Not every lesson is remarkable or a success, but this one had a good activity that the students really enjoyed.
Algebra II is not everyone's cup of tea. Some students prefer geometry and other students really dislike math all together. The first section of the summer was all about functions. Students learned about function notation and how to evaluate functions. But, a particularly challenging topic, is composition of functions. Lucky for my students, this lesson fell in the first week of classes.
A Source of Inspiration
I was wracking my brain on how to make this lesson more interesting and more engaging. Naturally, I consulted the best source for any teacher which is TeacherPayTeachers. There are so many activities on this website that other teachers have created. Not all of them cost money, but I'm usually just looking for some inspiration. I found this one activity that involved solving a mystery using composition of functions. Instead of paying, I adapted it into my own.
How It Worked
One day was completely dedicated to learning the lesson. As this was a more challenging topic, I wanted to give two days for this. One was heavy in instruction with some time for practice. But the bulk of the structured practice was on the second day. The activity had 10 different stations (or clues as I called them). At each station was a problem relating to composition of functions. Listed underneath were four potential answers. Each answer correlated to a clue. The correct answer helped students get one step closer to the answer.
At the end of their packet was a list of suspects, locations, and the murder weapon. The mystery was centered around the murder of one of my coworkers (she graciously allowed me to use her in this activity). The other suspects were the student's teachers and the locations also correlated to the school.
I had so much fun watching my students walk around and trying so desperately to solve the mystery. They were also interrogating my coworkers to see if they knew what happened. I heard one student continually say "Maddy did it. I know that she did it." By the end, they had a better grip on the information and were able to solve a lot of the problems by themselves.
Always Room to Improve
Of course, not every lesson is perfect. Breakthrough provides sample lesson plans that we can adapt each week. The sample lesson had students learning composition of functions where they evaluated at a given number or just in general. The picture above shows (f o g)(x). Since there is an 'x' (and not a number), you evaluate the problem in general. When there is a number, say (f o g)(2) then you evaluate the functions at 2. It is easier for students to understand the latter because they just learned about evaluating functions. I included both because the sample lesson plan had that, but in the future I would just do evaluating at a given point.
More Information
Here is a link to my presentation that I used to teach composition of functions: https://view.genial.ly/62a699305293c4001a7b3c06/presentation-composition-of-functions