# The Common Factor

Jose Vilson Education

“The mediocre teachers tell. The good teachers explain. The superior teachers demonstrate. The great teachers inspire.” – my good friend Indira, who quoted someone else, but thought about me when she read the quote

I’ve grown more excited about the possibilities I have to nurture and inspire the kids I have. As I mentioned previously, I was teaching the Fundamental Theorem of Arithmetic with the 6th graders, a lofty feat considering that I recently learned FTA in my masters program, and I instantly wrote about in this here blog. As many of my readers know, the FTA states:

every natural number greater than 1 can be written as a unique product of prime numbers.

Ha! This is cool, but on the same end, this is nowhere in the NYS Math State Standards nor was it something I could prove to kids who just learned what primes were. Fine.

So we go through using a factor tree, and little tricks like using all the primes to find all the factors for numbers, and such. A natural progression from that discussion is the topic of common factors i.e. when two or more numbers share a factor in common. After that discussion, I get the teachable moment:

“Mr. Vilson, I still don’t get it.”

“Well, it’s like this. Me and Boy X are male. We have a common factor. We’re both male. This girl and I have a common factor, too, because we both have black hair. As different as we may seem, we at least have that in common. We’re all in this room right now, so we have a common factor. The Fundamental Theorem of Arithmetic states that every natural number greater than 1 can be expressed as a unique set of primes. Well look, if we’re all different people with different factors, but we might all have something in common, a factor. That’s what I mean.”

She just nodded her head and went about her business. I got a couple of smirks, and a couple of acknowledging nods. I didn’t have to really ask for feedback on the explanation. Just the fact that they understood the next assignment was enough for me.

jose, who really did shed a tear in a segment of the movie Across the Universe