# Optical Illusions in Mathematics and Reading

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```					    Optical Illusions
in
Kenton Middle School
Study Skills
Amanda Ritzler
ritzlera@kentoncityschools.org
Co-Presenters today:

Jenifer Stauffer
- Elementary Educator

Robin Hughes
-KMS Technology Teacher
Goals for this presentation today…
1. Build interest about optical illusions.
2. Show how illusions relate to math and reading.
3. Create an atmosphere where each child can learn
at his or her own pace and ability.
4. Differentiate instruction using 21st technology.
5. Give teachers the standards used to combine
reading and math (Content Skills) in order to
create a well rounded educational experience.
6. Have FUN with your students.
the Student Goals
Have students research on the internet how math
relates to our everyday lives through studying optical
illusions.
Ask the students how perception can change the
way we can see objects?

When we see an illusion, is it math related?

Does the brain use prior knowledge and
information when perceiving pictures?
Technology ideas that can be
used for this project…
   2. PowerPoint
   3. Blogging/Moodle/Social Networking
   4. E-mail
   5. Inspiration
   6. Movie
   7. Animation techniques
January 8, 2007
By:Alysha
Coulson
Does this image appear to be an
impossible Triangle?
Penrose Impossible Triangle

This triangle appears to be
impossible, But it isn’t because a
man made this illusion to make it
appear to look impossible to trick
image was made out of paper.
He connected the sides in 3-D
form to make it an illusion.
•Can you feel the "motion" of the
image?……
•There is an exact number of squares,
but while your trying to count them
your eyes and brain are trying to work
• Your eyesight gets blurry so you
can’t count the exact number of
squares!
Look carefully at any of the white dots in the grid below.

How many black or grey dots can you see elsewhere in the grid.?
Look again!
•You can’t see any black or grey dots.
•You’re seeing things in the illusion
because there is so much black in it and
only a little white.
•This makes your eyes see it blend
together when you are focusing on the
illusion.
•The blending is making you see grey
from where the black and white blend
together.
This one will make you dizzy. Try focusing on
Did it work?

you dizzy from focusing on the
center of the object while the other
part of the object is appearing to go
around the other way as you turn
Are the
cubes
moving
backward
and forward?
 No, nothing in this illusion is moving. But
the cubes are getting smaller, as it appears
the cubes are moving in and out of the
object.
 The cubes were made to look like they are
moving so the ones around the outside of
the page are larger and as they get closer to
the middle they are reducing!
Stare   at the four
black dots in the
center of the image
for 30 - 60
seconds.
Then quickly
and look at
something bright
(like a lamp or a
window with
sunlight coming
through it).
You should see a
white circle with an
image inside it.

ARE THE SPIRALS ROTATING?
These spirals should appear to move!
As you look at the spirals,
they will appear to move. This
is called "illusory movement"
and the same technique has
been explored.
Move your
the screen.
Do the perfect
blue cubes
appear to be
distorted?
Absolutely... this is due to the black
figurations in the back moving
and twisting it in your mind.
But they are really perfectly cubed.

What an eye trick!
Terms…
Image-An optical counterpart or appearance of an
object, as is produced by reflection from a mirror,
refraction by a lens, or the passage of luminous
rays through a small aperture and their reception
on a surface.

Grid-A network of horizontal and perpendicular
lines, uniformly spaced, for locating points on a
map, chart, or aerial photograph by means of a
system of coordinates.

Object-Anything that is visible or tangible and is
relatively stable in form.
Inspiration
From the Inspiration website:
“Inspiration's integrated
diagramming and outlining
environments work together to
help students comprehend
concepts and information.
Educators use Inspiration to
customize instruction, achieve
standards, assess student progress
and energize learning.”
Inspiration
 Visual Thinking and Learning
 Learning to think. Learning to learn. These are the essential skills for student
success in every curriculum area and academic pursuit.

Visual Learning Techniques
 Data Literacy

 Visual thinking and learning utilize graphical ways of working with ideas and
presenting information. Research in both educational theory and cognitive
psychology tells us that visual learning is among the very best methods for teaching
students of all ages how to think and how to learn.
Inspiration Concept Map
OPTICAL
ILLUSIONS
(Visual Phenomena)

-Direct students                                                                             The Body
Fun Pictures
and Puzzles
Mathematical
Concepts
- Everyone has the                                            and
Optical Illusion                                          How do
Vocabulary                                                 eyes
same resources        Artistic
Diagram
of the
Brain
form
images?
Illusions
Animated
proof of                                                          Vision
Try this
Pythagorean        Beginner             Basic
-independent                            Therom         activity below       Patterning

Why do

learning                                                   Spatial
we see
illusions?       Color

Ability
Through
G eometry     Interactive
Imagery

--differentiated work
Tesselation
Activity
Visual learning helps students:
* Make abstract ideas visible and concrete

* Connect prior knowledge and new concepts

* Provide structure for thinking, writing,
discussing, analyzing, planning and reporting

* Focus thoughts and ideas, leading to
understanding and interpretation.
Discuss with the class the basics of optical
illusions in Mathematics and their background
knowledge.

Have students write down some questions that they
of this project.
Share past projects and books on optical illusions
to build interest and give concrete examples on how
they relate to Mathematics.
Research Questions
The students can use these questions as to
guide them in their RESEARCH efforts. They
are open ended and can have many different
I provide a folder with sites, topics and
resources in my shared folder.
If you do not have a shared folder; then an
email can be sent to your students with the
STUDENT CHECKLIST
 1-2 days to explore and bookmark sites

 Complete the research/question packet

 Write a 1-2 page paper

 Draw diagrams of the eye, brain and correlations (use
mathematical terms such a reflection,angles, distance… etc.)

 Explain to the class how your brain and eyes work together
to see an illusion. (Do they really work together? Or… Do they play tricks on each
other?)

 Create a final presentation
(Googles Doc,Power point, movie or Inspiration) to present to the Class. It will be used to learn
Mathematical terms and concepts)
Requirements for
optical illusion project
Choose from the following kinds of
presentations:
PowerPoint Presentation
 Movie
Inspiration Concept Map

List and define 5 to10 Mathematical
FINAL PRESENTATION
Title page with your name and date
At least 5 or more Optical Illusions
At least 5 or more summaries of the above
illusions. (What should we see?)
 Highlighted math terms and definitions
Creative style and personality
Informational ( summaries, descriptions…)
Oral Presentation
Students use the computer, TV and/or the Smart
Board to present their projects to the class.

The students are engaged and interacting with the
student presenter…

The class takes notes and records on their own
new vocabulary they have learned.
Rotate-To cause to turn around an axis or
center point; revolve.

Figure-Form or shape, as determined by
outlines or exterior surfaces: to be round,
square, or cubical in figure.

Figuration-The resulting figure or shape.
Cube-A solid bounded by six equal squares, the
angle between any two adjacent faces being a
right angle.

Spirals-A three-dimensional curve that turns
around an axis at a constant or continuously
varying distance while moving parallel to the axis.

Reducing-To bring down to a smaller extent, size,
amount, number, etc.

3-Dimensional-Involving or relating to three
dimensions or aspects; giving the illusion of depth;
"lifelike three-dimensional characters."
QuickTime™ and a
decompressor
are neede d to see this picture.
ttfn…rofl…ttyl…r u jk ?…g2g…brb…

ta ta for now…rolling on the floor
laughing…talk to you later… got to go…be
right back…Are you just kidding?
QuickTime™ and a
decompressor
are neede d to see this picture.
VOCABULARY WALL
Just to name a few….
Ambiguous         rotate     perceive
Movement          pattern    transform
Symmetry          arch       intercept
Distorted         net        parallel
Bisector          angles     transparent
Flip              tile       ascend
Tessellations
Preparation for you
before we go over all the
Curriculum Standards.

Here are a few cute cartoons before I talk
to you about the ins and outs of the
standards, benchmarks and curriculum
guides from the state of Ohio.
Does this describe your life as an educator?

And of course… curriculum standards
to read and apply to our lessons.
Do you ever feel like this?
Have you ever felt this pressed for time?
Did you know your brains can
read a passage even when the
letters are in a different order?

HOW DOES YOUR BRAIN DO IT?
Try to read the handout quietly to yourself
Curriculum Benchmarks,
Indicators, and Standards
Acquisition of Vocabulary
A Context   Clues and Text structures to determine the meaning of
new vocabulary.

B   Infer word meanings by examining relationships of analogical
statements.

E    Apply knowledge of roots and affixes to determine meaning of
complex subject area words.
Curriculum Benchmarks,
Indicators, and Standards
Persuasive Text C         Analyze whether graphics
supplement textual information
and promote author’s purpose.

Persuasive Text E          Utilize multiple resources to
critique the various ways authors
develop their ideas.
Curriculum Benchmarks,
Indicators, and Standards
Writing Process
A Formulate writing ideas and identify a topic appropriate to the purpose and the audience.
B Organize and apply appropriate pre-writing tasks.
C Use revision strategies to improve the style, variety of sentence structure,clarity of controlling idea,
logic, effectiveness of word choice and transitions between paragraphs, passages and ideas.

D Edit to improve sentence fluency, grammar and usage.
E Apply tools to judge the quality of writing.
F Prepare writing for publication that is legible, follows an appropriate format and uses techniques such
as electronic resources and graphics.
Curriculum Benchmarks,
Indicators, and Standards
Research
A Formulate open-ended research questions suitable for investigation and adjust questions as necessary
while research is conducted.

B Evaluate the usefulness and credibility of data and sources.
C Organize information from various resources and select appropriate sources to support central ideas,
concepts and themes.

D Use style guides to produce oral and written reports that give proper credit for sources.
E Communicate findings, reporting on the substance and process orally, visually in writing or
multimedia.
Curriculum Benchmarks,
Indicators, and Standards
Communication, Oral and Visual
A Use a variety of strategies to enhance listening comprehension.
C Evaluate the content and purpose of the presentation by analyzing language and delivery

D Demonstrate an understanding of effective speaking by selecting appropriate language

E Give informational presentations that present ideas in a logical sequence,include relevant
facts and details from multiple sources and use a consistent organizational structure.

F & G Controlling ideas or thesis; give presentations using a variety of delivery
methods, visual displays, and technology.
Math Standards
 Geometry and Spatial Sense 1, 2, 5,& 6

 Patterns, Functions and Algebra 2, 7, 14 &
more

 And other Science and Technology
standards
With all of these standards.. We
can proudly say….
Why does this happen?
Comprehension is important!
These are people of courage...
General Rubric for Project
   4 The student fully achieves all mathematical and project goals. The
presentation demonstrates clear thinking and explanation. All work is
complete and correct.

   3 The student substantially achieves the mathematical and project goals. The
main thrust of the project and the mathematics behind it is understood., but
there may be some minor misunderstanding of content, errors in computation,
or weakness in presentation.

   2 The student partially achieves the mathematical and project goals. A
limited grasp of the main mathematical ideas or project requirements is
demonstrated. Some of the work may be incomplete, misdirected, or unclear.

   1 The student makes little progress toward accomplishing the goals of the
project because of lack of understanding or lack of effort.
By:
1/6/09   Collin Roll
Circles in optical illusions can
make an object look like it is
rotating..
 Lines can appear to make an
illusion look as if it is
disproportioned with the mix
of colors.
 This illusion is creating the
effect of letters and numbers.

 Which can you see?
 This illusion creates an
illusion of 3D or 3-
dimentional.
 It means that there is the
view of something realistic.
 People can be hypnotized by an
illusion.
 One that is created with circles
can look as if they are rotating
when they are really not moving
at all.
The End
Optical Illusions

By: Graham Reese
01/05/09
Optical Illusions
 Optical illusions are pictures that are visually
perceived to be something that they aren’t.
Optical Illusions
 Circles are a very important part of an optical illusion. They
can create the illusion that a picture is spinning or tilting
irregularly.

Above: Which of
the center dots
are bigger?

Right: The circle
This illusion makes the circles    appears to be
look like they are spiraling.      facing 2 directions.
Optical Illusions
 Line segments are also important. They might seem
to bend, but are straight.

The illusions above all make the line segments look
like they are not straight.
Optical Illusions
 Another important object of optical illusions is the
color of an object.

Above: The color of the boat’s sail is the
same color as the sky, giving the boat the
ability to transform from the sky.

Left: The color of the people’s robes is the
same as the water,giving them the illusion
of being water.
The End
 http://www.michaelbach.de/ot/
 http://www.moillusions.com/
Geometry Illusions

http://www.palmyria.co.uk/illusio
ns/illusions.htm
 http://www.coolopticalillusions.com/
 http://www.archimedes-
lab.org/Gallery/new_optical_illusions/index.htm
l
 http://www.wyrmcorp.com/galleries
/illusions/index.shtml
 http://www.colorcube.com/illusions/
illusion.htm

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