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STEAMLesson Breifk12HartmanVTiSTEMedHow to Build Fractals Into Optical Illusions STEAM Education© Lesson Brief

Educators’ Names (with Titles): Mrs. Claudia Hartman

Trained (When/Where): Chariho Middle School 2016-2017

Claudia,

Thank you for your hard work. It is obvious you really enjoy fractals! They are fascinating. I would like to make a suggestion on your lesson plan. You provide a good deal of information about fractals that would help a teacher start to understand them and share them with students. For our certification, we need to see how each subject and their standards are connecting to the overall theme of fractals. Perhaps it would be easier as the reader to understand if you were to pull the supporting fractal information out and put it at the end of the lesson plan as additional or supporting material. This would then clear up the different sections to see what part of the project or smaller projects are happening in each different subject area that relates to the fractals. For each subject area, you need to have all parts of the lesson plan filled in. Each subject should have their specific standards, a project element (individual project for the subject or a part of an overall project) and an assessment component that shows if the student has conceptual understanding of the standards in that subject.

The section of the plan that I turned blue- this section could be broken apart into the different sections. Unfortunately I am not able to see without permission what you have in your fractal google doc. If you have questions, please include them in you revision in the section where you might have a question. I look forward to your revision and learning more about fractals. I know that the students will really enjoy them. Thanks ~KS

Lesson OverviewSkill Level

(Grade Range)

Middle School Grades 5-8

Central Theme

Understanding Fractals

Topic Concept of

Theme

Building Fractals that are 3-Dimensional Optical Illusions

Summary of Essential

ConceptsThe students will research (SS) Fractals Globally. They will study (S) how they are made and constructed. They will execute a design plan and build (E) a three dimensional prototype that is both optical illusion and fractal combined. The student will design and create (FA) two Fractals that are the same in design but in different colors that create and optical illusion of movement. They will measure and cut each Fractal by one inch increments and attach them both to the three dimensional piece that is built like an accordion. This piece will be

folded into one inch increments as well. Organize the folds by an A-B sequence, and glue each section of the two differently colored fractals in opposing order of A-B as well. (E) They will research by using (T) a computer to research what Fractals and Optical Illusions are and how they are connected to STEAM. They will observe an actual computer generated Mandelbrot Zoom by watching a video in Google Classroom. The students will learn (M) the numbering sequence within these designs. They will engage in groups to discuss and share(LA) (FA) information on various Fractal and Optical Illusion designs. They will discuss, in groups how the Sierpenski Triangle, Fibonacci Spiral, and Koch Curve works as a Fractal. They will be able to choose one as their final design. They will work on body motions (E) and building Fractal with their bodies. The students will listen to and then create (Mu) a unique body of music with progression in vocals and or instruments according to how fractals are used in musical compositions.

RBL(reality-based

learning)

Lesson Plan

OverviewIntegrated Basic Plan

Fractals cover most subjects today in STEAM Fractals has become a new tool for modeling in biology, geology, and other natural sciences. The students will learn, discuss and generate ideas of the many ways we can create a variety of Fractals in art. They will learn that a Sierpinski Triangle, Koch Curve, Fibonacci Spiral is a Self Similarity. They will also research the famous scientist, Mandelbrot, and the use of technology and the Mandelbrot Zoom and how it was created by Scientists discovering and measuring the coastlines. They will also discover Self Similarity and also by researching Sierpinski’ Triangle with STEAM especially integrating math science, technology and art. Mostly the math that we study in school is based geometry, in that you study about circles, squares, and triangles was organized around 300 B.C. by a man named Euclid in ancient Egypt and Greece. Fractal geometry, however, is much more modern. Research on fractals is being carried out right now by mathematicians, artists, scientists, engineers, social and cultural analysts and the technology world. Currently, research in mathematic and scientific fractals are being studied and used all over the world. Fractals often look like objects in nature. Many objects in nature aren't necessarily formed of squares or triangles, but of more complicated geometric and organic figures. Many natural objects - ferns, coastlines, etc. - are shaped like fractals. This picture is actually an example of a fractal coastline.

You could measure it with mile-long rulers and get a certain measurement. You could really get into the teeniest and tiniest of crannies, measuring with the smallest of rulers. This is only one example of a fractal. Self -similarity is a type of fractal that is a Sierpinski Triangle, Fibonacci spiral or a Koch Curve studied by scientists and Mathematicians.One can observe that the African culture uses Fractals it its’ architecture and design

patterns in clothing, textiles and industry.Ron Eglash investigates fractals in African architecture, traditional hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, practical craft, quantitative techniques, and symbolic systems.

Assessment

Evidence Based

The students will collaborate their research Fractals and Optical Illusions. They will watch several videos on the Mandelbrot, Sierpinski, Fibonacci (T) (M) and use journaling as note taking and log entries on specifics areas that spark interest in their design plans. They will report back in groups on what they discovered and learned from analyzing the Mathematician's work and how it’s affected modern society. (S) The students will research and problem solve on what optical illusions are and how artist such as Victor Vasarely created them. They will engage in discussions on how color theory, complementary colors to be exact, effect the optical illusion. They will pose questions on these topics to one another and report back. The students will then create two designs of Fractals based on those areas. (FA) They will then create a model of the Fractal turning into an Optical Illusion that is three dimensional. (E) They will evaluate their level of creativity and strength of idea based on a rubric. By the end of the lesson the students will have created a body of work that is highly organized as a completed portfolio of work.

Student Team

Selection(if applicable)

The students being assigned to small teams that will engage in discussions in the type of Fractals and the types of Optical Illusions, by gathering information through watching videos and by reading the research on the Mathematicians and artist alike. The project can be done as a 2 person group or individually, depending on the level of learning and engagement of the class.

Time Frame of

Lesson All Subjects: Science, Technology, Engineering, Art, Music,, Math . Weeks:4-5 Days:2 per week

Times per Day:1 class 50 mins. Research and Note taking Group Discussion : Days: 1 class Videos: 1 class Composition or Design : 8 classes or 4 weeks

Basic Supplies

Basic list of supplies required to complete the project.You may want to break this down by subject.Oak tag paper80wt. drawing paperGlueScissorsColored PencilsPaintColor WheelComputer

IT and Additional Resources

Links:www. cynthialanius.comFractalsGoogle Docs

Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3]YouTube video 5 minutes How To Draw Fractals - Golden Ratio Star Pattern - Sacred Geometry TutorialYouTube video 10 minutes Fractals - Hunting The Hidden Dimension [Full - Hd 720p]YouTube video 53 minutes Mandelbrot Zoom 10^227 [1080x1920]YouTube video 16 minutes

Career Clusters

Professional / Community Connections

Careers as Web designers and Digital Illustrators will be using patterns and designs that resemble Mandelbrot, Seirpinski and Fibonacci designs. Publishing, Visual Editors,Entertainment and Communication, Digital Illustrator, Animation and Design: 3-D Illustrator are all motivated by data driven information on what product works best a t that given time.. Earth Scientists that research natural disasters also use Fractals to (Mandelbrot Zoom) to discover the branching system of a river. Small tributaries join to form larger and larger

How are students engaged in the lesson plan going to have experiences that relate what they are learning to a current and/or future opportunity for work? Students can research 3D Fractals that are animated on You Tube. They can visit a Marine Biology department at the local college and tour the coastline by boat or land. They can create a Skype video of their tour and report back to the class of interesting facts and data supporting the Mandelbrot Zoom. They can also visit any science lab and learn about DNA, RNA, cells, venous systems. They can visit nature labs and speak with Botanists about

"branches" in the system, but each small piece of the system closely resembles the branching pattern as a whole. Marine, Ecology Scientists and Engineers that work in those fields are driven by data to research current problems such as weather and natural disasters.People or organizations that could be used as resources.How is their work a current and/or future opportunity for students engaged in the lesson plan?

plant growth. Students can visit a local nursery, agricultural center or department.Consider people or organizations within careers associated with the subject lessons and how students may connect with them as a resource for their project (e.g., site visit, Skype, video, etc.).Name - Title - Connection to Project - Website/Contact Info

Audience

Who will see the final products or presentations of this lesson? Student Educator Other students in class Other students in grade level Students throughout school

Other educators Parents/guardians Community members Local professionals

Miscellaneous

(Extensions and

Variations)

General or specific to a subject area. Enrichment for Learners-Videos, Handouts Modifications for Challenged Learners-Just Fractals-Sierpinski Triangle Variations to appeal to learning strengths/Preferences-Building Fractals to #-D Optical

Illusions, Color Theory Extensions for deeper learning-Value Development along with Complementary Color

Theory

Rufus Butler Seder tells the story of his optically-animated LIFETILES murals and his best-selling Scanimation(r) books in the context of the history of motion pictures. This engrossing, video-packed, half-hour discussion includes clips of works by other artists and inventors who work in related optical motion mediums.

Photos

Subject Templates & InstructionsEssential

Concept(s)

Sierpinski Triangles, Koch Curves, Fibonacci Sequence, Mandelbrot, Optical Illusions

Goal/Objectives When all of the benchmarks for the lesson are considered, The overall goal and objectives is to create a Fractal that has pattern quality that grows and repeats. it can be duplicated twice to become a three dimensional Lineal Optical Illusion that appears as it were moving, for students by mastering those standards. What capabilities and understandings will they have that go beyond the individual content and structure of each standard?The student will realize that the purpose of creating a three dimensional Optical Illusion from Fractals will help them understand how to build and measure using math, engineering, science, history, language arts and visual art.They are learning to build by using a number sequence during

the fractal set up and to build the optical illusion by measuring each fractal design to fit onto the accordion paper that appears to be moving. In other words they will measure the accordion paper to be the measurement of both fractals. They will measure each of their two fractals simultaneously to fit onto the accordion paper to it appears to be an illusion of movement. By doing this they have also learned and created a design principle such as movement/motion.

Standard(s)

National Art Educators Association (NAEA) Know that students may take different paths to the

understanding and creation of art and are able to plan instruction that allows for these differences

Help students create, experience, and understand art relevant to their experiences and interests;

Provide opportunities for students to work cooperatively as well as individually;

Promote student experiences in art by equipping students with a knowledge base that includes concepts related to presentation and exhibition as well as historical, critical, and aesthetic concepts;

VocabularyFractals, Fibonacci Sequence, Sierpinski Triangle, Mandelbrot Zoom, Optical Illusions

Career(s) Tie-In

The students now have a more deeper understanding of Art and STEM They are learning what Fractals are and how to design them into art. They are also making a historical connection to the mathematician Sierpinski and Fibonacci as well as the scientist Mandelbrot, to their field of study. They learned about artist Victor Vasarely and the art and science of optical Illusions of the 1950’s-60’s. They now understand the career tie in to STEAM. Graphic Design, Engineering, Web Design,

Project Elementand

Educator / Student Feedback

(student application of

Links:www. cynthialanius.comFractalsGoogle Docshttps://youtu.be/mmGB9ADKr5Y Lenticular Design Videos-You TuveDoodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3]YouTube

https://youtu.be/mmGB9ADKr5Y

standard/benchmark/goal)

RBL Component &Product

video 5 minutes How To Draw Fractals - Golden Ratio Star Pattern - Sacred Geometry TutorialYouTube video 10 minutes Fractals - Hunting The Hidden Dimension [Full - Hd 720p]YouTube video 53 minutes Mandelbrot Zoom 10^227 [1080x1920]YouTube video 16 minutes

AssessmentEvidence Based

End Product + Interview

The students will be evaluated using an art rubric designed and used in our districts art departments. It involves Development of the Idea -Fractals which is 20%. The Elements of Art, focused on Color, Form, Pattern and Shape, which is 20%. The Principles of Design focuses on Movement/Repetition and Balance which is 20%. Creativity and Risk taking as a unique representation which is 20%

Development of Idea-20%-Did the student have a clear understanding of what a Fractal is and how it is used as an interesting 3D moving form?Element of Art-20%-Is the use of shape, form, color and pattern used as a fractal that appears to be uniformly growing?Principle of Design-20%-Does the fractal and optical illusion appear to have movement/repetition, contrast of color along with balance of patterns and color?Creativity and Risk Taking-20%-Does the Fractal appear to be uniquely designed by the student? Is there an apparent reference to assessment in the design?Craftsmanship-20%-Is the fractal accurately and precisely designed, measured and cut to accurately fit onto the 3-d moving optical illusion? Is there an even tone of color and contrast of complementary color?

This is our current rubric in our art department. It has been validated and is the only rubric we use at this time. I found a great video on the history of this art. There is a major connection to science, technology and art here. The students will love it!

Miscellaneoushttps://youtu.be/JLfLSjbm4s8 You Tube Video: Rufus Butler Seder tells the story of his optically-animated LIFETILES murals and his best-selling

https://youtu.be/JLfLSjbm4s8

Scanimation(r) books in the context of the history of motion pictures.

1. Science

Essential Concept(s)

Research then make the connection to the art, technology and science of Fractals and Optical Illusions. Study motion with Lenticular Designs relating to technology and science, that leads into 3D animation using Lenticular photoshop and printing which is the most current trend.

Goal/ObjectivesEvaluate information on Fractals and optical illusions and by using geometry and technology. You will study the rate of motion in reference to the linear fractal device that is moving.

Standard(s) National Science Teachers Association (NSTA): NSTA StandardsNext Generation Science Standards: Next Generation Science Standards

1. Interdependence of Science, Engineering, and Technology

K-2 Connections Statements

3-5 Connections Statements



Science and engineering involve the use of tools to observe and measure things.

Science and technology support each other.

Tools and instruments are used to answer scientific questions,

while scientific discoveries lead to the development of new technologies.

Engineering advances have led to important discoveries in virtually every field of science and scientific discoveries have led to the development of entire industries and engineered systems.

Science and technology drive each other forward.

Science and engineering complement each other in the cycle known as research and development (R&D).

Many R&D projects may involve scientists, engineers, and others with wide ranges of expertise.

2. Influence of Engineering, Technology, and Science on Society and the Natural World

K-2 Connections Statements




Every human-made People’s needs and All human activity

draws onModern civilization depends on

April 2013 NGSS Release Page 3 of 6

product is designed by applying some knowledge of the natural world and is built by using natural materials.

Taking natural materials to make things impacts the environment.

wants change over time, as do their demands for new and improved technologies.

Engineers improve existing technologies or develop new ones to increase their benefits, decrease known risks, and meet societal demands.

When new technologies become available, they can bring about changes in the way people live and interact with one another.

natural resources and has both short and long-term consequences, positive as well as negative, for the health of people and the natural environment.

The uses of technologies and any limitations on their use are driven by individual or societal needs, desires, and values; by the findings of scientific research; and by differences in such factors as climate, natural resources, and economic conditions.

Technology use varies over time and from region to region.

major technological systems, such as agriculture, health, water, energy, transportation, manufacturing, construction, and communications.

Engineers continuously modify these systems to increase benefits while decreasing costs and risks.

New technologies can have deep impacts on society and the environment, including some that were not anticipated.

Analysis of costs and benefits is a critical aspect of decisions about technology.

English National Curriculum: Science StandardsPlease include the numbers and written standards that you are addressing as the science component of the fractal unit. I believe these standards address the connection of Science and Technology.

VocabularyFractals, Fibonacci Sequence, Sierpinski Triangle, Transformations, Kinetic Movement, Optical Illusions

Career(s) Tie-In Fractal Design Research, Digital Illustrators, 3-D Illustrators/animators will use new technology to show movement of these fractal designs, computer Systems Designer, System and Database Administrator can use data driven information to create new fractal systems. Together, advances in science, engineering, and technology can have—and indeed have had—profound effects on human society, in such areas as agriculture, transportation, health care, and communication, and on the natural environment. Each system can change significantly when new technologies are introduced, with both desired effects and unexpected outcomes. (NRC, 2012, p. 210)

The fields of science and engineering are mutually supportive, and scientists and engineers often work together in teams, especially in fields

at the borders of science and engineering. Advances in science offer new capabilities, new materials, or new understanding of processes that can be applied through engineering to produce advances in technology. Advances in technology, in turn, provide scientists with new capabilities to probe the natural world at larger or smaller scales; to record, manage, and analyze data; and to model ever more complex systems with greater precision. In addition, engineers’ efforts to develop or improve technologies often raise new questions for scientists’ investigations. (NRC, 2012, p. 203)

The careers need to relate to the specific subject and also show the connection of the career to the activity. I have highlighted the word movement because they are learning the optical illusion of moving designs. Fractals are not static patterns, but then we have taken that to special effects in the illusion of moving designs, camera and video.

Project Elementand


(student application of standard/benchmark/goa

l)RBL Component &

Product

The student come to an awareness that fractals are organized chaos and are the study of chaos. Fractals is more than just a new field in science that unifies mathematics, theoretical physics, art, and computer science - it is a revolution. It is the discovery of a new geometry, one that describes the boundless universe we live in; one that is in constant motion, not as static images in textbooks.

Was the student able to use the research and come up with a unique idea using organic or geometric shapes that become moving Lineal Fractals. Fractals are not just complex shapes and pretty pictures generated by computers. Anything that appears random and irregular can be a fractal. Fractals permeate our lives, appearing in places as tiny as the membrane of a cell and as majestic as the solar system. Fractals are the unique, irregular patterns left behind by the unpredictable movements of the chaotic world at work.

The student will engage and share out in learning about Optical Illusions and how color and design can influence the illusion? Fractals have always been associated with the term chaos. One can describe fractals as "the patterns of chaos." Fractals depict chaotic behavior, yet if one looks closely enough, it is always possible to find self-similarity within a fractal. The student understands that science is related to major technological systems, such as agriculture, health, water, energy, transportation, manufacturing, construction, and communications. The student learned that scientific discoveries lead to the development of new technologies. The student realized that new technologies can have deep impacts on society and the environment, including some that were not

anticipated.

Create a descriptive paragraph to explain to other educators what students will do with respect to science and the science standards that you are selecting. What is the specific project or part of the project that will be accomplished to meet the goals and standards selected?How will students apply their knowledge of the content standards?

o Make sure that your project includes goals that frame these benchmarks under the theme, and in the project area how you will have students practice these concepts and in your assessment show how each benchmark addressed will be evaluated.

What feedback and checkpoints will students receive?What element of this project helps society solve a problem or interacts with real people/community members? (RBL)Begin with: “Students will…”.

o This needs to be a paragraph that explains the project and includes the standards formally. Many of the things you put in goals and assessment should be replicated here to show what students will do to address learning the benchmarks through the project.



Did the student find a unique fractal design that can be connected to their field of study within the various sciences such as..

the branching of tracheal tubes, the leaves in trees, the veins in a hand, water swirling and twisting out of a tap, a puffy cumulus cloud, tiny oxygen molecule, or the DNA molecule, the stock market

Did the student learn by researching how 3D Lenticular designs can be used in photoshop and printing?

Miscellaneous(Enrichment,

modification, extension, alternate methodology)

https://youtu.be/qS6oGQmpdRM You Tube Video, Lenticular production Photrogram is a world wide leader in HD Dynamic Printing, Lenticular, 3D, Stereoscopic printing. More powerful then holography / holograms, this is a unique marketing tool.https://youtu.be/JLfLSjbm4s8 You Tube Video on 3d Lenticular Murals


https://youtu.be/qS6oGQmpdRM

Rufus Butler Seder tells the story of his optically-animated LIFETILES murals and his best-selling Scanimation(r) books in the context of the history of motion pictures. This engrossing, video-packed, half-hour discussion includes clips of works by other artists and inventors who work in related optical motion mediums.

2. Engineering & 3. Technology& 3. Engineering


T=create google slide show and 3-d optical illusionE= engineering design processT = The students are going to create a google slideshow presentation after they have watched videos on google classroom on fractals and have done their own research. They can research videos on how to make an optical illusion move, and further research on the mechanics of movement in design. Kinetic movement would be a start. See the work of Alexander Calders mobiles. The Cubist and Futurist movement all used ‘moving’ images in a modern way. Researching the work of MC Escher and Victor Vasarelys’ optical illusions of movement would be a great inspiration to the students.E = The part of the lesson has design and innovation elements would be choosing the design of the fractal and then creating the 3-d optical illusion. They may choose a step further to create actual movement of the accordion pieces within a frame. They can create any 3D design that appears to be moving, such as MC Escher did in his staircase series. They can use levers for lineal pictures. (moved to project element section)

Goal/ObjectivesThe students will be able to research and construct a fractal design that is 3-d and possible components that move. This can be done with plastic , wood, books that move like a phyloscope.

Standard(s) International Technology and Engineers in Education Association (ITEEA): Standards for Technological Literacy ITEEA Standards (See Appendix B, p. 210)

Students will develop an understanding of the relationships among technologies and the connections between technology and other fields of study.

o Technology is closely linked to creativity, which has resulted in innovation.

New products and systems can be developed to

solve problems or to help do things that could not be done without the help

of technology.English National Curriculum: Design and Technology

Standards

Design

design purposeful, functional, appealing products for themselves and other users based on design criteria

generate, develop, model and communicate their ideas through talking, drawing, templates, mock-ups and, where appropriate, information and communication technology

Make Evaluate explore and evaluate a range of existing products evaluate their ideas and products against design

criteria select from and use a range of tools and equipment to perform practical tasks [for example, cutting, shaping, joining and finishing]

select from and use a wide range of materials and components, including construction materials, textiles and ingredients, according to their characteristics

Technical knowledge build structures, exploring how they can be made

stronger, stiffer and more stable explore and use mechanisms [for example, levers,

sliders, wheels and axles] in their products

American Society for Engineering Education (ASEE): ASEE K-12 STEM Standards

The following topics are the initial ideas

Declarative (Understands) that lead to this dimension for all Americans:

o Engineers design and conduct experiments, as well as analyze and interpret data as it relates to product design.

Engineering and Design -Problem-Solving National Science Standards (ITA) 9C/P. 102 and G/P. 103;

Atlas of Science Literacy (Project 2061) Chapter 3; National

Math Standards P . 52

Procedural All Americans will apply concepts of engineering design to solve problems.

o Apply a structured approach to solving problems including: defining a problem, brainstorming, researching and generating ideas, identifying criteria and constraints, exploring possibilities, making a model or prototype, evaluating the design using specifications, and communicating results.

English National Curriculum: Computing StandardsComputing Programmes of StudyKey Stages 1 and 2

Aims can evaluate and apply information technology,

including new or unfamiliar technologies, analytically to solve problems

are responsible, competent, confident and creative

users of information and communication technology.

International Society for Technology in Education (ISTE): ISTE Standards * *(ISTE & the Computing Standards should be reflected as being used throughout all subjects when IT/ET is available to students. Using only ISTE IT/ET standards will rarely cover the scope of technology and engineering in an integrated lesson plan. These standards can usually only be relied on to cover engineering when creating a computer program).

You do not need to use all of the standards from all of the organizations, you may select one groups and use those. We normally recommend the ITEEA standards for the T&E section. I think all of these are important to the skills of building using technology.

VocabularyFractals, Fibonacci Sequence, Sierpinski Triangle, Optical Illusion, Kinetic Movement

Career(s) Tie-In

Mechanical Engineer, Design Engineer, Structural Engineer, woodcutter, welder, project managerHow do the careers listed connect to the activities that the students are completing, make sure to explain the connection.

Project Elementand


(student application of standard/benchmark/goal)


T = The students are going to create a google slideshow presentation after they have watched videos on google classroom on fractals and have done their own research. They can research videos on how to make an optical illusion move, and further research on the mechanics of movement in design. Kinetic movement would be a start. The works of MC Escher and Victor Vasarely would be a great inspiration. Even the works of Cubists and Futurism show movement. They were way ahead of their time.E = The part of the lesson has design and innovation elements would be choosing the design of the fractal and then creating the 3-d optical illusion. They may choose a step further to create actual movement of the accordion pieces within a frame.

T = using tools, E = designing a new elementEngineering includes students doing research to be able to propose a new tangible or systems design and/or make an evaluative test to show something new. Computer programs and systems planning are not tangible, but they are creating something new. Did the students plan and measure appropriately to create this 3-d Fractal. Have they come up with an innovative plan to make it move? If so, how did they design this to move?



T = Did the process, use of computer for research, videos and the end product meet the specifications?E = How does the Fractal/Optical Illusion meet the design parameters and how well does it function or does it move? How innovative was it? This will be evaluated using a rubric. It is expected that every assessment be rubric-based. Rubrics with a clear set of criteria for students’ work that includes descriptions of levels of performance quality on the criteria. Use the educational standards associated with each subject to develop criteria.

Be sure to align the educational standards within each subject to the outcomes of performance, project and reporting that prove conceptual understanding.

Remember to put a focus on the process as well as the result.Recommended: place 40% value on the process, 20% on the product, 40% on the report after the process.

How are each of the standards and the overall goals assessed from

entries in a portfolio, the end product, and the report?

Miscellaneous(Enrichment, modification,

extension, alternate methodology)

https://youtu.be/JLfLSjbm4s8 You Tube Video: Rufus Butler Seder tells the story of his optically-animated LIFETILES murals and his best-selling Scanimation(r) books in the context of the history of motion pictures.

4. Math Mathematics

Essential Concept(s) Understand the number sequence of the Fractal design that you create.

Goal/Objectives Create a Fractal design using the Fibonacci, Serpinski or Transormation sequence.

Standard(s) National Council of Teachers of Mathematics (NCTM): NCTM Standards Geometry

o Understand congruence and similarity using physical models, transparencies, or geometry software.

Understand and apply the Pythagorean theorem.o Solve real-world and mathematical problems

involving volume of cylinders, cones and spheres.

Common Core: Math Standards Common CoreGeometry

Understand congruence and similarity using physical models, transparencies, or geometry software.

Verify experimentally the properties of rotations, reflections, and translations:

Lines are taken to lines, and line segments to line segments of the same length.

Angles are taken to angles of the same measure. Parallel lines are taken to parallel lines.

English National Curriculum: Math Standards

Geometry - properties of shapes

Pupils should be taught to:

identify 3-D shapes, including cubes and other cuboids, from 2-D representations

know angles are measured in degrees: estimate and


compare acute, obtuse and reflex angles draw given angles, and measure them in degrees (°) identify:

o angles at a point and 1 whole turn (total 360°)

o angles at a point on a straight line and half a turn (total 180°)

o other multiples of 90°o use the properties of rectangles to deduce

related facts and find missing lengths and angles

o distinguish between regular and irregular polygons based on reasoning about equal sides and angles

VocabularyFractals, Fibonacci Sequence, Serpinski Triangle, Transformations,

Career(s) Tie-InData Analyst, Marketing, design, technology, financial investment services

Project Elementand




Math is integral to almost all building, testing, analyzing, and marketing of projects.Fractals are characterized by the repetition of similar patterns at ever-diminishing scales. Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced by computer graphics.Create a descriptive paragraph to explain ot other educators what students will do. How will students apply their knowledge of the content standards for math?



Does the student understand the numbered patterns using the Fibonacci Sequence in their design? Do they choose the numbered Sierpinski Triangle design instead?



5. Language Arts Language Arts


Research, expressing and communicating knowledgeStudents can create a Google Slideshow Presentation, an artist Reflection, or Narrative account by researching information on the historical impact of Fractals as well as Optical Illusions.

Goal/ObjectivesResearch information on Fractals and Optical Illusions and create a Google Slideshow Presentation or a narrative account on how they created their fractal.

Standard(s)

National Council of Teachers of English (NCTE) Language Art Standards:7.Students conduct research on issues and interests by generating ideas and questions, and by posing problems. They gather, evaluate, and synthesize data from a variety of sources (e.g., print and non-print texts, artifacts, people) to communicate their discoveries in ways that suit their purpose and audience.8. Students use a variety of technological and information resources (e.g., libraries, databases, computer networks, video) to gather and synthesize information and to create and communicate knowledge.Language Arts StandardsCommon Core: Comprehension and Collaboration:CCSS.ELA-LITERACY.SL.8.1

Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 8 topics, texts, and issues, building on others' ideas and expressing their own clearly. English Language Arts Standards

CCSS.ELA-LITERACY.SL.8.1.C

Pose questions that connect the ideas of several speakers and respond to others' questions and comments with relevant evidence, observations, and ideas. English National Curriculum: English Standards

VocabularyFractals, Fibonacci Sequence, Sierpinski Triangle, Transformations, Optical Illusions, Kinetic Movement

Career(s) Tie-In

Web Publishers, Editors, Design Research ManagementMake sure to show the connection between the activity and the career.

Project Elementand




Students can write a narrative account or procedure on how to build any two dimensional fractal, optical illusion or further study the concept of becoming three dimensional. They can also design a google slide presentation individually or a a group and present it to the class. https://sites.google.com/a/bvsd.org/google-for-bvsd-educators/presentationswww.academycharter.org/wp-content/uploads/.../GooglePresentationrubric-1.docx



Did the student research information on Fractals and Optical Illusions and create a Google Slideshow Presentation or a narrative account on how they created their fractal.



66.S66. Social Studiesocial Studies

Essential Concept(s) Research the time period of Optical Illusions and Fractals in an essay and create a project with choice of materials such as clay.

Goal/Objectives

The student will learn how to research the historical and cultural significance of the time period of the creation of Fractal and Optical Illusions. They will be able to relate it to Modern or historical Geography, Cultures, Society and Historical importance.

Standard(s) National Council for Social Studies (NCSS): Social Studies Standards TIME, CONTINUITY, AND CHANGEStudying the past makes it possible for us to understand the human story across time. The historical experiences of societies, peoples and nations reveal patterns of continuity and change. Historical analysis enables us to identify continuities over time in core institutions, values, ideals, and traditions, as well as processes that lead to change within societies and institutions, and that result in innovation and the development of new ideas, values and ways of life.

Common Core: ELA = History/Social Studies StandardsIntegration of Knowledge and Ideas:CCSS.ELA-LITERACY.RH.6-8.7

Determine the central ideas or information of a primary or secondary source; provide an accurate

summary of the source distinct from prior knowledge or opinions.

Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts.

English National Curriculum: Geography Standards History Standards Citizenship StandardsHuman and physical geography

use basic geographical vocabulary to refer to:o key physical features, including: beach,

cliff, coast, forest, hill, mountain, sea, ocean, river, soil, valley, vegetation, season and weather

Geographical skills and fieldwork

use aerial photographs and plan perspectives to recognize landmarks and basic human and physical features; devise a simple map; and use and construct basic symbols in a key

o


Career(s) Tie-In

Historian, Art historian, Museum Curator, Art History Specialist, Historical Advisor, Logistics Analyst, Science and Math Historian

Project Elementand



RBL Component &

Fractals are characterized by the repetition of similar patterns at ever-diminishing scales They have no characteristic lengths, but are a state of broken pieces that are gathered together irregularly. Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced by computer graphics. It has become a new tool for modeling in biology, geology, and other natural sciences. Anthropologists have observed that the patterns

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produced in different cultures can be characterized by specific design themes. In Europe and America, we often see cities laid out in a grid pattern of straight streets and right-angle corners. In contrast, traditional African settlements tend to use fractal structures-circles of circles of circular dwellings, rectangular walls enclosing ever-smaller rectangles, and streets in which broad avenues branch down to tiny footpaths with striking geometric repetition. These indigenous fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs and knowledge systems. Drawing on interviews with African designers, artists, and scientists, Ron Eglash investigates fractals in African architecture, traditional hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, practical craft, quantitative techniques, and symbolic systems. He also examines the political and social implications of the existence of African fractal geometry. His book makes a unique contribution to the study of mathematics, African culture, anthropology, and computer simulations. The students will learn that Geometry was created by Euclid in ancient Egypt and Greece. What is the project and how are the students being assessed based on the standards for this section?



How does the student integrate Fractal knowledge in creating the cultural designs? What is the end product? Was it a mask, architecture, carving in clay? Does the project clearly represent the idea of growth in the fractal design element, such as patterns that grow?Does the student gather and reflect the idea that the historical experiences of societies, peoples and nations reveal patterns of continuity and change in their designs on their mask or aritechture?Assessed with Art Rubric



Some students may have the depth of understanding to create a 3-D model with a Fractal design. There may be some that will just be able to create a simple repeating pattern. Several students may not understand the Fibonacci Sequence but will understand the Sierpinski Triangle as their choice of design.

ne F7. Fine Artsine ArtsF

Essential Concept(s) Create a Fractal design that becomes a three dimensional accordion Optical Illusion

Goal/Objectives

The student will understand and create a fractal that is from the Sirpenski, Fibonacci, self similar or from transformation. This fractal is turned into a 3-D optical illusion.

Standard(s) We often cross-correlate to standards for other subjects in these areas: science (materials), technology (processes), research (LA, history, SS) engineering (creation) and math (structure).National Art Educators Association (NAEA): NAEA Fine Arts

StandardsNational Core Art Standards:V A:Cr2.3Enduring Understanding: People create and interact with objects, places, and design that define, shape, enhance, and empower their lives.Essential Question(s): How do objects, places, and design shape lives and communities? How do artists and designers determine goals for designing or redesigning objects, places, or systems? How do artists and designers create works of art or design that effectively communicate?Anchor Standard 7: Perceive and analyze artistic work V A:Re7.1

Enduring Understanding: Individual aesthetic and empathetic awareness developed through engagement with art can lead to understanding and appreciation of self, others, the natural world, and constructed environments.Essential Question(s): How do life experiences influence the way you relate to art? How does learning about art impact how we perceive the world? What can we learn from our responses to art?

V A:Re7.2Enduring Understanding: Visual imagery influences understanding of and responses to the world.Essential Question(s): What is an image? Where and how do we encounter images in our world? How do images influence our views of the world?

CN Connecting-Anchor Standard #11. Relate artistic ideas and works with societal, cultural and historical context to deepen understanding.- See more at: http://www.nationalartsstandards.org/content/national-core-arts-standards-anchor-standards#creating

Pupils should be taught to develop their creativity and ideas, and increase proficiency in their execution. They should develop a critical understanding of artists, architects and designers, expressing reasoned judgments that can inform their own work.

Pupils should be taught:

to use a range of techniques to record their observations in sketchbooks, journals and other media as a basis for

exploring their ideas to use a range of techniques and media, including painting to increase their proficiency in the handling of different

materials to analyze and evaluate their own work, and that of others,

in order to strengthen the visual impact or applications of their work

about the history of art, craft, design and architecture, including periods, styles and major movements from ancient times up to the present day

NCAS Fine Arts StandardsEnglish National Curriculum: Art and Design Standards


Career(s) Tie-In

Web design, Publishing, Visual Editor, Entertainment and Communication, Digital Illustrator, Animation and Design: 3-D Illustrator

Project Elementand




How has the student related their artistic ideas and works within a matter of historical context to deepen their understanding of the lesson?Was their research thorough and do they see how art has a connection to science, history and math by creating the accorian optical illusion?Has the student shown an evaluation of both their own work and other optical illusion artists of that time period?Has the student shown the creativity by using Fractals and optical Illusions in a highly creative manner?Has the student understood how to measure using a ruler and how to construct a three dimentional Fractal that appears to be moving, as an optical illusion would?What is the project and how are the students being assessed based on the standards for this section?



For this assessment there should be a rubric, using color, shape, and form as Art Elements. Movement a/Repetition is key as well as balance, as a Principle of Design. The student must choose an appropriate medium for durability, ergonomics. All as related to the grade-level arts standards.


extension, alternate

Some students may have the depth of understanding to create the 3-D model of the optical illusion. Several students may not understand the Fibonacci Sequence but will understand the Sierpinski Triangle as

methodology) their choice of design.

8. Physical Education ArtsPhysical Arts

Essential Concept(s) Research Fractal Growth in Trees, the human body.

Goal/ObjectivesTo show the growth in trees are a fractal, by using the human body to represent a growing tree that has self similarity and transformation.

Standard(s)

Shape America: National PE StandardsStandard 2 - The physically literate individual applies knowledge of concepts, principles, strategies and tactics related to movement and performance.English National Curriculum: PE StandardsKey stage 1

Pupils should develop fundamental movement skills, become increasingly competent and confident and access a broad range of opportunities to extend their agility, balance and coordination, individually and with others. They should be able to engage in competitive (both against self and against others) and co-operative physical activities, in a range of increasingly challenging situations.


master basic movements including running, jumping, throwing and catching, as well as developing balance, agility and co-ordination, and begin to apply these in a range of activities

participate in team games, developing simple tactics for attacking and defending

perform dances using simple movement patterns

VocabularyFractals, Fibonacci Sequence, Sierpinski ,Triangle, Self Similarity Transformations,

Career(s) Tie-In

Sports Therapist, Sports Science, Science of movement, Dance therapist,

Project Elementand

Educator / Student

Take a tree, for example. Pick a particular branch and study it closely. Choose a bundle of leaves on that branch. To archeologists, all three of the objects described - the tree, the

Feedback(student application of

standard/benchmark/goal)RBL Component &

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branch, and the leaves - are identical. The students will form a Fractal Tree by drawing the life size and progression of individual branches and show the length and width of its growth. They can lie on the drawing and form the trunk and branches with their bodies as a fractal form that grows. They can also draw the Fibonacci design from the human body configurations. They can incorporate dance routines as kinetic movement using the tree or Fibonacci Fractal. Fractals have more and more applications in science. The main reason is that they very often describe the real world better than traditional mathematics and physics.



Did the student understand that tree fractals grow as self similarity and can also connect this science to veins in the human body? Do they understand that the human body is made up of interconnection fractals? Do they understand the human body is made up of a Fibonacci design? Did they take it a step further and incorporate dance as kinetic movement?



Some students may have the depth of understanding to create a moving 3-D model with a Fractal design. There may be some that will just be able to create a simple repeating pattern of movement. Several students may not understand the Fibonacci Sequence but will understand the Serpinski Triangle as their choice of movement design.

9. Music ArtsMusical Arts

Essential Concept(s) Design a song with Fractal components.

Goal/Objectives Create a song or melody using the physics of sound to design a Sierpinski structure.

Standard(s) National Association for Music Education: Music Standards

ImagineGenerate musical ideas for various purposes and contexts.

Enduring Understanding: The creative ideas, concepts, and feelings that influence musicians’ work Essential Question: How do musicians generate creative emerge from a variety of sources. ideas?

MU:Cr1.1.C.Ia Describe how sounds and short musical ideas can be used to represent personal experiences, moods, visual images, and/or storylines.

Plan and Make

Select and develop musical ideas for defined purposes and contexts.Enduring Understanding: Musicians’ creative choices are influenced by their expertise, context, and Essential Question: How do musicians make creative expressive intent. decisions?

MU:Cr2.1.C.Ia Assemble and organize sounds or short musical ideas to create initial expressions of selected experiences, moods, images, or storylines.

Evaluate and Refine

Evaluate and refine selected musical ideas to create musical work that meets appropriate criteria.Enduring Understanding: Musicians evaluate and refine their work through openness to new ideas, Essential Question: How do musicians improve the quality of persistence, and the application of appropriate criteria. their creative work?

MU:Cr3.1.C.Ia Identify, describe, and apply teacher-provided criteria to assess and refine the technical and expressive aspects of evolving drafts leading to final versions.

English National Curriculum: Music StandardsKey stage 2

Pupils should be taught to sing and play musically with increasing confidence and control. They should develop an understanding of musical composition, organizing and manipulating ideas within musical structures and reproducing sounds from aural memory.


play and perform in solo and ensemble contexts, using their voices and playing musical instruments with increasing accuracy, fluency, control and expression

improvise and compose music for a range of purposes using the interrelated dimensions of music

listen with attention to detail and recall sounds with increasing aural memory

use and understand staff and other musical notations appreciate and understand a wide range of high-quality

live and recorded music drawn from different traditions and from great composers and musicians

develop an understanding of the history of music

VocabularyFractals, Fibonacci Sequence, Serpenski Triangle, Transformations,

Career(s) Tie-InOften Music careers are similar titles for most projects, as industry will hire people with similar skills for various applications. E.g., composers, performers, conductors, lyricists… Careers?

Project Elementand




Research songs or musical genres that include a progression of sounds created by fractals. Create a unique melody, song or instrumental using the progression of Fractals seen in most music or song writing. Sometimes it can be making music with the elements of the project or the project itself. It can also be the physics of sound to recognize what is happening with a project, a product, an environment, a tone for something on a device needing attention, etc. One example occurs in Beethoven’s Sonata 15 op. 28 third movement which is a combination of binary and ternary schemes similar to the Sierpinski triangle structure.



Does the student create a musical project using fractals as part of their composition? do they use an instrument or sing a song to create the fractal composition?



Some students may have the depth of understanding to create a Fractal composition. Several students may not understand the Fibonacci Sequence but will understand the Sierpinski Triangle as their choice of identifying a repeating rhythm or chorus in their design composition. There will be some students who will not understand a Fractal but understand repetition in music.

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