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How do you teach this topic so that students don’t make this mistake? (Or do you just rail on their earlier teachers?)

Thanks to Kristen Fouss for the submission.

  • I don’t allow the word “cancel” to be used in these situations. They have to say a whole big sentence like “Dividing both sides of the equation by …” or “dividing top and bottom of the fraction by …” or “because these are inverse functions…”

    I also tell lots of jokes like 16/64 = 1/4 (by canceling the 6) and sin x / n = 6 (by canceling the n) and so on. It’s always illuminating to see whose number sense treats the “canceling the 6” operation as potentially plausible.

  • Oh boy do I see this a lot. I’ve adopted Bowman’s DPT (well, I’m not sure it’s his, but he made these cool posters: for convincing students not to do that.