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Patterns in Nature

Peggy Welch


  • Interdisciplinary Project
  • Group/Cooperative Learning
    • Mentoring


  • Prime Target is biology and geometry classes


Materials Needed:

  • art supplies
  • videotapes
  • computer software
  • reference books
  • computers
  • tape recorder


Students will research patterns in nature which illustrate biological and mathematical concepts. They will design group projects which will model these concepts in a cooperative setting with fourth graders.


This math/science project was centered around patterns in nature and was funded by an Appalachian Educational Laboratory grant. The grant paid for travel between the three schools, materials for research, and the Science/Math showcase. It involved fifty sophomore students who were taking biology and geometry with the same two teachers for the last two periods of the school day. It also involved two fourth grade classes at different elementary schools. High school students researched math/science topics including fractals, Fibonaccis numbers, whale and butterfly migration patterns, whale identification, flower patterns, biorhythms, fingerprints, planetary alignment, fossils, human body proportions, bee and wasp nests and spider webs. Working in cooperative groups with fourth grade students, they designing models of these concepts. The culminating event was a Science/Math showcase where the students displayed and explained their models.

Project Time Live:


High school students designed the application and mailed a copy to all fourth grade teachers.


High school students chose two fourth grade classes, based upon the application.

High school students chose their groups and their research topics. They sent a list of these topics to the fourth grade teachers.

Fourth graders chose their groups and their research topics.


First visit between high school students and fourth graders. The purpose of this visit was to form collaborative groups and decide on their project. They made a list of the materials needed to complete the project.


Second visit between students. The purpose of this visit was to begin designing the project.


Third visit between students. The purpose of this visit was to complete the project and practice the presentations for the Science/Math showcase.


Science/Math Showcase. Students from the elementary school visited the showcase in the morning. In the afternoon, parents of the students, along with other community members viewed the projects.

Examples of Projects:


  • constructed models of the different kinds of caddisfly cases, relating their structure and components to the caddisflyUs niche.

  • displayed specimens such as pine cones and pineapples which illustrate the Fibonaccis sequence. Detailed descriptions and explanations were included.

  • constructed spider webs using tree branches and string.

  • collected data from a tape of crickets chirping at different temperatures and graphed and displayed the results. They also kept a 2-week log of evening temperatures based on the frequency of the cricketUs chirping.

  • plotted the migration routes of the monarch butterfly on a map of North America and described the routes using vectors.

  • analyzed the fingerprints of their classmates and graphed the frequencies of different patterns such as loops and whirls.

  • drew detailed drawings of monocots and dicots and also displayed dissected and preserved specimens of both flower types.

  • designed snowflakes, using black poster board and white yarn, illustrating the self-similarity of fractals.

  • constructed a 3-D honeycomb, illustrating the geometric patterns found inside a bee hive.

  • mapped the migration routes of whales, estimating miles traveled and describing patterns.

  • constructed a mobile, with each piece being a cut-out of a different whale, illustrating the fluke pattern that is used for identification.

  • constructed paper mache scale models of the planets and then hung them from the ceiling, again using scaling to illustrate their distances from the sun and from each other.

  • charted the biorhythms of their classmates using a computer program. They displayed these charts on the classroom wall, and students periodically checked them for accuracy.

  • constructed detailed drawings of bee dances. They included detailed explanations of the dance patterns.

Method of Evaluation:

High School students were assessed in two ways. The first assessment measured the research skills used to gather information on their topic. The second assessment evaluated their ability to work cooperatively with each other and with the fourth graders. Students were assessed over specific content they had learned throughout the project; and they were also asked to assess the cooperative venture between high school and elementary students.

Elementary students gave an oral presentation of their project in their classroom and also at the showcase. Each elementary teacher also used the project to generate ideas for mathematics portfolio entries. The elementary students also evaluated the cooperative venture between high school and elementary students.


Ahlgren, Andrew and Franz Halberg. Cycles of Nature: An Introduction to Biological Rhythms. National Science Teachers Assoc. Washington, DC. 1990.

Ahouse, Jeremy John. Fingerprinting (TeacherUs Guide) University of CA, Berkeley. 1987.

Biological Science: Patterns and Processes. Kendall/Hunt Publishing Co. Dubuque, IA, 1986.

Briggs, John. Fractals: The Patterns of Chaos. Simon & Schuster. New York. 1992.Z

Brooks, Bruce. Nature by Design. Farrar Straus Girous. New York. 1991.

Crump, Reva. RSnowflake Science.S The Science Teacher. J an. 1994

Garland, Trudi Hammel. Fascinating Fibonaccis: Mystery and Magic in Numbers. Dale Seymour Publications, Palo Alto, CA. 1987.

Gleick, James. Chaos: Making a New Science. Penguin Books. 1987.

Jones, M. Gail. R Biological Clocks.S The Science Teacher. Mar. 1991.

Martin, Glen. RKiller Culture.S Discover. Dec. 1991

Moore, Randy. RThe Numbers of Life.S The American Biology Teacher, Vol. 54, No.2 Feb. 1992.

Patterns in the Wild. National Wildlife Federation. Washington, DC. 1992

Peitgen, Heinz-Otto and Hartmut Jrgens. Fractals for the Classroom:

Strategic Activities Volume One. Springer-Verlag, New York. 1991.

Schattschneider, Doris and Wallace Walker. M.C. Escher Kaleidocycles. Pomegranate Artbooks, Inc. 1987.

Schmidt-Nielsen, Knut. Scaling: Why Is Animal Size So Important? Cambridge Univ. Press. Cambridge. 1991.

Sylvestre, Jean-Pierre. Dolphins & Porpoises: A Worldwide Guide.

Sterling Publish Co., Inc. New York. 1993.

Vogel, Steven. RLife in a Whirl.S Discover. Aug. 1993.

Whale Adoption Project. International Wildlife Coalition. East Falmouth, MA.

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