SuccessLink Missouri Department of Elementary & Secondary Education Friday, September 3, 2010

Great Teaching Ideas

lesson & unit viewer

Tipi Math

published on: 2/11/2005

Contributing Teacher(s): Clarice Nelson

Subject Area: Math/Geometric/spatial--Geometry, Fine Arts/Performing Arts/Art

Grade Range: High School (9-12)

Materials Needed:

Internet

Library resources

Word processor (optional)

Compass

Protractor

Ruler

Graph paper

Unlined paper

Dowel rods or straight saplings

Butcher paper

Research for dimensions and construction of a tipi.

Completed model of a tipi

Paint

Brushes

Pencils & pens

Markers

Research for authentic designs

Objective:

Research Project:

Students will investigate the Plains Indians and their use of the tipi.

Students will produce a written report from the research.

Math Project:

Students will draw to scale a two-dimensional plan of a tipi and all its parts.

Students will construct a three-dimensional model of a tipi.

Art Project:

Students will research typical designs used by the Plains Indians to decorate their tipis.

Students will decorate their two-dimensional scale drawing or their three-dimensional model with typical designs used by the Plains Indians.

Instructional Strategy: Evaluating Student Understanding

Process Standards:

Goal 1.8 organize data, information and ideas into useful forms (including charts, graphs, outlines)
Goal 2.5 perform or produce works in the fine and practical arts

Content Standards:

Mathematics 2. Geometric and spatial sense involving measurement (including length, area, volume), trigonometry, ...
Fine Arts 4. Interrelationships of visual and performing arts and the relationships of the arts to other disciplines

G.L.E.:
- Ma - GS - 4 - B - 09
  (Geometric and Spatial Relationships, Use visulization, spatial reasoning and geometric modeling to solve problems, Draw and use visual models, Grade 9.)
Time Allowance: 10-12 Days based on 50-minute daily class periods.

Description: Through an integrated curriculum, students will research, design, build, and decorate accurately a scale model of a Plains Indian tipi.

Comments:
- RESEARCH: Discuss project on Thursday, allow Friday for computer lab/library research. Use Monday for a check-up and question day. Tuesday completed report is due. Presentations can follow if desired.
- MATH: Discuss project on Monday. Give Tuesday to work in class. Project due on Thursday.
- ART: Introduce ways to make a scale model on Friday. Require students to gather materials over the weekend and bring them to class on Monday. Allow 1 or 2 days to work in class.
Classroom Component:
Pre-Test and Post-Test for Tipi Math

Name:_______________________________________
1. Name three Plains Indians tribes and describe the cultural differences between those tribes.
  
  A.
  
  B.
  
  C.
2. Use a scale of 1 inch - 2.5 feet to convert all measurements on the sketch of a bookcase to actual dimensions in feet. (use sketch on next page). Clearly show work for each conversion.
3. How tall will the tipi be if the diameter of the floor of the tipi is 21 feet? (Use the value 22/7 for pi.) How long will the poles be if they extend seven feet beyond the top of the tipi? Show and clearly label all of your calculations.
Pre-Test and Post-Test Answers for Tipi Math
1. (Refer to your research. A wide variety of answers are possible.)
2. (Typical calculations and organization.)
Implementation

RESEARCH PROJECT

Give the students the RESEARCH QUESTIONS HANDOUT (1) and the NATIVE AMERICAN TIPI BACKGROUND SUMMARY HANDOUT (2) for the research project. Introduce the subject in class and discuss what quality of research you are looking for.

If you simply want the students to find information, completing the questions asked on the RESEARCH QUESTIONS HANDOUT could be the extent of the research portion.

If you wish to work with the English Department and have the students write a formal report for dual credit, you will need to set up a scoring guide in conjunction with the English Department.

If you wish to handle the formal report in math class, the scoring guide for the report is given in the Native American Tipi Background Summary Handout.

After presenting the project in class, be sure the students know how to start the research.

An excellent book for background research is The Mystic Warriors of the Plains by Thomas E. Mails. (Barnes and Noble, Inc., 1972. ISBN 1-56619-657-4.0)

MATH PROJECT

After the students complete the RESEARCH QUESTIONS HANDOUT or after students present their reports, use the information in class to discuss the designing and building of a tipi. As a teacher, you need to research the same information as the students, but the TEACHER INFORMATION SHEET HANDOUT (3) will give you a quick idea of some basic facts.

Be certain the students are familiar with the following math concepts and techniques or be willing to teach the skills:
- Drawing models to scale.
- Using compass, straightedge, protractor, and ruler.
- Finding area and circumference.
- Surface area of a cone.
- Difference between height and the slant height of the cone.
- Properties of circles (circumference, radius, diameter, concentric)
Depending on your time and the interest of the students, you can take this information to several degrees.
1. On graph paper, design a scale drawing of a tipi, both the two-dimensional cover and liner, and the three-dimensional drawing of a tipi.
2. Build an actual table model using the design from number one.
3. Build a full scale tipi for use in a particular project. (Summer school display, project in conjunction with a scout troop, school project to celebrate the Commemoration of the Corps of Discovery: Lewis and Clark.)
Refer to the student's TIPI DESIGN INSTRUCTION SHEET (4) that will help the students with their scale model drawing.
The following web sites give information on actual construction of tipis.

http://www.seawell.net/ybms/ "Young Blood's and Morning Star's Home of Information" —Click on "Blackfoot Crafts" and then click NEXT at the bottom until you come to "How to Make a Tipi (Lodge)." (Clear, simple information and instructions.)

http://collections.ic.gc.ca/notukeu/tipi_e.htm "Tipi Construction" (Good photographs of steps in erecting a tipi.)

ART PROJECT

Make a separate project of researching the designs Native Americans used on their tipis. These projects could be assigned on the basis of the particular tribes involved and the significance of symbols and designs they use.

Some excellent sources for designs include the following:
1. North American Indian Motifs CD-ROM and Book, Dover Publication Electronic Clip Art (ISBN 0-486-99945-9) Contains almost 400 copyright-free designs.
2. American Indian Design and Decoration by Leroy H. Appleton, Dover Publications, ISBN 0-486-22704-9 Contains stories and myths of American Indians and over 700 designs typical of each tribe.
GRAPHIC ORGANIZER FOR TIPI COVER DECORATION

Using a large bulletin board or a wall where signs and materials can be taped, mark off the available area in a grid with headings similar to those listed below. Leave enough space for actual sketches or photocopies of these designs. Ask the students to pin or tape the symbols up in the appropriate category as they bring them in. Spend a few minutes each day discussing the new additions. Decide if they have been classified correctly.
GRAPHIC ORGANIZER HEADINGS

TRIBE

Animal

Plant

War

Deities

Natural Forces

Depending on the research the students develop, other categories may be needed in order to include all the research.

After the students have a collection of typical designs, discuss how to apply these items geometrically to a hemispheric plane.

This may involve designing on polar graph paper, or students can make their own rough polar graph by inscribing concentric circles on the scale model of their tipi cover. They will also need to lightly pencil in radii at even intervals using a protractor. With these guidelines, students can do a good job designing (on a hemispheric plane) objects which will be seen on a three-dimensional cone when erected as a tipi cover.

EXTENSIONS
1. Cooperate with the art department researching the materials used by Native Americans to paint the designs on the tipi covers.
2. Involve the local Historical Society by having them help locate authentic materials in the area to use in building the tipis.
3. Research other Native American habitations and create a similar research-math-art project that uses those architectural forms. (Igloo, long house, hogan, cliff dwelling, wikiup) www.pbm.com/~lindahl/articles/yurt/
4. Extend this project to trigonometry and conic sections. Investigate the details of tipi building such as the fact that tipis were set up with a much steeper slant to the windward side for stability. (This means the floor area was actually an ellipse, and interesting calculations can be developed based on the conic section of an ellipse.)
  The following web sites give brief, concise descriptions of the trigonometry involved in conic sections:
  www.math2.org/math/algebra/conics.htm
  http://mathworld.wolfram.com/ConicSection.html
5. Some groups used a basis of three initial poles to set the framework for the tipi poles instead of four poles. How would this fact change the calculations for the initial poles? (Equilateral triangle? Isosceles triangle? Circular base? Elliptical base?)
6. Involve the Family Arts department by researching and cooking Native American foods. One excellent book is American Indian Food and Lore by Carolyn Niethammer. (Collier Books, 1974. ISBN 0-02-010000-0)
Student and Teacher Handouts

Research Questions Handout (1)

These questions are meant to guide your research. The answers are not simple one-word answers. Some questions may require paragraphs, measurements, calculations, or sketches. Be sure you supply complete information for each question on notebook paper. Number your answers to match the number of the question.
1. Which Native American tribes used tipis?
2. For what purposes did they use tipis?
3. Where were these tribes located?
4. What materials did they use for tipis?
5. How and where did they obtain these materials?
6. What quantities of each material did they need?
7. Describe the parts of a tipi.
8. Describe the typical dimensions of a tipi.
9. How were the tipis transported from one place to another.
10. Who was responsible for the building, assembly, and care of the tipi?
11. How was it possible to have a fire in a tipi without burning it down?
NATIVE AMERICAN TIPIS
Background Summary Handout (2)

RESEARCH
Using the Internet, research the group of Native Americans known as the Plains Indians.

KEY WORDS:
- Native American History
- Plains Indians
- Tipi or Teepee
- Native American Shelters
PRINT three to five of the sites you visit. Be sure you include all the documentation for the web site, the author, or the group responsible. I want to be able to retrace your exact route to find the same information.
WRITING
Using the printed research, you will summarize what you have found in your own words when answering the questions on the Research Questions Handout. To begin your report, you need to write three to five topic sentences from the information you have gathered. Each sentence should be about a separate aspect of the Plains Indians and Tipis.

For each topic sentence, you will write three to five sentences explaining the details about that topic.

For example, one topic sentence might be "The term 'Plains Indians' referred to several tribes who occupied the portion of the United States known as the Great Plains." Then you would use several sentences explaining such things as what states the Great Plains covers, which particular tribes lived in that area, and characteristics typical of those tribes.

GUIDELINES FOR WRITING
1. Use a word processor if you can. Otherwise, neatly write your summary. Remember that the body of a report is double-spaced. Use this format for the summary:
2. On a separate sheet of paper you will list the complete documentation for each of the research pieces you printed. Use this format:
3. Staple your work in this order to hand in:
Grading criteria
1. Three to five printed sources with complete documentation by first due date 10 points
2. Written report (Topic sentences and supporting sentences)
  1. Format was followed correctly 5 points
  2. Each paragraph contains three to five sentences 5 points
  3. Information is in student's own words 5 points
  4. Grammar, spelling, punctuation are correct 5 points
  5. Sentences exhibit a variety of constructions 5 points
3. Source sheet
  1. Format was followed correctly 5 points TOTAL 40 POINTS
Teacher Information Sheet Handout (3)

Sources:
- The Indian How Book by Arthur C. Parker
  The Indian Tipi: Its History, Construction, and Use by Reginald and Gladys Laubin
Originally, tipis of the Plains Indians were semicircular covers with particular extensions made of 12 to 20 tanned buffalo hides sewn together. Later, canvas was used for the covers. They were supported by 16 to 24 straight, trimmed pine, cedar, or spruce saplings about 25 feet tall. 8 to 16 pins were needed to pin the cover together and 40 to 50 pegs needed to anchor it to the ground. Erecting a tipi required a working knowledge of geometry. Poles were placed by twos in a parallel position and originally crossed within a foot of the top at nearly right angles. (Later, as horses were available to carry longer, heavier poles, the intersection allowed much longer extensions of poles at the intersection. The longer the "topknot," the wealthier the owner.) This intersection was tied securely with a rawhide thong and about 15 feet of length allowed to hang down to be used as an interior anchor for the tipi during storms. These four poles were then set up in a square, forming a quadrangle that supported the other poles and located the circumference of a circle matching the bottom size of the tent. The tipi was finished on the interior by hanging a soft leather liner halfway up the poles to form an inner wall. The tipi door, an oval opening, was located 12 to 18 inches from the ground and was 3 to 4 feet high. A movable leather shield covered the opening.
One interesting web site discussed the Pole Values specific First Nations hold. This web site bears more investigation before the information is taken as truth.
PLAINS INDIAN TRIBES

According to Thomas E. Mails in The Mystic Warriors of the Plains, those tribes generally termed "Plains Indians" include the following:

Blackfoot, Cree, Assiniboine, Hidatsa, Ojibwa, Mandan, Crow, Cheyenne, Sioux, Arikara, Ponca, Omaha, Pawnee, Arapaho, Kansa, Osage, Kiowa, Comanche, Wichita

Tipi Design Instruction Sheet Handout (4)

Your job is to construct a scale model drawing of a tipi. This drawing should contain all the information necessary for another person to actually build a tipi from your instructions.
1. You should have answers to the following questions before beginning your design.
2. Design a tipi cover on graph paper.
Plains Indians Designs Handout (5)

Teacher Reflections

I have taught all portions of Tipi Math for many years. I have never been able to teach all three components consecutively to the very same students. However, I have taught portions of all three components in a self-contained seventh and eighth grade classroom and to ninth and tenth graders in a large high school. Some of those high school students were in both my geometry classes and in my English classes.
The research component is effective in guiding students with average writing skills through a basic research project. It is important for the students to realize normal rules of English grammar, sentence structure, paragraph assembly, and spelling and punctuation will be enforced no matter what academic areas present the unit.
Even when the only research presentation required is simply answering the questions posed, the teacher should require that all answers be given in acceptable paragraph form.

I have enjoyed the math portion of the unit most since it is an opportunity to teach scale, geometric construction techniques, and sketching. However, the students must have some skill with manipulating a compass and straight edge or they will become frustrated. It is well worth the time to practice some simple construction skills before introducing the project.

Constructing the scale drawing of the tipi and its parts will be much easier if it is done on graph paper, quad ruled. Even with graph paper, the teacher must be sure students are familiar with the idea of graphing. Using polar graph paper is very effective in the art portion of the unit if the students are at ease with polar graphing.
I found that constructing a model is least frustrating when the determining factor, the size of the paper, is located first. Then the poles and other portions can be scaled in keeping with the paper for the tipi cover. Having a large, smooth surface to work with facilitates the transfer of the scale drawing to the model.

Time spent on the project can easily expand and become unmanageable. To avoid that problem, I found that it was best to clearly announce the portions of the project to be done in class and adhere to the time allocated. Those portions to be done outside of class should be clearly delineated, and deadlines should be kept.

The subject of Native American habitations has always appealed to me since childhood. As children on a farm, we were encouraged by our parents and grandparents to build tipis, wigwams, long houses, and other types of shelters in the wooded areas on the farm. They supported our interest in outdoor experiments and encouraged us to explore many aspects of Native American culture.

Therefore, it seemed natural to me that students would best remember the principles of subjects like geometry if they had hands-on experience designing and building something like a tipi. The opportunity to investigate the culture and history and culminate with a creative art project seems a logical teaching opportunity.

Students who participate fully in such a unit gain in several ways. Analytic skills are strengthened when students collect, organize, and reinterpret information as they prepare reports. Practical and theoretical math skills must be developed and used in order to design plans for tipis and the accompanying items. A combination of cultural, aesthetic, and artistic sensibilities must come into play as students decorate the tipis authentically.

It is true that implementing even one portion of this project takes time and effort to prepare, and others may feel that the classroom time used should be spent on other things. Sometimes students want to attempt projects that simply are too expensive or are beyond their skill level. Sometimes there simply isn't room to work on such a project.

Those considerations in various forms have, in part, prevented me from ever completing this entire unit at one time with one specific class of students. But the beauty of the project is that the parts may be separated to some extent, or some parts may be de-emphasized and others emphasized.

Even if only one portion of the unit is all that a teacher ever uses, I feel the rewards will justify the time and effort spent.

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For additional information contact :
Clarice Nelson
California High
Moniteau Co. R-I
(573) 796-4911
EMAIL: CNDNelson@socket.net