I wasn’t going to blog about my lesson on expanding binomials from earlier in October. It did not work out nicely at all. But it wouldn’t be right to only ever blog about the things that go pretty well. So here’s a quickie to share how it all went downhill …
I had students cut out a set of paper algebra tiles for themselves to store in their binder. We started with the 1 tiles and I asked them to show me a rectangle measuring 2 x 3 and then 4 x 5 and so on. Each time I asked them what the area of each rectangle was. So far so good – they got it.
Next we introduced some x tiles & I asked them to represent 3 x (x + 2). And I can’t remember now if it was at this point, or when I asked for a rectangle with width x+2 and length x+4, but somewhere in here my lesson went off the rails because my students were not building the correct rectangles. They were confusing the concepts of area versus width and length. They were getting confused about what each algebra tile represented.
I abandoned my carefully planned out prompts and remembered thinking after this lesson last year that perhaps it would be better to have them factor a trinomial first. That way, you give them a trinomial, have them take out the tiles needed to represent it & then use those tiles to form a rectangle. Once you get the rectangle you simply have to interpret the width & length of it. Boom – factoring.
Well, I’m not sure it went Boom per se. I had to do a lot of direct teaching about where to position the x squared tiles versus the x tiles versus the ones (with no better explanation than because that’s where we put them – help me out on that one!).
By the time the bell rang, some kids had figured out the side lengths, but other groups had not. They were using x^2 in their width and/or length. I did not feel good about the lesson or my students’ learning.
I didn’t assign any homework on the topic as we hadn’t dealt with any negative numbers in there yet, and the first Khan Academy exercise set includes some negatives. I did however put a very simple factoring question on our first monthly test later that week. All positive numbers, nothing tricky. And many students did OK or even well on the question. So all is not lost.
All this to remind those following my blog that not all my activities or lesson work out well. It’s good to reflect and share the times things don’t work out. Next year I will start with factoring first instead of multiplying or expanding. And I’ll hopefully do a bit better. We can always get better.
– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)