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Teaching on topic: Follow up on logarithms

March 3, 2010 am31 7:29 am

So yesterday I was fretting about logs. But the lessons went ok. I used a small modified bit of Kate(t)’s approach (explicitly, I used her notation as a transition) but stayed true to the puzzle/game spirit.

I’ll share what I thought were two highlights/key elements.

1. The warm-up (I don’t call it that; I don’t call it anything, actually) was:  Hand-graph y = 2^x, -5 \leq x \leq 5

2. I diverted their attention to a problem that was framed as the “Tuesday Challenge.”  As my “challenges” are generally unrelated to the lesson/topic/unit, this was a bit of misdirection.

Without any explanation:  L(8) = 3, L(32) = 5, L(1/2) = -1. Find L(0).

And then the first kid with a hand up, I called on, because it looked like 2 or 3 kids figured it out, and I took the answer with no explanation, but I asked the kid to give us the next question. L of what? And so he said L of 16 (it was different in each class) and I asked for new volunteers to find the value of L(16). And I made that volunteer pose a new question. And another, and another. And without explanation you could see the lights turning on and more and more hands going up.

Now, I didn’t call on every single kid in each class, but maybe three-quarters. And others were ready to answer. And when I asked “What is L?” I got a nice batch of responses, including the inverse of $f(x) = 2^x$. (Reverse instead of inverse a few times – that’s from me overemphasizing the exchange of x and y coordinates).

Log laws, applications, etc, those come over the next few days.

8 Comments leave one →
  1. March 3, 2010 am31 7:52 am 7:52 am

    I’m very pleased to have found your blog: filled with all of my favourite education hubs.

    I have been meaning to tell you about a new maths resource that is one of my new favourite links, Although the site is new, it has a lot to offer and new maths games are being added frequently.

    I have been using it in the classroom and for homework. A great teacher’s resource they have put together is a lesson plan guide:

  2. March 3, 2010 am31 9:47 am 9:47 am

    Nice! (Now how do I extend that for a college class? Hmm…)

  3. Stan Rabinowitz permalink
    March 19, 2010 am31 10:10 am 10:10 am

    This is a response to your question: L(8) = 3, L(32) = 5, L(1/2) = -1. Find L(0).
    Let c be any complex number. It’s well known that there’s a fourth degree polynomial P such that: P(8) = 3, P(32) = 5, P(1/2) = -1 and P(0) = c. Unless you tell the students that L is a logarithmic function, the problem as stated has no solution. A little knowledge is a dangerous thing.

    • March 19, 2010 pm31 9:24 pm 9:24 pm

      Stan, good point.

      In fact we worked forwards without considering multiple answers, but later that period we did come back.

      In particular they already knew how to fit a parabola to three points – which I used to open that discussion.

      But I wanted an intuitive jump to inverses, and I got it. Some refinement, later the same hour, not such a big deal.

  4. July 8, 2010 pm31 1:55 pm 1:55 pm


  5. October 20, 2011 pm31 5:35 pm 5:35 pm

    I did my lesson something like this today. One of my students told me after class how much she liked it. I used P(x) instead of L(x). Thanks!


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