No more. It's time to give the comma a voice.
We were getting ready to add rational expressions and I wanted my students do have a workable rule for adding fractions with like and unlike denominators. My goal was to develop the idea that when adding fractions with unlike denominators:
A lot of students don't see this very clearly. They do what they do to jump from [this] to [that]. And most of the problems end up looking a lot like
Time to talk about the comma. It was actually a pretty simple adjustment to a simple question, but the conversations it generated made all the difference in the world.
This quickly became
See, the beauty here is that the process became the outcome. The numbers become the variables and we get a good grip on how one-third plus two-sevenths becomes thirteen-twentyfirsts. The abstract isn't so abstract and the easy part is swapping out the 1, 2, 3, and 7 for a, b, c, and d.
Mission accomplished. Now, lets hope they remember it tomorrow.