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 Desmos graph pasted into Smart Notebook. No way my handwriting is that neat! If you use a smart board and you graph/discuss functions as much as I do, I think you’ll love this tip. Even some of the veteran teachers in my dept. loved this and didn’t know how easy it was.
Our Department abolished the phrase “Cancels out” a long time ago, and now we use phrases such as “reduces to 1“, “divides to 1 over 1“, etc. which demonstrates the math operation not some magic. We also always replace numbers and variables that reduce with a number even if it’s one (see below right). I actually start my students on Day 1 teaching them the fundamentals of both derivatives and integration. I started teaching AP Calculus (AB) for the first time about 10 years ago. My students didn’t do so well my first 2 years (the class average grade was below 3). The third year I taught the class I started seeing much better grades. Now our AP scores average is above 4.0. Here are 3 things that I did differently that I think made all the difference: |
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Matter and anti-matter cancels out (violently I might add). The airlines can cancel your flight. You can’t cancel out in Math (instead you “reduce” or “divide”). If you do try to cancel out, bad things can happen. Let me explain.