1. Elapsed Time & Determining Start and End Times Mountain-Hill-Rock Strategy
By Linda Ewonce

2. First, lets review telling time
O’Clock
First, lets review telling time
Remember: The short hand shows the hour and the long hand shows the minutes.
Past or After
To or Until
A Quarter to
A Quarter past
Half Past

3. Ten minutes after three
What time is it?
How many ways can you say it?
3:10
Ten minutes after three

4. What time is it?
How many ways can you say it?
1:30
Half past one

5. What time is it? 6:45 15 minutes until 7 Quarter til 7
How many ways can you say it?
6:45
15 minutes until 7
Quarter til 7

6. What time is it? 4:36 36 minutes after 4 24 minutes before 5
How many ways can you say it?
4:36
36 minutes after 4
24 minutes before 5

7. What is elapsed time? Elapsed Time: 4 hours
The word elapsed means “pass” or “go by”.
Elapsed time is the amount of time that has passed or gone by when given two sets of time.
Elapsed Time: 4 hours S
Start Time: 7:00 S
End Time: 11:00: S

8. We will use the Mountain-Hill-Rock strategy for elapsed time.
A mountain represents 1 hour
A hill represents 10 or 5 minutes
A rock represents 1 minute

9. Read the elapsed time problem and draw a timeline.
Peter began his homework at 5:12pm and finished at 6:34pm. How long did it take him to do his homework?

10. Place the start time and end time on the time line at both ends.
Peter began his homework at 5:12pm and finished at 6:34pm. How long did it take him to do his homework?
5:12
6:34

11. Add hours with mountains but be careful not to go over the end time
Add hours with mountains but be careful not to go over the end time. Label the 1 hour increment inside the mountain.
Peter began his homework at 5:12pm and finished at 6:34pm. How long did it take him to do his homework?
5:12
6:34

12. Place the time under the timeline.
Peter began his homework at 5:12pm and finished at 6:34pm. How long did it take him to do his homework?
5:12
6:34
6:12

13. Add 10 minutes or 5 minutes with hills but be careful not to go over the end time. Label the 10 or 5 minute increments inside the hills. Add the time under the timeline as you go.
Peter began his homework at 5:12pm and finished at 6:34pm. How long did it take him to do his homework?
5:12
6:34
6:12
6:22
6:32

14. Add 1 minutes with rocks but be careful not to go over the end time
Add 1 minutes with rocks but be careful not to go over the end time. Label the 1 minute increments inside the rocks. Add the time under the timeline as you go until you get to the target end time.
Peter began his homework at 5:12pm and finished at 6:34pm. How long did it take him to do his homework?
5:12
6:33
6:34
6:12
6:22
6:32

15. To determine the elapsed time, add up the mountains, hills and rocks.
Peter began his homework at 5:12pm and finished at 6:34pm. How long did it take him to do his homework?
1 mountain = hour
2 hills = minutes
2 rocks = minutes
1 hour + 20 minutes + 2 minutes = 1 hour 22 minutes

16. You try. Jenn took her little sister shopping
You try! Jenn took her little sister shopping. They left their house at 11:09 am and returned home at 2:55 pm. How long were they gone?
Add it up!

17. You try! An airplane left the Pgh International Airport at 9:50 am and arrived at Orlando, Florida at 12:15 pm. How long did the trip take?
Add it up!

18. You can use the Mountain-Hill-Rock strategy to determine the start or end time when given an amount of elapsed time.
Jason is going to swim practice. Practice begins at 7:23 pm and it will take 1 hour and 52 minutes to finish. What time will it be when he finishes practice?
Start by making the timeline and placing the start time on the left side. On the right, place a box. You will be solving for the end time.
7:23

19. Add the elapsed time (time needed for swim practice) using mountains, hills and rocks.
Jason is going to swim practice. Practice begins at 7:23 pm and it will take 1 hour and 53 minutes to finish. What time will it be when he finishes practice?
Add 1 mountain and label the time under the timeline.
7:23 pm
8:23
8:33
8:43
8:53
9:03
9:13
9:14
9:15
Add the hills and label the time under the timeline.
Be careful adding the 10 minutes here. You are going over a new hour.
Add the rocks and label the time on the timeline and in the red box.
The answer is, Jason will finish practice at 9:15 pm.

20. You can use the Mountain-Hill-Rock strategy to determine the start or end time when given an amount of elapsed time.
Erica is making dinner for her family. She wants to serve dinner at 5:35. According to the recipe, it will take her 2 hours and 26 minutes to prepare the meal. What time should she begin preparing dinner in order to serve it on time?
Start by making the timeline and placing the end time on the right side. On the left, place a box. You will be solving for the start time by working backwards.
5:35

21. Add the elapsed time (time needed to make dinner) using mountains, hills and rocks.
Erica is making dinner for her family. She wants to serve dinner at 5:35 pm. According to the recipe, it will take her 2 hours and 26 minutes to prepare the meal. What time should she begin preparing dinner in order to serve it on time?
Add 2 mountains and label the time under the timeline.
3:09
3:10
3:15
3:25
3:35
4:35
5:35
Add the hills and label the time under the timeline.
Add the rocks and label the time in the red box.
The answer is, Erica should begin preparing dinner at 3:09 pm.

22. You try. Andrea’s bedtime is 9:00 pm
You try! Andrea’s bedtime is 9:00 pm. She wants to watch a movie that is 3 hours and 9 minutes long. What time should she start the movie in order to be in bed on time?

23. One More. Mario is taking a trip to the beach
One More! Mario is taking a trip to the beach. He wants to arrive at 3:15 pm. The trip will take 6 hours and 12 minutes. What time should he leave?