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 |