Using Proportions: What If Our High School Was Our Geometry Class?

With the big push for proportional reasoning in Common Core, I wanted to find a way that I could make the whole idea meaningful for my students.  Teaching Geometry requires that I teach a unit on similarity (mostly related to triangles), but I wanted to do things a little differently.  I started the unit by having students create a scale drawing of the classroom, so they had practice setting up and solving proportions with an application.  It was cool to hear the issues that came up around converting units and the accuracy of their drawings.  I felt that the engagement was high and that students were seeing the use of a proportion.

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!

Transformations Test

I work with a lot of Geometry teachers in my consulting work and the question of assessment comes up a lot.  I have made a point of making my classroom a place where we focus on understanding and reasoning as opposed to number-crunching and doing math without context.

I wrote this assessment back in September and used it as my unit test on transformations, but I didn't realize how many teachers would find it useful. So, here it is!!  By far, it is the one assessment that I am most proud of because I feel as though it is a genuine representation of what I find important: balance.  You will notice that there are some procedurally driven questions, but also lots of questions that asses student understanding of the concepts.

In the past, when I would write assessments, I would do my best to come up with a clever extra credit question that was challenging, but doable, so long as students extended their understanding of the given topic.  Oddly enough, I rarely had students even attempt the extra credit question because they thought it was too hard.  That was NOT the case on this test.  I would say that 80% of my students tried it and of those who attempted it, more than 50% of them got it right!  I could not have been happier!

So, take a look, let me know what you think.  I'd love to hear your ideas for additional/other questions, what has worked for you, and any other nuggets of wisdom you have to share.

Link to the Test