Art and Culture Center
of Hollywood
Integrated Art Lesson Title:
Optical Illusion: Creating a Mathematical
Tessellation
Description and Overall Focus:
This project will allow students to learn how to
create illusory optical effects by combining
multiples of geometric shapes (patterns) resulting
in art that tricks the eye.
45 minutes – 1 hour
Elementary School
VA.68.S.2.1 VA.68.S.2.2 VA.68.S.3.5
Length of Lesson
Grade Range
Sunshine State Standards
and National Art Standards
Objective(s)
Materials: PLEASE NOTE: Some materials
must be acquired prior to this lesson.
Note: Previously cut-out template pieces
by the teacher will facilitate the ease of
student completion of the project within
the time frame of the project.
Introductory activity
Core activity
VA.912.C.1.7 VA.912.O.3.2 VA.912.S.3.1
Students will learn about the art of Maurits
Cornelius Escher (1898-1972), a predecessor to
the Op Art movement, as well as Bridget Riley of
the Op Art movement. Students then will learn
how to use geometric shapes to create a
tessellation – a visual art piece that appears to
feature a three-dimensional construction.
Teacher Supplies:
Tessellation (gray) & parallelogram (black)
templates - one set per student printed on white
card stock
Student Supplies:
8 ½ ” X 11” sheet of gray construction paper
8 ½ ” X 11” sheet of black construction paper
8 ½ ” X 11” sheet of red construction paper
Drawing pencil and eraser
Glue (stick glue recommended)
scissors
Students will begin by learning about the art of
M.C. Escher and its relationship to the Op art
movement. Students will be shown some
examples of his most famous work and work by
Bridget Riley. Students will also learn about
methods in which the artist can trick the eye to
see impossible “constructions” where there are
none. This will be accomplished through the
placement of shapes on the page to create a
tessellation.
Students will begin by tracing parallelograms in
black and gray to begin to develop a
tessellation. The parallelograms will then be
glued in place completing their tessellations in
order to achieve the optical illusion of a 3-D
construction.
Closure activity
Assessment
Teacher follow-up idea
Student follow-up idea
Cooking Lesson
Book/Web references
Art and Culture Center of Hollywood
www.artandculturecenter.org
Lesson plan prepared by Traci Petersen, MFA
Students will complete their creations making
sure that the tessellations are completed in order
by color and secured to the red background.
Several students will then share their completed
pictures with the rest of their classmates.
Students will have learned about the history and
works of art of M.C. Escher and Bridget Riley. They
will also have learned the application of tonal
gradation in geometric shapes to help achieve a
3-D illusion. Geometry will have been learned
and discussed (parallelogram, hexagon, square)
as well as Mathematical terminology (pattern,
tessellation, symmetry, etc.).
The classroom teacher can use the websites
below to present more of the information
surrounding the subsequent Op Art movement
and artists such as Victor Vasarely.
Students can continue to make optical illusions,
based on M.C. Escher’s work using tessellations
or they may even try to draw the Penrose Tribar
(impossible triangle).
Chocolate Berry Tessellations
www.mcescher.com
www.visual-arts-cork.com/famous-artists/bridgetriley
www.wikihow.com
Tessellations
Tessellation is the process of creating a twodimensional plane using the repetition of a
geometric shape with no overlaps and no gaps to
create a pattern. Generalizations to higher
dimensions are also possible. Tessellations
frequently appeared in the art of M. C. Escher,
who was inspired by studying use of symmetry in
tile art. Tessellations are seen throughout art
history, from ancient architecture to modern art,
as in the Op Art movement of the 1960s.
Bridget Riley, Cataract 3, 1967.
Bridget Riley
A honeycomb is an example of a natural tessellated structure.
M.C. Escher
M.C Escher’s work also strongly influenced the
Modern art movement called Op Art, or optical
art. Bridget Riley is an English painter who is one of
the most well-known artists of Op Art. Riley’s work
mostly consists of black and white art created by
using repeated geometric shapes, or tessellations.
She currently lives and works in London, Cornwall,
and France. Much of her art work evolved into
optical art showing the illusion of movement.
It’s fun and simple to create your own
Maurits Cornelis Escher (1898-1972) is one of the
tessellations, or optical illusion-style art. Just
world's most famous graphic artists. His art is
choose a shape and repeat it in a pattern that goes
enjoyed by millions of people all over the world.
from left to right, up and down, turning and
changing the shape’s colors as you go!
He was quite famous for his transformation prints,
such as Metamorphosis I, II & III. He is well known
for using mathematical tessellations in his work, as
in Symmetry #45. He played with architecture,
perspective and impossible spaces. His art
continues to amaze millions of people all over the
world.
TEMPLATES
1. Enlarge templates until the gray-outlined Parallelogram Tessellation is approximately 6 ½ to 7 ½
inches wide. Print the templates on white cardstock. Cut-out the entire gray template as one
piece, and the two parallelograms separately. One set per student.
2. The black-outlined Parallelogram templates (diamonds) are to be traced onto black and gray
construction paper. Students will need 7 black and 7 gray to complete the tessellation.
Preparation
Active Time: 25 min
Total Time: 1 hour, 25 minutes
Recipe Ingredients
•
•
•
1/3 cup + 1 Tbsp extra virgin
coconut oil, warmed
1/2 cup natural unsweetened
cocoa
3 Tbsp fruit juice
concentrate*** thawed
Chocolate Berry Tessellations
Recipe Instructions
1.
In a small container, warm coconut oil and stir in powdered cocoa. Add juice concentrate and
stir well to blend flavors and create a smooth internal texture – the surface tessellation occurs
naturally. “Tessellation” refers to the surface texture of the chocolate and to the repeating
geometric pattern created when the chocolate is sliced into bite-size servings.
Pour warm chocolate mixture into a 9x9” pan lined with wax paper. Cover and refrigerate for
several hours until firm.
3. When the chocolate is firm in the center (not completely hardened), slice into pieces and store
in a covered container in the refrigerator.
2.
*** Juice concentrate should have the consistency of syrup. Use a single concentrate or combine
several to create enticing flavors (try blueberry, cranberry, pomegranate, or black cherry).
ENJOY!