As children in my math group can tell you, we've been working hard on our numerical palindrome project. This project has really engaged the group, as they look for number patterns, both visually and numerically. It is also excellent practice in addition with renaming, and persistence.
A palindrome is a number that reads the same forward and backward, such as 8008. A number that is not a palindrome, such as 13, can be changed into a palindrome by using a particular procedure: You reverse the digits and add. 13 is a one step palindrome, because 13 and 31 is 44.
Some numbers take more than one addition. I demonstrated this with 68 (86), which took 3 steps to make it into the palindrome 1111.
Each child is currently investigating all the numbers from zero to ninety-nine. We record our information on data sheets - the number, how many steps it took to get to the palindrome, and the resulting number. After we record this information, we will transfer the information on a hundred chart, coloring the numbers that are already palindromes with one color, coloring the two-step palindromes with another color, and so on.
As a class, we are tackling ninety-eight and eighty-nine. This takes twenty four steps, with the resulting palindrome of 8,813,200,023,188! So far we are up to step 12 (85,189,247). Half-way there!
Igor, Sophie's dad, even devised a computer program that instantly tells the numerical palindrome of any number you plug in. He came yesterday to show us. The children got to guess any number under 2000, to see which numbers resulted in the most steps.
I wrote the numbers that seemingly don't have a palindrome on the board. These numbers were off limits, although Igor was nice enough to try one just so the children could be amazed at the pages and pages of script.
Bora ended up making a lucky guess - his number, 1,897 had 16 iterations! Several children are already savvy enough to immediately recognize that a number like 2000 was a bad choice -"obviously, that will only be a one-step!"