Neft Teacher · Learn It

Unit 3 · Standard 6.AT.2

Understand Rates and Unit Rates

Lesson 3-2 · Learn It — how the math works

Why we're learning this

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!

✱ Math Workbench

Learn It

What is a unit rate, and how does it help me find the better buy?

A rate compares two amounts with different units. A unit rate tells you the amount for just 1 of something, like the cost for 1 game.

Picture itSee what the math looks like before you read about it

Two arcade booths sell game tokens. One booth advertises 5 tokens for $3.00, and the booth next to it advertises 8 tokens for $5.00. The signs are big and colorful, and each lists a different number of tokens for a different price.
Where you see this in real lifeTwo arcade booths sell game tokens. One booth advertises 5 tokens for $3.00, and the booth next to it advertises 8 tokens for $5.00. The signs are big and colorful, and each lists a different number of tokens for a different price.

Watch me solve itI do — read one step at a time

The problem looks like this
Double number line: 5 games cost $3, so 1 game costs $0.60.Games15Cost$0.60$3
  1. Booth A charges $3 for 5 games. I want the cost for just 1 game.
  2. I the cost by the games:$3 ÷ 5 = $0.60
  3. So Booth A costs $0.60 game. That is the .
  4. Because this is money for one item, it has its own name: it is the .
  5. Now I can compare this booth's fairly with any other booth's.

Watch out — mistakes students make here

  • Divide the cost by the number for each pack. You should get $0.25 and $0.28.
  • Compare the cost per token, not the total price or the total number of tokens. Divide each pack's price by its tokens and compare those results.
  • A bigger pack is not automatically cheaper for each token. Work out price ÷ tokens for every pack before deciding.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. A booth charges $4 for 8 games. What do we ?
  2. We cost by games: $4 ÷ 8 = ?$4 ÷ 8
  3. What is the , the cost for just 1 game?
    Check this step
    ($0.50 game.)

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the table, find the cost game for each booth by dividing.
  • Then decide which booth has the lowest — that is the .

Solve: Complete the table to find and determine the best deal.

DealQuantityCostUnit Rate
Tokens Pack A20 tokens$5.00
Tokens Pack B35 tokens$7.00
Tokens Pack C50 tokens$12.50

Stuck? Open one hint at a time.

Hint 1

Each pack lists tokens and a total cost. The unit rate column wants the cost of ONE token, like '$0.25 per token'.

Hint 2

Divide the cost by the number of tokens for each pack — dollars ÷ tokens = dollars per token.

Hint 3

For Pack A, divide $5.00 by 20 tokens. Then repeat: $7.00 ÷ 35 for Pack B and $12.50 ÷ 50 for Pack C.

Check my answer
✅ Answers:
  • Tokens Pack A → Unit Rate: $0.25 per token
  • Tokens Pack B → Unit Rate: $0.20 per token
  • Tokens Pack C → Unit Rate: $0.25 per token
Dividing the cost by the number of tokens gives the price of a single token: $5.00 ÷ 20 = $0.25, $7.00 ÷ 35 = $0.20, and $12.50 ÷ 50 = $0.25 per token. The unit rates show Pack B is the best value, even though it is neither the biggest pack nor the cheapest total.

Turn & TalkSay it out loud with a partner

Booth A charges $3 for 5 games and Booth B charges $5 for 8 games. Just by looking, which booth seems like the better deal, and what makes it hard to be sure?

Try starting with:

  • Booth ___ looks better because ___.El puesto ___ se ve mejor porque ___.
  • It is hard to compare because the ___ are different.Es difícil comparar porque los/las ___ son diferentes.
Use these wordsrateperratiocompare