Math IS Real Life: Playing with Palindromes on the Odometer

I've been trying to hook up with the Math IS Real Life Linky for quite some time. It makes me crazy when my students don't see that math is everywhere and that they use it regularly; so I like to point out these real-life examples whenever I can.

For my maiden voyage, I want to share how much fun you can have with palindromes, one of my favorite number patterns! Palindromes are numbers (or words- race car) that are the same regardless of which direction you read them- forward or backwards. We can find them on our grocery receipts, our digital clocks, anywhere there is (at least) a two digit number.  (EX:  The date, 12/21, a friend's birthday, is a palindrome. 1221 is the same read either direction.  I'm sure that's good luck for her!)

One of my all-time favorite games to play is Odometer Palindrome, a great way to pass time at stop lights or on a road trip.

Here's how it works- Read the mileage on the odometer and figure out how many miles it will be until your next palindrome.  If it's close, try to figure out where you might be in your travels when it hits.  The hard part is remembering to look.  You don't win the game unless you actually see the palindrome, and I've missed many of them by just a mile or two, even knowing they were close.  Sigh.

Here's a fun one I did capture.  I had just left my house, when I saw I was about to hit this milestone palindrome in a couple tenths of a mile.  So, of course, I had to stop on the side of the street and take a picture.  After all, this was a momentous event!

And then, knowing the store was farther than my next palindrome, and I didn't want to be a distracted driver, so I decided I would just drive around my neighborhood until I got there. (I live in a mostly quiet neighborhood.)

Yes, the neighbors probably wondered if I had completely lost it, but I couldn't let these two great palindromes go unrecorded!

Here's a fun activity to do with your students. Have everyone take a snapshot of their parent's odometer and bring it in.  Some, of course, will forget, so ask your staff to help out by snapping their odometers to have some extras on hand.

Have students figure out how many miles it's been since the last palindrome and then how many miles it will be until the next one shows up.  Write each number on the front and back of an index card, labeled "previous palindrome" on one side, and "next palindrome" on the other.  Have them record their answers.

Label one spot in the classroom Previous Palindrome and across the room as Next Palindrome.

Have everyone rank/order themselves according to who is closest to their last palindrome.  Make it a silent ranking, where they hold up the number of miles since the last palindrome and fit themselves in their number line.  No talking!  What will they do if there is a repeated amount?  Take a snapshot of the class lined up.

Next, have them rank/order themselves according to how far they have to travel until they reach the next palindrome, from closest to farthest away.  Again, no talking.  Take another snapshot and compare the two.

What do they notice about each line of students? How did their positions change? Are some students about the same place? What does that mean?  What else do they notice?
If there's time, break them up into groups of five and compare their previous and future palindromes. Who has the largest mileage span between the the two palindromes?  What interesting patterns do they see? 

Playing with palindromes reminds kids math is all about patterns.  I hope you get a chance to use this fun little activity.  Challenge your students to find other palindromes that appear around them.  It's quite habit forming!      

  "You teach best what you most need to learn." Richard Bach

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