Math Activity: Number Palindromes

When we hear the word "palindrome," we usually think of words.  Palindromes can also be numbers, and  there's potentially an interesting math activity in discovering how many steps it takes to turn a number into a palindrome.


You'll want to explain to your students what a palindrome actually is (something that, whether read from left to right or right to left, is the same... like the word "level" or 141).  To find how many steps it takes to create a number palindrome, you may want students to work with calculators, or use paper and pencil.


Use Jason Doucette's site as a model.  He's posted the method for finding number palindromes:

1. Pick a number.
2. Reverse its digits and add this value to the original number.
3. If this is not a palindrome, go back to step 2 and repeat.

For instance, 104.  104 + 401 = 505.  505 is a palindrome, so it takes just one step to turn 104 into a palindrome.  Try it with most numbers (80% of numbers under ten thousand, according to his site), and you'll see that you can do it within 4 steps or less. 

Once you have students test this out, ask them to figure out how many steps it takes to turn 87 into a palindrome.  87 takes 4 steps to create a palindrome.  How many steps for the number 264?  79?

Jason even posted this page from Canada's YES Magazine that explores number palindromes, including the elusive 196.

This is a good activity because it's simple, requires few materials, and it works for multiple grade levels and abilities.  Really, students only need to be able to do addition to discover numerical palindromes.  As we've seen, though, some numbers require multiple steps.  Some require millions of steps done by computers!  Even advanced students who've mastered addition could be appropriately challenged by discovering how many steps it takes to form a palindrome from 89, or numbers with many digits.

There are many ways you could do this activity:

• It could be a whole class activity in which you let students use calculators, pencil and paper, or markers and dry erase boards to find their answers.  Have some fun with it and turn it into a race!
• Numerical palindromes could be a quick activity when you have a few minutes to fill, or a morning work assignment.
• Palindromes could also be a math center, or independent activity for students who finish their work quickly.
• Do your students need some practice with addition?  Try this activity as a group in lieu of a worksheet or textbook assignment.

Remember, students can find many palindromes fairly easily.  But there are some numbers that require several steps, and lots of math.  You can, therefore, just as easily try this activity with a bunch of second-graders as you can with middle-schoolers.  Again, use Jason's site to pick numbers that will give your students an appropriate challenge.