# Real World Equations!

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 Keywords: real world, photography, MATH, modeling, equations, algebra Subject(s): Grades 9 through 12 School: Lyme Central School, Chaumont, NY Planned By: Lisa Blank Original Author: Lisa Blank, Chaumont
Students will use digital cameras to gather photos which will enable them to model the shape of an item, pathway, or situation using algebraic equations.

To accomplish this, parameters must first be set. In a basic algebra class, students could gather photos that involve linear equations. Examples of such situations might include equations to model pathways of linear motion in the photograph, such as that of cars moving down a straight road or they could consider a linear equation to represent the line in a photograph that shows where a wall meets the floor in a room. More advanced algebra students, such as those in Algebra II, could find situations that involve quadratic equations. Examples of such situations might include equations to model the arc formed by water at a drinking fountain, or the path of a basketball to reach the basket from a shooter's hands.

Once students have gathered appropriate photos, these photos can be uploaded into graphics programs such as Geometer's Sketchpad, Cabri II Plus, or Texas Instuments' Navigator software, where students can explore entering equations and modifying them to create equations that model the situation displayed in their photographs. The software programs named will allow students to overlay equations on top of the photographs they have gathered.

Students may then incorporate their work into a presentation, such as a Power Point presentation to be shared with their peers, or they could create a document for placement in a student portfolio.
 Follow-Up As a result of this activity, students should develop an understanding of how to modify equations to fit a model. To follow this up, students need to engage in equations on the cause and effect of modifying equations to solidify the key ideas involved in this work. The teacher must also check for understanding through additional project work, quizzing, or testing to evaluate student understanding. Materials: Slideshow, Math, Batteries, Camera Bags, Point and Shoot