🎯 What is 6.RP.A.2?
The Big Idea — from ratio to rate to unit rate
📌 Standard
Understand the concept of a unit rate a/b associated with a ratio a:b (where b ≠ 0), and use rate language in the context of a ratio relationship.
Unit Rate = Total Amount ÷ Number of Units
📊 Ratio compares two quantities.
Example: 12 apples for 4 students → 12:4
Example: 12 apples for 4 students → 12:4
⚡ Rate is a ratio comparing different units.
Example: $75 for 15 burgers = rate
Example: $75 for 15 burgers = rate
🏆 Unit Rate
Denominator is always 1.
"…per 1 unit" — "$5 per burger"
"…per 1 unit" — "$5 per burger"
📘 Real-World Examples
| Situation | Unit Rate |
|---|---|
| $75 for 15 burgers | $5/burger |
| 240 miles in 4 hours | 60 mph |
| $8.40 for 12 eggs | $0.70/egg |
| 150 words in 2 min | 75 words/min |
| 18 push-ups in 3 min | 6/min |
📏 Double Number Line Model
Each "jump" represents the same unit rate — see the pattern!
Example: $15 for 3 pounds of cherries → Unit rate = $5 per pound
💵 Money ($)
$0
$5
$10
$15
$20
⚖️ Pounds
0
1
2
3
4
✅ For each pound, the price increases by $5. That's the unit rate: $5 per pound.
✍️ TWR Frame — Describe the Unit Rate (EN/ES)
The unit rate is per , because ÷ = .
🇪🇸 ES: La tasa unitaria es ___ por ___, porque ___ ÷ ___ = ___.
📖 Key Vocabulary
Academic language for 6.RP.A.2 — with Spanish translations
Ratio / Razón
RA-shee-oh
A comparison of two quantities. Can be written as a:b, a/b, or "a to b."
🍕 3 slices to 4 students → ratio 3:4
Rate / Tasa
rayt
A ratio comparing two quantities with different units.
💰 $30 for 6 hours of work
Unit Rate / Tasa Unitaria
YOO-nit rayt
A rate with denominator = 1. Tells you the amount per one unit.
🚗 60 miles per 1 hour = 60 mph
Unit Price / Precio Unitario
YOO-nit prys
Cost per 1 item or 1 unit of measure.
🛒 $2.50 per can of soup
Denominator / Denominador
deh-NOM-ih-NAY-tor
The bottom number in a fraction — what you divide by. For unit rates, denominator = 1.
In 18/6, denominator is 6
Per / Por
pur
Means "for each one" — the key word that signals a unit rate.
"$5 per burger" = unit rate language
🧠 Morphology: "Unit" comes from Latin unus = "one." A unit rate always means per ONE. "Rate" from Latin rata = "reckoned/calculated."
🪜 How to Find a Unit Rate — 5 Steps
Follow every time — never skip step 4 (labels!)
1
Identify the two quantities and their units
Read carefully. What are you comparing? Label each quantity.
Example: "Jayla earns $56 in 8 hours." → $56 and 8 hours
2
Write the ratio as a fraction
Put the quantity you want "per 1 of" on TOP (numerator).
$56 / 8 hours
3
Divide numerator ÷ denominator
Divide until denominator becomes 1.
$56 ÷ 8 = $7
4
Write the unit rate with labels!
Always include units. Use "per" language.
Answer: $7 per hour
5
Check — multiply back
Unit rate × denominator = original numerator
$7 × 8 hours = $56 ✅
📘 Three Worked Examples
Money · Speed · Recipe contexts
💰 MONEY
Marcus paid $4.50 for 3 avocados. Unit price per avocado?
→
Write ratio: $4.50 / 3 avocados
→
Divide: $4.50 ÷ 3 = $1.50
→
Check: $1.50 × 3 = $4.50 ✅
Unit Price = $1.50 per avocado
🚗 SPEED
A train travels 360 miles in 6 hours. Unit rate in miles per hour?
→
360 miles / 6 hours
→
360 ÷ 6 = 60
→
Label: 60 miles per 1 hour
Unit Rate = 60 mph
🍳 RECIPE
3 cups flour for 4 cups sugar. Cups of flour per 1 cup of sugar?
→
3 cups flour / 4 cups sugar
→
3 ÷ 4 = 0.75 (or 3/4)
→
3/4 cup flour per 1 cup sugar
Unit Rate = 3/4 (0.75) cup of flour per cup of sugar
✍️ TWR — Unit Rate Explanation Frame
To find the unit rate, I divided by to get per . This means for every 1 , the train travels .
🏅
Your Score
0 / 6
Progress
✏️ Practice Problems
Type your answer · Click Check · Use hints if stuck
Problem 1
Basic
A car travels 180 miles in 3 hours. Unit rate in miles per hour?
miles per hour
Divide 180 ÷ 3. How many miles for every 1 hour?
Problem 2
Basic
A store sells 5 oranges for $2.00. Unit price in cents per orange?
cents per orange
$2.00 = 200 cents. Divide 200 ÷ 5 oranges.
Problem 3
Apply
A factory produces 840 bottles in 7 hours. Bottles per hour?
bottles per hour
840 ÷ 7 = ? bottles for every 1 hour
Problem 4
Apply
Destiny reads 96 pages in 4 days. Pages per day?
pages per day
96 ÷ 4. How many for each 1 day?
Problem 5
Extend
A recipe calls for 2.5 cups of milk for 5 servings. Cups per serving?
cups per serving
2.5 ÷ 5. Your answer will be less than 1.
Problem 6
Extend
Store A: $13.50 for 9 pens. Store B: $11.20 for 8 pens. Enter the lower unit price in cents.
cents per pen
A: $13.50÷9=$1.50=150¢ · B: $11.20÷8=$1.40=140¢ · Which is lower?
🛒 Best Buy Challenge
Calculate unit price to find the best deal — click Reveal to check!
Round 1 of 4
✍️ TWR — Best Buy Explanation
Store ___ is the better deal because its unit price of $ per is lower than $ at the other store.
🔀 Sort: Rate or Not a Rate?
Drag each card into the correct category
Cards to Sort
$5 per pizza
3 cats
60 miles per hour
12 students
$1.50 per egg
30 laps in 5 min
8 pages per day
7 apples
25 words per minute
$18 for 3 hours
⭐ Unit Rate
Denominator = 1 ("per 1")
⚡ Rate (not unit rate)
Different units, denom ≠ 1
❌ Not a Rate
Just a quantity, no comparison
🔁 Flash Review Cards
Tap each card to reveal the unit rate
$24 for 8 gallons of juice
Tap to reveal ↩
$3 per gallon
$24 ÷ 8 = $3
150 km in 3 hours
Tap to reveal ↩
50 km/h
150 ÷ 3 = 50
72 push-ups in 6 minutes
Tap to reveal ↩
12 push-ups/min
72 ÷ 6 = 12
$9.60 for 4 notebooks
Tap to reveal ↩
$2.40 per notebook
$9.60 ÷ 4 = $2.40
45 tacos for 9 people
Tap to reveal ↩
5 tacos per person
45 ÷ 9 = 5
$32 for 8 pounds grapes
Tap to reveal ↩
$4 per pound
$32 ÷ 8 = $4
270 words in 3 minutes
Tap to reveal ↩
90 words/min
270 ÷ 3 = 90
$5.25 for 3 muffins
Tap to reveal ↩
$1.75 per muffin
$5.25 ÷ 3 = $1.75
⚠️ Common Mistakes — Watch Out!
Real student errors and how to fix them
❌
Mistake #1 — Dividing Backwards
Error: For "$75 for 15 burgers," student divides 15 ÷ 75 = 0.2 instead of 75 ÷ 15 = 5.
Fix: The unit you want "per 1 of" goes on TOP. Ask: "per 1 ____?" Put that unit's total on top.
Fix: The unit you want "per 1 of" goes on TOP. Ask: "per 1 ____?" Put that unit's total on top.
❌
Mistake #2 — Missing Labels
Error: Writing "5" instead of "$5 per burger."
Fix: A unit rate is meaningless without labels. Always write: [number] [unit] per [unit].
Fix: A unit rate is meaningless without labels. Always write: [number] [unit] per [unit].
❌
Mistake #3 — Confusing Ratio and Unit Rate
Error: Saying "the rate is 3:4" when a unit rate is needed.
Fix: Unit rate has denominator = 1. Keep dividing until you reach "per 1."
Fix: Unit rate has denominator = 1. Keep dividing until you reach "per 1."
❌
Mistake #4 — Adding Instead of Dividing
Error: Thinking "3 miles per hour" means add 3 each hour rather than dividing to find the rate.
Fix: Unit rates use division. Multiplication/tables scale from a known unit rate.
Fix: Unit rates use division. Multiplication/tables scale from a known unit rate.
🎯 Self-Check Rule: After finding a unit rate, multiply back. Unit rate × denominator = original numerator. If it doesn't work → re-do the division.