Lesson 3.2Understand Rates and Unit Rates
Start hereWords, worked example, and sentence starters
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!
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| Rates and Unit RatesSpanish: Tasas y tasas unitarias | A rate compares different units; a unit rate compares a quantity to 1 unit. | 180 miles in 3 hours = 60 miles per 1 hour. |
| RateSpanish: Tasa | A ratio comparing two amounts with different units, like miles per hour. | 96 pages / 3 hours |
| Unit RateSpanish: Tasa unitaria | A rate for just 1 of something, like cost for 1 item. | 32 pages per 1 hour |
| PerSpanish: Por | For each one. Example: 5 dollars per book. | miles per hour, cost per pound |
| RatioSpanish: Razón | A way to compare two amounts, like 3 to 2. | 5 to 3 or 5:3 |
| Unit priceSpanish: Precio unitario | A unit rate that gives the cost of exactly 1 item, like $0.60 per game. | $3 for 5 games → $0.60 per 1 game |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A printer prints 90 pages in 6 minutes at a steady rate. How many pages in 7 minutes? How long for 45 pages?
- Divide: 90 ÷ 6 = 15 pages per minute.
- 7 minutes: 15 × 7 = 105 pages.
- 45 pages: 45 ÷ 15 = 3 minutes.
Answer: 105 pages; 3 minutes
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A booth charges $4 for 8 games. What do we divide?
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The rate is for every .
- I divided by to find the unit rate.
- The unit rate is per .
- To find the amount for , I .
Word bank rateunit ratepereachdividemultiplyfor everyspeedpredictconstanthourpound
Watch out!A common mistake
A common mistake in Rates and Unit Rates is comparing total costs instead of unit rates: a student sees Pack X at $4.00 for 10 tokens and Pack Y at $6.00 for 16 tokens and picks Pack X just because $4.00 is the smaller number, without dividing to find the cost per token ($0.40 for Pack X vs. $0.375 for Pack Y
Lesson 3.2Understand Rates and Unit Rates
Level 0Most support · every hint printed
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!
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A printer prints 90 pages in 6 minutes at a steady rate. How many pages in 7 minutes? How long for 45 pages?
- Divide: 90 ÷ 6 = 15 pages per minute.
- 7 minutes: 15 × 7 = 105 pages.
- 45 pages: 45 ÷ 15 = 3 minutes.
Answer: 105 pages; 3 minutes
-
1Circle the letter of the best answer. Show how you know.
A booth charges $4.50 for 9 games. What is the unit rate?
- A$0.45 per game
- B$0.50 per game
- C$2.00 per game
- D$4.50 per game
Steps to try- You know the total cost ($4.50) and the total games (9). A unit rate tells the cost of just ONE game.
- To find a unit rate, divide the total cost by the number of games so the second quantity becomes 1.
- Set up the division: $4.50 ÷ 9. Think of $4.50 as 450 cents if that makes the division easier.
per 1 - 1LabelWrite what each column is.
- 2Find per 1Divide to get one.
- 3ScaleMultiply up to what is asked.
- 4CheckDoes the size make sense?
-
2Circle the letter of the best answer. Show how you know.
A car travels 180 miles using 6 gallons of gas. What is the unit rate in miles per gallon?
- A6 miles per gallon
- B30 miles per gallon
- C36 miles per gallon
- D180 miles per gallon
Steps to try- Notice the units in the question: miles PER gallon. That tells you miles go on top and gallons on the bottom.
- Divide the total miles by the total gallons so you get the miles for just 1 gallon.
- Start the division: 180 ÷ 6. Think: 6 × what number lands on 180?
per 1 - 1LabelWrite what each column is.
- 2Find per 1Divide to get one.
- 3ScaleMultiply up to what is asked.
- 4CheckDoes the size make sense?
-
3Circle the letter of the best answer. Show how you know.
A pack of 8 markers costs $6.00. What is the cost per marker?
- A$0.60
- B$0.75
- C$0.80
- D$1.33
Steps to try- You have 8 markers costing $6.00 total. 'Cost per marker' means the price of ONE marker.
- Divide the total price by the number of markers — cost goes first, markers second.
- Set up $6.00 ÷ 8. Tip: $6.00 is 600 cents, so try 600 ÷ 8 cents.
per 1 - 1LabelWrite what each column is.
- 2Find per 1Divide to get one.
- 3ScaleMultiply up to what is asked.
- 4CheckDoes the size make sense?
-
4Circle the letter of the best answer. Show how you know.
Which is a unit rate?
- A12 miles per 1 hour
- B24 miles in 2 hours
- C36 miles for 3 gallons
- D100 points in 5 games
Steps to try- A unit rate always compares to exactly ONE of something — look at the second number in each choice.
- Check each choice: is the second quantity (hours, gallons, games) equal to 1? Only one choice passes that test.
- Start with '24 miles in 2 hours' — the second quantity is 2, not 1, so that one is not a unit rate. Test the rest the same way.
Show your work
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 ___.