FIRST Robotics - Recycle Rush - The Rush is over! and the Teflon Moment.

After 6+ weeks of building our robot is now complete.  I hope to upload some photos and videos later, but just suffice to say, very tired. Need lots of rest, and looking forward to competition.  Also as you will see when I do show the video.  You will see sometimes some of your best designs are well thought about with lots of work, effort, and thought, and other time you get lucky and have what I call a "Teflon Moment"  the accidental discovery.  We had one of those that more than tripled our scoring capability.  I hope to reveal the Teflon Moment soon.

Introducing Logs by Inverse not Definition

Well as you can probably notice by the long dry spell, I haven't quite got into the Blogging thing yet.  Anyhow as I was introducing logs this week, I had kind of a "eureka" moment on how to introduce them.  In the past I sort of done the typical textbook approach here is the definition, now lets use it.  I took a slightly different approach in hopes of getting the kids to appreciate why we have logs.  I'm not sure how much they appreciated it, but I felt like it was a better way to introduce them than just stating the definition.  So here it goes....

I started off by talking about how to find an inverse for a function.   This is something we did earlier in the year.  So here are a couple of examples showing the process I use.  Write as y=, switch y & x variable, then solve for y..

s

Then I asked what operation did we have to use to find the inverse of the function for multiplying.  The answer was obviously division, and to find the inverse of the subtraction function became addition.  So they were able to see these as "inverse" operations to find the inverse functions.

Then we looked at 

Again, I' not sure how much the students appreciated this, but I like the idea of claiming we needed to have an "inverse" operator so we define the log to get this new operator.

After writing this I did happen to look in two other textbooks from different publishers than the one I am stuck with, both of them seem to do an approach similar to what I just showed.  So my approach isn't novel, but just another nail in the coffin that my textbook is pretty bad.