As a mathematics teacher, I have discovered that my students respond most enthusiastically when they can understand the rationale for studying new topics, when they recognize interesting applications of this subject material, and when they experience some personal connection with the information. The challenge of course is to find a balance of teaching traditional mathematical material while allowing students to experience something extraordinary.
This Conic Sections Extension activity is to be used at the conclusion of studying Conic Sections in either an Advanced Algebra II class or a Pre Calculus class. It consists of two exercises with the first consisting of three tasks. The first task asks students to identify the appropriate conic section that is described through real life applications and natural occurrences. The second task outlines a procedure to create parabolic envelopes while the remaining task uses algebraic, geometric, and calculus concepts to outline a proof to establish that the envelope is indeed a parabola.
The final exercise enables students to engage in a creative process of needle and thread designs that not only connects art with mathematics, but displays the beauty of mathematics.