1. For example:
A person walks ½ mile each ¼ hour. How far do they walk in one hour? How long does it take them to walk one mile?
I say “How do you find unit rates in situations involving fractions. A person walks 1/2 mile each 1/4 hour. How far do they walk in one hour? How long does it take them to walk one mile?”

2. I say, “In this lesson you will learn how to find unit rates in situations involving fractions by using simplification.”

3. Unit Rate
How many of a given quantity that you have “for every” or “per” another quantity.
I say, “Putting these two concepts together, you already know that one way to find a unit rate is by simplification where we divide one of the measures, let’s call it measure a by the other measure, let’s call it measure b, for any a, and b. You have experience doing this with whole number quantities for measures a and b, but in this lesson you will extend your understanding to include unit rates which include measures that are fractions. Overall, it is important to remember the concept of unit rate tells you how many of measure a you have “for every” or “per” one of measure b. For example, 2 dollars for 1 slice or 2 dollars per slice, or 1/2 slice for 1 dollar or 1/2 slice per dollar.”

4. I say, “Dividing by a fraction is the same as multiplying by the reciprocal. So a over b over or divided by c over d equals a over b multiplied by d over c.”

6. Ann and Brian were at track practice
Ann and Brian were at track practice. The track is kilometers around. Ann ran 1 lap in 2 minutes. Brian ran 3 laps in 5 minutes. How many minutes does it take Ann to run one kilometer? What about Brian? How far does Ann run in one minute? What about Brian? Who is running faster? Explain your reasoning.
I say, “Ann and Brian were at track practice. The track is 2/5 kilometers around. Ann ran 1 lap in 2 minutes. Brian ran 3 laps in 5 minutes. How many minutes does it take Ann to run one kilometer? What about Brian? How far does Ann run in one minute? What about Brian? Who is running faster? Explain your reasoning. Note that in this question it is assumed that Ann and Brian are running at a constant rate. When running most of us slow down, speed up, and stop. Average speed is the total distance traveled compared to the total time it takes to travel that distance (rather than the average of all of the individual segments of a trip). It is important to realize that although we find average speed and constant speed the same way, they represent two different situations in the real world.”

7. Laps
kilo-
meters
Ann (in min)
Brian (in min) 1 2 3 5
1 lap = km
1 5
2 5 x = = 1 5
3 5
1 2 lap = km
4 5
5 5
6 5

8. # of laps x 2 5 = total km # of 1 2 laps x 1 5 = total km 1 5 3 5 4 5
kilo-
meters
Ann (in min)
Brian (in min) 1 2 3 5
# of laps x = total km
1 5
# of laps x = total km
3 5
4 5
5 5
6 5

9. 2 min km
Laps
kilo-
meters
Ann (in min)
Brian (in min) 1 2 3 5
= x = = 5
1 5
3 5
5 min km
4 5
= x = =
5 5
6 5

10. 1 lap 2 min 1 2 lap 1 min 1 lap = 2 5 km 2 5 x 1 2 = 2 10 = 1 5 1 5
Laps
kilo-
meters
Ann (in min)
Brian (in min) 1 2 3 5
1 lap 2 min
1 5
1 2 lap 1 min
3 5
1 lap = km
4 5
5 5
2 5 x = = 1 5
6 5

11. Laps
kilo-
meters
Ann (in min)
Brian (in min) 1 2 3 5
3 laps 5 min
1 5
3 5 lap 1 min
3 5
2 5 x = 6 25
4 5
5 5
6 5

12. 5 minutes per 1 kilometer 4 minutes per 1 kilometer = kilometers per
Ann
Brian
5 minutes per 1 kilometer
4 minutes per 1 kilometer
= kilometers per
1 minute
kilometers per 1 minute

14. I say, “In this lesson you have learned how to find unit rates in situations involving fractions by simplification.”

15. Ann
Brian
Kilometer per minute
Minutes per kilometer

17. 120 and 1/2 miles in 2 hours and 45 minutes.
5 and 3/4 pizzas for 3 teenagers
50 GBP (British pounds) being equivalent to $88.48 USD (U.S. dollars)

20. Amy and Matt were at track practice. The track is 2/9 kilometers around. Amy ran 1 lap in 5 minutes. Matt ran 4 laps in 19 minutes. How many minutes does it take Amy to run one kilometer? What about Matt? How far does Amy run in one minute? What about Matt? Who is running faster? Explain your reasoning.