Graphing: Its a beautiful thing! Students at all levels employ graphs, points, domain and range as...

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