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Thrill U. the PHYSICS and MATH of AMUSEMENT PARK RIDES

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Thrill U. the PHYSICS and MATH of AMUSEMENT PARK RIDES Thrill U. THE PHYSICS AND MATH OF AMUSEMENT PARK RIDES Algebra © Copyrighted by Dr. Joseph S. Elias. This material is based upon work supported by the National Science Foundation under Grant No. 9986753. KUTZTOWN UNIVERSITY OF PENNSYLVANIA Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Dorney Park/Kutztown University Thrill U. - Algebra Introduction Welcome to Thrill U.! This set of mathematics activities focuses on Algebra . We believe there is something for everyone as the collection represents a breadth of adventures. There are activities that address algebra topics for beginning students (Survival of the Fittest), for mid-level students (Dominator), and for more advanced students (Thunderhawk). Some activities require straightforward data collection and calculations (Waveswinger), while others require collaboration (White Water Landing - The Bridge) or interdisciplinary considerations (Create a Park). Several of the activities can be easily adapted for special needs students, some can be adapted for use as follow-up activities, and still others are appropriate for schools with intensive scheduling programs. Each activity is preceded by an "Information Sheet" to help guide teachers in selecting appropriate activities for their particular group(s) of students. In addition to identifying objectives based on state and national mathematics standards, these pages provide a list of equipment needs and suggestions that may lead to the activity's successful completion. Teachers should feel welcome to adapt activities to the specific needs of their students. Teachers may request a “solution manual.” Contact Dr. Joseph S. Elias at [email protected] Join us in May and challenge your students to experience algebra in action! Dr. Kathleen Dolgos Dr. Deborah Frantz Professor Emeritus Professor Emeritus Mathematics Department of Secondary Education Department of Mathematics/CIS College of Education College of Liberal Arts and Sciences Kutztown University Kutztown University KUTZTOWN UNIVERSITY OF PENNSYLVANIA Thrill U. Table of Contents Acknowledgments Page i Tips for Mathematics Teachers Page ii Things to Bring/Dorney Park Information Page iii Algebra Activities Specific Rides: The Antique Carrousel Page 1 The Dominator Page 7 The Enterprise Page 13 The Sea Dragon Page 17 Thunderhawk Page 23 The Waveswinger Page 26 White Water Landing – The Bridge Page 29 White Water Landing – The Ride Page 33 Whole Park: Create a Park! Page 37 Entertainment Values Page 39 A Group of Friends at Dorney Page 55 Geometry Activities (Separate manual) KUTZTOWN UNIVERSITY OF PENNSYLVANIA Thrill U. Dorney Park/Kutztown University Acknowledgments During the winter of 1997, area teachers of physics and mathematics, professionals from Dorney Park, and faculty from Kutztown University gave birth to Thrill U.: The Physics and Mathematics of Thrill Rides. In May 1999, the Thrill U. - Physics Planning Committee presented physics activities in the form of (Coaster Quest) Thrill U. The Thrill U. - Mathematics Planning Committee was established in the fall of 1999. The Committee began by creating algebra activities that would help teachers achieve goals set forth by the state and national “Mathematics Standards.” As a result, the mathematics component of Thrill U. consisted of algebra activities that were introduced in May 2001. Geometry activities have been developed and have been a part of the mathematics component since May 2002. Thrill U. is the culmination of effort and time of many people. Its existence would not have been possible without the collaborative efforts of: the professional staff at Dorney Park and Wildwater Kingdom; the administrators and academic faculty at Kutztown University; teachers who had taken students to the Park and provided feedback; and (most importantly) members of the planning committees. Each planning committee consists primarily of area high school teachers of physics or mathematics. The leadership and creativity of these teachers resulted in impressive sets of activities. Members of all planning committees have worn out shoes in the Park, endured days of inclement weather, fretted over success (or failure) of their students to complete preliminary versions of activities while in the "piloting" stages, spent many hours in meetings, and countless hours designing and editing the activities. In short, we admire and appreciate the efforts of all who have contributed to the success of the Thrill U. project. Algebra Planning Committee Mr. Ray Cianni Upper Perkiomen High School Dr. Kathleen Dolgos Kutztown University Dr. Joseph Elias Kutztown University Mr. Gerry Farnsworth Parkland High School Dr. Deborah Frantz Kutztown University Mr. Keith Koepke Dorney Park and Wildwater Kingdom Ms. Laura Leiby Emmaus High School Mrs. Kim Reiter Emmaus High School Mrs. Brenda Snyder Kutztown University Mrs. Beth Stoudt Emmaus High School Mrs. Michelle Wiley Dieruff High School Ms. Maggie Woodward Upper Perkiomen High School KUTZTOWN UNIVERSITY OF PENNSYLVANIA i Thrill U. Tips for Mathematics Teachers Think of this as an adventure! To help make a "stress-free" day at the Park, we have created this list of suggestions to guide you through your planning stage of Thrill U. • Above and beyond all else, bring your sense of humor. Experienced teachers know that there will be mistakes. Allow students to have fun as well as complete your selection of activities. • While mathematics is an "exact" discipline, applications of mathematics are much "less exact." ALL measurements and collected data will have inherent errors. Accept it. • Please do not forget copies of activity sheets, equipment and supplies. You might also consider bringing a camcorder to record aspects of the rides for use in the classroom after Thrill U., or to use as introductory preparation for next year. • If your comfort level is low with orchestrating lab-type activities, consider consulting a science teacher for assistance with logistics. • Carefully peruse the complete list of activities and select those that will best fit the needs and abilities of your students. (That is, do not expect your students to complete all of these activities!) The difficulty levels are quite varied among the activities. Consider doing parts (but not all) of some activities. You may modify them, or assign groups of students to them. • Some activities take longer than others to complete. Keep in mind that it may be necessary to observe, ride, or take measurements several times in order to obtain good data. • As much as is feasible, introduce the students to the concepts to be studied during the weeks leading up to the event. Consider planning time in class for calculations and analysis during the days following the experience. • In our opinion, students who may be fearful of some rides should not be forced to ride. • Kutztown University students will serve as general assistants for you. They will be stationed at designated Thrill U. rides from approximately 10:00 A.M. to 2:00 P.M. Inform your students that they may ask the university students questions related to the activities. University students will help students discover the "answers," but will not give them answers. Instruct your students NOT to ask Dorney Park employees to give answers. • Teachers are welcome to utilize a designated grove at Dorney Park to chat with other teachers and members of the planning committees, or to use as a place for your students to work. Please do not leave equipment and other valuables unattended at the grove. KUTZTOWN UNIVERSITY OF PENNSYLVANIA ii Thrill U. Things to Bring We present this list for your convenience and hope that it helps make your day at the Park enjoyable as well as productive. You may wish to bring some or all of these items with you to Thrill U.. • tickets for you, your students and your chaperones • copies of your selection of activities, enough for your group • pencils and paper • stopwatches • calculators (depends on activities: basic, basic with tangent key, or graphing) • camcorder • clipboards • inclinometers or protractors with a plumb bob • appropriate clothing and perhaps a change of clothing • sunscreen, hats, raincoats • money for food, drinks, phone • measuring tape or string • masking tape • backpacks or plastic bags to keep papers and equipment dry and together • maps of the Park (can be picked up at the entrance to the Park) • a good reserve of energy and enthusiasm for exploration Dorney Park Information General Information: (800) 551-5656 or (610) 395-3724 Group Sales Information: (610) 395-2000 For specific questions about ticket sales for Thrill U., call Matt Stoltzfus at (610) 391- 7607 or e-mail him at [email protected] Visit our websites: Dorney Park Thrill U. KUTZTOWN UNIVERSITY OF PENNSYLVANIA iii Thrill U. Algebra KUTZTOWN UNIVERSITY OF PENNSYLVANIA Antique Carrousel Information Sheet topics: radius and circumference of a circle average distance average velocity d use of formulas ( C = 2 πr, v = , etc.) t use conversion formulas ( meters to feet, meters per second to miles per hour ) objectives: to use formulas to calculate the average linear velocities of different rows of the carrousel equipment : activity sheets pencil basic calculator stopwatch notes for the teacher: Activities that are marked "optional" are not "harder" than those not so designated. These are optional because of the amount of time that students would need to complete the entire set of activities for this ride. The Antique Carrousel takes about 1 revolution to get to full speed, which is relatively constant. It begins slowing by the end of the fourth revolution. Timing of 3 revolutions should take place between the first and fourth revolutions. KUTZTOWN UNIVERSITY OF PENNSYLVANIA 1 Antique Carrousel Notice that there are two carousels at Dorney Park. The Chance Carousel has 3 rows of "seats" and the Antique Carrousel has 4 rows. Be sure that you are working with the Antique Carrousel. PART 1: The Antique Carrousel is a "circular" ride at Dorney Park. Because of its historical significance, it is a most treasured ride as well.
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