Introduction to Elapsed Time (Hour Steps) - Second Grade Mathematics

Time does not stand still; it elapses, meaning it passes or ticks forward from a starting moment to an ending moment. The amount of time that passes between the start of an event and the end of that event is called elapsed time. In second grade, you master elapsed time in whole-hour steps: calculating how many hours a movie lasted, finding what time soccer practice will end, or figuring out what time you must leave home to arrive on time. In this chapter, you will learn the three components of elapsed time—Start Time, Elapsed Time, and End Time—and use timeline hops and clock models to calculate time with confidence.

The Three Components of Elapsed Time

Every elapsed time scenario connects three fundamental quantities.

The Elapsed Time Formula:
      START TIME  +  ELAPSED TIME  =  END TIME

Alternative Inversions:
      END TIME  -  START TIME    =  ELAPSED TIME
      END TIME  -  ELAPSED TIME  =  START TIME

The Three Unknown Problem Types:

Type 1: End Time Unknown: You know when the movie started (2:00 P.M.) and how long it lasted (2 hours). What time did it end? (2:00 + 2 hours = 4:00 P.M.). Type 2: Elapsed Time Unknown: You know when soccer practice started (4:00 P.M.) and when it ended (6:00 P.M.). How long was practice? (6:00 - 4:00 = 2 hours). Type 3: Start Time Unknown: You know a birthday party ended at 5:00 P.M. and lasted 3 hours. What time did the party begin? (5:00 - 3 hours = 2:00 P.M.).

Solving Elapsed Time with an Open Timeline

An open timeline is simply a number line where the tick marks represent hours of time.

Finding End Time for 1:00 P.M. + 3 Hours:

            +1 hour         +1 hour         +1 hour
        +------------>  +------------>  +------------>
--------+---------------+---------------+---------------+--->
    1:00 P.M.       2:00 P.M.       3:00 P.M.       4:00 P.M.

Forward Hops for End Time

When you need to find an end time, place the start time on the left of your timeline. Draw forward hops for each hour that passes: Start: 1:00 P.M. Hop 1 (+1 hr): 2:00 P.M. Hop 2 (+1 hr): 3:00 P.M. Hop 3 (+1 hr): 4:00 P.M. The end time is 4:00 P.M.

Backward Hops for Start Time

When you know the end time and need to find the start time, place the end time on the right of your timeline and hop backward to the left! End: 6:00 P.M., lasting 2 hours: Start at 6:00 P.M. Hop back 1 hour to 5:00 P.M. Hop back 1 hour to 4:00 P.M. The event started at 4:00 P.M.

Counting Hours on an Analog Clock Face

You can also find elapsed time by watching the short hour hand step around an analog clock.

Counting Around the Clock from 8:00 A.M. to 11:00 A.M.:
Start: Hour hand points at 8.
Count: From 8 to 9 is 1 hour.
       From 9 to 10 is 2 hours.
       From 10 to 11 is 3 hours!
Elapsed Time: Exactly 3 hours!

Keeping Track of Whole Hours

Because we are working in whole-hour steps, the minute hand stays pointed directly at the 12 (or at the exact same minute mark) the entire time. You only need to watch the hour hand advance from number to number.

Crossing the 12:00 Boundary

Be especially alert when elapsed time crosses over 12:00, because the hour numbers reset from 12 back to 1!

Starting at 10:00 A.M. and Adding 4 Hours:
Hop 1: 10:00 A.M. + 1 hr = 11:00 A.M.
Hop 2: 11:00 A.M. + 1 hr = 12:00 NOON (A.M. switches to P.M.!)
Hop 3: 12:00 P.M. + 1 hr =  1:00 P.M. (Numbers reset from 12 to 1!)
Hop 4:  1:00 P.M. + 1 hr =  2:00 P.M.
Final End Time: 2:00 P.M.!

Two Critical Shifts at 12:

Shift 1: After 12 comes 1 (not 13!). Shift 2: When crossing 12:00 Noon, the label changes from A.M. to P.M. (or from P.M. to A.M. when crossing midnight).

Practice Exercises

Exercise 1: A school science fair started at 9:00 A.M. and ended at 1:00 P.M. Use a timeline or clock counting to find how many hours the science fair lasted.

Exercise 2: Marcus started reading his book at 3:00 P.M. He read continuously for 2 hours. What time did Marcus finish reading?

Exercise 3: A family arrived at a campground at 6:00 P.M. They had been driving for 4 hours. What time did the family begin driving?

Exercise 4: Explain what two important changes happen when you count forward across 12:00 noon on a clock timeline.

Solutions and Explanations

Solution to Exercise 1: Count the hours forward from 9:00 A.M. to 1:00 P.M.: 9 to 10 is 1 hour; 10 to 11 is 2 hours; 11 to 12 is 3 hours; 12 to 1 is 4 hours. The science fair lasted exactly 4 hours.

Solution to Exercise 2: To find the end time, add 2 hours to 3:00 P.M.: 3:00 + 1 hr = 4:00 P.M., and 4:00 + 1 hr = 5:00 P.M. Marcus finished reading at 5:00 P.M.

Solution to Exercise 3: To find the start time, subtract 4 hours backward from 6:00 P.M.: Hop back 1 hr to 5:00 P.M.; hop back 1 hr to 4:00 P.M.; hop back 1 hr to 3:00 P.M.; hop back 1 hr to 2:00 P.M. The family began driving at 2:00 P.M.

Solution to Exercise 4: When counting forward across 12:00 noon: First, the clock number resets from 12 back to 1 (since clock numbers only go up to 12). Second, the time-of-day label flips from A.M. (morning) to P.M. (afternoon).