An Interdisciplinary and Lively Application Project (ILAP)
Principal Author: Richard T. Seitz
Editors
and Consultants: Marie Vanisko , Jack Oberweiser
Mathematical Subjects: Algebra and Geometry High School Mathematics (all levels)
Disciplinary Subjects: US History,
World Cultures, and Native American Studies
Concepts: Nomadic lifestyles, tipi design, and modeling
Materials Included: Introductory setting, assumptions, tepee data, and problem requirements
Materials and Computing Requirements:
Access to pictures of tepees, graphing calculator (TI-83 or comparable),
small sticks, cloth or paper and glue.
Introduction:
Imagine
yourself on the plains of Montana in 1700. You are an American Indian.
This fall you are following the American Bison. The bison is linked to
your survival. This noble beast provides warmth, shelter, food, decoration,
and tools. Late at night this hunted beast also provides you with tales
and memories of hunts to share around a campfire.
How can your people live with the uncertain challenges of a rugged climate as they follow the game across the west? One key to that survival was the tepee (also spelled teepee or tipi). This honored structure provided protection from heat and cold and allowed proud hunting bands the chance to live a lifestyle that measures time and distances in days and moons.
This ILAP investigates the tipi of the plains Indians.
You will reflect, plan, and consider designs for building tipis. Once done
you will be able to demonstrate a strong understanding of the architecture,
design, lifestyle and cultural significance of the tipi in the American
culture.
Basic Information about Tipis:
Some people prefer to
model a tipi with a right polygonal prism. That is by a hexagon, octagon
or polygon base going straight up to a point over the center. In this case
you have to utilize two different formulas.The formula for the areas of
a regular polygon (the base of the tipi) is
Requirement
0:
Make a large circle and mark a radius.Cut a line along the radius and
“roll” the circle into a cone.What happens to the surface area, volume,
slant height, radius and height as you roll the cone tighter?Contrast this
shape to the basic shape of a tipi.
Requirement 1:
Find from three to five pictures of tipis with people in the picture.
Measure the people and the tipi and come up with a reasonable scale to
compute the height of the tipi in each picture. Combine your data
with the class. Write a paragraph and create a box and whisker plot
that explains the average height of a tipi.Make sure you explain the relationship
between the height h the slant height s and the radius r or diameter d
of a tipi.
Requirement
2:
Make a scale model of a tipi. Include traditional Native American
decorations the sides of the tipi. Calculate the area of the sides
and the volume of the tipi. Calculate the floor area of the tipi.
Requirement 3:
Create a net (a net is a two dimensional cut out for a pattern that
will fold into the shape) for a right hexagonal prism. Compare and
contrast the net for the hexagonal prism with a 6-pole tipi.
Requirement 4:
Design a tipi with the most space (volume) inside. Use 21-foot
poles with slant height of 18 foot (three feet will extend beyond the sides).
Explain how you determined the best shape for the most volume. Describe
the height and the radius of the tipi with the most volume.
You are asked to set up a tipi using from 3 to 12 poles (the poles are
16 feet long) on the edge of a 10-foot circle. Make a table of values
and graph the relationship of the area of the floor of the tipi based on
the number of poles. Describe the advantages and disadvantages of
the number of poles.
Requirement 6:
Develop a scale drawing for a tipi that would hold 18 people sitting
around the edge of the tipi.Include design notes and your calculations
alongside the drawing.
Requirement
7:
Investigate the uses of tipis in today’s society.Contact a local Native
American organization and create a report or web page on customs and traditions
for your region of the country.Investigate getting a full size tipi set
up at your school.
Requirement 8:
Design an improvement to the tipi.Describe the advantages and prepare
sketches and ads to market your idea.
Afterthoughts