MPM2D - Day 58: Solving Quadratic Equations by Factoring

I was planning on giving my students today's class to practice more factoring, but changed my mind part way through first period (it's at times like this that I am really glad that I'm the only one teaching this course in this way!). Instead, we solved quadratic equations by factoring - this gave them the factoring practice, but also moved us forward.

We spent a bit of time talking about how great 0 is. We looked at a product like a * b = 12 and determined, after a long list of possibilities, that there was an infinite number of combinations of values for a and b that would make this true. However, if a * b = 0, we know that a or b must be 0. Many students have been struggling with finding the zeros of questions like these:

I think they now understand why you can just take the opposite of the constant term in every case.

We consolidated the process of solving a quadratic equation that can be factored and then followed up with a lot of practice questions.

The next few questions were a little more challenging as some students have yet to master factoring complex trinomials. I used both the box and decomposition. I did an informal poll of the class and they are pretty much split half and half between the methods.

Then we hit one with a common factor and I, of course, did what my students suggested and factored it without taking the common factor out first.

We talked a lot about this one. If you are factoring, but not solving, you must take the common factor out either at the beginning or the end. They saw pretty quickly that taking it out at the beginning made their solution much easier. We talked about why you could divide by 3 when you are solving, but not when you are just factoring. After class a student asked me about using the box method for example 2a. I had not tried one that contained a common factor and it is not as obvious as you might think (well, it was not obvious to me, anyway). I will go over it with him tomorrow, stressing that taking the common factor out first will make it all work much more nicely.

Part (c) gave us the opportunity to look at a difference of squares. I drew the corresponding tiles on the whiteboard and they all remembered factoring these types of quadratics. Part (d) was gave them the tools to deal with a -1 coefficient of the variable squared. We finished with this one:

Today's homework was the second box of the handout from yesterday.