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How to navigate the space-time continuum (or, a visual way to solve elapsed time problems)

Wednesday, January 5th, 2011

When I was growing up, I learned to do elapsed time problems by subtracting the start time from the end time (and when necessary, borrowing while keeping in mind that there are 60 minutes in a hour).

This technique always seemed convoluted, so when a fifth grade tutoring student of mine was working on elapsed time problems, I tried this visual way of solving them, which seemed to be much more intuitive for my student.

Let’s say you have a problem like this: A train departs at 2:55 and arrives at 5:18. How long is the train ride?

First, draw a timeline:

Draw in the beginning and ending times, marking the hours as you go:

Draw loops to count the hours:


Add up the hours:

Draw loops to count the minutes left at either end:

Add the minutes together:

Combine the hours and the minutes, and you’re done!


That’s it!

Once you do a few of these, there’s lots of different ways to draw the loops. For example, you could start at 2:55 and loop to 3:55 (1 hour), 4:55 (2 hours), and then from 4:55 to 5:18 (4:55 to 5:00 is 5 minutes; 5:00 to 5:18 is 18 minutes; 5 + 18 = 23 minutes) to get 2 hours and 23 minutes.


And after drawing some of these out, you can use the same process to do elapsed time problems mentally, too. Just think about counting from one time marker to another and adding up the different loops.

*Visiting from this week’s Carnival of Homescooling? Welcome, I’m glad to see you here! Below are some more posts you may enjoy.

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Gallon Man to the Rescue!
An easy way to remember how logarithms work
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Confused about fractions? Visualize brownies, not pizzas

21 Comments on “How to navigate the space-time continuum (or, a visual way to solve elapsed time problems)”

  • Caroline Mukisa on January 18th 6:33 am

    Rebecca, what a cool and easy to understand visual. I remeber trying to explain a similar method to my daughter when she was younger but I’m sure she would have “got it” much faster if I’d illustrated it.

  • Rebecca Zook on January 18th 2:58 pm

    Thanks, Caroline! When my student came to me, I had just done a similar problem by myself the day before, calculating how many minutes were on a tape recording that started and ended at a particular time. So I remembered how I had done it by myself — count the hours, then the minutes on either end — and just tried to draw out what I had done in my head.

    I’m always looking for ways to make things more visual, so please keep me posted on whatever tricks you come up with too! πŸ™‚

  • KelleyH on March 7th 9:03 am

    This is awesome! I’m going to teach my students today this strategy! It’s a great way for visual learners to understand elapsed time! Thanks for sharing!

  • Rebecca Zook on March 7th 2:24 pm

    Thanks, Kelley! I’m glad you found found this useful. Let me know how it goes, and thanks for stopping by!

  • Stephanie on March 22nd 8:04 am

    This is great! I tried this, and some of my students “didn’t get it”. I taught a T-Chart for those students, and between the 2 methods all my students “got it”!
    The hours are figured in the first column and the minutes in the other.

    2:55 5:18
    3:55 Tally marks in sets of 5 to count from 55 to
    4:55 60, then start at one and make marks to 18.
    2 hrs 23 min

  • Rebecca Zook on March 22nd 3:11 pm

    Awesome! I’m so glad it was helpful! The t-chart is a good idea, too. Thanks for sharing that because I am always collecting different ways to explain! πŸ™‚

  • Jennifer on November 9th 6:30 pm

    I tried this with my son and it worked so well. Thank you for the tip. Finally a night with math homework and no headache!

  • Rebecca Zook on November 9th 7:18 pm

    Jennifer, it’s so nice to ‘meet’ you here! Thank you for your comment, which brought a smile to my face. I’m so glad to be of service. πŸ™‚

  • liz on December 15th 8:18 pm

    this did not work m y students are getting 53 and you supposed to do all that except the numbers on top

  • liz on December 15th 8:22 pm

    we tried everything this does not work i even dicused this with my staff members they said it dosent work ethier sorry maybe you can help us online to understand

  • liz on December 15th 8:23 pm

    your stratiges

  • Rebecca Zook on December 15th 9:13 pm

    Hey Liz, thanks for posting. Could you explain where you’re getting 53 from? What do you mean by “across the top”?

    Also, if you don’t like this method, there are definitely other ways to approach this kind of problem. The comment from Stephanie above has an alternative approach with a t-chart that might be helpful. πŸ™‚

  • Esme Deanda on March 1st 10:16 pm

    Thank you, this helped my child alot thank you so much πŸ˜€ <3 i cant thank u OMG it even helped me lol

  • Esme Deanda on March 1st 10:16 pm


  • […] posts: A visual way to solve elapsed-time problems Gallon Man to the Rescue! An easy way to remember how logarithmic notation works […]

  • Shelli on November 13th 8:15 pm

    I REALLY like this because it is visual. I plan to use it tomorrow. I think I will “loop” the hours on top and the minutes on the bottom so the numbers aren’t as confusing. Thanks!

  • Rebecca Zook on November 13th 8:39 pm

    Hey Shelli, it’s so great to “meet” you here! Thank you for your feedback. Let me know how it goes! I’m glad to help!

  • Jamie on January 16th 11:03 pm

    Im teaching a 5th grade class and im kinda confused.
    You left the PM and AM out, and my kids were having trouble with this.
    Any solutions?

  • Amelia on April 20th 8:57 am

    hello this is really easy

  • Amelia on April 20th 8:57 am

    hello this is really easy

  • Madalyn on April 27th 9:29 am

    i love this its so so super easy

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