I started systems of equations with graphing because it's the hardest, most useless, and the one I wanted to teach least. I did a bad job on it and they didn't really even understand the concept of 0 or infinite solutions. And when they tried graphing on their own, it went horribly. They suck at graphing. Everyone always got different answers. Here are two of the worksheets I used.
From there we went on to solving systems by substitution. I think this is the easiest method but the students struggled with it more than I expected. They were fine is y = 5 or x = -3 but when it got to y = x + 2 they panicked and made it harder than necessary. And oh lord when we got to x - y = 6 they were clueless. I always had to remind them to get x or y alone. They could do it when they heard that, but they always stared cluelessly when they first saw the problem.
From there, we went to elimination (I stole this ppt). They liked this much better and tried to use it on every problem by default. I don't think we ever got to the point where they could look at a problem and pick which method would work best. Here is a trashketball review game that I stole and modified and here is a quiz.
I do the same order (graphing, then substitution, then elimination). I think that graphing is the easiest for most students to visualize (obviously) and the idea of a point that lies on both lines, i.e. at their intersection, seems fairly apparent. I usually talk about how if you stand in the middle of an intersection of two streets, you're really standing on BOTH streets at the same time, and that seems to click.
ReplyDeleteBut yeah, transitioning to substitution is sometimes more difficult because it is less tangible.... But it seems that you mostly have to do it before elimination, since the second half of solving a problem by elimination is still substitution. For most of us (usually including me?) elimination becomes our method of choice.
This year in one of my classes I had a motivated student who had begged to teach a lesson, so I asked her to take elimination using multiplication, and she really did great. She also got to see how it's NOT likely for the entire class to "get" an idea at the same time, so she had to work with some students a lot one-on-one while others zipped right along.
I'll probably stick with the same order but I need to do something 100 times better with graphing to start with.
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