I typed out the notes. This is a first. Usually, I just show my students how to do it. But, I do recognize the importance of them having something to look back on if they forget the process.
This was a first attempt at writing out the steps. I'm sure these will morph and grow over the years like the rest of my notes do!
Then, we did some practice problems together.
I had them note the degree of each polynomial to see if it has any 0 terms in it that need to be taken into account. At the multiplying stage, you can leave out the zeros, and everything will work just fine. But, the like terms won't always be on the diagonals. Plus, having the zeros is essential when using the box method to divide. So, I want my students to get in the habit of including the zeros now.
I think the moment when my students really started buying into this method was when we color-coded the diagonals and saw the like terms. If all the terms in a diagonal are not like terms, we know we made a mistake somewhere!
One student raised his hand to say he liked this method a lot better than the way a previous teacher taught him with drawing arrows all over the place. That's the way I was taught, and it worked just fine for me. But I've seen students forget to distribute a term to every other term so many times. Drawing the boxes (if drawn correctly) shows students just how many times they have to multiply.
They often get frustrated trying to figure out where the zero rows/columns go. But, they definitely get a sense of satisfaction when they get to fill in that whole row or column with zeros!
Here's what the problems end up looking like when we work them out on the SMART Board. My boxes were a bit wonky, and it definitely showed when I used the highlighter tool...
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