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Graphing: Its a beautiful thing! Students at all levels employ graphs, points, domain and range as artistic media. A GEMS/ALEX Submission Submitted by: E. Thompson, PhD Summer 2008

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The Process Have students create an original piece of art using their graphing knowledge and listing each equation (or coordinate) used in the piece. The list should be kept on a separate sheet so another student can attempt to replicate the artwork.

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Available knowledge This lesson extension can be used at different levels by utilizing the students available knowledge as shown below Pre-Algebra: Points Algebra: Points, linear equations, quadratic equations, range and domain Algebra II w/Trig: Points, linear equations, quadratic equations, circles, ellipses, hyperbolas, exponential growth/decay, sine, cosine, tangent, range and domain

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Level: Plotting Points These are student generated plot-dots. For advanced students: USE POLAR COORDINATES.

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Level: Linear equations This student employed linear equations, points, domain and range to create this work of art. Nose: y=0 when -1 x 1 y= -2x+2 when 0 x 1 y = 2x+2 when -1 x 0 X = 0 when -4 y 0 Mouth: Start:(-3,-4), (-2,-5), (-1,-5), (0, -4), (1,-5),(2,-5), (3,-4) lift pencil

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Level: Knowledge of multiple graphs, range, domain and points. The equations on the following chart include circles, ellipses, linear and absolute value graphs.

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The equations on the chart include circles, ellipses, linear and absolute value graphs. Put together they make the picture on the following slide Graph the following equations w/ respect to parameters Part EquationRange/Domain Facey 4 Haty 4 and -6 x 6 Hat Bandy = 4 y = 6 -6 x 6 -5 x 5 Eyes PupilsPoints (-3,2) and (3,2) Nosey = 1 y = x 2 -1 -1 x 1 -1 y 0 MouthAll when -4 y -2 Whiskersy = 0 y = - ¼ y = 1/6 x y = ¼ x All when -5 x -1 and 1 x 5

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Halloween Cat PartEquationRange/Domain Facey 4 Haty 4 and -6 x 6 Hat Bandy = 4 y = 6 -6 x 6 -5 x 5 Eyes PupilsPoints (-3,2) and (3,2) Nosey = 1 y = x 2 -1 -1 x 1 -1 y 0 MouthAll when -4 y -2 Whiskersy = 0 y = - ¼ y = 1/6 x y = ¼ x All when -5 x -1 and 1 x 5 This Algebra II w/ Trig student used circles and an ellipse, but did not incorporate a trig graph which would have added points to the final grade.

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Grades: Be sure to outline requirements This assignment can be used as: part of a final exam, formal assessment, extra credit, Homework extending traditional textbook assignment. Final art on clean graph paper List of equations/points on separate paper –neatness matters (do you want it typed?) Originality/appropriateness for school Minimum number of equations to be employed Types if equations to be used (linear, quadratic…) Behavior/participation/focus

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