I went ahead and taught the power rule today in calculus. Every year, I’ve been disappointed at how hard the computations have been for my kids. This is supposed to be the easiest lessson of the year, I’ve thought to myself year after year. As all calculus teachers know, it’s not the calculus that trips them up; it’s the algebra.
This year I finally got my act together and before we did any calculus, we did two days of “Algebra Bootcamp” a la Sam Shah.
Oh. My. Word.
This lesson has never gone so smoothly. Each class was able to compute -16(4)^(-3/2) without a problem. “So what did you all get for the slope of the tangent line?” I asked, cringing, expecting to get confused and frustrated looks. Instead? “-2,” without a bit of fanfare. Like it was no big deal. Like, “Duh, Mrs. P, please stop talking and let us get on with our homework.”
I am so delighted.
I’m thrilled that I’m still coming up with ways I can better serve my kids. I’m so thankful for a job that I’ll never master.
We’ve been working on combined work word problems in Intermediate Algebra. I had a problem on the board, and one of my calc kids asked if it was a Calc BC question (I don’t even teach BC). I thought that was so cute though, and shows that our Intermediate kids are doing some math that impresses even my calc kids.
Speaking of combined work problems, we watched Dan Myer’s classic “bean counting” videos yesterday. If you’re not familiar with it, Act 1 shows Dan counting beans (takes him 22.6 minutes) and Chris counting beans (takes him 5.6 minutes). After watching Act 1, I asked the kids for predictions. “How long would it take if Chris and Dan worked together? Person with the closest time gets a cookie.”
After their predictions, I showed them how to solve the problem algebraically (takes 4.5 minutes if Dan and Chris work together). And then a winner was named.
Then I played Act 2, which shows Dan and Chris actually counting together, and lo and behold, it takes them 4.5 minutes.
One of my kids said, “But we already found that.”
He was basically saying that we didn’t need to watch the second video. Obviously our math was correct.