I was given a book a few years ago called "If the World Were a Village" and I thought this would be a great way to continue the application and help give context to similarity and proportional reasoning.
I started this section of the unit by reading the students the book and had them brainstorm questions that they would be interested to know about the population of our high school. Students worked in their table groups of four to generate questions and they came up with ones that I would have expected and others that surprised me. There were questions like, How many people drive to school? and How many people play a sport? And then there were also questions such as, How many students own a pair of designer jeans? or How many students have lost their virginity? I typed up all the questions as they read them to me and then I narrowed them down to a list of appropriate questions that were reasonable to put into a survey.
Here's the final survey that I used to collect data:
The way that our schedule is structured, all students are enrolled in an English class, so I asked the English teachers if they would be willing to survey the students. They were more than accommodating and within a couple of days we had our data.
Through all of the "number crunching" it became obvious that students struggled to keep their data organized, but they eventually had some totals that they could work with. If I were to do this project again, I could see taking my students to the computer lab to work with Excel. The big, overarching question here was, "What if our high school was our Geometry class?" There were roughly 1,300 students surveyed and we wanted that population scaled down to the size of our Geometry class of 32 students. This is, of course, where the proportional reasoning comes in. If 472 students (I made that up) said that they drive to school, students solved the equation 472/1300 = x/32.
As a final product, I wanted students to create an info-graphic that could show the relationship between the entire surveyed population and our own Geometry class. I had them choose 6 of the 19 survey questions that they liked and put the data into the info-graphic. Also, I asked all the students to represent the ratio of boys to girls in their info-graphics (that was the only required survey question to represent). I recommended that they use easel.ly or Pictochart to generate their graphics. I've included some of my favorite info-graphics, please enjoy!