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Geometry and Algebra: the Future Flight Equation Educational Product Educators Grades 6-8 EG-2001-09-30-LARC Geometry and Algebra: The Future Flight Equation A Lesson Guide with Activities in Mathematics, Science, and Technology Test airplanes PGC Geometry and Algebra: The Future Flight Equation is available in electronic format through NASA Spacelink - one of NASA’s electronic resources specifically developed for the educational community.This publication and other educational products may be accessed at the following address: http://spacelink.nasa.gov/products A PDF version of the lesson guide for NASA CONNECT can be found at the NASA CONNECT web site: http://connect.larc.nasa.gov Geometry and Algebra: The Future Flight Equation A Lesson Guide with Activities in Mathematics, Science, and Technology Program Overview Student Worksheets Summary and Objectives . 5 Data Chart . 13 Student Involvement . 5 Wing Chart . 14 Cue Card Questions . 5 Experimental Data and Wing Charts . 15 Hands-On Activity . 5 Delta WIng Template . 16 Instructional Technology Activity . 5 Oblique Wing/Stabilizer Template . 17 Resources . 5 Straight Wing/Stabilizer Template. 18 Swept-Back Wing Template . 19 Hands-On Activity Graph Paper . 20 Background . 6 Fuselage Template. 21 National Standards . 6 Cue Cards. 22 Instructional Objectives . 7 Vocabulary . 8 Teacher Materials Preparing for the Activity. 8 Cue Card Answers . 23 Student Materials . 8 Teacher Materials. 8 Instructional Technology Activity Time . 8 Description . 24 Focus Questions . 8 National Standards . 24 Advance Preparation . 8 Instructional Objectives. 25 The Activity . 9 Resources Extensions . 12 Books, Pamphlets, and Periodicals. 26 Web Sites . 26 Acknowledgments: Special thanks to Summer 2001 Educators in Residence, Jennifer Pulley, Chris Giersch, Bill Williams, and NCTM. NASA CONNECT is a production of the NASA Langley Research Center, Hampton, VA. All Rights Reserved. Broadcast and off-air rights are unlimited and are granted in perpetuity with the following stipulations: NASA CONNECT shall not be used for commercial purposes; used, in whole or in part, to endorse a commercial product; stored, in whole or in part, in a commercial database; altered electronically, mechanically, or photographically without the expressed and prior written permission of NASA.This publication is in the public domain and is not protected by copyright. Permission is not required for duplication. 2001-2002 NASA CONNECT Series 5 Program Overview SUMMARY AND OBJECTIVES In Geometry and Algebra: The Future Flight Equation, Flight Equation.They will observe NASA engineers students will learn how NASA engineers develop using geometry and algebra when they measure experimental aircraft. They will learn about the and design models to be tested in wind tunnels. By Hyper-X Research Vehicle, an experimental plane conducting hands-on and web activities, students that uses scramjet engine technology to propel will make connections between NASA research and itself to ten times the speed of sound. Students will the mathematics, science, and technology they learn understand how the Hyper-X is part of the Future in their classrooms. STUDENT INVOLVEMENT Cue Card Questions standards. Students are designated as Aeronautical Norbert, NASA CONNECT’s animated cohost, poses Engineers in Training (AET).They will analyze wing questions throughout the broadcast.These geometry based on measurements and questions direct the instruction and observations. Students will use geometry and encourage students to think about the algebra to design, construct, and test an concepts being presented. When viewing a experimental wing. videotaped version of NASA CONNECT, educators have the option to use Norbert’s Instructional Technology Activity Pause, which gives students an opportunity PlaneMath, the instructional technology activity, is to reflect and record their answers on the Cue aligned with the National Council of Teachers of Cards (p. 22). Norbert appears with a remote to Mathematics (NCTM) standards, the National indicate an appropriate time to pause the videotape Science Education (NSE) standards, the International and discuss the answers to the questions. Technology Education Association (ITEA) standards, and the National Educational Technology (NET) Hands-On Activity standards.This online interactive activity lets The hands-on activity is teacher-created and is students learn, design, and test experimental aligned with the National Council of Teachers of aircraft.The students will learn about the forces of Mathematics (NCTM) standards, the National flight, wing shape, propulsion, experimental design, Science Education (NSE) standards, the International and several other topics.To access PlaneMath, go to Technology Education Association (ITEA) standards, Dan’s Domain on NASA CONNECT’s web site at and the National Educational Technology (NET) http://connect.larc.nasa.gov/dansdomain.html. RESOURCES Teacher and student resources (p. 26) support, http://connect.larc.nasa.gov, offers online enhance, and extend the NASA CONNECT program. resources for teachers, students, and parents. Books, periodicals, pamphlets, and web sites provide Teachers who would like to get the most from the teachers and students with background information NASA CONNECT web site can visit the Lab Manager, and extensions. In addition to the resources listed in located in Dan’s Domain, this lesson guide, the NASA CONNECT web site, http://connect.larc.nasa.gov/dansdomain.html. EG-2001-09-30-LARC Geometry and Algebra: The Future Flight Equation 6 2001-2002 NASA CONNECT Series Hands-On Activity BACKGROUND Aeronautical research usually begins with wings. They fly with jet engines, rocket engines, computers, wind tunnels, and flight simulators, but piston engines, solar-electric engines, and even eventually the theories must fly. That is when flight without engines. Some research planes are too research begins, and aircraft are the primary tools of small for a pilot; some are as large as an airliner. the trade. There are four stages in the development of new aircraft: mission (purpose), design The first experimental planes designed exclusively (aerodynamics, propulsion, stability, control), for research were the XS-1 and the D-558-1. They computer modeling, and testing. were made in 1946 to enable scientists to study flight near the speed of sound. Custom-made Flight research involves doing precision maneuvers planes were the only way to accomplish this in either specially built experimental aircraft or in an objective because supersonic wind tunnels were not existing production aircraft that has been modified. accurate enough, and no other planes had flown All research aircraft are able to perform scientific that fast. The supersonic era began when the XS-1 experiments because of the onboard instruments broke the “sound barrier” in 1947. that record data about its systems, aerodynamics, and the outside environment. In the 1950s the famous “X-Planes” continued to take people to higher altitudes and greater speeds. NASA pilots work closely with engineers to conduct They were the first aircraft to fly at Mach 2 and Mach carefully constructed flight programs that gradually 3, and the studies performed with them influenced probe an aircraft’s capability; edging toward the the designs of all supersonic planes. speed, altitude, and structural limits that will define the final performance of an aircraft. This procedure In the 1960s, the X-15 rocket plane became the first furnishes answers that will verify, extend, and aircraft to fly into space. The projects done on this perhaps correct the inputs from computer studies, aircraft benefited not only NASA’s Apollo Lunar wind tunnel tests, and simulations. It is the last step Landing Program, but also the Space Shuttle, nearly in the developmental process and leads the way for 15 years later. designs that can be put into production. It also Since the 1970s, NASA flight research has become delivers the final word on a most crucial question: more comprehensive with flights involving everything How well does it fly? from Space Shuttles to ultralight aircraft. NASA now Experimental research aircraft are tools of flies not only the fastest airplanes, but some of the exploration, incorporating the newest ideas in every slowest as well. Flying machines continue to evolve aspect of aerospace flight. For this reason they come with new wing designs, propulsion systems, and in many shapes and sizes. They have short wings, flight controls. As always, a look at today’s delta wings, swept wings, moveable wings, and no experimental research aircraft is a preview of the future. NATIONAL STANDARDS Mathematics (NCTM) Standards • Develop and evaluate inferences that are based on • Compute fluently and make reasonable estimates data • Understand measurable attributes of objects and • Build new mathematical knowledge through the units, systems, and processes of measurement problem solving • Apply appropriate techniques, tools, and formulas • Apply and adapt a variety of appropriate strategies to determine measurements to solve problems Geometry and Algebra: The Future Flight Equation EG-2001-09-30-LARC 2001-2002 NASA CONNECT Series 7 • Recognize, use, and learn about mathematics in • Physical Science contexts outside of mathematics • Motions and forces • Analyze characteristics and properties of two- and • Science and Technology three-dimensional geometric shapes and develop Abilities of technological design mathematical arguments about geometric Understanding about science and technology relationships
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