Advanced Algebra 2/ Intro to Precalculus Designing Ferris Wheels Challenge

By Irina Uk – Math Specialist, Education & Innovation Program Manager

Introduction: What do Ferris wheels have to do with trigonometry? In our latest hands-on math challenge, students became engineers as they used sine and cosine functions to design and model their own Ferris wheels. 

Background: We have been studying trigonometry, specifically periodic functions– we are using sine and cosine functions to model various contexts. With this, we are exploring key features of those functions, including the midline, amplitude, and period of the function and what information those features reflect from any given context. One context we have been looking at in depth is the motion of ferris wheels.

Challenge: Students had to create a description of two Ferris wheels with the same radius, height of center, and angular speed. One wheel had to have clockwise rotation, while the other had to have counterclockwise rotation. Then they had to model both the vertical and horizontal motion of the two ferris wheels with a graph and an equation of each.

Process: Both Serena and Joshua came up with equations and graphs that accurately reflected the periodic behavior of the equations. We then reflected on what their equations informed us about the ferris wheels’ design- how large were the ferris wheels, how many spokes did they have, and how fast were they moving? Serena reflected on how her ferris wheel was very small and sat only six people – a wheel of radius 10 ft and having 6 spokes. Yet it’s large enough to fit all six people of average height. As Joshua reflected he realized that his functions reflected ferris wheels that were large with 30 spokes, but the wheels were so large that they would dip under the ground. The first image of student work reflects ferris wheels that would dip under the ground. The second image reflects corrections to the equations modeling the ferris wheels, placing them above the ground. His wheel more resembles the traditionally large wheels we see as landmarks in major cities, such as the London Eye.

Student Takeaways: Besides learning more about the behavior of sine and cosine functions, Serena and Joshua had an opportunity to think like engineers. They examined what sound and effective design involve. Students also tapped into their creativity and innovative spirits. For example, when examining the ferris wheels that dip under the ground, we discussed when such a design might be viable– students suggested ferris wheels that went through a transparent tunnel at an archeological dig site or a “haunted ferris wheel” that dipped into a tunnel under the ground. 

Next Steps: To take this exploration further, it would be great for students to build physical models of their ferris wheels reflecting features of the periodic functions inherent to their equations.

[/vc_column_text][/vc_column][/vc_row]