Cogito
Grade 6 Math · Chapter 2 · Lesson 1
Unit Rates
How much for exactly one.
10 problems · about 17 minutes · 6.RP.A.2, 6.RP.A.3
What this lesson teaches
The child finds a unit rate from a ratio and uses it to compare and to solve problems.
- A unit rate says how much goes with exactly one.
- Divide to find it.
- Two rates can only be compared once both are per one.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Comparing Two Ratios: Scale 4 : 7 so the first number is 12. What is the second?
Answer 21
Why 12 : 21.
Review — Double Number Lines: Ratio 2 : 9. If the top shows 6, what does the bottom show?
Answer 27
Why 3 × 9 = 27.
Warm Up
Straightforward practice. Get the method working first.
4 problems84 miles in 2 hours. How many miles per hour?
Answer 42
Why 42 miles per hour.
Why write two deals as unit rates before comparing?
Answer Both are then per one, so they can be compared.
Why Per one makes them directly comparable.
20 pens for 5 pounds. How many pens per pound?
Answer 4
Why 20 ÷ 5.
150 km in 3 hours. How many km per hour?
Answer 50
Why 150 ÷ 3.
Build It Up
The same ideas with more to keep track of.
2 problems8 pencils per pound. How many for 6 pounds?
Answer 48
Why 6 × 8.
90 pages in 6 days. How many pages per day?
Answer 15
Why 90 ÷ 6.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Car: 240 miles on 8 gallons. How many miles per gallon?
Answer 30 miles per gallon
Why 30 miles per gallon.
The Typing: 180 words in 4 minutes. How many words per minute?
Answer 45 words per minute
Why 45 words per minute.