Albert+Gallatin+High+School+(AGSD)

=Albert Gallatin and the Mattress Factory Activity= 1. Title: **Making A Link Between Aesthetics and Math**

2. Subject/Course: identifies the targeted subject area and/or course
 * Subject - Mathematics, Arts and Humanities
 * Course – Geometry, Physics, Visual Arts

3. Standard/Eligible Content (alignments): shows the connection between standard, anchor, anchor descriptor, and/or eligible content and the curriculum framework
 * [|2.3.G.C], [|2.3.G.E] , [|2.9.G.A] , [|2.9.G.C] , [|G.1.1.1.1] , [|G.1.1.1.2] , [|G.1.1.1.4] , [|G.2.1.2.1] , [|G.2.1.2.2] , [|G.2.1.2.3] , [|G.2.2.1.1] , [|G.2.2.1.2] , [|G.2.2.2.2] , [|G.2.2.2.5] , [|G.2.2.3.1] , [|G.2.3.1.1] , [|G.2.3.1.2] , [|G.2.3.1.3] , [|G.2.3.2.1]
 * Standards [|9.1.12.A], [|9.1.12.B] , [|9.1.12.C] , [|9.1.12.E] , [|9.1.12.H] [|9.1.12.D] , [|9.1.12.E] , [|9.1.12.J] , [|9.1.12.K] [|9.4.12.A] , [|9.4.12.B] , [|9.4.12.D]
 * Eligible Content
 * National Standards for Visual Arts: The learner will understand the visual arts in relation to history and cultures.
 * __BIG Ideas:__ __Spatial reasoning and visualization are ways to orient thinking about the physical world.;__ Similarity relationships between objects are a form of proportional relationships. Congruence describes a special similarity relationship between objects and is a form of equivalence.; The skills, techniques, elements and principles of the arts can be learned, studied, refined and practiced. The arts provide a medium to understand and exchange ideas. People use both aesthetic and critical processes to assess quality, interpret meaning, and determine value.
 * Concept(s)
 * 2- and 3- dimensional figures
 * Geometric Representations
 * Multimedia artists employ sound, image, and text together to communicate ideas.
 * The study of aesthetics includes the examination of the nature and value of art.
 * Competencies: Define, describe, and analyze 2- and 3-dimensional figures, their properties and relationships, including how a change in one measurement will affect other measurements of that figure.;Use concepts of congruence and similarity to relate and compare 2- and 3-dimensional figures, including trigonometric ratios.
 * Artists and designers use the elements of arts and principles of design in strategic ways to convey meaning.
 * [[image:IMG_8409.jpg width="402" height="315"]] || [[image:IMG_8408.jpg width="390" height="311"]] ||
 * [[image:IMG_8410.jpg width="390" height="311"]] || [[image:IMG_8411.jpg width="390" height="311"]] ||

4. Vocabulary: Similarity, congruency, angle bisector, median, altitude, complementary, supplementary, diagonals, tetrahedron, polyhedron. Visual art: installation art, elements of design (line, shape, color, form, space) principles of design (rhythm, pattern, unity, emphasis, movement, contrast, balance), origami

5. Objectives: the goal(s) of the unit; a subsequent measure of the student’s performance How can a change in one measurement of a 2- or 3-dimensional figure effect other measurements such as perimeter, area, surface area or volume of that figure? How can you explain the relationship between congruence and similarity in both 2- and 3-dimensional figures? How does multi-media art help people understand ideas? Why do people value and engage with art? How are the elements of art and principles of design used to convey meaning in graphic design?
 * Demonstrate that figures are congruent, Determine if figures are similar
 * Use properties of lines, angles, and triangles
 * Define and build upon cummulative knowledge and experience of art in order to grow in the ability to describe, interpret, evaluate, respond, and produce.
 * Demonstrate the ability to construct a 3-D figure from a 2-D surface
 * Express and build upon their cumulative knowledge and experience of art in order to grow
 * 6. Essential Question(s):

7. Duration: 2 weeks

8. Materials: square paper (variety of colors and textures), colored markers, straight edge, triangles, rulers, protractors, pencils, dowel rods, nylon cord, digital projector, white panels

9. Instructional Procedures: Students will measure angles. Students will construct three dimensional polyhedras from tetrahedras or 2-dimensional paper folds.

10. Suggested Instructional Strategies: strategies embedded within instructional procedures (this will include check boxes to select from universal principles and other strategies). optional

11.Assessment: Geometry vocabulary test and problems. Art vocabulary(Principles of Design Composition) test. //A process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students’ achievement of intended instructional outcomes *discuss pre/post test//

12. Related Materials & Resources: Amazing Origami, Geogami, art works of Alexander Calder, M.C. Escher, 12th-16th century artists (such as Leonardo DiVinci, el Greco, Masaccio), Greek and Egyptain architecture using Golden Ratio, Chinese and Japanese origami works (traditional and modern).Origami artist/mathematician Robert Lang and Industrial and medical uses of origami, e.i. air bags in automobiles.



Students in the Junior class at AG have been making connections between MATH and ART through a project brought to them by The Intermediate Unit 1 and The Mattress Factory Art Museum. Because of this project the AG students have a better understanding how Math uses Art and vice versa. This project, called "The Space I'm In" was created to identify weaknesses in math and to determine what course of action could be taken to enhance academic skills. The final work was to create an Installation--defined as a site specific, 3-D work designed to transform a viewer's perception of space--using visual, auditory, or combination.
 * STUDENTS AT ALBERT GALLATIN SENIOR HIGH MAKE CONNECTIONS BETWEEN MATH AND ART**

A view of the Parthenon and the use of the Golden Ratio to create this piece of architecture was then used as the beginning or introduction to this lesson. The Golden ratio was used also by the ancient Egyptians and both regarded it as an aesthetically pleasing ratio. However, it wasn't put into mathematical text until Pythagoras and later by Euclid in the 5th century.
 * Artists have always used math in some form, e.i. geometry or physics to create sculpture, architecture, or painting.**

The students viewed a video of the work of Alexander Caulder and discussed how he used physics to create his giant mobiles. An example of Caulder's work is part of the interior of the Pittsburgh International Airport. Then the students viewed the works of Masiccio (The Trinity), El Greco (The Burial of Count Orgaza), and Leonardo (Mona Lisa). Each work used geometry to divide the picture plane for placement of characters called Triangular Configuration for one example.

M.C. Escher, another artist that used math, created what we all know today as tesselations. Escher often consulted mathematitians before he carved his work from wood or used lithograph for each perceptually defying piece.
 * [[image:IMG_7985.JPG width="367" height="265"]] || [[image:IMG_7987.JPG width="367" height="265"]] ||
 * [[image:IMG_7978.JPG width="368" height="266"]] || [[image:IMG_7990.JPG width="368" height="266"]] ||
 * [[image:IMG_7973L.JPG width="240" height="360" align="center"]] || [[image:IMG_7976R.JPG width="240" height="360" align="center"]] ||
 * [[image:IMG_7983.JPG width="368" height="266"]] || [[image:IMG_7970.JPG width="368" height="266"]] ||
 * [[image:IMG_7980.JPG width="368" height="266"]] || [[image:IMG_7989.JPG width="368" height="266"]] ||

This lesson then brought the class to Eastern art forms e.i. ORIGAMI. The juniors were show a few simple folds,such as boxes, water balloons and cranes and as each fold took place they reflected on making these pieces in elementary school. The students never thought that at that time they were being introduced to geometry in 4th grade. After viewing a short you-tube video about the origami of Robert Lang they were enthusiastic to start creating their own pieces. The class learned that several traditional Origami folds are now part of some modern engineering. The air bag in todays automobiles, the stint used in artery repair is from the water ballon fold and the space telescopes mirrors were folded into origami in order to transport them into space. The students were given an assignment to find more engineering uses from origami. They found that cardboard boxes used by the postal service, FEDX, UPS are all origami based.

The math pre-test consisted of a matching section with 10 vocabulary terms and 9 PSSA-based multiple choice questions. The most commonly missed terms were incorporated into the tetrahedron lesson. These words included complementary, supplementary, median, and altitude. Students were given a square piece of paper. Printed on it were the lines created from an "unfolded" tetrahedron. The students calculated the measures of each angle using geometric properties. Next they answered some questions based on their angle calculations (for example, what is the complement of angle ADG). Then they used a protractor to double-check their work. Finally, they folded the lines to create the tetrahedron. media type="youtube" key="wcSB_cUZq6Y" height="349" width="560"

To entice the students the Art teacher had several polyhedrons sitting on the desk. Curiosity gave way to enthusiasm to create their own. Thus, the four pointed star from a tetrahedron (2-dimensional object) was transformed into a polyhedron (3-dimensional) was born. Each student was given several sizes of white paper from 4" x 4" to 24"x 24". The largest polyhedras were used for the installation exhibit and the smaller pieces were used to construct mobiles. The students were given a quick lesson on the Elements and Principles of Design Composition and the smaller ones were decorated, using markers, to change the surface quality. The large pieces were glued together to form larger sculptures and placed inside an 8'x8'x8'x8' square white tent. After several minutes of moving the pieces to their best spots, the class was given the assignment to create a powerpoint presentation. They were told to include vocabulary (art, geometry) and to include photographs. The students chose as photos the work of Massico, El Greco, Escher, manmade structures and such and photos from nature that resembled geometry such as honeycombs, sun flowers, and crystals. They also found several textures and colors to fill in between the reading information. A few student went beyond the assigned work and folded other forms..dodecahedrons-any polyhedron with 12 flat faces, and stellated stars-6 points, 12 points, 24 points.
 * [[image:IMG_7744L.JPG width="240" height="360" align="center"]] || [[image:IMG_7994R.JPG width="240" height="360" align="center"]] ||
 * [[image:IMG_7745.JPG width="368" height="266"]] || [[image:IMG_7721.JPG width="368" height="266"]] ||
 * [[image:IMG_7752L.JPG width="240" height="360" align="center"]] || [[image:IMG_8000R.JPG width="240" height="360" align="center"]] ||
 * [[image:IMG_7742.JPG width="367" height="265" align="center"]] || [[image:IMG_7996.JPG width="240" height="273" align="center"]] ||

Finally, the exhibit took place. The students arranged the polyhedrons inside the tent. They viewed the powerpoint making sure it was "perfect". The evening of May 11, 2011 it was show time. The installation was set up at the entrance of the high school auditorium and the district had a night of art and music. There was also a performance by the school chorus, therefore, a sizeable crowd was in attendance. A committee of students (2) were appointed to answer any questions the visitors might have had.

Please enjoy the photos, also taken by students, of the work that the AG Art and Math classes have done.
 * [[image:IMG_7995.JPG width="384" height="253"]] || [[image:IMG_8005.JPG width="384" height="253"]] ||
 * [[image:IMG_7997.JPG width="384" height="253"]] || [[image:IMG_8001.JPG width="384" height="253"]] ||
 * [[image:IMG_7737L.JPG width="240" height="360" align="center"]] || [[image:IMG_7749R.JPG width="240" height="360" align="center"]] ||
 * [[image:IMG_7728.JPG width="384" height="253"]] || [[image:IMG_8002.JPG width="384" height="253"]] ||