Palindromes

When students would rather stay in class and work on a math investigation than go to P.E., you know they are excited about math!  I couldn't be more thrilled with the way our palindrome investigation has gone over the past three days.

On Tuesday, I introduced the students to the concept of palindromes (words, phrases or numbers that are the same forward and backward, ex: wow, Hannah, race car, 303, 99).  I told them that there were palindromes in numbers, but not all numbers started as palindromes.  For instance, 13 is not a palindrome.  However, if you add the reverse of it, 13 + 31, you get 44, a palindrome.  We called this a "1-step" palindrome.  Some numbers take more steps, like 39.  39 + 93 = 132.  132 + 231 = 363, so 39 is a "2-step" palindrome.

The students quickly dove into the investigation eager to find patterns in numbers 10 - 99.  They worked as groups dividing up the work and quickly noticed patterns in palindromes and the number of steps.  To show these patterns, we color-coded our 0-99 chart so that 0-step palindromes were red, 1-step were orange, 2-step were yellow and so on.

Students worked eagerly, enthusiastically and cooperatively to complete the task.  Sure, the only "math skill" they were working on was addition, but as far as the mathematical practices go, those eight standards we expect all students to show when solving math problems, well, they showed practically every one. They solved problems without giving up (just ask them about 89 and 98); they thought about numbers in many different ways; they defended their thinking to one another; they used math tools such as a chart and a calculator (only for 89 and 98); they worked carefully and checked their work; they used what they knew to solve new problems and they looked for patterns.

I am so proud of these students for their hard work, perseverance, and for their attitude as they investigated numbers.