Wednesday, May 22, 2013

Pythagorean Slap

Too long for twitter, but probably a little short for a blog post.  This line got a laugh today:
"If any of you try to use the Pythagorean Theorem with a triangle that's not right when I test you next week, I'm gonna come over there and slap you.  Not joking.  I'm tellin' you - I don't like this job that much.  I am gonna come over there and put a handprint on your face."
This, of course, in the name of being memorable.  Let's hope I don't have to follow through.

Wednesday, May 8, 2013

Lottery Tickets

I taught probability distributions today, and their associated expected values, variances, and standard deviations. It's one of my favorite lessons, so I thought I'd blog about it.

Prior to the lesson, I print off pages for scratch off tickets from the Minnesota State Lottery website. You know, tickets like this:



And the state lottery site is also nice enough to put up the probability of winning and how many of each prize was printed:


So I print off enough pages for everyone or every pair.  I used to just give them out randomly, but I find it fun to hype the tickets a little bit.  Ohhhh, $100,000 Poker Night?  That's a good night!  ELECTRIC 8's!!?!?  Whoa that sounds dangerous AND FUN.  Double Dollar Fortunnnnnnne in the mfing house!!!  The TWINS may suck, but you could win big!  Worth a MILLION??!?!  Are you kidding me?!?!?!  I'm never coming to work AGAIN!  You know, that sort of thing.

Pause: Those links above will expire; I promise.  If you're reading the post later than Summer 2013 you'll need to use your imagination or make up your own.

So I go through the tickets after I've hyped them a little and I tell them that I'll give the ticket page to the first hand I see.  I read them off.  There are some weird titles like "Scratch Me" that if you deadpan the delivery can get a big laugh.  I tell them that if they don't raise their hand I'll assign them one.  And nobody wants that.  The hype works.

I take the leftovers and pick the one with the smallest number of rows in the distribution table.  Today it was MONOPOLY.



If winning up to 27 times doesn't get you excited, I don't know what will.

So everybody's got their ticket, and I've got mine.  And the questions are obvious:

"Who's got the best ticket?"

"Which one will win the most money?"

"What's the probability of winning?"

"How many do I need to play on average before I win?"

Those types of questions.

Of course, I have hidden motives.  To answer the question, it's helpful to write it as a probability distribution table.

Whoops, we forgot a row.  Can anyone think of what we may have forgotten?


At this point it's important to leverage technology, so we put the $ list & probabilities into our calculators.  And we take a brief pitstop in the land of cumulative probability distributions.  I'm doing mine and they're doing theirs.  Everyone has a different ticket, and this is the part where it's helpful to have kids who know how to use their calculators.  If you don't know, the "cumsum("  button works very well for this.


Very easy now to know the probability of winning $15 or less, for example.

But that is not the meat of the lesson.  Here it comes.  Expected value.  How much, on average, will you win if you play a lot?  Time to define expected value.  Note the beautifully well-written mu.  I have incredible mus.



We delete L3 and put in a new calculation: L1*L2.  Add it all up and that is our expected value.  If we play a lot, I will win, on average, $7.00 in the long run.  I NEED TO BE PLAYING MONOPOLY; I'M GOING TO MAKE BANK AND QUIT MY JOB!!!

(Groans, boos, and a couple of cheers, as you might expect.)

Turns out I spent $10 on the ticket so I'm actually losing an average of $3 every time I play.  Now we go around and share out how much we'd lose if we play their respective games.  Interestingly, but not surprisingly, you lose about the same amount for each type of ticket of the same denomination.

Who's ticket is the best?  Depends upon how you define "the best"?  Scratch Me, a $1 game, could be the best because you lose the least every time you play.  Or maybe it's Worth a Million, because you can win a million dollars.  "Actually they all suck because you lose money on all of them," says a student.

Life lesson intersects math.  That's a win.

Here's where I insert my story about a buddy who uses the lottery to hide money from his wife.  I really hope his wife never comes across this blog because she'll know who I am talking about and he'll get into trouble.

He plays $5 or $10 tickets once or twice a week.  His wife never notices because the denominations are small and they don't really factor into their budget.  But when he hits a winner, that money is all his.  Money he can spend on booze, drugs, hookers, whatever.  OK, it's not that exotic.  Usually, we just get a couple of beers and play a little Golden Tee at Buffalo Wild Wings.

I'd suggest he just stuff $10 into a hidden pillow case every week, but I suppose that's not as fun.

Now I hit them with this.  They saw variance for data distributions earlier in the year, but it's a bit different with probability distributions.


AND, we calculate our variances in our calculators without much thought about what it means.  I got 120849.  What the heck does THAT mean?

We need to do some more splorin.  Who's got a $5 ticket?  I'll bet yours is less than mine.  $2?  Less than that.  $1?  Yeah, much smaller.  How about my $30?  Is yours over a million?  Discuss with your partners what this number might tell us.

We finish boringly with a small note about standard deviation.  Yes, it's still the square root of the variance.  And it still measures spread.  Lesson ends on a whimper.

Overall , although I am sure many out there do something similar, it's a still a lesson that I love; one that brings the math home to real life.  It really energizes me when I can do this kind of thing.  It put me in just the right mood to teach solving rational equations to Algebra 2 students later in the day, completely devoid of context and without any application to anything any of them will ever do again.

Monday, May 6, 2013

Portfolios in SBG

I was talking crazy the other day trying to figure out ways we can make our SBG classroom better.  Seems like it's all test test test test test test test test test test test, and I'm getting sick of it.

So I was talking this out with my colleague, Stacey Haas, and I was telling her my vision.  I suggested that instead of taking each test as a snapshot of what students know at a particular time, why don't we create "evidence folders" for each learning target?  Students could put whatever they see fit into the folder as long it's truly their own work, including warm-ups, skills sheets, tests, whatever.  At the end of the unit we as teachers can grade the folder holistically to determine the extent to which the student has learned the content.




And then Stacey said, "You mean, like a PORTFOLIO?!"

And yeah, I guess this evidence folder would basically be a portfolio.  I've never been a portfolio kind of guy, but I am intrigued by this idea.  We'd give feedback along the way and multiple opportunities to put in or take out whatever pieces of evidence the student chooses.  We could use those problems from our current assessments to provide opportunities for evidence.  Or maybe we could give the tests as we do now and they would be part of the evidence folder.

It would help to alleviate the problems caused by my district's asinine rule regarding the scores we must use for retakes.  It changes the cheating dynamic.  It seems easier to add a communication & problem solving piece.  All work we do in or out of class may impact their grade.  It gives me more control over their grade and I won't be bound to a single score or just a couple of scores.

I'm going to bounce this idea off of the walls of my brain for a summer and see where my colleagues Stacey & Matthew Sauter come down on it.  I think it could work.

Do you have anything you might suggest to make this idea better?  Don't let me down, Internet.