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.
JD2718 
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, Mangahigh.com. 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: http://www.mangahigh.com/
Nice! (Now how do I extend that for a college class? Hmm…)
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.
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.
there
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!