Palindromes by Marilyn Burns -
from A Collection of Math Lessons grade 3 - 6
Numbers that are palindromes read the same forward and backward
such as 55, 737 and 9,753,579.
Numbers that are not already palindromes can be turned into palindromes
by reversing the digits and adding the 2 numbers.
For example, 31 is not a palindrome.
Reverse the digits to make 13 then add the two numbers: 13 + 31 = 44, a palindrome!
Not all numbers are so cooperative.
It might take 2,3,4 or more steps to reach palindrome land,
but with a few exceptions they all get there eventually.
For example 361 is not a palindrome.
Reverse the digits to get 163. Add the two numbers and you get 524.
Still not a palindrome. Reverse the digits again and add: 425 + 524 = 949.
A palindrome!
Try some numbers on your own.
How many steps does it take for each number to reach palindrome land?
Do you want to find out more?
You can work on this project alone or with some friends.
Be sure to read the directions and organize your work before you start.
You will need the following materials:
• 0 to 99 chart
• Record sheet of numbers and their palindromes:
• Several colored highlighters
• Paper and pencil for addition work
Choose a number less than 100.
Follow the steps to make it a palindrome
(reverse the digits and add).
When it has reached palindrome land,
count the number of steps it took.
Record the number of steps
and the final palindrome on the record sheet.
Choose a colored marker for 1 step palindromes,
another color for two step palindromes and so on.
Be sure to have a color
for numbers that are already palindromes like 44 or 77 too.
Now fill in the square for your number on the 100 chart
using the correct color marker.
For example, if blue was the one step color
you would color 13 with blue.
If red was the two step color you would color 58 red.
Continue getting your numbers to palindrome land
and coloring in the number of steps it took.
Look for patterns on your list and on your chart.
You will discover something interesting as you work!
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Teacher page for Palindromes
From A Collection of Math Lessons from grades 3 through 6 by Marilyn Burns
This lesson is found on page 159 (a two step palindromic number) and requires only basic addition skills. It offers arithmetic practice in an interesting format, as well as “ higher-order thinking skills - looking for and analyzing patterns, making conjectures and testing their validity, and formulating generalizations.”
Ms. Burns describes a classroom presentation of this lesson, but it is also well suited to individual or small group work. It is well worth taking the time to read this lesson (10 pages) and having 100’s charts available.
The format of the attached 100 chart works best with this lesson.
Note: All 2 digit numbers will take 1 - 4 steps except 89 and 98. They take 24 steps and the resulting palindrome is 8813200023188. That should keep a few budding mathematicians busy for while.
Questions for classroom discusion:
What patterns do you see on the list?
What patterns do you see on the chart?
What statements can you make about 1 step palindromes?
About 2 step palindromes? Etc.
Super challenge questions: ( multiples of eleven ) Use calculators.
Here are some questions you might want to ask students who are ready for more:
1. Do you notice something about the numbers that are already palindromes?
2. Are all the final palindromes on your list multiples of 11? What are the factor pairs for the final palindromes on your chart. What do you notice?
3. Are all multiples of 11 palindromes? Check it out on a calculator counting up by 11’s. If not all multiples of 11 are palindromes, which ones are?
4. Are all palindromes divisible by 11? Make up several palindromes and divide by 11. What are the factor pairs?
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