Perimeter, Area, Volume, and All That: A Study of Measurement

CONTENTS OF CURRICULUM UNIT 19.05.03

  1. Unit Guide
  1. Introduction
  2. Background
  3. Content
  4. Native Dwellings
  5. Perimeter and Area
  6. Perimeter 
  7. Area
  8. Surface Area
  9. Strategies
  10. Vocabulary
  11. Visuals
  12. Math Discourse
  13. Hands on Activities
  14. Teaching Activities
  15. Architecture Activity
  16. Resources
  17. Websites
  18. Appendix

Native American Geometric Community

Marnita A. Chischilly

Published September 2019

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Native Dwellings

Tipi

Most people are familiar with the symbolic structure of North American conical dwellings best known by the Sioux word “tipi” (also spelled teepee). These structures have such international fame and recognition relating to the Native American people. These dwellings are from the plains nomadic tribes who were buffalo hunters. The tipi dwellings were common among the Plains tribes when the first Europeans came into the country during the 1500s. Tipis were not too big and had meager furnishings since everything had to be packed and hauled to different places. Long heavy poles were out of the question for these nomadic people who needed to follow the buffalo herd. These transportable dwellings were made to protect the people in their daily struggle for survival in a harsh and ruthless environment. So, the tipi has more meaning to the tribe than just a home, but as a sacred place of being for family and friends to keep the relationship bond strong.

The foundation for the tipi framework was four forked poles, interlocking at the top, with an additional dozen poles with no forks placed to make a complete circle.  The cover consisted of rectangular shaped pieces of skin that were pierced at the corners so the skins could be tied or sewn together in a series, and with a slight overlapping so water would run off. The bottom series is longer than the top series of hides, which were then put together and cut to form the conical shape. Thus, when it is set up for living in, the tipi has the shape of a cone.

Pueblo

The longest enduring Native architecture in North America was built about three thousand years ago by the Native tribe that roamed the mountains and plateaus of the southwest. By the late 1190s, after primarily living on the mesa top for over 600 years, the native tribe began living in dwellings they built beneath the overhanging cliffs. The structures ranged in sizes from one-room storage units to villages of more than 150 rooms. While still farming the mesa tops, they continued to reside in these cliff dwellings, with continuous repairing, remodeling, and construction of new rooms for family. In the late 1270s, the population began migrating south into New Mexico and Arizona. From the ancient cliff dwellings evolved the kiva and above-ground dwellings called pueblos, named according to their resemblance to the houses and courtyards in Spain. Most pueblo villages housed family members and extended family relations. Families typically had several connecting rooms, which are often arranged in a line radiating out from the central plaza. Additions to a family’s section of the pueblo are generally added above or behind the original rooms. Traditionally, each pueblo also had two or more kivas or ceremonial rooms situated in the center of the complex.

The Pueblo structures were made of adobe and built like an apartment complex. Usually each floor is set back from the floor below, so it kind of looked like a stepped pyramid. This architectural form provided the roof of each level to serve as a terrace for the level above. Movement between the levels was accomplished by using wooden ladders. Most rooms above the ground floor could be entered by doorways between the adjoining rooms. However, the at the ground level, there were no doors because these rooms were used for storing grain.  They were entered through rooftop openings. This limited the access to the buildings, so movable ladders were important and also used as a defense mechanism.

Pueblo buildings feature a box base, smaller box on top, and an even smaller one on top of that, with the tallest reaching four and five stories. Therefore, this dwelling uses the rectangular prism for their architectural design, with several prisms stacked up, each one smaller than the one below it.

Hogan

The hogan is an important part of the Navajo culture as it is defined as a sacred home for the Diné (Navajo) people. In the Diné culture a majority of the families have a hogan nearby even if they live in a modern style home, so that they can continue their traditional ceremonies, and to keep themselves in balance with mother earth. Today, although there is a decrease in Diné families living in hogans, as trailers or modern houses are becoming the trend on the reservation, the hogans are still built alongside these homes.

The older form of the dwelling is round and cone-shaped, but hogans are now made of logs in a polygonal form. The traditional hogans are built with wooden poles, tree bark and mud. The doorway of a hogan faces to the east to receive blessings from father sun. Except for a circular opening in the roof to allow smoke to escape, the traditional hogans are without windows or interior divisions. By the early 21st century, the architectural design of the hogan went through a few changes due to new construction materials and techniques. Hogans are now being built with windows and sometimes built into the floor plan of a modern home. Hence, hogans are still hexagonal or octagonal in shape with an open circular floor plan, an eastward-facing door, but currently being built with notched-log construction. For the Native village activity, I will use the hexagonal shape.  The following is common knowledge amongst the older generation of the Diné people regarding the hogan.

Hooghan baah hashne’ dooleeł (I will speak about the hogan.)

East. Ha’ahaahdéé’ yah ajighááh. Ákwe’é nitsáhákees silá. (You enter from the East. Here ideas exist.)

South. Shádi’ááhjigo dashdiighááh. Ákwe’é nahat’á silá. (You head toward the South. Here planning exist.)

West. Áádóó E’e’aahjigo dashdiighááh. Ákwe’é iiná silá. (You head toward the west. Here life exist.)

North. Áádóó Nahookǫsjigo dashdiighááh. Ákwe’é sih hasin silá. (You head toward the west. Here older life exist.)

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