1. Trigonometry Superbowl Aimee Frame 1, Gabrea Bender 2 1 Department of Engineering, University of Cincinnati, Cincinnati, OH; 2 Newport High School, Newport, KY AbstractPlaybook ActivityPrerequisite Knowledge Goals Reflections & Modifications Objectives State Standards Pre/Post Assessment References & Acknowledgments Conclusions Project STEP is funded through NSF Grant # DGE058532. Students will be able to: Determine the right triangles in a real-world problem. Use right triangle relationships to find the unknown length and angle measurements. Kentucky Core Content: MA-HS-2.1.3: Students will apply definitions and properties of right triangle relationships (right triangle trigonometry and the Pythagorean theorem) to determine length and angle measures to solve real-world and mathematical problems. Ohio Standards: Geometry and Spatial Sense Standard, Grades 8-10, I: Use right triangle trigonometric relationships to determine lengths and angle measures. Geometry and Spatial Sense Standard, Grades 11-12, A: Use trigonometric relationships to verify and determine solutions in problem situations. Mathematical Processes Standard, Grades 11-12, J: Apply mathematical modeling to workplace and consumer situations, including problem formulation, identification of a mathematical model, interpretation of solution within the model, and validation to original problem situation. The purpose of this lesson is to show the students how trigonometry can be applied to real-world problems. The students are given a set of football plays which they need to complete in order for the play to be successful. Using the given information and the basic trigonometry functions (sine, cosine, and tangent), the students will be able to determine the unknown values that will make the play a success. After applying trigonometry to football, extensions to other real-world and engineering applications will be discussed. http://www.eng.uc.edu/STEP/activities/ This lesson is intended to be a fun way to show how trigonometry can be used in a real-world situation. The students are given a playbook in which some of the route information is missing. They are asked to determine the missing information using their knowledge of trigonometry and right triangles. The first play is completed as a class with guidance from the instructor to familiarize the students with the terminology and the idea of creating right triangles that can help solve the problem. The class is then divided into groups to complete the rest of the playbook. Once completed, the instructor can review the solution process as a class, showing that there can be more than one way to solve the problem and reach the correct answer. Afterwards, a short presentation on how this idea is applied in other real-world applications is given. This lesson provides an interesting application for trigonometry, encouraging the students to apply their knowledge a different manner. Most of the students seemed to like the real-world application of football and were engaged throughout the activity. Although it can be challenging to those students that are struggling with the prerequisite knowledge, the use in a different setting may help their understanding of the basic trigonometric functions. Finally, this lesson can be extended to the concept of vectors and vector addition for use in a physics class. This lesson was adapted from Amy Dimmerling’s Geometry Superbowl lesson Pythagorean Theorem Basic Trigonometric Functions (SOH-CAH-TOA) Sine Cosine Tangent Solving Equations Special Right Triangles (optional) 90 o -45 o -45 o 90 o -30 o -60 o PosYard LineField PositionPattern QBOwn 30 yd line Centera) 30 yd pass 45 o to his left WROwn 30 yd line 10 yds left of center a) Runs 15 yds at 0 o (straight) b) ? a)If the pass is to be completed, at what angle does the WR need to run to catch the ball? b)How far does the WR run (total yards)? c)Where is the pass caught? PosYard LineField PositionPattern QBOpp 20 yd lineCentera) Under pressure, runs 90 o left 10 yds b) ? WROpp 20 yd line5 yds right of centera) Runs 30 yds 40 o to his right a)At what angle does the QB need to throw to connect with the WR? b)How far is the ball thrown? c)Is it a touchdown? 30 feet 45 o 650 m 30 o 4 ft 1.Find the HEIGHT of the tree. 2.Find the HEIGHT of the Eiffel Tower. 3.Find the ANGLE the 15 ft ladder makes with the floor. PosYard Line Field PositionPattern QB50 yd line5 yds right of center a) Runs backward 45 o left to the 45 yd line b) Throws 15 o left WR50 yd line15 yds left of center a) Runs 0 o (straight) 4. a)How far does the WR have to run to catch the football? b)How far is the ball thrown? c)Is it a touchdown? Pre-Test The first three questions are good indicators of how well the students understand the basic trigonometric functions Students that did well on these questions were better able to figure out how to apply the trigonometry functions during the activity It may be a good idea to ensure that each group has a student that did well on the pre-test Playbook Although there are five plays listed, there is not enough time in one class period to get through all of them. Complete the first play as a class The terminology has to be explained well to help prevent confusion on the remaining plays Players face the end zone Left/Right refer to how the players are facing Angles are measured from “x-axis” to line Show how to make right triangles by using the “slanted lines” as hypotenuses Explain that there is more than one way to solve the problems May need to reconvene as a class periodically For bigger classes, may not be able to get to all the groups individually Can clarify any questions about terminology Discuss/show different approaches to the problem