GRADE FIVE: the required elements

Theory: With the gradual evolution from village gardening under the guidance of women to city-state agriculture--with its male-driven oxen and plows and state-controlled systems of irrigation--there occurred a coevolution from oral traditions and custom-based forms of matristic authority to new political systems of power in which literate priests and organized warriors restructured society in a formation scholars term "civilization." This transformation of culture involved a shift from shamanism to organized religion, as well as a shift from the generative values of procreation and numeration-- embodied in the icon of the Great Goddess and the prehistoric Arithmetic Mentality--to a new and more abstract Geometrical Mentality embodied in writing, temple architecture and astronomy--all three of which were articulated in the new system of male power and written laws controlled by high priests and military leaders.

Practice: The study of geometry, irrigation systems, architecture, the simple physics of civil engineering, and the origins of literature in mythology and folklore.

Integrated Studies Project: Inannas Descent into the Netherworld.

Math Units:

• Topics:
  • Euclid, Books I & II, constructions only
  • Topics from the history of math in Egypt, Mesopotamia, India, China, and Megalithic Western Europe
  • Pythagorean triangles and triples
• Activities:
  • Graphical solutions for problems
  • Chinese proof of the Pythagorean theorem
• Suggested Integrated Projects (one required):
  • Stonehenge and carved balls of Scotland
  • The Golden Ratio in the art and architecture of ancient Egypt
  • The monochord and the scales of Sumer with musical arithmetic
  • The rope-stretchers of Egypt and the orientation of temples
  • The squareness of the pyramids
  • The relations of Phi and Pi
  • Musical arithmetic of the Rig Veda
  • Binary arithmetic of the I Ching