Integrating Factors and Harry Potter

Calculus II has been a lot of fun lately. (It’s an independent study.) My student is willing to ask questions, and she’s willing to explore with me. She’s ok with me not knowing the answer, and she’s willing to find out together.

Today, we were discussing first order linear equations; you solve them with an integrating factor. I pointed out that you don’t have to add C when you take the antiderivative to find the integrating factor. She paused, cocked her head to the side, and said, “Ok, but why?”

Asking why on its own is enough of a victory – she didn’t just take my word for things, and she wants to understand! But then we worked the problem again adding in a +C, and she saw why it wasn’t needed without me telling her. Plus, it was fun.

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The Algebra II teacher last year did an amazing job and was very thorough. So when we got to introducing angles today, they’d seen almost everything before, which was awesome, because if they’re comfortable with angles, we can start reasoning about them and doing trig. We even got to play a card sort/matching game that someone came up with and I blatantly stole. (Sorry, can’t remember who!)

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Math club – which is student-led, but I’m the faculty sponsor – met today and took personality type quizzes, then listed them by Harry Potter houses, then looked for trends and asked if it’s what we’d expect. Not super mathy, but awesome thinking. Plus, we got to talk about Harry Potter.

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