THE BEAUTY AND ART OF THE GOLDEN SECTION
INDEPENDENT ART CURRICULUM PROJECT UNIT
CREATED BY: DEBRA TROYANOS
For Graduate Program at University of Florida, Master's of Art Education
THE BEAUTY AND ART OF THE GOLDEN SECTION
Targeted Grade Level: Junior High or High School
*Could be cross-curricular with science, math, English (poetry) or music.
Unit Overview
For as long as humans have existed there has been a universal standard of beauty that seems to be inherent in nature, and that appeals most to the human eye. The Golden Ratio is also known as the Golden Section, The Golden Mean, The Divine Proportion, The Fibonacci Sequence or Phi. They are all based on the proportion: 1 to 1.618. The Golden Ratio exists in art, nature, architecture, music, poetry, even in the proportions and DNA of humans themselves. It can be found throughout the universe; from the spirals of galaxies to the spiral of a Nautilus seashell, the harmony of music, the growth patterns of flowers and plants, to the beauty in art. It is like a design blue print that the entire universe is founded upon. It is seen as the beauty and organization within the cosmos. It is the harmony underlying the universe. Some call it the Divine Proportion because it seems to be the very nature of creation.
Artists from Leonardo DaVinci and Michelangelo, to Egyptian and Greek architects, to contemporary website and product designers, will be included in this unit as it examines the use of golden proportions in art. The Golden Mean is important because this will help students develop a clearer understanding of aesthetics and what is considered beautiful.
Big Ideas:
Essential Questions:
Lesson One: What Is The Golden Ratio?
Introduction:
During this lesson class will first watch one of the you-tube videos, movies, or powerpoints listed below which explains what the Golden Section is. This will be an introduction in the study of aesthetics, from the viewpoint of art history and various cultures that have incorporated this topic. A powerpoint presentation, movie, or you-tube videos can be shown as introduction to the topic, and showing various artists from history who have utilized this in their artwork. Then, a class
demonstration and discussion will take place looking at various objects designed in this way. Finally, students will draw a golden rectangle and spiral, utilizing these universal design principles.
Big Ideas:
Essential Questions:
Lesson Objectives:
Students will be aware of what and why certain things are considered beautiful in art and in nature and learn about proportion which is the geometry of aesthetics. They will recognize the Golden section, and be able to see it in nature, artwork or design.
Tools and Materials:
Teacher will bring in examples of objects from nature, art history, and everyday objects, that show the Golden Ratio such as: several pinecones, a whole pineapple, a sunflower, a nautilus shell, a picture frame, a laptop, an I-phone, a credit card, a book, a coffee table, a T.V. screen, etc. Teacher should also prepare photo examples of artists such as DaVinci whose work used the Golden mean, and photos of the Universe taken by Nasa, which show spirals in the cosmos. Challenge them to find more around the classroom- sometimes windows, desks, whiteboard, erasers, text books, cabinets, and other items are good examples.
In addition, students will need paper, pencils, compasses, rulers and erasers for the drawings. These can be colored in for fun using any media, if preferred. ( I use 12x18 watercolor paper, which I point out that even this art paper is made of the Golden Proportion!!)
Process:
First start by viewing this awesome Disney video entitled Donald in Mathmagic Land:
http://www.youtube.com/watch?v=YRD4gb0p5RM&feature=related
Or there is an 8 minute mini-version of it at this link:
http://www.youtube.com/watch?v=YVODhFLe0mw
Students draw a golden rectangle, pentagram, and golden spiral to become familiar with them. These can be colored with media of your choice and the Fibonacci numbers can be added for interest. These can also be made into multi-media collages. While students work, play Beethoven’s Fifth Symphony, which is an example of the Golden Ratio used in music.
Alternate or Additional Project:
Create a collage using images collected that maintain the golden proportions. When dry draw a Golden Spiral over it using a dark pencil or sharpie marker.
Extend this lesson, by looking at images of Davinci’s Vetruvian Man, and Mona Lisa, and pointing out the many golden proportions on the human body and face as well. As you explain, students can test out the measurements on themselves. You can also have them go to some of the websites below for more information on this.
Assessment:
Self Reflection/ Assessment: Does the project show good craftsmanship? Does student work demonstrate an understanding of the proportion used in the Golden Ratio? Has student learned to properly use compass and straight edge ruler?
(Or Use Rubric Attached Below)
Artists:
Leonardo DaVinci, Albrect Durer, Michelangelo, Beethoven, ancient Egyptian and Greek architects, and Nasa photographers.
Helpful Links and Information for Lesson One:
History of Phi, the Golden Ratio:
http://goldennumber.net/history.htm
http://unfoldingcreativity.com/beauty-in-art-%E2%80%93-part-3.htm
http://en.wikipedia.org/wiki/List_of_works_designed_with_the_golden_ratio
You-Tube videos:
Good for showing to high school students to explain Golden Ratio:
http://www.youtube.com/watch?v=fmaVqkR0ZXg&feature=related
http://www.youtube.com/watch?v=U2bAlIK4KkE&feature=related
Great for showing junior high school students:
30 minute Disney movie Donald in Mathmagic Land:
http://www.youtube.com/watch?v=YRD4gb0p5RM&feature=related
How to create the golden proportions:
rectangle-
http://www.youtube.com/watch?v=FJvTncKLiIQ&feature=related
spiral-
http://www.youtube.com/watch?v=RjM8AaNSjhA&feature=related
circle theory:
http://www.circular-theory.com/absolute-intelligence
Golden Ratio on Human Faces (a good one!-could be used with portrait drawing too):
http://mrloken.wikispaces.com/Golden_Ratio_Page2
The Parthenon & Greek architecture and modern architecture using golden mean:
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html#parthenon
The mind of Leonardo- Uffizi gallery:
http://brunelleschi.imss.fi.it/menteleonardo/
Lesson One Resources:
Lesson Two: How Artists and Designers Today Use Golden Ratio
Introduction:
In teaching composition in artwork we often point out that it is better to position objects not in the center of the picture but about one-third of the way across, and to use lines which divide the picture into thirds. The preferential placement of the horizon line in an image is at the top one third line, or the bottom one third, rather than in the middle. This seems to make the picture design more pleasing to the eye and relies again on the idea of the golden section being "ideal". This 2:1 ratio approximates the Golden Ratio proportions.
Big Ideas:
Essential Questions:
Lesson objectives:
Recognizing and discover the pervasiveness of The Golden Ratio in looking at modern products, logos, advertising and designs that use the Golden Proportions. Students will create their own original logo or design a brand for a product using the golden proportions. Remember: The whole has the same ratio to the larger segment as the larger segment has to the smaller segment.
Tools and Materials:
Show some examples of how Golden Section is used in current brands and logos- for example, Mastercard & Visa, Pepsi, Kit Kat Candy Bars, National Geographic logo (yellow rectangle), a cereal box.
Students need: paper, sharpie pens, pencils, markers or colored pencils, rulers, compasses.
Process:
A. First, students will demonstrate their understanding by researching or finding three logos or products which have been designed in this way.
B. Create an original logo or product design using the Golden Proportions to create the design.
C. Alternate project: Using scientific images of space, human DNA Strands, or microscopic images of cells, students create a chalk or oil pastel drawing on black paper.
Assessment:
Short Constructed Response Questions:(Students write a brief response to the questions below).
1. Did you find 3 good examples of logos or brands?
2. Did student show their awareness of the Golden proportion by using it to create their design?
3. Name three products or every day items that are designed with the Golden Proportion: _____________________, __________ , _________________.
4. Explain briefly what the Golden Ratio is:
5. Name three artists who used the Golden Ratio in their work: ___________________________, ________________________, __________________________.
6. How does your artwork use the Golden ratio in the design? _________________________________________________________________________________.
Artists:
Various designers of different modern products, logos, and brands. A few of their websites are below:
http://www.webdesignstuff.co.uk/nl004/golden-ratio/application-examples-in-modern-design/
http://www.smashingmagazine.com/2008/05/29/applying-divine-proportion-to-web-design/
http://nexusartcafe.com/2011/09/exhibition-preview-the-golden-ratio/ (a contemporary art exhibit)
Recommended links for this lesson:
http://en.wikipedia.org/wiki/Fibonacci_numbers_in_popular_culture
http://www.artyfactory.com/graphic_design/graphic_design_lessons.html
Golden Ratio Art Projects | eHow.com
http://www.ehow.com/list_6388716_golden-ratio-art-projects.html#ixzz1Zlb703OL
Beauty of the human face:
http://www.beautyanalysis.com/
How to use golden section proportions in your designs:
Bradley Steven, May 16, 2011, Web Design at
http://www.vanseodesign.com/web-design/golden-section-proportions/
Creating a Sense of Beauty in -Design & Composition-
http://www.goldennumber.net/design.htm
Resources:
CREATED BY: DEBRA TROYANOS
For Graduate Program at University of Florida, Master's of Art Education
THE BEAUTY AND ART OF THE GOLDEN SECTION
Targeted Grade Level: Junior High or High School
*Could be cross-curricular with science, math, English (poetry) or music.
Unit Overview
For as long as humans have existed there has been a universal standard of beauty that seems to be inherent in nature, and that appeals most to the human eye. The Golden Ratio is also known as the Golden Section, The Golden Mean, The Divine Proportion, The Fibonacci Sequence or Phi. They are all based on the proportion: 1 to 1.618. The Golden Ratio exists in art, nature, architecture, music, poetry, even in the proportions and DNA of humans themselves. It can be found throughout the universe; from the spirals of galaxies to the spiral of a Nautilus seashell, the harmony of music, the growth patterns of flowers and plants, to the beauty in art. It is like a design blue print that the entire universe is founded upon. It is seen as the beauty and organization within the cosmos. It is the harmony underlying the universe. Some call it the Divine Proportion because it seems to be the very nature of creation.
Artists from Leonardo DaVinci and Michelangelo, to Egyptian and Greek architects, to contemporary website and product designers, will be included in this unit as it examines the use of golden proportions in art. The Golden Mean is important because this will help students develop a clearer understanding of aesthetics and what is considered beautiful.
Big Ideas:
- What makes something “beautiful” to humans? Is it intuitive or cultural?
- Does art have to be beautiful? Is beauty in the eye of the beholder?
- Once you become “aesthetically aware” you can find joy and delight in viewing art, and nature, as well as many other objects in the world at large.
Essential Questions:
- Where did the Golden Ratio come from?
- What artists are known for using it?
- What makes something “beautiful” to humans?
- Can artist’s imitate nature in design?
Lesson One: What Is The Golden Ratio?
Introduction:
During this lesson class will first watch one of the you-tube videos, movies, or powerpoints listed below which explains what the Golden Section is. This will be an introduction in the study of aesthetics, from the viewpoint of art history and various cultures that have incorporated this topic. A powerpoint presentation, movie, or you-tube videos can be shown as introduction to the topic, and showing various artists from history who have utilized this in their artwork. Then, a class
demonstration and discussion will take place looking at various objects designed in this way. Finally, students will draw a golden rectangle and spiral, utilizing these universal design principles.
Big Ideas:
- Many things exist in nature that have one astounding correlation, the same ratio of height to width which is 1: 1.618.
- Artists from the ancient Egyptians, Mayans, and Greeks, to Renaissance artists like DaVinci, Michelangelo, and Albrect Durer, up to contemporary artists and designers today have used this principle in their art, architecture, and designs since it is most appealing to the human eye.
- Using the rules of The Golden Ratio produces artwork with balance and harmony.
Essential Questions:
- What makes something beautiful to humans?
- Why have artists chosen to use the Golden Ratio in their art or design today?
- Does Art have to be beautiful?
- What is proportion?
Lesson Objectives:
Students will be aware of what and why certain things are considered beautiful in art and in nature and learn about proportion which is the geometry of aesthetics. They will recognize the Golden section, and be able to see it in nature, artwork or design.
Tools and Materials:
Teacher will bring in examples of objects from nature, art history, and everyday objects, that show the Golden Ratio such as: several pinecones, a whole pineapple, a sunflower, a nautilus shell, a picture frame, a laptop, an I-phone, a credit card, a book, a coffee table, a T.V. screen, etc. Teacher should also prepare photo examples of artists such as DaVinci whose work used the Golden mean, and photos of the Universe taken by Nasa, which show spirals in the cosmos. Challenge them to find more around the classroom- sometimes windows, desks, whiteboard, erasers, text books, cabinets, and other items are good examples.
In addition, students will need paper, pencils, compasses, rulers and erasers for the drawings. These can be colored in for fun using any media, if preferred. ( I use 12x18 watercolor paper, which I point out that even this art paper is made of the Golden Proportion!!)
Process:
First start by viewing this awesome Disney video entitled Donald in Mathmagic Land:
http://www.youtube.com/watch?v=YRD4gb0p5RM&feature=related
Or there is an 8 minute mini-version of it at this link:
http://www.youtube.com/watch?v=YVODhFLe0mw
Students draw a golden rectangle, pentagram, and golden spiral to become familiar with them. These can be colored with media of your choice and the Fibonacci numbers can be added for interest. These can also be made into multi-media collages. While students work, play Beethoven’s Fifth Symphony, which is an example of the Golden Ratio used in music.
Alternate or Additional Project:
Create a collage using images collected that maintain the golden proportions. When dry draw a Golden Spiral over it using a dark pencil or sharpie marker.
Extend this lesson, by looking at images of Davinci’s Vetruvian Man, and Mona Lisa, and pointing out the many golden proportions on the human body and face as well. As you explain, students can test out the measurements on themselves. You can also have them go to some of the websites below for more information on this.
Assessment:
Self Reflection/ Assessment: Does the project show good craftsmanship? Does student work demonstrate an understanding of the proportion used in the Golden Ratio? Has student learned to properly use compass and straight edge ruler?
(Or Use Rubric Attached Below)
Artists:
Leonardo DaVinci, Albrect Durer, Michelangelo, Beethoven, ancient Egyptian and Greek architects, and Nasa photographers.
Helpful Links and Information for Lesson One:
History of Phi, the Golden Ratio:
http://goldennumber.net/history.htm
http://unfoldingcreativity.com/beauty-in-art-%E2%80%93-part-3.htm
http://en.wikipedia.org/wiki/List_of_works_designed_with_the_golden_ratio
You-Tube videos:
Good for showing to high school students to explain Golden Ratio:
http://www.youtube.com/watch?v=fmaVqkR0ZXg&feature=related
http://www.youtube.com/watch?v=U2bAlIK4KkE&feature=related
Great for showing junior high school students:
30 minute Disney movie Donald in Mathmagic Land:
http://www.youtube.com/watch?v=YRD4gb0p5RM&feature=related
How to create the golden proportions:
rectangle-
http://www.youtube.com/watch?v=FJvTncKLiIQ&feature=related
spiral-
http://www.youtube.com/watch?v=RjM8AaNSjhA&feature=related
circle theory:
http://www.circular-theory.com/absolute-intelligence
Golden Ratio on Human Faces (a good one!-could be used with portrait drawing too):
http://mrloken.wikispaces.com/Golden_Ratio_Page2
The Parthenon & Greek architecture and modern architecture using golden mean:
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html#parthenon
The mind of Leonardo- Uffizi gallery:
http://brunelleschi.imss.fi.it/menteleonardo/
Lesson One Resources:
- Doczi, G. (1994), The Power of Limits: Proportional Harmonies in Nature, Art, and Architecture Shambala Press.
- Livio, Mario. The Golden Ratio. New York: Broadway Books, 2003.
- Runion, Garth. The Golden Section. Palo Alto, CA: Dale Seymour Publications, 1990.
Lesson Two: How Artists and Designers Today Use Golden Ratio
Introduction:
In teaching composition in artwork we often point out that it is better to position objects not in the center of the picture but about one-third of the way across, and to use lines which divide the picture into thirds. The preferential placement of the horizon line in an image is at the top one third line, or the bottom one third, rather than in the middle. This seems to make the picture design more pleasing to the eye and relies again on the idea of the golden section being "ideal". This 2:1 ratio approximates the Golden Ratio proportions.
Big Ideas:
- People today are inundated with visual images in our culture. Most are made to capture our attention. Those made for ads or products, are meant to appeal to us psychologically and visually.
- Students can learn to interpret visual images, and understand the design process which is used by contemporary artists and designers which dates back to the discovery of the Golden Section.
- There is an element of visual harmony and order in proportions,that is innately appealing to our human aesthetic sensibility even today.
- Art does not exist as an isolated subject. It is interconnected with the world and other “academic” studies such as geometry, science, history, psychology, sociology and cultural anthropology.
Essential Questions:
- What techniques can designers use to make their products or ads appealing to consumers?
- How can artists influence a viewer or consumer’s opinion of their artwork?
- Could this be why artists like DaVinci and Michelangelo have become as famous as they are, and why their artwork has endured?
Lesson objectives:
Recognizing and discover the pervasiveness of The Golden Ratio in looking at modern products, logos, advertising and designs that use the Golden Proportions. Students will create their own original logo or design a brand for a product using the golden proportions. Remember: The whole has the same ratio to the larger segment as the larger segment has to the smaller segment.
Tools and Materials:
Show some examples of how Golden Section is used in current brands and logos- for example, Mastercard & Visa, Pepsi, Kit Kat Candy Bars, National Geographic logo (yellow rectangle), a cereal box.
Students need: paper, sharpie pens, pencils, markers or colored pencils, rulers, compasses.
Process:
A. First, students will demonstrate their understanding by researching or finding three logos or products which have been designed in this way.
B. Create an original logo or product design using the Golden Proportions to create the design.
C. Alternate project: Using scientific images of space, human DNA Strands, or microscopic images of cells, students create a chalk or oil pastel drawing on black paper.
Assessment:
Short Constructed Response Questions:(Students write a brief response to the questions below).
1. Did you find 3 good examples of logos or brands?
2. Did student show their awareness of the Golden proportion by using it to create their design?
3. Name three products or every day items that are designed with the Golden Proportion: _____________________, __________ , _________________.
4. Explain briefly what the Golden Ratio is:
5. Name three artists who used the Golden Ratio in their work: ___________________________, ________________________, __________________________.
6. How does your artwork use the Golden ratio in the design? _________________________________________________________________________________.
Artists:
Various designers of different modern products, logos, and brands. A few of their websites are below:
http://www.webdesignstuff.co.uk/nl004/golden-ratio/application-examples-in-modern-design/
http://www.smashingmagazine.com/2008/05/29/applying-divine-proportion-to-web-design/
http://nexusartcafe.com/2011/09/exhibition-preview-the-golden-ratio/ (a contemporary art exhibit)
Recommended links for this lesson:
http://en.wikipedia.org/wiki/Fibonacci_numbers_in_popular_culture
http://www.artyfactory.com/graphic_design/graphic_design_lessons.html
Golden Ratio Art Projects | eHow.com
http://www.ehow.com/list_6388716_golden-ratio-art-projects.html#ixzz1Zlb703OL
Beauty of the human face:
http://www.beautyanalysis.com/
How to use golden section proportions in your designs:
Bradley Steven, May 16, 2011, Web Design at
http://www.vanseodesign.com/web-design/golden-section-proportions/
Creating a Sense of Beauty in -Design & Composition-
http://www.goldennumber.net/design.htm
Resources:
- Rayo, N. (2009) The Golden Ratio of Branding and Success: Role of Logo Design in Branding Success. Retrieved from: http://knol.google.com/k/logo-design-consultant/the-golden-ratio-of-branding-and-success/3ud8y8mxjwj8m/6
- Meisner, G. (2011) The GoldenNumber.Net, retrieved from http://www.goldennumber.net/phiguy.htm
- Doczi, György (2005) . The Power of Limits: Proportional Harmonies in Nature, Art, and Architecture. Boston: Shambhala Publications
Rubric attached here:
troyanos_golden_rubric.pdf | |
File Size: | 79 kb |
File Type: |
Lesson Three: Create Your Own Artwork or Design Using Golden Proportion
Introduction:
Artists, architects and designers have proportioned their works to approximate the Golden Ratio, especially in the form of the Golden Rectangle. They believe this proportion to be universally and aesthetically pleasing. The Golden Ratio plays an essential role in human perception of beauty. Students will now attempt to create their own original artwork using these proportions.
Big Ideas:
Once you become “aesthetically aware” you can find joy and delight in viewing art, and nature, and potentially many other objects in the world at large. You can use the Golden Proportion in creating your own art or designs for a more universally appealing outcome.
Essential Questions:
How can an artist use the Golden Ratio in their art? Why does it become more aesthetically pleasing?
Lesson Objectives:
The student will be able to create a photograph, artwork, or website design, applying the Golden Proportion. This can be done using the Fibonacci sequence to create the pattern, using the rule-of-thirds in creating composition, using the golden rectangle or spiral, and even including using the dimensions of the artwork itself.
Tools and Materials:
Tools and materials vary according to student choice of project. Could be done with any media, and could also be digital design (such as website) as an option.
Process: Students create their 2-D or 3-D artwork interpreting and using the Golden Proportions underlying their design.
Vocabulary Terms:
Pattern, balance, unity, proportion, and symmetry.
Assessment: When project is complete students will share their work with the class (class critique). Students should be able to explain how the Golden proportion was used in their design (self-assessment). Final assessment is unit test of Golden Ratio in Art. See attached.
Some Contemporary Artists Using Golden Ratio:
Patricia Bennett and Mary Miller (Quilt Design), Steve Plummer and Pat Ashforth (knitting and crocheting), Billie Ruth Sudduth (basketwork), Kees van Prooijen, Fletcher Cox (wood), Pietro Malusardi and Karen Wallace (Furniture Design), David Weitzman (sacred geometry jewelry artist) and Mario Merz (environmental artist).
Artist links:
http://www.ka-gold-jewelry.com/
http://www.summum.us/philosophy/phi.shtml
http://www.spiralzoom.com/Culture/ContemporaryArt/Contemporaryart.html
Cool Widget Link for this lesson:
Phiculator, is a simple flash application that does the math for you. You enter in a dimension and it will calculate the corresponding dimension based on the golden ratio. I know it’s not hard math to do (divide your larger side by 1.618), but the calculator makes it easier and more fun.
http://www.thismanslife.co.uk/projects/phiculator/
Other Helpful Links:
http://www.youtube.com/watch?v=U2bAlIK4KkE&NR=1
http://www.youtube.com/watch?v=2zWivbG0RIo&feature=player_embedded
http://www.presentationzen.com/presentationzen/2005/08/from_wabisabi_t.html
http://www.youtube.com/watch?v=fmaVqkR0ZXg
http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golde
http://www.youtube.com/watch?v=U2bAlIK4KkE&NR=1
http://www.youtube.com/watch?v=2zWivbG0RIo&feature=player_embedded
Art 21 video: The Need for Beauty
Resources:
Golden Ratio, Wikipedia(2010)Retrieved from http://en.wikipedia.org/wiki/Golden_ratio
Click on the links below for a Powerpoint I created for my class on the Golden Ratio In Art:
the_beauty_of_the_golden_ratio_in_art.pptx | |
File Size: | 2401 kb |
File Type: | pptx |
golden_section_in_art__architecture.pptx | |
File Size: | 7831 kb |
File Type: | pptx |
See my following website page for further contemporary artists who use the Golden Proportion to create their art.
A quilt designed using the Golden Proportion
Massachusetts Curriculum Frameworks Visual Arts Standards (used in this unit):
1. Methods, Materials, and Techniques. Students will demonstrate knowledge of the methods, materials, and techniques unique to the visual arts.
2. Elements and Principles of Design. Students will demonstrate knowledge of the elements and principles of design. (In particular to this lesson- proportion, unity, rhythm )
3. Observation, Abstraction, Invention, and Expression. Students will demonstrate their powers of observation, abstraction, invention, and expression in a variety of media, materials, and techniques.
4. Drafting, Revising, and Exhibiting. Students will demonstrate knowledge of the processes of creating and exhibiting their own artwork: drafts, critique, self-assessment, refinement, and exhibit preparation.
5. Critical Response. Students will describe and analyze their own work and the work of others using appropriate visual arts vocabulary. When appropriate, students will connect their analysis to interpretation and evaluation.
6. Purposes of the Arts. Students will describe the purposes for which works of dance, music, theatre, visual arts, and architecture were and are created, and, when appropriate, interpret their meanings.
7. Roles of Artists in Communities. Students will describe the roles of artists, patrons, cultural organizations, and arts institutions in societies of the past and present.
8. Concepts of Style, Stylistic Influence, and Stylistic Change. Students will demonstrate their understanding of styles, stylistic influence, and stylistic change by identifying when and where art works were created, and by analyzing characteristic features of art works from various historical periods, cultures, and genres.
9. Inventions, Technologies and the Arts. Students will describe and analyze how performing and visual artists use and have used materials, inventions, and technologies in their work.
10. Interdisciplinary Connections. Students will apply their knowledge of the arts to the study of English language arts, foreign languages, health, history and social science, mathematics, and science and technology/engineering.