# Reverse Add Rule for finding Palindromes

Given any number, you can use the following simple algorithm to find other palindromes.

Step 1:

**Start with any number.** Call it

original number. **Reverse the digits **

**of the original number**

Step 2:

Call the number whose digits are

reversed new number. **Add the new **

**number to your original number**.

Call the number found by adding

the new number to the original

number test number

Step 3:

If test number is a palindrome, you

are done. If not, use your test

number as your original number

and **repeat the steps above**

I told the children that they can be playfully “evil mathematicians” if they teach someone how easy it is to reverse add to find a palindrome and then gave that person a Lychrel number like 196 or 295 which they would never be able to solve.

K-2nd grade I simply want them to do one step reverse add palindromes because they would not have to carry to the next place value. All 2+ step reverse add palindromes require carrying the tens value to the next column in the addition problem. For many of my 2-4th graders they were learning vertical addition with carrying for the first time with me. This will take weeks to master but we will stay at it. They should practice a lot so it becomes second nature.

3-7th graders can solve any multi-step palindrome up to 24 on the pdf.

For my 4-7th graders, I challenged them to LIST AS MANY **PRIME** PALINDROMES AS YOU CAN: __________________________________________

Note: Prime numbers must have only two distinct (different) factors, 1 and the prime number itself.

LIST AS MANY **SQUARE** PALINDROMES AS YOU CAN:

There are five types of square palindromes:

1. One-digit squares: _______ ________ ________

2. Sequences of 2, 3, 4 ...-digit numbers that are squared to palindromes (can you find a pattern?):

11^2 = 121

101^2 = 10,201

1001^2 =

10001^2 =

1000000001^2 =

22^2 =

202^2 =

2002^2 =

20002^2 =

2000000002^2 =

3. Numbers with multiple 1s squared (how many are there?)

11^2 = 121

111^2 =

See the answer keys on the pdfs. Have fun.

Attachment | Size |
---|---|

Palindromes_K-3.pdf | 2.03 MB |

Palindromes_Reverse_Add_and_Squares_4-7th_Grade.pdf | 2.4 MB |