Teaching on topic: Follow up on logarithms
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
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.