## Evolution of a Theorem (or How to Save All the Animals)

[Edited 7/31/2018 with further information and credit about the origins of the theorem]

Greg (@sarcasymptote) is responsible for the first known instance of puppies in peril. Chris Lusto formalized it into a theorem.   It all started when Bowman Dickson posted The Dead Puppy Theorem and Its Corollaries. Others joined in on the effort, most notably the additional corollaries developed by Math Curmudgeon   I also joined the cause, making a worksheet that covered the do’s and don’ts of exponents.   Lisa Winer at eatplaymath took that idea and made an a full-page warning worksheet for her Algebra II students.

Lisa posted her worksheet at just the right time as I was about to start one of the more dangerous chapters: Trig Identities and Equations!  EEEEK!  So I made this and we spent about 15-20 minutes discussing the various problems that come up, why they’re illegal and what to do instead.

(file here) We also added more to the back as we needed them (e.g. can’t cancel sin x in 1/sin x + sin x.)  I really think it worked as the identities section of their quiz was really quite pretty!  Only 4 kittens were harmed in 75 tests!  It really made them think about each step and I got a lot of “Mrs Craig, is this hurting an animal?” or “Mrs Craig, is this legal?” questions when we were working on them, whereas before I think they just did magic and didn’t care.

What are some constant mistakes that you would want to warn your students about?

## #mtboschallenge 1-2-3 Sunday Summary

Going to change up my order a bit so I can start with:

One Totally Awesome Way to Deal with Complex Fractions (complete with poor cell phone visuals)

I don’t know where I picked up this method (I actually want to say it was a textbook and not MTBoS, but that doesn’t sound right, so if it was from you that I got this, let me know) but it is a totally awesome way to deal with complex fractions.  Before, I would simplify the top and bottom, then multiply the numerator by the reciprocal of the denominator.

I was going to use arrows to show the two different ways on the same page but I ran out of room.  It’s not that I don’t think you could follow my steps without them.

Maybe to save time, once I simplified the top and bottom, I’d use “outers over inners” to get the next step, while pretending I didn’t know what this Nix the Tricks thing was all about.

Now here is the totally cool, time-saving, wait-til-you-get-to-cal-to-see-how-awesome-this-is, not-a-trick way instead.

Multiply the top and bottom by the LCD of the “tiny denominators.”

WHAT???  How amazing is that?  We just have to choose a “convenient one” and all that middle work is taken care of.  Some more examples:

I need to set up some sort of royalty system where I get 3 cents every time you use this rule and are completely amazed by it (because I still am amazed after using it for a year).  (I also think all those Shark Tank viewings may be going to my head.)

Two Other Cool Things To Share

1. What reminded me about the cool fraction trick was the fact that we were working with trig identities and double/half angle formulas this week.  Here is a lovely handout (.doc file with “running for a cause” font) for trig identities:

The order of the identities works out nicely to do 1-6 as a group, 7-12 as individual practice, then the rest as group practice (and yes, 11 and 19 are the same. My laziness strikes again.)  I also tried to disperse the more difficult ones throughout the worksheet instead of all at the end.

2. Mattie B (@stoodle) sent out this plea this week:

Which led to a discussion of Bowman’s Dead Puppy Theorem, which then led to my sharing of this handout, (.doc file with “running for a cause” font) which has all of the ways to save animals.

You’re welcome, I already test drove this and therefore changed save “yourself” to “your grade” to avoid the awkward “don’t kill yourself” statement.

The arrows at the top are a reference for this fabulous way to think about exponents from Sweeney Math

Shoot, Now I Need to Think of Three Other Things to Talk About

1. I tried to go vertical with my group whiteboards this week by having my Precal classes work on their identities.  It was AMAZING!!  I could do a quick scan to see where everyone was, 98% of the kids were engaged, if we had time at the end of class I could say “to the boards!” and they would pick up where they left off the day before.  Then all the whiteboards fell off the wall overnight.  I’m just thankful the one that did fall off during class wasn’t where any students were sitting.  I put in a request to see if someone would mount them for me (or if I would be allowed to mount them), but haven’t heard back yet.

2. Like many of the other MTBoSers, this has not been a very positive year overall for me.  All the grand plans I had at the start of the year have been squashed and now I’m basically back to doing the same things that I’ve always done.  But now with 20% more stress.

3. Have you tried showme? I was introduced to it by a new teacher at my school, and it is pretty cool.  Unlike some of the other ipad whiteboard apps, this one makes and stores the video for you–no need to find a place to upload it or deal with a password-protected site.  The only thing I wish it had would be the ability to import PDFs, but another teacher had the brilliant idea of taking a screenshot of the PDF and importing the picture.  Clever!