Learning Goal: Use unit rates to solve real problems about speed, price, and steady amounts.
Vocabulary
constant speedA speed that stays the same the whole time.
unit priceThe cost of exactly 1 item or 1 unit.
totalThe full amount you get after combining all the units.
What You Need to Know
First find the unit rate, then multiply to get a bigger amount.
Distance = speed × time when speed stays constant.
To find the better deal, compare the unit prices (cost per 1).
At a steady rate, you can scale up or down to any amount.
Example: if 1 hour = 50 miles, then 4 hours = 50 × 4 = 200 miles.
Lining up the unit (per 1) makes multiplying easy.
Worked Example I Do — watch how it works
A train travels at a constant speed of 60 miles per hour. How far does it travel in 4.5 hours?
Step 1. The unit rate is 60 miles in 1 hour.
Step 2. Multiply the unit rate by the number of hours: 60 × 4.5.
Step 3. 60 × 4.5 = 270.
Answer: 270 miles
Guided Practice We Do — try it together
1. Oranges cost $0.40 each. How much do 7 oranges cost?
💡 Hint: Multiply the unit price by the number of oranges: 0.40 × 7.
2. A walker moves at 3 miles per hour. How far in 2.5 hours?
💡 Hint: Multiply 3 by 2.5.
3. Store A: 6 pens for $3.00. Store B: 10 pens for $4.50. Which is cheaper per pen?
💡 Hint: Find each unit price: 3.00 ÷ 6 and 4.50 ÷ 10.
Independent Practice You Do — show your work
1. A car goes 55 miles per hour. How far in 3 hours?
2. Bananas cost $0.25 each. How much for 12 bananas?
3. A pump moves 8 gallons per minute. How many gallons in 15 minutes?
4. A cyclist rides 14 miles per hour. How long to ride 42 miles?
5. Which is the better buy: 4 lbs for $10 or 6 lbs for $13.50?
MCAP-Style Practice
Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.RP.A.3b.
Item 1Selected Response6.RP.A.3b
A runner keeps a steady pace of 8 minutes per mile. How long to run 5 miles?
Select the correct answer.
Item 2Selected Response6.RP.A.3b
Apples are $1.80 for 3 pounds. How much for 5 pounds at the same rate?
Select the correct answer.
Item 3Constructed Response6.RP.A.3b
A boat travels at a constant 22 miles per hour. Fill in: in 3 hours it travels ____ miles.
Enter your answer in the space provided. Show your work.
Enter your answer:
Teacher Answer Key (click to show)
Independent 1
165 miles
Independent 2
$3.00
Independent 3
120 gallons
Independent 4
3 hours
Independent 5
6 lbs for $13.50 ($2.25/lb vs $2.50/lb)
Item 1 · 6.RP.A.3b
C — 8 minutes × 5 miles = 40 minutes.
Item 2 · 6.RP.A.3b
B — Unit price is $0.60/lb, so 0.60 × 5 = $3.00.
Item 3 · 6.RP.A.3b
66 — 22 × 3 = 66 miles.
Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.RP.A.3b