Title: Mathematics with Native American Tepees

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

Prerequisite Skills: Understanding of basic volume formulas for cones and pyramids.

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.

Mathematics with Native American Tepees

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.

Tipis can have up to 18 poles. Traditional tipis are covered with bark, or hides. New tipis can be covered with any material. Tipis can be many different heights. One part of this activity will be to gather a range of information on common sizes. A simple mathematical model for a tipi is a cone. The Volume of a cone = (Area of the base) times (the Height) divided by 3. The Surface Area of the Curved Section of a Cone = (pi) times (radius) times (slant height squared) divided by 180.

Note that the Pythagorean Theorem allows us to find a relationship between the slant height s, the radius r, and the height h

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.

Requirement 5:

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

If you enjoyed investigating tipis, have ideas for how to use mathematics to model other projects that relate to the West, or would like to make suggestions for improving this ILAP web page, please contact the author at Rseitz@metnet.state.mt.us