Introducing Properties of Logarithms (Find the pattern!)

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:

Properties of logs slide

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!

Multiple Methods for a Simple Problem

For each video I have students watch I ask them, among other things, to submit one question they have after watching the video. After a student watched the “Solving Logarithmic and Exponential Equations” video, he submitted the following question.

How would you solve 8^x = 16^x ?

The following day I used this question in our WSQ chat over the video. What appeared to be a simple problem revealed some interesting solutions. I’ve provided the main types of solutions that I found.

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I anticipated the second method from most students but only two of the five groups approached it that way. All methods are valid and what I really liked is that not only were they different methods but also different thought processes that led to the method/solution.

I would love to hear your feedback or observations that you have seen in your class!