Monday, September 22, 2008

Algebra 2: Intro to Logarithms


Tomorrow, I will introduce the students to logarithms. I decided to start them early in the year for a couple of reasons. Our first unit is on the Real Number System, along with the operations that can be done on real numbers that we don't study in Algebra 1: nth-roots and rational exponents, absolute value, and logarithms. Secondly, students have lots of trouble mastering the log properties. We typically teach it all at once; my thinking is that front-loading what logarithms are, and how to convert back and forth between logs and exponential form, will make it easier to teach log properties later in the year. There are quite a few log problems on the STAR test, so I'm hoping that this is one standard in which we can make some real growth.

I wrote about using the Big L notation a while back. We used it a little bit last year, and I have anecdotal evidence that it improved students' learning. This year, I am going to go full-on with the Big L, and only practice converting from regular log notation as we approach the STAR test. Just to summarize why I am using Big L:
1) Clearer notation - symbolic instead of a "word"
2) Easier to compare/contrast to radicals
3) Helps students understand that log is an operation, not a number or variable
4) Makes it easier to read and remember log properties

There was a bit of discussion on this on the previous post, but it kind of fizzled out. I'm hoping to get more feedback on this from you all, especially if anyone else decides to try it out.

Here are the files for the next lesson:

Lesson 11 (Intro to Logs)

Lesson 11 Keynote
Keynote Quicktime

4 comments:

jd2718 said...

I want my students to memorize the following:

log_2 (8) = 3 == 2^3 = 8

and to reproduce it any time they are called upon to work with exp or logs.

I think it helps. It can't hurt.

Jonathan

Dan Greene said...

I agree, and I do the same with the Big L notation.

I think the payoff will come when we do the log properties later in the year. They are much easier to read and understand (in my opinion) when written with Big L. I'll post about how it goes when we get there.

samjshah.com said...

Howdy! I was wondering if you came back to logarithms yet and if so, how the students did on them.

sI curious to know how the idea of starting logarithms early and leaving them for a long while went.

Also I'm curious to know how your "big L" notation went!

Best,
Sam

Dan Greene said...

Hey Sam,

Well, we move slow in DCP math... we haven't gotten to the logs/exponential unit yet, and we're not going to before the STAR test. Too bad.

They definitely liked using the big-L notation, and it seemed to help them work with the basic problems back at the beginning of the year. I'll post how it goes when we get back to it. With spring break and STAR testing in the way, that won't be until the second or third week of May.