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!