Tuesday, March 19, 2013

Properties of Logarithms Question

In Algebra 2, we are working on logarithms right now. I am pretty much sticking with what I did last year - I was pleased with the results and the students have continued to respond well. Mathy McMatherson's post on sharing assessments caught my attention as I was catching up on GReader posts. Since I am getting ready to assess properties of logarithms, I thought I'd share a question I am considering.

As I was teaching today and we were discussing the change of base formula, I was thinking about how it tied in with the properties of logarithms we did the day before. Traditionally, some of the problems give the student the value of a logarithm they don't know (like log_2_3) and ask the student to approximate, say, log_2_12. So here's my thought:

Question Version 1
a) Write log_5_200 as a sum or difference of logarithms.
b) If you are given that log_5_8 = 1.2920, use the expression you wrote in part a to find the value of log_5_200.
c) Find the value of log_5_200 to the nearest ten-thousandth.

Question Version 2
Use the properties of logarithms and that log_5_8 = 1.2920 to find the value of log_5_200. Then use the change of base formula to find log_5_200.

I like the multiple representations idea here. I like the second version but I am afraid that there is not enough structure for my students to grasp what I am going for. The first version is very structured and gets at what I want them to demonstrate.

As I am preparing for review, I am also pondering how to review this with them. I can put the exact question on the review (changing numbers) but on the other hand, I can also give them problems of each type on the review and not give them the exact wording of this on their assessment. Usually I give them review sheets that have pretty much the exact type of problems on the assessment but the numbers are changed. I am nervous that if I don't give them the exact type of problem to practice that they won't do well with it and fuss if they don't get what to do. Still debating what I am going to do here, but I need to decide shortly since I begin review tomorrow.

Comments are certainly welcome. Thanks!


JFairbanks said...

I just tested on logs. I like your questions. I just did something similar with a thinking question let b = log5 and c = log 4, find log 80. I put this one in a review millionaire game and they really had to think about it. I gave them time, hints, eventually some got it. Then, I put a similar one c=log5 and c=log3, find log75, but it was a bonus(which I don't usually do) and only about 1/2 the kids got it. Just my results to share with you.

Laura @ Frugal Newlyweds said...

Thanks for posting this! I've always been stumped on the change of base problems because most of my students see it as the property that makes it so you can type things in a calculator. This is a way that will show a bit more meaning:).