Unit 4 · Standard 6.RP.2
Rates and Unit Rates
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
$12 for 4 games is a rate
Rate
A ratio comparing two amounts with different units, like miles per hour.
$3 per 1 game
Unit Rate
A rate for just 1 of something, like cost for 1 item.
60 miles per hour means 60 miles for every 1 hour
Per
For each one. Example: 5 dollars per book.
5 to 3 or 5:3
Ratio
A way to compare two amounts.
Pack A: $0.50 per pencil vs Pack B: $0.40 per pencil — Pack B is the better buy
Better Buy
The choice that costs less for each item.
$12 ÷ 4 games = $3 per game
Divide
Splitting a total into equal groups.
Key Ideas & Notes
- 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!
- Calculate the unit rate (cost per game) for each arcade booth. Divide the total cost by the number of games.
Think About It
- What two quantities are being compared at each booth?
- Which booth seems like a better deal at first glance?
- How can you compare prices when the number of games is different?
My Notes
Guided Examples
Example 1
A booth charges $4.50 for 9 games. What is the unit rate?
Solution: $4.50 ÷ 9 = $0.50 per game.
Answer: A. $0.50 per game
Example 2
A car travels 180 miles using 6 gallons of gas. What is the unit rate in miles per gallon?
Solution: 180 miles ÷ 6 gallons = 30 miles per gallon.
Answer: A. 30 miles per gallon
Example 3
A pack of 8 markers costs $6.00. What is the cost per marker?
Solution: $6.00 ÷ 8 = $0.75 per marker.
Answer: A. $0.75
Write About the Math The Writing Revolution
I can explain my choice using the words rate, unit rate, per, and better buy.
1. Kernel Sentence subject + verb
Model: Rate is a ratio comparing two amounts with different units, like miles per hour.Tasa es una razón que compara dos cantidades con unidades distintas, como millas por hora.
Write a kernel sentence about rate. Use a subject and a verb.Escribe una oración base sobre tasa. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Rate matters in mathTasa importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Rate matters in math because ___.Tasa importa en matemáticas porque ___.
Rate matters in math, but ___.Tasa importa en matemáticas, pero ___.
Rate matters in math, so ___.Tasa importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about rate.Di un hecho verdadero sobre rate.
Rate ___.
Ask a question about rate.Haz una pregunta sobre rate.
How does ___ ?¿Cómo ___ ?
Show excitement about rate.Muestra entusiasmo sobre rate.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with rate.Dile a un compañero qué hacer con rate.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
The unit rate is ___ per one ___.La tasa unitaria es ___ por un ___.
I divided ___ by ___.Dividí ___ entre ___.
The best buy is ___ because ___.La mejor compra es ___ porque ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Which token pack from the table above is the best deal?
- Pack A
- Pack B
- Pack C
- They are all the same
2. Runner A completes 4 laps in 12 minutes. Runner B completes 5 laps in 14 minutes. Who runs more laps per minute?
- Runner B
- Runner A
- Same rate
- Cannot determine
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
An arcade sells tokens in three packs: 25 tokens for $5, 60 tokens for $10.80, and 100 tokens for $19. A student says the 100-token pack is always the best deal because you get the most tokens. Is the student correct? Find all three unit rates and explain.
Sentence starter: The student is ___ because the best deal is the ___ pack with a unit rate of $___ per token.
Reflect — Exit Ticket
A store sells 6 pencils for $1.50 and 10 pencils for $2.80. Which is the better buy?
- 6 for $1.50 — $0.25 each
- 10 for $2.80 — $0.28 each
- They cost the same per pencil
- Not enough information
Answer Key & Teacher Guide
- Try It 1: B. Pack B — Pack B has a unit rate of $0.20 per token, which is the lowest cost per token.
- Try It 2: A. Runner B — Runner A: 4÷12 ≈ 0.33 laps/min. Runner B: 5÷14 ≈ 0.36 laps/min. Runner B runs slightly more laps per minute.
- Exit Ticket: A. 6 for $1.50 — $0.25 each — $1.50 ÷ 6 = $0.25 per pencil. $2.80 ÷ 10 = $0.28 per pencil. $0.25 < $0.28, so 6 for $1.50 is the better buy.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Rate is a ratio comparing two amounts with different units, like miles per hour.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).