# Day 80: Folder Trig

One activity I started last year to get students thinking about constraints and possibilities of an application problem is what I call the “Folder Activity.”  This time around, I wanted my students to be thinking about what makes a problem sinusoidal and what information from the situation helps to create a mathematical model (equation).  In addition, I want them to be thinking about what kinds of questions could be asked about the situation that can be answered with the graph and/or the function equation.

To set up this activity, I needed lots of sinusoidal application situations that are different from the typical situations of ferris wheels, merry-go-rounds and oscillating springs.  The internet is a great source for these and I found many!  I then “pull apart” the problem situation from the questions asked.  The students only get the problem situation…here is one example of the eight different problems I had available:

First of all, students open the task card on their iPad.  This includes group roles, materials needed, the task and the product.  Here is a copy of the tasks and folder layout.

The groups then get a folder, a quarter sheet headed with “Known Information,” a second quarter sheet headed with “Mathematical Relationships,” and a half sheet of graph paper.  At this point they read and discuss the problem information, determine known information and identify potential useful mathematical relationships…they know not all of the possible mathematical relationships will be used, but it is helpful to think about them.  The discussions are rich, the misconceptions get “fixed” most of the time, and once the questions are actually asked, they already have a plan to answer them.

Once the information is organized and glued to the folder, then the group can pick up the actual questions and begin working on them.

The final product is the folder with the solution written out neatly…each person’s handwriting needs to be apparent in the solution write-up.  All is glued in the proper places and finally the group evaluates to what extent they used the 8 Math Practices along with a 1-2 sentence summary for each practice.