# ZeroSum Ruler (home)

## Blogging on math education and other related things

### Awesome Euclid and his AlgorithmNovember 19, 2010

One of my favorite things that I learned while in graduate school for math education was the Euclidean Algorithm for finding the Greatest Common Factor of two numbers.  If you click on the  picture to the left, you’ll get to a very informative YouTube video on the Algorithm.  It’s a bit boring, but very educational, and it shows exactly how to go about using Euclid’s method to find the biggest number that divides into two numbers.

(The screenshot to the left will bring you to the YouTube video on the Euclidean Algorithm)

The alternative, but mainstream, way using factor trees and circling primes always confused my students.  “Do I count the 3 twice since I circled it as a factor in both 81 and 57?”

If Euclid’s method was the mainstreamed one, math would be a lot more interesting and one more confusing topic could be checked off the list.  Euclid, you rock!

(The screenshot here of the kids is a funny video about Euclid and his algorithm)

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### To the Zero! [power]June 15, 2010

Filed under: calculator,zero — ZeroSum Ruler @ 11:28 am
Tags: , , , , ,

“Any number to the zero power is equal to 1,” my teachers would say. “Why?” the students would ask. “Because.” the teachers would declare. And this would usually end it. Sometimes a persistent student would again ask, “Why?” to which he’d get the slightly more creative answer, “That’s just the way it is.” Because of the mystery surrounding the zero power as a kid, I always got the feeling that there was something supernatural about it; my teachers held the key and didn’t want to share.

It wasn’t until graduate school that I finally found out why a number to the zero power always equaled one and how to explain this once mysterious phenomenon.

Now as a math teacher, I take the time to explain the zero power. It’s not mysterious, it’s just division. Whenever a question about the zero power comes up, I stop, go to a side board, and ask “What’s 2^3? How about 2^2?” When the kids answer “8” and “4”, I then ask, “Ok, what’s “2^1?” I create a table of their answers on the board:

2^3             2^2              2^1

8                 4                   2

We then step back and look at the pattern.

Soon the students see that the common difference between numbers is 2. “We divide by 2 to get to the next number,” they say. I then go on to ask, “Then what’s 2^0?”

Of course most students will answer 0 at first. I’ve realized that it’s a natural reaction to answer “zero” whenever hearing “zero” and “multiply” or “divide” within the same lesson. Other students will put 2^0 into the calculator and answer “1”, but that’s what I did as a student and it wasn’t good enough. I always wanted to know why.

I direct all students back to the table we created to find the next term “2^0”.

2^3             2^2              2^1             2^0

8                  4                 2                ??

“If we divide by 2 each time to get to the next term, what’s 2 divided by 2?” I ask. The students will answer, with an “oh, obviously!” tone, “1.”

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Another way to think of this concept is through exponent rules:

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To divide terms with exponets, we subtract the exponents, here giving us a 0 exponent.  If we then back up and look at the original fraction, we have a number over itself, which is equal to 1.  Therefore, any number to the 0 power is equal to 1.