Log to Exponential Form & My Two Favorite Words

I don't know where I first I heard this, but I've had such success with it in both my teaching and my tutoring that I wanted to share it.  When students are converting from logarithmic to exponential form (or vice versa) there are two words that have become my new best friends.

Ready?

Basement and base.

For the most part, students seem to know exactly where to go when switching from one form to the other as long as they start out right.  How do I ensure I start out right?  I just remember:  "What's in the basement becomes the base."  (Or vice versa)

Does this solve all my problems?  No.  Does it guarantee that students fully understand what a log function is?  Absolutely not.  But, I want my students to be able to covert from log form to exponential form like it's nothing.  And this helps that process some.

Maybe this is widely known already.  But I still heart it.

Spring Break Surveys

A dear friend of mine from grad school recently told me she created a survey for one of her college classes through surveymonkey.com.  I was very intrigued by this idea, so I decided to create one as well.  It's nothing fancy, but it was super easy to make.  We do end-of-the-semester evals, but I don't see those until final grades have been submitted.  So, the students really don't have a chance to give their thoughts on how they'd like to see the course changed in a way that would directly affect them.

So far I haven't gotten too many bites, but I'm hoping by the end of Spring Break I'll have a few solid ideas I can work with.  I'll post them if they're useful.

Here's what my survey looks like (click to enlarge).  I stole the majority of the wording from my friend, who's ridiculously good at coming up with cool ideas to interact with her students.

Happy Pi Day! (And happy birthday, Albert Einstein!)

I made this picture tiny on purpose 

Today at the college a man was handing out mini pies in honor of Pi Day.  "It's Pi Day!  3.14--March 14th, get it?!"

It was corny, but it still brought a smile to my face.

This is my third year to make Oreo Truffles for Pi Day.  I mean, everyone makes a pie.  And Oreo Truffles are...spherical...ish.  (Ok, making a pie makes more sense, but my palate favors Oreos.  Sue me.)

Every year I forget how ridiculously time-consuming these are to make, and every year they turn out so much more beautiful in my head than in real life (last year I was able to drizzle a π on each candy...this year I couldn't quite master it so I just plopped chocolate on each one).  But...they sure are tasty.

In other news, today is also Einstein's 133rd birthday!  So, happy birthday to one of the most brilliant minds of the 20th century.

Exponential Functions: Folding and Shopping

I've never been all that happy with my presentation of exponential functions.  I usually slap a couple of functions on the board, plot some points with the class, and then write up a list of these functions' characteristics.  Boring.

Thankfully, I recently came across Sam Shah's method of exploring exponential functions using paper folding.  I like this idea so much more than plain old point-plotting (though I ask the students to do that as well).  Here's the worksheet I had my classes fill out before introducing the formal definition of an exponential function:

Paper Folding Exponential Functions



We spent 15-20 minutes on this worksheet in class before diving into the lecture.  That's a lot of time for a college class, and I felt rushed the rest of period, which is never good.  So, next semester I may assign it for homework the day before instead to save some time.  I would have to give some kind of hint as to how to find f(x) and g(x) though, because the students were a bit unsure of the pattern going on.  I don't think anyone got 2^x, but most did see that we were multiplying (or dividing) by two each time.

Once we got into the lecture part, I gave the students a great cheesy word problem:

One of my students noticed that it didn't take much time for the spending to increase significantly, which I was quite happy about.  "So the moral of the story," I began to say...

"Is not to be exponential when you're shopping!"  she finished for me. 

Perfectly said.

Polynomial and Rational Function Review Day

Review days are a continual dilemma for me.  After each unit is finished and before each test day, I schedule a Review/Catch Up Day.  I'm not sold on this format, but I'm not opposed to it either.  Due to the fact that we live in Oklahoma, I definitely have to have a few built-in catch up days since we close our schools and colleges at the slightest sign of snow/"cold" weather.

I've been using these built-in catch up days for review, which seems natural enough.  The downside is that I often have very low attendance on these days. So, today I tried something new.  I offered something that nearly every one of my students will come to class for:  extra credit. 

You would think I would have had this revelation a while ago...alas.   

Math Mama wrote about a game of "Risk Your Beginning Algebra Skills."  I really liked the idea of the students having to wager a certain amount for each given question:  they have to be honest with themselves and decide how well they think they know something before seeing the answer.  So, I adapted Math Mama's idea and made a game of "Polynomial and Rational Function Jeopardy."  Before I showed them the answer slide, I would ask which students felt confident about their answer and then I had one of these students share with the class.  They were usually right on the money.  

I chose to do this in a slideshow format as opposed to a worksheet format because I know my students well enough to know that half of them would be working ahead and hence not contributing to the overall discussion (all my students are concurrent high school juniors and seniors).  Even if the overall discussion is not always where I would like it to be, some discussion still beats no discussion.

Overall, I think this review day was a success.  Students participated and hopefully got a good sense of what they needed to study for the upcoming test.

Here's the wager sheet I gave my students in Word format and PDF format.

Polynomial and Rational Jeopardy

View more PowerPoint from Rebecka Peterson