Chapter 13: Spaghetti Trig

The spaghetti task is designed to help students better their understanding of the unit circle, as well as develop a relationship between the unit circle and the graphs of trig functions. Essentially, students either develop, or are provided with a unit circle. They are then asked to wrap a length of string around the circumference of the unit circle. At each of the ordered pairs of each special angle, students should place a "dot" on the string using a marker. Once this is completed, the students would straighten the string and glue (or tape) it to a piece of paper (see the image below).

Next, students will measure and break pieces of spaghetti that run from each ordered pair point back to the baseline (horizontal axis) of the circle. These pieces would be glued (or taped) to their corresponding point on the string. The pattern created would either be a sine or cosine wave (see image below) depending on whether students measured the distance of an ordered pair to the vertical or horizontal axis.

https://www.pinterest.com/lesfleur87/trig/

I found this task to be a super refreshing take on a unit circle activity. The context of this sort of task almost always involves a Ferris wheel, which means the activity is typically completed on paper, and best-suits theoretical thinkers (most schools do not typically have a Ferris wheel on hand...). This activity however, is highly differentiated; I believe that students who have more success with visual/hands on thinking will be able to grasp the innately theoretical trig concepts presented in this unit. Another benefit of this activity would be the fact that students actually create a product that can be kept or displayed in order to "recall" the concepts learned.

These are the types of tasks that mathematics educators should aim to present as often as possible. Students want to create things, they want to discover relationships, and they want to have fun! I truly believe that we can tap into this intrinsic desire to learn math through this type of lesson.

Thanks for reading!