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!

Let Students Explore and Collaborate (week 1)

We had a great first week! This is my third year of teaching and this is by far the most excited I have been for the rest of the school year. Steve Kelly and I tried a few new things last year in pre calculus and calculus that we didn’t care for, so we revamped the prerequisite units in pre calculus and calculus (again). I have provided links to both documents.

In pre calculus we created a packet for the students with 5 activities. The first asked them to make a piece of art using Geogebra or Desmos and then upload that art to their blog. This had kids a little confused and some weren’t really sure how to begin. It helped that I gave them an example of art I made with Desmos. I don’t think this was a terrible situation as I think it gave activity 5 more meaning and the final works of art were much better. The intermediate activities build on one another And are designed to lead the student to an understanding of the families of functions and transformations. This should be review, but quite often the families of functions are taught in isolation and students lose the big picture. This is especially true for the understanding of how any function is moved left, or right or up-and-down, or reflected. Our objective was that by the end of the packet students would be able to create a better piece of art and understand why their art looked the way that it did.

In calculus, Steve and I sat down together and determined the concepts in mathematics that are most important to be successful in calculus. These included skills like understanding composition of functions, graphical reasoning skills, algebraic manipulation skills, domain and range analysis, and a myriad of other skills. This was successful, as students were given an opportunity to refresh their brains, get back into math mode, and collaborate.

Both of these activities, although in structure were quite different, set the stage for a year full of collaboration and communication.

(I will post some the artwork in another post.)

Calculus packet

Precalculus Packet