The Common Factor - The Jose Vilson

The Common Factor

by Jose Vilson on September 24, 2007

Factor Tree“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

p.s. – This article I wrote about adrienne curry seems to have gone over well …

{ 5 comments… read them below or add one }

Miss Profe September 24, 2007 at 6:01 pm

I like the way you broke it down for the student. And, isn’t it cool when we reach them?


Repairman September 25, 2007 at 1:54 am

What Miss Profe said about the connections. As for the math part, it makes my head spin. ;-)


angelamichelle September 25, 2007 at 3:48 pm

jumping on the bandwagon: that explanation was very good. i found that when terms were demonstrated to me in terms that i could “see”, i picked up the lesson easier. yet another confirmation of the type of teacher you are.

oh and by the way, what happened to that “tutor my daughter” thing i volunteered you for? HA!


LuzMaria September 25, 2007 at 7:05 pm

The beauty of your lesson was that you made the material accessible to your kids. I struggled with mathematics in the latter part of middle school because it no longer made sense. The numbers and equations became another language which I feared. Where were you when I needed an explanation like the one above? Great job, Mr. Vilson. It is wonderful to see the manner in which you facilitate abstract concepts to your kids by creating teachable moments.


pissedoffteacher September 25, 2007 at 9:37 pm

Good example. I use similar stuff in my classes. I am doing geometric proofs and the kids are struggling. To get them to see how things must relate I ask them is a dog can have kittens or if a cat can have puppies. Then I use this to point out how ridiculous it is to say a median makes a right angle with the base of the triangle.


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