Teacher Guide: Unit Rates
Learn how to find and use unit rates to compare quantities and solve real-world problems.
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Class quiz
10 questions on Ratios. Students join with a name, you see everyone's score.
For Teachers
- Define unit rate as a ratio comparing a quantity to one unit
- Calculate unit rates by dividing the total by the number of units
- Compare quantities using unit rates to make decisions
- Apply unit rates to solve real-world problems involving price, speed, and work
- • Understanding of ratios and what they represent
- • Division of whole numbers and decimals
- • Basic understanding of fractions as division
- 1. Where have you seen unit prices displayed in stores?
- 2. Why do you think speed limits are given as unit rates (km/h) instead of total distances?
- 3. A car gets 8 liters per 100 km and another gets 6 liters per 100 km. Which is more fuel-efficient?
- 4. If two workers have different hourly rates, how would you decide who completes a job faster?
Thinking the larger number always goes on top
Believing unit rates must be whole numbers
For Struggling Students:
- • Start with whole number division only (120 / 4, not 75 / 4)
- • Use visual tape diagrams to show the division
- • Provide unit rate templates with blanks to fill in
For On-Level Students:
- • Calculate unit rates with decimal answers
- • Compare two different unit rates to find better deals
- • Solve two-step problems using unit rates
For Advanced Students:
- • Work backwards from unit rate to find original quantities
- • Compare rates with different units (convert first)
- • Create real-world problems involving multiple unit rates
- 6.RP.A.2 (CCSS.MATH.CONTENT.6.RP.A.2)
Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0
- 6.RP.A.3b (CCSS.MATH.CONTENT.6.RP.A.3.B)
Solve unit rate problems including those involving unit pricing and constant speed
- visualUnit Rate Tape Diagram
Interactive diagram showing how rates become unit rates
- activityShopping Comparison Game
Find the best deals by calculating unit prices
- worksheetSpeed and Distance Problems
Practice calculating speeds and travel times
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Definition
- Price per item: 12 dollars for 4 apples = $3 per apple
- Speed: 150 km in 3 hours = km per hour
- Efficiency: 240 pages in 8 days = pages per day
Worked Examples
A pack of 8 water bottles costs 12 dollars. What is the price per bottle?
Identify the ratio
12 dollars for 8 bottles →
Divide to find unit rate
→ $1.50
Write the unit rate
1.50 dollars per 1 bottle → $1.50/bottle
Answer: The unit rate is 1.50 dollars per bottle.
Common Mistakes
Dividing in the wrong order
Why it's wrong: Students sometimes divide 8 by 12 instead of 12 by 8 when finding price per item.
Correct: Always divide the quantity you want to find (price) by the number of units (items). 12 dollars / 8 items = 1.50 dollars per item.
Forgetting the units
Why it's wrong: Writing just '70' instead of '70 km/h' loses important information.
Correct: Always include both units in your answer: km/h, dollars/item, pages/day, etc.
Comparing rates with different units
Why it's wrong: You cannot directly compare 2 dollars/bottle with 50 cents/ounce.
Correct: Convert to the same units first, then compare the unit rates.
Why It Matters
- Shopping: Which cereal is the better deal - 500g for 4 dollars or 750g for 5 dollars?
- Travel: If you drive 240 km in 3 hours, what's your average speed?
- Work: A painter covers 120 square meters in 6 hours. How fast do they work?
- Cooking: A recipe uses 6 eggs for 24 cookies. How many eggs per dozen cookies?
Real World Applications
Smart Shopping
Stores often show unit prices on shelf labels, but you can calculate them yourself when they are missing.
Example:
A 750ml bottle costs 3 dollars. Unit rate: dollars per liter.
At the grocery store, you see two options for orange juice: 2 liters for 4 dollars OR 1.5 liters for 3.30 dollars.
Which is the better value?
Step 1: Write the mathematical expression
Find unit price for each: Price / Liters
Travel Planning
Speed is a unit rate that helps you plan trips and estimate arrival times.
Example:
If you drive at an average speed of 80 km/h, a 320 km trip takes hours.
A cyclist travels 45 kilometers in 3 hours.
At this rate, how long will it take to travel 75 kilometers?
Step 1: Write the mathematical expression
First find speed, then divide distance by speed
Key Takeaways
- 1A unit rate compares a quantity to exactly ONE unit of another quantity
- 2To find a unit rate, divide the total by the number of units
- 3Unit rates let you compare different quantities on equal terms
- 4Common unit rates: price per item, speed (km/h), rate of work (items/hour)
- 5Always include units in your answer (dollars/item, km/h, pages/day)
Frequently Asked Questions
What's the difference between a rate and a unit rate?
Why do we use unit rates instead of regular rates?
How do I know which number to divide by?
Glossary
- Rate
- A ratio that compares two quantities with different units
- Unit rate
- A rate where the second quantity is exactly 1 (e.g., 5 dollars per item)
- Per
- Means 'for each' or 'divided by' - indicates a unit rate
- Speed
- A unit rate that measures distance traveled per unit of time
Formula Card
Unit Rate
Divide the total by the number of units to get the rate per one unit
Using Unit Rates
Multiply the unit rate by any number of units to find the total