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Golden Mean - Math Integration

Submitted by: Grace Hall, Wilkes Central High School in Wilkesboro, NC.
UNIT: Golden Mean - Math/Science Integration
Lesson: The Golden Mean Project - Design in Nature
Grade Level: High School (grades 10-12)
Approximate Time Needed: 5 to 7 class periods

 

Preparations:
1. Download the Power Point Presentation PPT (To download this to your hard drive, right-click on the link and select "save link as.") , review it and research the topic to become familiar with how the Golden Mean connects with art.
2. Collect materials needed from the list above.
3. Make transparencies with the 4 different styles of the Golden Mean by either tracing them on transparencies, or by using a copy machine.

4. Make copies of the Golden Mean handout or use it as a transparency.

Procedure:
1. Begin by posing the first essential question to the class and discuss the ideas they come up with. Conclude by informing students of the theory of the Golden Mean.
2. Use the Power Point Presentation PPT to instruct students on the background of the Golden Mean.
3. The presentation concludes with the activity including the rubric that will be used to assess the final product.
4. Distribute the handout. Begin the activity.
5. Set a due date; depending on the class give them from a week to 2 weeks.
6. Conclude with a group critique discussing issues included in the rubric.
7. Allow students to make changes if necessary.
8. Display the artwork for the class or the school including a brief description of the goal of the assignment.

 

golden mean      golden mean      golden mean
Click images for larger views

Activity:
1. In this assignment students will choose a pattern from nature which is created through the phenomenon of the Golden Mean such as the pattern in a Nautilus Shell or the pattern from the seed pod of a sunflower to inspire an original design.


2. Students will use the layouts provided on the transparencies to create an original work of art for the composition. The solutions to this problem are infinite.


3. Show students books and magazines with patterns from nature and suggest ways they could use them. Allow them to use the Internet to further research natural patterns.

4. Demonstrate how students are to tape down their canvas paper so as to leave an even white border around the edge of the paper.

5. Have students select a background color for the entire painting and paint that color within the masking tape area, overlapping enough to create a straight edge when the tape is removed.

6. Demonstrate using the overhead projector to project one of the Golden Ratio transparencies over the background and trace it in chalk over the background.

7. Using the Golden Ratio pattern that they chose, they must determine what part of the design will be the center of interest and place it in the section of the pattern of the Golden Ratio.

8. Students may use chalk or pencil to draw in the composition.

9. If students have not used Acrylic Paint before, a discussion of the nature, care and cleaning of acrylics should be discussed including the fact that acrylics dry fast and that they will harden in the brushes and at the bottom of the sink.  Acrylics may be used transparently by adding an acrylic medium or water.  Alternately, by adding Gesso. they may also become more opaque.  Acrylics will not come out of clothes unless they are removed while still wet and that isn’t guaranteed.  Acrylics can be covered with plastic wrap in order to keep them moist for the next day.

10. Instruct students on the importance of good craftsmanship and technical accuracy.

11. Circulate to be sure students understand the concept and are using the paints appropriately.

12. When the paintings are finished have students sign their work in one of the lower corners of the painting and carefully remove the masking tape to reveal the white border around the painting.

13. Upon the due date, conclude the lesson with a critique using the rubric as a foundation for the discussion.

14. Allow students to make changes to their work based on suggestions during the critique before grading or displaying the work.

 

National Visual Arts Standards for Grades 9-12:
1. Using knowledge of structures and functions. (other National Standards below)


State Visual Arts Standards for Art II-IV:
(North Carolina) COMPETENCY GOAL 3: The learner will organize the components of a work into a cohesive whole through knowledge of organizational principles of design and art elements.


Benchmarks:
(North Carolina) 3.06 Demonstrate the ability to form and defend judgments about the characteristics of structures to accomplish commercial, personal, communal or other purposes of art.

National Educational Technology Standards:
V. TECHNOLOGY RESEARCH TOOLS
    * Students use technology to locate, evaluate, and collect information from a variety of sources.
    * Students evaluate and select new information resources and technological innovations based on the appropriateness for specific tasks.

Goal: To understand the Golden Ratio as a means of organizing a work of art.


Objectives:

  • TLW: Observe and recall information regarding the mathematical properties of the Golden Mean.

  • TLW: Associate how artists have used the Golden Mean to create masterpieces throughout history.

  • TLW: Demonstrate knowledge of the Golden Mean using one of the formulas of organization to create an original work of art.

  • TLW: Select a pattern from nature to inspire an original composition.

  • TLW: Design a composition organized using the Golden Mean and inspired by a pattern from nature.

  • TLW: Verbally assess the value of using the Golden Mean to organize their own compositions as well as those of their peers in a class critique.

Parthenon divided by golden ratio

Elements:

Space

Principles:

Balance, Proportion, Movement, Emphasis

Vocabulary:
Golden Mean (Archive)
The Divine Proportion
Golden Ratio
Phi
Golden Spiral
Fibonacci Numbers

 

Essential Questions/Aesthetic Questions:

  1. Did you know that math and geometry are very closely related to art? Brainstorm different ways that math and geometry could be used in art.

  2. Do you know of any artists who use math in their artwork?

  3. How might science and art be related? Brainstorm ways artists may use science to inspire artwork.

  4. Do you know of any artists who have used science in their artwork?

  5. How effective was the use of the golden rectangle in Leonardo’s Mona Lisa?

  6. What buildings in the community use the same ratio of the Golden Mean in the architectural design?

  7. Do you think a rectangle is more interesting that a square in art? Explain why.

Technology:

A Computer with a Projector“.” to show the teacher made Power Point Presentation to teach the theory and background about the Golden Mean.

Students will use the computer to discover a wide range of natural patterns to use in their compositions.

Overhead Projector“.” used to transfer the pattern of the Golden Mean to students canvas.

 

Web Resources:

Video on the golden ratio

 

 

Other Resources:
"Vitruvian Man". by Leonardo da Vinci

The Parthenon.

 

Integrated Studies:

Math, Science, and History

 

Artist Connections:

Leonardo da Vinci,. M.C. Escher,. and Piet Mondrian.

Materials:
Power Point Presentation PPT
Prints of artworks that demonstrate the Golden Mean

List of art that uses the Golden Mean

Transparencies with Golden Ratio diagrams
Chalk
Masking Tape
Paper Canvas
Acrylic Paint - pallets or pallet paper - Acrylic Gloss Medium - variety of Brushes
Drawing Boards. or mats to tape canvas paper down
Drawing Pencils. - Kneaded Rubber Erasers. - Sketchbooks.
Books and magazines with pictures of animals and nature

Assessment:
• Is the design original?
• Did the composition use the Golden Mean?
• Did the painting use a pattern found in nature to inspire the design?
• Does the design demonstrate knowledge of space as an element of design?
• Did the student use acrylic paint properly and/or creatively?
• Does the design show technical craftsmanship?
• Did the student use proper care and conservation of tools and supplies?
• Was the project completed in a timely manner?


Rubric for the Golden Mean Project

Student Name: _______________________________Section________ Date______

 

Student is able to:

Consistently Evident
(9 - 10 pts)

Evident

(8 - 9 pts)

Somewhat Evident
(7 - 8 pts)

Not Evident

(6 pts or less)

Comments

Design is original

Golden Mean used in the composition

Design inspired by a pattern from nature.

Composition demonstrates knowledge of space as an element of design.

Technical craftsmanship.

Proper care and conservation of tools and supplies.

Use of acrylics as a media.

Project completed in a timely manner

Total Points:                  Average Score:                    Percent:

 

(Points added above are only a suggestion)

 

National Standards:

 

1. Understanding and applying media, techniques, and processes

2. Using knowledge of structures and functions

3. Choosing and evaluating a range of subject matter, symbols, and ideas

6. Making connections between visual arts and other disciplines

(connections to math and science)

Students apply media, techniques, and processes with sufficient skill, confidence, and sensitivity that their intentions are carried out in their artworks

Students demonstrate the ability to form and defend judgments about the characteristics and structures to accomplish commercial, personal, communal, or other purposes of art

 

(Advanced) Students synthesize the creative and analytical principles and techniques of the visual arts and selected other arts disciplines, the humanities, or the sciences

Students conceive and create works of visual art that demonstrate an understanding of how the communication of their ideas relates to the media, techniques, and processes they use

Students evaluate the effectiveness of artworks in terms of organizational structures and functions

Students apply subjects, symbols, and ideas in their artworks and use the skills gained to solve problems in daily life

 

 

Golden Means Handout

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Golden Section - Rule of Thirds - make transparency

Golden Section

Rule of Thirds

Golden Spiral - Harmonic Triangles - make Transparency.

Golden Spiral

 

Harmonic Triangles





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