A version of this has been floating around Twitter lately and I thought it would be a good way to get them thinking about common factoring and would lead us to finding the greatest common factor. Here are some of what they came up with for parts (h), (e) and (g) (ignore the simplification of x^5 over x^2 in the middle!). I asked them why my version was "better" (I showed them all my questions which are also at the top of each column, below). Someone said that what was left was in lowest terms. Loved that!
So then we moved into the lesson itself.
I emphasized the why, giving examples of quadratics in factored and standard forms and asking which was more helpful for graphing.
I tied factoring to area and showed an example with algebra tiles.
I break up the skills, to make sure that students can do each part correctly. Many don't remember the exponent rules well (hence the example on the picture of the whiteboard above). The answers below may look messy, but are all correct. We haven't worked with negative exponents, so that was fairly new to most.
Next, we looked at finding the greatest common factor.
I randomly drew names to get six students up writing answers and 5 of the 6 answers were incorrect. I told them that and asked them to talk in their groups to see if they could figure out what was wrong. They had only written the GCF (in one case not even the greatest) of the coefficients. Not one student had a variable in the GCF. I found this really interesting as there was no connection made to today's initial activity. Once they figured out that we needed some variables in the mix, corrections were made pretty quickly.
Having both pieces in place, we now moved on to actually factoring.
We did the first few examples explicitly showing the process then continued and only explained the calculations that were being done in our heads instead of writing them all out. At this point I saw one of my student acting like her brain was exploding so I went to ask what was up and she said that it was miraculous because she understood it all!
Here is today's homework.