 The Swing Lab is a dynamic problem that will help your students explore the motion of a Swinger by modeling the horizontal and vertical positions of the Swinger over time. In this video, we'll show you how to use the Swing Lab in a classroom setting. To do this lab, you'll need the video, the animation, the handouts, data sets, and a calculator. Links to these files are provided in the YouTube description of this video. First you'll want to show the movie of the Swinger to the entire class. As you watch the Swinger with your students, ask your students to think about breaking up her motion into her vertical position and horizontal position over time. The distance between the top of the two orange cones is approximately 72 inches. Ask your students to think about how high she swings or how far left or right she is from the center of her swing. We can use the animation of the Swinger to help students see how the horizontal and vertical positions of the Swinger change over time. Well, we will overlay a coordinate system on the Swinger so that the middle position is zero. We will mark her starting position and we can see that her starting vertical position is shown by the blue arrow and her starting horizontal position is shown by the red arrow. In this system we can see that when the Swinger is to the left, her horizontal position is negative and when she is to the right of the middle position, her horizontal position is positive. As we watch the animation, we can see the graphs of the Swinger's horizontal and vertical position over time. As we step through the animation, we can point out important features of the graphs as the Swinger is in motion. For example, we can see that when the Swinger is at the bottom of her swing, the graph of the vertical position is at a minimum and the graph of the horizontal position is close to zero. Students should watch the video of the Swinger in the animation as many times as needed. When they're ready, it's time to work through the questions on the student handout lab sheet. They will need access to the actual data points for the vertical and horizontal position of the Swinger. The data is provided in two Excel files, one for vertical and one for horizontal, or TI-83-84 data sets. A partial data set is also provided at the end of the student handout. After students work on parts one and two of the lab sheet, you should show the video again and have half of the students say up and down when the Swinger is at the top and bottom of her swing. Then have the other half of the students say left and right when the Swinger is at the left-most position and right-most position. We can hear one group of students talking more frequently. This helps to illustrate that the Swinger moves up and down twice as often as she does left and right. This should help students understand why the period of the horizontal graph is half of that of the vertical graph. We can also see this important relationship between the periods of the two functions by comparing the graphs on the same set of axes. Finally, we will use the TI graphing calculator to graph the horizontal position of the Swinger against the vertical position of the Swinger. Press mode, choose parametric. Press y equals. Type your equations in x of t and y of t. Press the window button. Set an appropriate window. For example, t min equals zero, t max equals eight, since this is time in seconds, t step equals zero point one. x min equals negative seventy, x max equals seventy, x scale is ten. y min equals zero, which represents the ground, y max equals one thirty, y scale is ten. You can change the trace type in y equals. Now press graph. This lab activity gives students an opportunity to create trigonometric functions to model a real-world problem.