Sinusoidal Spaghetti

When I was first learning about sinusoidal functions we were taught using a very direct teaching method. My math teacher showed us the equation, the graph and a number of key features of the function. The teacher then compared and contrasted these portrayals of the function, all the while the class (and my self) copied down the notes. The way I retained this knowledge was through reviewing my notes and slowly memorizing the function and it's properties. 

Retrieved from: https://mathbitsnotebook.com/Algebra2/TrigGraphs/phasepic5.gif 

During our course this week I was introduced to a student centred learning model for the sinusoidal function. My peer introduced this activity as sine wave spaghetti. We were given a bit of review of content the students would need to know before attempting this activity. Then we were partnered up and worked as a team to co-create the sine wave. We used a cartesian plane with a circle thats radius was 1. From here we found the sinx=opposite/hypotenuse values for a many points along the circle. We cut pieces of spaghetti to this length. Then we placed them at corresponding locations on a graph. Finally we drew out the lines to show the representations. 

This activity would have really helped me grasp the relationship of the sinusoidal function if I had been given the opportunity to do it as I learnt functions. As an educator it is important to explore various ways of representing content to students. This is a direct example of differentiating instruction and how it can benefit a number of students.