Never, Ever Simplify
Today in calculus I taught the chain rule. We started class with some warm-up problems based on what we'd been learning before. At the end of the warm-ups, I had some algebra questions.
First I asked if the following expression was equal to x2 + x.
The vast majority of the students said that yes it was. (That's the great thing about having the clickers; as soon as the question ends, a bar graph of the responses appears on my screen.) I explained that it didn't simplify like that.
Then I asked whether this expression equals x + 2.
Again, most of the students answered yes.
At this point I told them that for the rest of the semester that they should assume that radicals never simplify.
First I asked if the following expression was equal to x2 + x.
The vast majority of the students said that yes it was. (That's the great thing about having the clickers; as soon as the question ends, a bar graph of the responses appears on my screen.) I explained that it didn't simplify like that.
Then I asked whether this expression equals x + 2.
Again, most of the students answered yes.
At this point I told them that for the rest of the semester that they should assume that radicals never simplify.
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