I begin this lesson by asking my students what they know about earthquakes and the Richter Scale because it's engaging for my students and helps them makes connections as discussed in my video. This link has additional information about the Richter scale if you are interested. Although we haven't had any earthquakes in our immediate area recently, many of my students have family or friends on the west coast, so they are very aware of the potential dangers earthquakes pose. We discuss the meaning of the Richter Scale and why we need a logarithmic scale for this kind of data. I ask my students to graph the function and then find the input values that correspond to the first eight positive integer output values. (MP1) This is tougher for some students than it sounds, because they have to recognize that their window and/or table settings for the x-axis will need to extend to at least 10^8. When they've had a few minutes to work on this, I ask for volunteers to post their answers on the board. Then I ask the class to look for patterns in the input values. (MP7) This should be a review of what logarithms are, but I find it helpful to review this pattern now so that my students can connect key features more easily later.
For this part of the lesson I tell my students that they will be teaming with their back partners to work through several more logarithm problems and that they will get to present at least one problem to the class. I distribute the Log functions worksheet, ask if there are any questions, and tell them they have about 25 minutes to complete this assignment before we begin presenting. (MP1, MP2) While they're working I walk around offering encouragement and redirection as needed. Some teams will struggle with discussing what the key features mean for the application problems. These are generally students who haven't made a good connection between the verbal part of the problem and the graph. I try to help them focus on just one part of the graph at a time and describe that, then move to the next part, instead of trying to see it all at once. After about 25 minutes or when everyone is done I randomly select teams to present, allowing each team to choose which problem they want to discuss. This takes some of the sting out of being selected first, because that team can choose from all of the problems, either the skills problems or the applications, whereas each subsequent team has one fewer to choose from. As each problem is presented the remainder of the students participate by critiquing and questioning. (MP3)
To close this lesson I ask my students to write a brief note for an absent student explaining the key features of log functions and how to interpret their meaning in terms of real-world problems. I remind them that they need to use mathematically appropriate and accurate language so that the absent student will understand. (MP6) This gives them an opportunity to reflect on what we've just studied and it gives me a snapshot of which students might need additional support as we move forward.