean the same thing. | 4:6 and 2:3 are equivalent (both simplify to 2:3) |
| CompareSpanish: Comparar | To look at ratios and see which is bigger, smaller, or equal. | 3:4 vs. 2:5 — which has more of the first ingredient per unit? |
| SimplifySpanish: Simplificar | To write a ratio with smaller numbers that still compares the same way. 6:8 and 3:4 are the same ratio. | 8:12 → divide both by 4 → 2:3 |
| Common denominatorSpanish: Denominador común | A bottom number that two fractions can share so you can compare them. | To compare 3/5 and 4/7, use LCD 35: 21/35 vs 20/35 |
| Common multipleSpanish: Múltiplo común | A number that both terms can be scaled to. | 2 and 3 both reach 6. |
How it worksWorked examplecomparing with a benchmark instead of dividing
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Store A sells 4 lb for $10.00. Store B sells 6 lb for $14.40. Which is the better deal?
- Pick a benchmark both can reach. 4 and 6 both reach 12 lb.
- Scale Store A. ×3 → 12 lb for $30.00
- Scale Store B. ×2 → 12 lb for $28.80
- Same weight, so compare the price. LOWER price = better deal.
Answer: Store B is the better deal: $28.80 for 12 lb.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
Runner A does 9 laps in 6 minutes. Runner B does 12 laps in 9 minutes. Who is faster?
- Pick a benchmark both reach. 6 and 9 both reach minutes.
- Scale A. × → laps
- Scale B. × → laps
- Same time, so compare the laps. MORE laps = faster. Runner
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- I scaled both to .
- At , costs and costs .
- is the better deal because .
- A benchmark helps because .
Word bank benchmarkrateunit ratescalecompareequivalentlowerhigherbetter dealpersame amountdivide
Watch outA common mistake
A common mistake in Compare Ratios is thinking the ratio with the bigger raw number automatically wins — like assuming Chef Tran's 8 tablespoons of cocoa must be more chocolatey than Chef Reyes's 6 tablespoons, without checking that the milk amounts (14 oz vs. 10 oz) are different. Never compare the raw numbers alone — always scale both ratios to the same amount or find each unit rate first.
Lesson 3.5Comparing Rates with Benchmarks
Apply Day · Version ASupported practice
Learning target I can compare ratios by finding unit rates or using equivalent ratios.
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1Complete each step, then write the final answer.
Shop A: first two columns. Shop B: last two. Shop A sells 2 cookies for $4. Shop B sells 3 cookies for $9. What is the lower price for 1 cookie?
Show your workHint Divide each cost by the number of cookies.
Final answer: -
2Complete each step, then write the final answer.
Drink A: first two columns. Drink B: last two. Drink A uses 1 cup of juice for 2 cups of water. Drink B uses 2 cups of juice for 3 cups of water. Scale both to 6 cups of water. Which drink has more juice?
Show your workHint With the same water, the drink with more juice wins.
Final answer: -
3Complete each step, then write the final answer.
Bag A: first two columns. Bag B: last two. Bag A has 4 oranges for $2. Bag B has 6 oranges for $4. Which bag costs less for 1 orange?
Show your workHint Divide each cost by the number of oranges. The lower price wins.
Final answer:
Lesson 3.5Comparing Rates with Benchmarks
Apply Day · Version BCore practice
Learning target I can compare ratios by finding unit rates or using equivalent ratios.
-
1Circle the letter of the best answer. Show how you know.
Box A: first two columns. Box B: last two. Box A has 10 granola bars for $4. Box B has 12 granola bars for $6. Which box is the better buy?
- ABox A — $0.40 per bar
- BBox B — $0.50 per bar
- CBox B — it has more bars
- DThey cost the same per bar
Show your work -
2Complete each step, then write the final answer.
Drink A: first two columns. Drink B: last two. Drink A uses 3 scoops of powder for 5 cups of water. Drink B uses 5 scoops for 8 cups of water. Scale both to 40 cups of water. For 40 cups of water, how many scoops does the stronger drink use?
Show your workFinal answer: -
3Complete each step, then write the final answer.
Store A: first two columns. Store B: last two. Store A sells 3 pens for $3.60. Store B sells 5 pens for $5.50. What is the lower price for 1 pen?
Show your workFinal answer:
Lesson 3.5Comparing Rates with Benchmarks
Apply Day · ChallengeExtension
Learning target I can compare ratios by finding unit rates or using equivalent ratios.
-
1Circle the letter of the best answer. Show how you know.
7:10: first two columns. 3:4: last two. Ty says the ratio 7:10 is greater than 3:4, because 7 > 3. Which statement is true?
- A3:4 is greater
- B7:10 is greater
- CThey are equal
Show your work
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2Circle the letter of the best answer. Show how you know.
Car A travels 180 miles on 6 gallons. Car B travels 225 miles on 9 gallons. Which car gets better gas mileage?
- ACar B, at 25 miles per gallon
- BCar B, because it traveled farther
- CThey are equal
- DCar A, at 30 miles per gallon
Show your work -
3Complete each step, then write the final answer.
Tea A: first two columns. Tea B: last two. Tea A uses 2 spoons of honey for 9 cups of tea. Tea B uses 3 spoons of honey for 12 cups of tea. Which tea is sweeter?
Show your workFinal answer: