Why this matters for FAST: Unit rates are essential for proportional reasoning and appear frequently on FAST in contexts like pricing, speed, and density. Students must calculate unit rates AND interpret what they mean in context.
Students think all ratios are rates. A rate specifically compares quantities with DIFFERENT units (like miles and hours).
"A ratio compares two quantities of any kind. A RATE is a special ratio that compares two quantities with DIFFERENT units. For example, 60 miles per 2 hours is a rate because miles and hours are different units!"
Students divide the wrong way. For "$15 for 3 items," they might calculate 3/15 instead of 15/3.
"For a unit rate, we want ONE of something. If we want price PER ONE item, divide the price BY the number of items: $15 / 3 items = $5 per 1 item. The unit you want 'per one' of goes in the denominator!"
Students write "5" instead of "$5 per item" or "60" instead of "60 miles per hour."
"A rate without units is meaningless! Always include BOTH units with 'per' between them. The answer isn't just '5' - it's '$5 per item.' What are we measuring? What is it 'per'?"
Review: "What is a ratio?" (compares two quantities) "Today we're learning about a special type of ratio called a RATE. A rate compares quantities with DIFFERENT units."
"A rate compares two quantities with different units. Examples: miles per hour, dollars per pound, words per minute. Notice the word 'per' - it means 'for each' or 'for every.'"
Examples of Rates
60 miles / 2 hours | $12 / 4 pounds | 150 words / 3 minutes
Notice: Each rate has TWO different units!
"A UNIT rate is when we have 'per 1' of something. To find a unit rate, divide to get ONE in the denominator."
Finding Unit Rate: 60 miles in 2 hours
60 miles / 2 hours = 30 miles per 1 hour
or simply: 30 miles per hour (mph)
Divide: 60 / 2 = 30
Finding Unit Rate: $12 for 4 pounds
$12 / 4 pounds = $3 per 1 pound
or simply: $3 per pound
Divide: 12 / 4 = 3
Which is the better buy?
Store A: 6 apples for $3.00 | Store B: 10 apples for $4.50
Store A: $3.00 / 6 = $0.50 per apple
Store B: $4.50 / 10 = $0.45 per apple
Store B is better - lower price per apple!
Work through these together:
"A runner completes 12 miles in 2 hours. What is the unit rate?"
A) 24 miles per hour B) 6 miles per hour C) 2 miles per hour D) 12 miles per hour
Correct answer: B) 6 miles per hour (12 miles / 2 hours = 6 mph)
For struggling students: Use concrete examples like counting items and money. Focus on the pattern: "divide to get per ONE." Use visual ratio tables.
For advanced students: Introduce unit rates with fractions (e.g., 1/2 mile in 1/4 hour) or have them create their own best-buy comparison problems from real advertisements.
For home: Send Parent Activity sheet. Families can compare unit prices while shopping or calculate miles per gallon on car trips.