MathChat

Isn’t it great when kids ask good questions?

(Rhetorical question, that, of course.)

I got a good question today, about factoring.

I was showing this student how to factor by taking out the GCG, and he asks me, “So what’s the difference between factoring and dividing?”

You see, we had been using dividing when factoring the GCF. For example, to factor an expression like 4x + 16, we divided both terms by 4 after seeing the 4 is the GCF. So in this boy’s mind, factoring seemed akin to dividing.

What I liked about the question is that it made me think … and clarify something.

I realized that when you factor, you do divide, but you do more than divide.

Essentially, when you factor, you use division to make rename an expression. 

In the example I gave, you equate 4x + 16 with its factored form, 4(x + 4)

When you divide, on the other hand, you are just doing a small piece of this.

You divide, for example, when you ask:  4x divided by 4 = what? Answer: x

You use that answer to lay out the factored version, but dividing is only a step.

So hooray for good questions and congratulations to those who ask and recognize them.  Good questions make the act of teaching come alive.