graphing: its a beautiful thing! students at all levels employ graphs, points, domain and range as...
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Graphing: It’s a beautiful thing!
Students at all levels employ graphs, points, domain and range as artistic media.A GEMS/ALEX SubmissionSubmitted by: E. Thompson, PhDSummer 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 knowledgeThis 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 PointsThese are student generated plot-dots.
For advanced students:USE POLAR COORDINATES.
Level: Linear equationsThis 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
Level: Knowledge of multiple graphs, range, domain and points.
The equations on the following chart include circles, ellipses, linear and absolute value graphs.
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
136
2
81
2
yx
15 xy
422
412
412
432
xy
xy
xy
xy
PartEquation Range/Domain
Face y ≤ 4
Hat y ≥ 4 and -6 ≤ x ≤ 6
Hat Band y = 4y = 6
-6 ≤ x ≤ 6-5 ≤ x ≤ 5
Eyes
Pupils Points (-3,2) and (3,2)
Nose y = 1y = x2 -1
-1 ≤ x ≤ 1-1 ≤ y ≤ 0
Mouth All when -4 ≤ y ≤ -2
Whiskers y = 0y = - ¼y = 1/6 xy = ¼ x
All when-5 ≤ x ≤ -1 and1 ≤ x ≤ 5
Halloween Cat Part Equation Range/Domain
Face y ≤ 4
Hat y ≥ 4 and -6 ≤ x ≤ 6
Hat Band y = 4y = 6
-6 ≤ x ≤ 6-5 ≤ x ≤ 5
Eyes
Pupils Points (-3,2) and (3,2)
Nose y = 1y = x2 -1
-1 ≤ x ≤ 1-1 ≤ y ≤ 0
Mouth All when -4 ≤ y ≤ -2
Whiskers y = 0y = - ¼y = 1/6 xy = ¼ x
All when-5 ≤ x ≤ -1 and1 ≤ x ≤ 5
136
2
81
2
yx
15 xy
123
12322
22
yx
yx
422
412
412
432
xy
xy
xy
xy
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.
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