Elapsed Time Word Problems

By the conclusion of 3rd grade students should be able to tell time to the nearest minute as well as calculating elapsed time problems within the hour using tools such as a number line. Targeting this skill, first, by using hands-on materials (like a model clock) will bring this concept to life for your students! You can then progress towards a more efficient model–solving elapsed time problems on a number line.

The 5 examples listed are certainly not an exhaustive list of tools and lessons that could be used to teach this skill.

They are rather a sample progression from hands-on to abstract thinking! 

Which step represents your students’ current level of understanding? 

Your first goal in helping your students to understand elapsed time is to make connections between time on a clock and a number line so that your students can use a skill they already have (how to navigate a number line) in order to understand a new skill (calculating elapsed time).

Begin the lesson by telling your students a story:

Last weekend I took a trip in the car. We left the house at 1:00 in the afternoon and didn’t arrive until 5:00 in the evening. It was a long trip! Let’s see if we can figure out how long we were in the car for.

Show your students the model clock and model how your trip began at one o’clock. Move the hour hand from one o’clock to two o’clock and tell your students “We were in the car all the way from 1:00 to 2:00- that’s a whole hour! But our ride wasn’t done yet.” Move the hand again from 2:00 to 3:00 “Look! We were in the car another whole hour from 2:00 to 3:00… but we still weren’t there yet!” Again, move the hand from 3:00 to 4:00 and, again, illuminate that this was yet another hour. “Look! Another hour has gone by and we were STILL in the car! But, believe it or not, we still weren’t there yet!” Move the hour hand one final time from 4:00 to 5:00 “Finally, one more hour in the car and we were at our destination!”

Ask your students if they can tell you how long you were in the car in all. Record your students guesses on a white board and ask your students to explain their thinking.

Next, translate this work to a number line and show how each hour on the clock can be translated to a “jump” on the number line. 

It’s time to start developing flexibility in your students by illuminating the fact that the missing number in an elapsed time problem can be the start or end time rather than only the elapsed time.

Conduct this step much in the same way you explored calculating elapsed time in the first activity. 

Next weekend I’m planning on going on a hike to [insert something local to you]. I’m going to get started on my hike at 3:00 but it’s expected to take 2 hours to finish my hike. What time do you think it will be when I finish my hike?

Ask your students if they have any ideas around how you might solve this problem. Have a clock with moveable hands and a whiteboard available to your students so that they can use the tools they practiced in the first activity. 

In the first two elapsed time activities your students showed each individual jump as an hour on a number line.

The biggest difference in the calculation of elapsed time in hours vs. minutes on a number line is that your students will want to work in more efficient jumps when calculating time in minutes. Rather than showing each individual minute jump on the number line your students will want to work in “easy to manage” jumps. There is not one correct way to work along a number line and the more flexible your students are in decomposing numbers, the more efficient they will have the ability to be!

Explore calculating elasped time to the minute in the same way you explored time to the hour using the clock with moveable hands as well as the number line but highlight for your students the different ways they can “jump” along the number line. For example, jumps of 10 minutes, jumps of 5 minutes, jumps to benchmark numbers, etc. 

Your students have been using a clock and number line to calculate elapsed for several days at this point. The purpose in this activity is two-fold.

First, in activity #2 you made the explicit connection that a number line could be used to find a start or end time rather than elapsed time alone. You are making that connection again for time to the minute.

Second, you are providing addition practice moving along the number line to increase your students’ flexibility and efficiency with this tool.

Begin this activity with a story context about a train station.

There was a big mix-up at the train station! Someone spilled their coffee on the train schedule and no one can read the train departures and arrivals! Your job will be to fill in the missing pieces of the schedule so that everyone can get to their destinations.

The orange train is set to leave the station at 3:20 for a 25 minute trip. What time will it arrive at it’s destination?

Allow your students to use the moveable clock and number line to solve for the missing time. You are looking first for students who are correctly using the number line- address any misunderstandings of students who may be incorrectly using the number line.

Your students have now had experience solving elapsed time problems to the hour, minute and including missing start and end times.

Be sure to provide your students opportunities to solve when you have mixed each of these experiences together so they can become flexible moving between each of these different problem types.

Consider using numberless word problems to promote a focus on the action of the word problem and to aid in overall comprehension. 

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