Posts Tagged ‘exponential functions’

Evaluating and Graphing Exponential Functions

By Kristina

I borrowed this from Sam Shah to use as the introduction to exponential functions.

I liked the self-guided aspect of this activity. I’m working on instilling more self-sufficiency in my students and learning to let go of the urge to have each minute of the class accounted for.  I would like to work on clearer directions, however. In the second section of class, I demonstrated the first few folds of the paper because many students in the first section just started trying to find the patterns without folding. Additionally, I would like to be able to guide discussions better on the “questions” and “properties” sections.

Unit 3, Lesson 2 (Evaluating and Graphing Exponential Functions)

Contagion

By Kristina

Photo Credit: trailers.apple.com

We started exponential functions today in IB Math Studies. The students attempted to guess the population of the U.S. and the population of the world. Surprisingly, most students guessed way over (about 2 billion). I showed them a clip of the Contagion movie trailer and had them write down the numbers spoken by Jude Law (so that they’d pay attention to the math rather than just the ominous nature of the movie), then see if the pattern matched up with his prediction of 1 billion deaths in 3 months, like in this MathsPig post. Some students asked “are you doing this to scare us away from bird flu?” I wish I had addressed the other factors that affect disease transmission at this point. Would 1 billion have been realistic for three months given geographic location (i.e., more time to transmit from continent to continent) and any slowing in disease transmission (i.e., if people were quarantined)?

We moved on to our Disease Detectives activity (based on this lesson from Georgia Southern University). I borrowed NaOH, phenolphthalein, graduated cylinders, and beakers from my science colleague in the room above mine.   During pre-class setup, I ended up rushing a bit because I had to fill the graduated cylinders with water from the cafeteria sink (the science sink water was cloudy ) and make handouts. I wouldn’t have been able to do this if I had a first period class.

The Setup

I handed out cups of clear solution to all the students, informing them that one student was “infected” (aka Gwyneth Paltrow in Contagion). I instructed the students to interact with two other students by mixing liquids and keep track of the students’ names. Then came the big test: who would be infected? I went around the room with a spray bottle of phenolphthalein to test each cup. The students waited in trepidation, and as soon as the first infected cup turned bright pink, they started screaming. I recommend using clear cups for this…it’s more exciting to see an infected one turn pink. During this round, four students were infected. I had them try to figure out who the original infected person was, but they couldn’t. Neither could I–I didn’t track the infected cup when handing it out.

Uh-oh…someone at this table was infected. Will the next person be too?

After round 1, we had the Great Spill of 2012 when trying to dispose of the liquids. I was hoping to carry them up to the science teacher’s classroom with a Halloween candy bucket, but the bucket started leaking all over the table. We lost about 10 minutes of instructional time sending students out for more paper towels, sacrificing a running trophy to catch the leak, mopping up the spill, and sending students out to wash their hands. However, the students were good sports and we still managed to do another round with three interactions. I forgot to have them estimate the number of students infected, so after we discovered 7 infectees (some of whom started screaming as soon as they realized they had traded with the first person whose cup turned pink), we looked at the theoretical numbers. In round 3, there should have been 8 infected people, but as my intern pointed out, the lower number could have been caused by two infected people trading.

Infected students in Round 2

I enjoyed doing this lesson because of the hands-on, visual aspect and the connection to real world issues. A few years ago, there was a swine flu outbreak at our school, so the issue of infectious disease transmission is very interesting to us.

Link to the lesson: Unit 3, Lesson 1 _Intro to Exponential Functions – Infectious Disease