My students recently took their end of unit test over exponential functions (writing them and graphing them)…and it was a disaster. They all went into a panic during the test, and their results were about as bad as they feared they would be. I clearly had not prepared them well enough.
I went into a panic of my own, decided that I could not put that test in the gradebook, went back to the drawing board, and came up with some review activities for us to do over the next few days. I also decided that engaging with real data in a way that would be pretty difficult would potentially prepare them to engage with the more sanitized numbers and scenarios of test problems more confidently. I employ this strategy frequently – putting problems in notes or practice that are more complex than any that will be on their tests, so that then the tests seem easy in comparison.
“What’s exponential in real life?” I thought to myself. “And what will I be able to get data for that is readily available and I can put together…in the next hour?” (I was trying to get something that we could use the next day in class). Many of our example problems involved populations, so my brain came up with world populations! “I can probably get a list of the populations of every country,” I thought. I searched country population growth rates and was led to this Wikipedia article (I know, Wikipedia as a source, cringe, but I was on a time crunch and THEIR data sources seemed pretty trustworthy). I copied the growth rates table into a spreadsheet, and then decided that I would only use the earliest year from each source, so deleted two of the columns.
Then I set out to find populations of every country for 2009, 2010, and 2012, the years the data came from. This was more difficult than I expected it to be, and I do not remember where I finally ended up finding the source I used that gave me downloadable or copyable data to put into my spreadsheet. I put this information into another tab on my spreadsheet, but I wish I had put each year into a separate tab because so many of my students ended up being confused by the fact that there weren’t the exact same countries on each list and so the countries didn’t line up in the same row for all 3 years. Some of them ended up with the population for the wrong country for one year and not realizing until they went to make their predictions and they were way different! (At least they realized it then, that’s great analyzing your solution for reasonableness!)
I gave the students a template to organize their information on. I chose to do this mostly because I only wanted to spend two class periods on this project, and if I had just given them a checklist of information to include and had them make their own posters, it would have extended the project to at least a week, and included so many “where should I write this?” “What should I title this section on the poster?” “Should these things go together?” questions, when I wanted them to focus on the math.
I gave them access to the spreadsheet via our Google Classroom, and told them they could select any country they wanted, as long as the dataset listed a growth rate for each year and a population for each year. This mainly excluded the tiny little countries, territories owned by other countries, and countries that stopped existing sometime during that time period. Some of my students found the weirdest name they could find, and some of them just went with Canada “because it was easy”. Several students chose Japan because my school has been really into anime and Yu-Gi-Oh!
After they chose a country, they started to fill the information in on their template. I got to conference with each student as they worked and help them transform the growth rate into a multiplier for their equation, help them set up some tables to find points for graphing, and help them make predictions using their equations. I think my written instructions were too wordy for my students’ taste, so I’d like to revise them in the future to be more bullet point-esque. I’m a very wordy person, as I’ve realized in grad school when I spend half of my time editing projects to be shorter so they fit the length requirements! (And also when I read my blog posts. I really need to figure out how to say things using fewer words)
I think my students got a lot of great practice writing and graphing exponential growth (and occasionally decay, some countries shrank in population!) functions through this project. They were also invested in their chosen countries – when it came time to think about why their predictions didn’t match the actual 2017 population of the country, so many of them came up with specific reasons that tied to their specific country and its culture. This could be a really cool project to tie in with your social studies teacher in that regard – if they could have researched more about their countries at the same time or beforehand, there could have been so much interesting knowledge for them to bring to their analysis of the population numbers!
I hung all of their projects on the glass wall that separates my classroom from the hallway, and one of my students excitedly showed his project and a bunch of his friends’ projects to his parents as they came in for conferences last week. I’m happy they took a lot of interest in this project, but I’m even happier that when they retook the test, most of them showed proficiency!
— Liz Mastalio (@MissMastalio) February 6, 2018
Here are all the resources I used for this project. I also found this site to be a good place to direct students to find current country populations. It still had 2017 populations when we did this project, but now appears to show 2018 populations, so you could adjust the project template to reflect that it is now officially 2018!