As the students enter the classroom, I already have the pendulum stations set up. At the front of the room I hang the largest pendulum from the ceiling, and begin class by asking them how long they think it will take for the plum-bob to swing back and forth one time - a.k.a. make one period. The students really enjoy guessing prior to the activity, and this immediately hooks them on the investigation (rather than having the pendulums make them sleepy... very sleepy.... very very sleepy...).
Once all of the students have recorded their guesses at the top of the paper, I have my students get out their iPads and pull up the stopwatch app. We record the actual time of the pendulum by finding the median at each table of students (a process that they can use if you rotate them in groups to complete the activity collaboratively). It is great to talk to the students about the value of finding the median. After this initial trial is done, tell the students that we will set out on a journey to determine the LENGTHS of the string through knowing only the period. At the end of class, I tell them, we will have a graph that models the period for any pendulum as a function of its length.
At the end of the class period, I have the students explain to me how we can graph our findings (MP4). If extra time is available, I like to adjust the length of the pendulum at the front of the room using a clothes pin - this allows us to get a few extra data points for our graph. I ask the students what they think the SHAPE of the graph looks like - - IT'S A RADICAL EQUATION! Just like we studied in a previous lesson! As an extension question, I ask the students about the behavior of pendulums with VERY long strings. What might be some issues with trying to gather this data through a test?