Unit Rate
Unit Rate:
120 miles in 2 hours → unit rate?
60 mph
Tables:
(2,4), (4,8), (6,12) → proportional?
Yes
Real World
A recipe uses 4 cups of flour for 6 batches. How much flour is needed for 1 batch?
2/3 cup per batch
Better Deal
Store A sells 5 bottles of water for $4. Store B sells 8 bottles for $6. Which is the better deal?
Store B is cheaper because each one is $0.75 versus Store A is $0.80 per bottle
What is a unit rate?
Rate per 1 unit.
Unit Rate
A car travels 150 miles in 3 hours. What is the unit rate?
50 mph
Tables
Find the constant of proportionality for the pair (5, 20).
4 because 20/5 = 4
Real World
A recipe uses 2 cups of sugar for 5 batches. How much sugar is needed for 15 batches?
6 cups
Better Deal
Which is the better deal: 10 granola bars for $4 or 12 granola bars for $6?
10 for $4 because it is $0.40 each instead of $0.50 each like the other deal.
Challenge
Explain how to find a unit rate.
Divide the total amount by the number of units to find the amount for 1 unit.
Unit Rate
A runner runs 6 miles in 48 minutes. What is the unit rate in miles per minute?
0.125 miles per minute of 1/8 mile per minute
Tables
Are these pairs proportional: (3, 6), (6, 12), (9, 20)?
No, because the ratios are not all equal.
Real World:
3 notebooks cost $6 → cost per notebook?
$2 per notebook
Better Deal:
8 apples for $4 OR 4 apples for $2?
Neither they are the same deal because both cost $0.50 per apple.
Why must ratios stay equal?
To be proportional.
A car travels 180 miles in 3 hours.
How far will it travel in 7 hours? Explain.
420 miles (60 mph × 7)
A table shows x=2,4,6 and y=8,16,24.
Predict y when x=9. Explain.
36 (k=4)
A recipe uses 3 cups for 4 servings.
How much for 10 servings? Explain.
7.5 cups
Store A: 6 for $5
Store B: 10 for $9
Which is better? Explain.
Store A ($0.83 vs $0.90)
A student says: “If numbers increase, it’s proportional.”
Explain why this is wrong.
Ratios must stay constant
A runner runs 9 miles in 1.5 hours.
How far in 4 hours? Explain.
24 miles
A table is proportional with k=3.
Create a pair and explain.
Example: (4,12)
A recipe doubles. Explain how all ingredients change.
Multiply all by 2
Which deal is better AND why using unit rate?
Must show unit rate comparison
Why is unit rate useful in real life?
Compare situations