# Failure Friday Fixed: A Better Logarithmic Application in Decibels

Here is my first success story from writing a “Failure Friday” post.  The “Failure Friday” idea is to give a lesson that failed and hopefully receive critical feedback on how to improve it, presumably for next year, although general suggestions could help one’s teaching throughout a year.  I am fortunate in that I teach 2 classes of Precalculus, one which is only a bit in front of the other in pacing, so I was able to use the suggestions and my improved lesson plan for the other Precal class.  Not only that, but my “failed” class, I was able to turn around and use the same lesson!

So the lesson is in this post if you care to read it.  The biggest problem that I had (even though I didn’t realize it at the time) was that I didn’t have a good way of visualizing loudness.  Thankfully, Kevin Laxton not only pointed this out for me, but also suggested the solution: Decibel Ultra on the iPads.  This was perfect because I have a class set of iPads, and I began brainstorming for a lab to do involving this app and students’ musical abilities (or lack thereof).

I started the with a very brief slide-show about sound.  Just enough to let them learn the basics, but not enough for them to lose interest yet.  Very soon after, I showed them the Decibel Ultra app.  All I did was hold it up.  My hope was that they would start yelling or slapping their desk in an attempt to make a loud enough sound.  What was funny was how self-conscious they became when they saw the meter move with their voice as they commented on it.

So I asked them an innocent question: “What different types of things could affect the decibel reader?”  They came up with the ones I was expecting, and a few neat other ones.  Included were distance to microphone, number of instruments/sources, pitch, as well as humidity, shape/size of room, number of other people in the room.  So I asked them if we could keep all of the variables the same except one of them (Oh, note: I did NOT use the word “variables”.  That’s one of those “Oh, you’re talking math, Mr. Newman, so I’m going to stop listening because it’s lame” words.  I said “things” and slipped in the word variables later when they were too into the project to notice.  Bwhahaha.).

Then I jumped into the hook and said “Okay, you guys are going to start a band!!”  You need a (1) Director (organizer and non-musical option), (2) “Sound Board” (Really just controls iPad and measure decibels), and (3) Musicians (really they could be slapping a stick on the ground to find decibels).

Here’s the powerpoint I went through with them during this.  Note: I did NOT show them the final slide, the one with the equations!! (It’s similar to my last slide with a few new edits).

After this, students broke up into groups, decided on a variable they were going to isolate and how they were going to “play” and measure the decibels.  Students had a blast going to different parts of the school (they couldn’t work in the same room as each other) and measuring their instruments.  Most of the data actually turned out really good!  Here are some pictures of them taking data:

When they came back together, the next day, I showed them Desmos (again) and modeled “playing with a log function” by adding, multiplying, etc. different parts of the function.  I was actually impressed with how quickly they found a function to fit their data once I released them to hunt on their own!  Here are some pictures of their graphs:

At the very end, I had the students find the real equation by doing some research on their own.  A few of the groups found really good equations, and one group found one that essentially matched their Desmos equation!! They were excited, and so was I for them. (It’s actually the 2nd graph above: you see their function was $y = 9.9 \log(x) + 70$ while they found $dB = 10 \log(x) + L_0$ so they did an incredible job collecting data and matching their graph in Desmos!

All, in all, I believe this was a much better lesson than the “application” worksheets I handed out a week ago.  True, there is not as much calculation here, but there is a lot more function manipulation, which connect to earlier in the course, so yay for that.  My next step on this subject: find a natural flow for that function manipulation.  And it may just have to be the worksheets, but we’ll see.

Thanks to Kevin and Tina for their help both in mentioning ideas and helping me to reflect!