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Capturing Conic Sections with Digital Cameras


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Keywords: Digital cameras, math, conics, Algebra 2, graphs, equations
Subject(s): Art, Technology, Animation, Calculus, Algebra, Photography, Geometry, Math, Physics, Trigonometry
Grades 9 through 12
School: Loyola High Sch of Los Angeles, Los Angeles, CA
Planned By: Emily Villa de Rey
Original Author: Emily Villa de Rey, Los Angeles
My goal is for students to be active participants in and take ownership of their learning. Students will appreciate the connections between mathematics and the world around them.

California State Standard for Algebra 2:
16.0 Students demonstrate and explain how the geometry of the graph of a conic section (e.g., asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation representing it.

First, students will be introduced to the four kinds of conic sections. Students will learn the formal coordinate geometry definition of the four conic sections, parabolas, circles, ellipses, and hyperbolas. Students will be introduced to the important parts of the graph of each conic section.

Students will then check out digital cameras and be tasked with finding examples of each conic section in their community. For example, satellite dishes are examples of parabolas. Students will be instructed in the use of the digital camera’s photo-editing software so that they can lay a coordinate grid over their pictures and write the equations for the conic sections they found out in the real world

Students will also be instructed in the use of movie editing and animation software that they will use to create a digital narrative. In their digital narrative, students will explain how they found the examples of conic sections in their communities, what they learned when they wrote the equations for those examples, and how mathematics is used in other fields. At the end of the project, students will present their digital narratives during an after school “film festival.” Parents, students, teachers, and community members will be invited to attend the film festival.
Comments
I currently have students complete a similar activity in which they draw pictures using conic sections and write the equations for the shapes they draw. The photographs extend the activity so that conic sections are connected to the real world.
Cross-Curriculum Ideas
This activity can be extended to Geometry by having students can take photographs of examples of different polygons. For an English class, students can take photographs of grammar errors found on local signs. For a foreign language class, students can take photographs of examples of influences of foreign cultures on their community. When students take digital cameras into their communities, learning is moved from the classroom into their daily lives.
Follow-Up
At the end of the project, students will present their digital narratives during an after school “film festival.” Parents, students, teachers, and community members will be invited to attend the film festival. Students' photos will be displayed in the main office and classroom.
Links: “Occurrence of the Conics”
“Cool Math: Circles”
“Cool Math: Ellipses”
“Cool Math: Parabolas”
“Cool Math: Hyperbolas”
Materials: Point and Shoot, Digital SLR, Graphing, Printers, Camera Bags, Flash/USB Drives, Tripods, Batteries, Memory Cards, CDs and DVDs, Cables, Power, Keyboards, LCD Monitors, Mice, High, Word Processor, Art Tools, Slideshow, Animation, Video Tools, Student Resources, Assessment, Prof. Dev. Workshops, Integrating Technology
Other Items: 1 Standard Digital Camera Lab, $2889 each, total of $2889.00