Palindrome Math in Third Grade

We've been having a lot of fun practicing double and triple digit addition using number palindromes this week.  Palindromes, as you may remember, are words, phrases or sequences of numbers that read the same forward and backward.  Before beginning palindrome addition, the third graders came up with words and names that were palindromes, such as mom, dad, Hannah, race car, and kayak.

They were then tasked with finding the palindrome for a variety of numbers.  This involved adding the number to its reverse until the answer was a palindrome.  In some cases, such as 45, this only took one step: 45+54=99.  Of course in other instances, it took multiple steps: 64+46= 110, 110+011= 121.

As third graders worked through their palindrome math, they noticed a number of patterns emerged.  They noticed that for some numbers, such as 62, they could just look at the answer they had gotten for 26, the reverse of 62, which they had already completed.

Many students began to to notice that the palindrome 121 came up multiple times as a number.  They discovered this was because any number that equaled 10 or 11 when the digits were added together (such as 37 or 38) would equal 121 after either one step or two.  When the digits equal 11, such as with 38, or 47, you get to 121 on the first step.  When the digits equal 10, such as with 37 or 46, you get to 110 after the first step, and 110 plus its reverse, 011, gets you to 121.  Our final step was for the students to figure out when the next 121 would be coming, and many of them were quite skilled at making accurate predictions.

To close, do you want to hear a palindrome math joke??

What did the mathematician say when she was offered cake?

Mathematician: I prefer pi! (yes, that's a palindrome!)