Teach 180: Planning to Discover Log Properties (Day 99)

Today we had our third (or maybe it was our fourth?) two-hour delay.  We were scheduled to originally have periods A, B, C, D and E.  I teach periods A, B, F and G.  With the two-hour delay, I had no classes today.  You may wonder why I even came into school.  Why not call in sick?  If you know me, you know that is not my style.  I had a meeting with a student planned and I also had a meeting with a colleague planned to discuss PreCalculus.

When I met with my colleague, we talked about the upcoming unit on logarithms in PreCalculus.  We wanted students to discover the properties for themselves, but we weren't quite sure how to do it.  For example, we want student to discover that log_b(MN) = log_bM + log_bN.  We could have them create a table of values like the one seen at the left on a spreadsheet.  But would they be able to see that log(2) + log(3) = log(6)?  I felt like there were too many numbers for the students to see that relationship.  Perhaps if we showed the values rounded to the nearest hundredth, it would be easier for the students to see that relationship.  Would it work?

My colleague had a suggestion for using index cards and placing log(M) on one side and the decimal approximation on the other side. Perhaps this might work.  We could tell students to look at the side with the decimal values and find three cards such the sum of two cards equals the third card.  Then, they flip the cards over and see if they can form a relationship with the numbers on the other sides of the cards.  We could also do this to also allow them to discover that log_b(M/N) = log_bM - log_bM.  Clearly, we are still in the planning stages on this.  But that's ok.  This lesson is for NEXT Monday, assuming no more two-hour delays or snow days between now and then.  If you have a way for students to discover log properties, let me know in the comments below.