Lesson Title: Patterns in Nature                             Grade Level:  4-8

 

Lesson Overview/Intro/Brief Description

This lesson brings Nebraska Science, Math, and National Visual Arts Standards together. Students will develop their understanding of patterns, specifically the Fibonacci sequence, and weaving through the study of Grid 8 by Larry Schulte.

 

Art Exemplar

            Title: Grid 8

            Artist: Larry Schulte

            Media: woven painted paper

            Plate/Date: no date

 

Standards/Curriculum

Nebraska Science Standards

4/8.1.1; 4.1.2; 4.3.1; 4.4.1

           

Nebraska Math Standards

4.1.3; 4.2.1; 4.6.2

 

National Visual Art Standards

Grades 5-8:  2; 3; 5; 6

 

Objectives

1.   Students will develop their understanding of key vocabulary (the Fibonacci Sequence, pattern, weave) by analyzing reproductions of Grid 8.

2.   Students will relate the Fibonacci sequence to the disciplines of Mathematics, Science, and Art by integrating the sequence by adding the sequence correctly, interpreting the sequence in nature, and using it in a drawn design.

3.   Students will compare the Fibonacci sequence to nature by identifying the curving movement in photographs of natural objects.

4.   Students will use the Fibonacci sequence to explore content in art by modifying the sequence into a design on graph paper.

 

Assessment

Use district assessment instruments for science, math, and visual arts.

Rubric generators available at:  http://www.teach-nology.com/web_tools/rubrics/

 

Resources                         

Museum Of Nebraska Art 

Reproduction of Grid 8 by Larry Schulte

Information on Fibonacci numbers and nature :  www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

Background knowledge on Fibonacci:  www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Fibonacci.html

Art information / vocabulary:  http://www.sanford-artedventures.com/

 

Materials   

Unifix Cubes

Graph paper

Photographs of natural objects (great examples on web site)

Markers

Colored pencils

                         

Vocabulary

http://www.artlex.com/

http://www.artincanada.com/arttalk/arttermsanddefinitions.html

Fibonacci Sequence - a series of numbers in which each number (Fibonacci number) is the sum of the two            preceding numbers (e.g. 1,1,2,3,5,8, 13, etc.); named after the Italian mathematician Leonardo           Fibonacci; the sequence is found in many instances in nature

Pattern

weave

 

Teaching

1.   Background of artwork / artist:  Larry Schulte http://monet.unk.edu/mona2/contemp/schulte/schulte.html

á    Larry Schulte was born in Kearney, Nebraska in 1949 and was raised on a farm near Pleasanton. He received his BS in Math, BA in Art, and MS in Art Education all from Kearney State College and went on to get his PhD from the University of Kansas. Schulte was a former teacher and worked as Assistant to the Dean at the Parsons School of Design in New York City and has spent the past ten years as a full time studio artist in New York City.

á    His work is based on a mathematical grid derived from the Fibonacci sequence, a numerical progression in which each number is the sum of the two that precede it. Schulte's work resembles that of Mondrian and Kandinsky and he considers himself to be a visual mathematician, "My work is about mathematical structure. It is based on creating visual order. Throughout the past twenty years, I have tried to invent ways to interpret mathematical concepts visually."

á    Artist Statement:  ÒMy work has developed out of a love of nature and a love of mathematics. Its shapes, colors and forms have been derived from realistic landscape painting to a personal abstraction of nature. Additionally, I have worked within grids based on the Fibonacci sequence, which is a mathematical basis of structure found in nature. Thus, I am combining the shapes, colors and forms of nature with a mathematical underpinning of the structure of nature.Ó

á    This mathematical sequence also reflects man's intuitive view of ratios of beauty, being closely tied to the "Golden Mean" that the Greeks found to be the ratio of beauty. The result is a personal view of the beauty of nature and the structure of nature. It is another example of man choosing to view his world as structured, and thus manageable, rather than random and chaotic.

2.   Introduce students to Larry Schulte and Grid 8 (Ideally on a field trip to MoNA).

3.   Analyze Grid 8 (or reproductions in small groups), by looking specifically for what makes this piece interesting. 

4.   As students share their ideas, direct the conversation toward patterns and the concept of weaving.  Also share the concept of Fibonacci numbers with students.

5.   As a class, create an addition sentence for the first seven numbers of the Fibonacci sequence (1+1+2+3+5+8+13).  This could be taken as far a you choose with older students (1+1+2+3+5+8+13+21+34+55...).

6.   Using Unifix cubes, have students build the addition sentence that the class has created.  Next, have students carry the sequence back down (8, 5, 3, 2, 1, 1). 

 

7.   Remind students that only a section of the sequence was carried out and then back down.  Help students to see the natural curving movement that is created in nature (ramÕs horn, the way sunflower seeds radiate from the center of the a sunflower, the way flowersÕ petals radiate etc.).

8.   Have students use graph paper to shade in the Fibonacci sequence.

 

Creating

9.   Encourage students to color and create 3 different examples of the Fibonacci sequence.  Elaboration, deletion, combining, and modifying the sequence should be encouraged.  Students may also elaborate on their use of color into the patterns.

 

                       

 

 

Closure

10. Display final designs.  Students should examine the designs and identify each sequence.  Discuss the individual variations in each design.

11. Have students individually, or in pairs, create a web on what they have learned about the Fibonacci sequence.

12. Share and make a class web that assembles their collective learning.

 

Extension/Related Activities

Art

á    Students could select 1 design sequence theyÕve created to complete as a finished art piece

á    Weavings with strips with widths that follow the sequence

á    Assembled collages with pieces that follow the sequence

Math

á    Figure and write out the sequence, as an addition sentence, as far as students are willing to go                            (could be a fun contest)

á    Symmetry
Science

á    Show students photos from nature.  The web site listed in the resources has some excellent examples.  On the first couple, show and mark, the natural curve that follows the Fibonacci sequence.  On more photos, have studentsÕ mark where they see the curve.

á    Students may choose an object from nature and demonstrate it with a Fibonacci sequence          drawing.