On Tuesday, my Pre-Calculus 12 class used our classroom clothesline to explore the magnitudes of radian measures.
When graphing sinusoidal functions, students have noticed that we can divide the period into four pieces (minimum, center, maximum, center) to help determine the location of a given function or to check the accuracy of our function after having graphed it. That said, they were also having trouble dividing a period into 4 equal parts, and if given a graph and asked to find points A to D as shown below, they struggled to find them. To get them to play around and explore strategies to find these points on our graph, it was clothesline time. 🙂
To play around with this concept, I selected random students and gave them each different values like pi/6, pi/2, 3pi/2, etc.. They were then asked to place them on our number line (as shown below). They were told that if they needed help or just wanted to feel like they were on the Price Is Right, they could ask for crowd input as well. 🙂 We then used the values to discuss if they were appropriately placed on the clothesline. Were they placed using the appropriate proportions? What values would fall between them? Were there any benchmark values that would have made placing their values easier?
The students shared their thought process and explained their reasoning in thoughtful ways. There were disagreements that were turned to agreements when students explained their reasoning in convincing ways. After playing with the values we had placed together, I then called attention to 2 values in particular: the value between pi/2 and pi/3, and the value between 0 and pi/6. (Notice that these are the x-values of points A and C on the trig function above.) After our number line discussion, students had many strategies for finding these and were much more confident in determining the value.
Once they had found these values (5pi/12 and pi/12), we then tried to find the midpoint of these values. The strategies shared were FANTASTIC! They had surprising ways to find the values, and it was overall a super worthwhile discussion.
The activity made me super curious what other strategies are out there, so if you have time I would love to know: How would YOU find point B on the trig function shown? I would love to hear your feedback and/or strategy in the comment section below! 🙂
I’ll gather my students’ strategies from yesterday and add them to a future blog post! 🙂