There is nothing earth shattering about this activity but I think it’s effective and worth sharing.
When I taught properties of logarithms last year this was the first slide I showed the students:
Yes, I know, boring. Not only is it boring but the notation can be confusing. On top of that, these properties aren’t exactly obvious. With all that on my mind, coming into this lesson today I wanted to start with something other than definitions. I came up with this activity.
This activity, as I mentioned above, will by no means change the world, but it gives students a “feel” for the properties before anything is formally defined. This is now how I start the lesson. This took my Extended Algebra II students 10-15 minutes to complete and I think it served it’s purpose. It also allows them to see the properties play out numerous times and should help them when they apply the properties to more complex problems. I also made sure to use natural logs and common logs so that they could quickly find the values and could use brain power to look for patterns.
Reflection: This went pretty well and even got a couple “wow, that is cool”s immediately following the activity. What I had trouble with was making it “stick” and helping students to extrapolate the rules to more complex expressions. I’m thinking about an extension activity in a similar format with variables and symbols instead of just numbers. This would allow them to immediately apply their new found rules and I think would be more advantageous than going straight into the direct instruction as I did this year.
As usual, any feedback is greatly appreciated!
Reflections on Holes in Graphs and Reasoning 