Advanced Algebra II Conic Section Webquest Project

The Task Your task is to model and explain each conic section as the intersection of a plane and cone. You will gather examples of each of the four conic sections and explain how the reflective properties are used in today's society to improve our lives. You will solve problems involving the conic sections and make a PowerPoint presentation that you could take back in time and show to Menaechmus, Euclid and Appollonius on your battery-powered laptop.

The Process 1. You will be assigned to a team of 4 students. Each team consists of four members: artist, astronomer, engineer, and historian. You will decide which position you will fill. The Artist will visually model and explain each conic section as the intersection of a plane and cone. This can be done with diagrams on a poster or by actually slicing a cone.Artist The Astronomer will solve problems involving ellipses and hyperbolas. The astronomer will share elliptical and hyperbolic graphics to the historian.Astronomer The Engineer will solve problems involving circles and parabolas. The engineer will share circle and parabolic graphics with the historian.Engineer The Historian will take pictures of conic sections with a digital camera, insert pictures into the SketchPad program and derive equations. The historian will make a PowerPoint picture album of the digital pictures and the graphics from the astronomer and engineer.Historian

ARTIST Make a poster or a three-dimensional model showing how a cone is slice to form each of the conic sections. Each section should be defined and labeled. Visual should be colorful and neat. Use the resources listed below. Videos: “Quadratics,” Unit 25, CORD Communications Applied Mathematics, February “Applications of Conic Sections,” Films for the Humanities & Science, 1992 Websites: Occurrence of the Conics The Conics Conics on Geometer's SketchPad Dave's Math Tables Conics in 3 Dimensions Interactive Conics Conic Sections Apollonius and the Conics

ASTRONOMER_____________ Choose and solve 2 elliptical problems and 2 hyperbolic problems from the applications below. Show all work. Use graph and/or diagrams to illustrate solutions. Locate real-life graphics showing applications of ellipses and hyperbolas. Share these with the historian for the Photo Album. Use the resources listed below. Applications Websites: Discovery School Math Helps White House Ellipse Ellipse Elliptical Orbits Kepler Motion Tycho Brahe Planetarium Habitat for the 21st Century Hyperbola The Hubble Project NASA Hubble Images Interactive Conics Properties of Projectile Motion Elliptical Pool Table Rose Bowl St. Louis Science Center The Comet's Tale Superdome Sonic Boom Channel One Sonic Boom Double Bubble Hyberboloid Videos “Quadratics,” Unit 25, CORD Communications Applied Mathematics, February “Applications of Conic Sections,” Films for the Humanities & Science, 1992

ENGINEER____________ Choose and solve 2 circular problems and 2 parabolic problems from the applications below. Show all work. Use graph and/or diagrams to illustrate solution. Locate real-life graphics showing applications of circles and parabolas. Share these with the historian for the Photo Album. Use the resources listed below. Applications Websites: Discovery School Math Helps Circles Circle Negative Pedal Curve Flying Circles VW Beetle: Round for a Reason Flower of Life Seed of Life Habitat for the 21st Century Interactive Conics Louisiana Superdome Parabola Parabolic Reflectors Sea World Physics Tycho Brahe Planetarium Paraboloid Videos “Quadratics,” Unit 25, CORD Communications Applied Mathematics, February “Applications of Conic Sections,” Films for the Humanities & Science, 1992

HISTORIAN_____________ Use the digital camera to take pictures around the school that represent each conic section. If you have a camera at home, you can take pictures in the community and bring your disk to school. Insert a picture of each conic section into the SketchPad program and derive equations. Make a PowerPoint picture album of the digital pictures (with equations), the graphics of each conic section from the astronomer and engineer, and a picture of the artist visual. Some resources to help you get ideas of where to find conic sections around the school are listed below.PowerPoint picture album Websites: Occurrence of the Conics Hyperbola Interactive Conics Parabola Parabolic Reflectors Videos: “Quadratics,” Unit 25, CORD Communications Applied Mathematics, February “Applications of Conic Sections,” Films for the Humanities & Science, 1992

3. On the assigned due date (March 30 and April 1 block days), your team will share with the class your PowerPoint or poster Photo Album. Each of you will explain your contribution to the Photo Album. The Artist will explain how the cone is sliced to form each conic section. The Astronomer will explain the elliptical and hyperbolic graphics. The Engineer will explain the circular and parabolic graphics. The Historian will explain the pictures taken around the school. You will turn in your word problems that day.

Beginning 1 Developing 2 Accomplished 3 Exemplary 4 Score Conic Visual Show conic sections as intersections of a plane and cone Cone is sliced incorrectly or incompletely. Attempts to identify intersections. Cone is sliced attempting to show all 4 conic sections. Identifies but does not explain each intersection. Cone is sliced correctly showing all 4 conic sections. Identifies and explains each intersection. Cone is sliced correctly showing all 4 conic sections. Identifies and explains each intersection. Model is eye-catching. Word Problems Solve conic section models Correctly solved 2 models (attempts at least one of each conic section). Correctly solved 4 models (attempts at least one of each conic section). Correctly solved 6 models (at least one of each conic section). All work shown. Correctly solved 8 models (2 of each conic section). All work shown. PowerPoint Presentation Application of Conic Sections Graphics showing application of conic sections incomplete. Graphics showing application of all 4 conic sections. Explanation insufficient. Graphics showing application of all 4 conic sections. Explanation demonstrates partial understanding. Graphics showing application of all 4 conic sections. Explanation of each demonstrates understanding. Student pictures Student pictures inserted in SketchPad. No derived equations. Student pictures inserted in SketchPad. Derived equation partially correct. Student pictures inserted in SketchPad. Derived equation correct. Student pictures inserted in SketchPad. Explanation of correct, derived equation demonstrates understanding. TOTAL