Graphing Its a beautiful thing Students at all

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

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.

Available knowledge This lesson extension can be used at different levels by utilizing the student’s 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

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

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= -2 x+2 when 0 ≤ x ≤ 1 y = 2 x+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

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

Graph the following equations w/ respect to parameters Equation Range/Domain Part The equations on the chart include circles, ellipses, linear and absolute value graphs. Put together they make the picture on the following slide Face y≤ 4 Hat y ≥ 4 and -6 ≤ x ≤ 6 Hat Band y=4 y=6 -6 ≤ x ≤ 6 -5 ≤ x ≤ 5 Eyes Pupils Points (-3, 2) and (3, 2) Nose y=1 y = x 2 -1 Mouth Whiskers -1 ≤ x ≤ 1 -1 ≤ y ≤ 0 All when -4 ≤ y ≤ -2 y=0 y=-¼ y = 1/6 x y=¼x All when -5 ≤ x ≤ -1 and 1≤x≤ 5

Halloween Cat Part Equation Range/Domain Face y≤ 4 Hat y ≥ 4 and -6 ≤ x ≤ 6 Hat Band y=4 y=6 -6 ≤ x ≤ 6 -5 ≤ x ≤ 5 Eyes Pupils Points (-3, 2) and (3, 2) Nose y=1 y = x 2 -1 Mouth 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. Whiskers -1 ≤ x ≤ 1 -1 ≤ y ≤ 0 All when -4 ≤ y ≤ -2 y=0 y=-¼ y = 1/6 x y=¼x All when -5 ≤ x ≤ -1 and 1≤x≤ 5

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