Great Teaching Ideas

lesson & unit viewer

Mimbres Geometry

published on: 2/28/2003

Contributing Teacher(s): Clarice Nelson,

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

Grade Range: Middle Grades (6-8)

Materials Needed:

• Access to the Internet
• Access to word processors
• Compass, protractor, straight edged ruler
• Unlined paper for practice
• Heavy paper plat such as Chinet (do not use plastic plates or flimsy plates)
• Handouts included in this packet

Objective:

Language Arts Component:

The student will research the Mimbres culture, geography, and art forms.

The student will complete a writing assignment as described in the Background Summary handout.

Geometry Component: The students will analyze a collection of Mimbres motifs and categorize each one using the Geometry Graphics grid.

Art Component: The student will design and complete a piece of Mimbres "pottery" on a paper plate or bowl.

NOTE: This unit is designed with a language arts component, a geometry component, and an art component. Collaboration among these teaching areas is encouraged, but the unit is set up so that it can be conducted entirely in the geometry classes.

Essential Question:

Instructional Strategy: Prior Knowledge & Connections

Process Standards: Goal 1.6 discover and evaluate patterns and relationships in information, ideas and structures
Goal 3.1 identify problems and define their scope and elements

Content Standards: FA5, MA2,

G.L.E.:
Ma - GS - 3 - A - 10
(Geometric and Spatial Relationships, Apply transformations and use symerty to analyze mathematical situations, Use transformations on objects, Grade 10.)

Time Allowance: Four to six days (see Comments)

Technological Resources:

Extensions:

Integration:

Differentiation:

Assessment:

Description: Explores the design motifs on black and white pottery through research and writing, analyzing and categorizing, and creative constructions.

Comments: Part I: Four days (Two homework assignment days when students are in school and one weekend)Part II: One classroom periodPart III: One classroom period and one homework assignment dayThis timeline can be altered to a great extent depending on the collaboration among the three departments.

---

Classroom Component:

Click here to see the video clip of this lesson.

Implementation

This unit is designed as a cross curricular unit for high school students or advanced 8th graders who have some experience with basic geometry construction techniques using compass, straight edge, protractor, and ruler.

Part One requires the student to research the subject on the Internet and write a guided five-paragraph summary.

Part Two requires students to analyze and categorize typical Mimbres motifs using a grid of geometric attributes.

Part Three requires the students to practice construction techniques in class and reproduce a Mimbres "pottery" piece using a heavy paper plate and black ink.

The teacher will only briefly introduce the topic, allowing students to research more thoroughly the culture, geography, religion, architecture, art, and disappearance of the Mimbres. A handout, "Teacher Summary: The Mimbres," is provided but it would be more satisfactory for the teacher to research the subject personally. Research suggestions appear on the student's handout, "Mimbres Geometry: A Background Summary."

Part I: Language Arts Component

Time Required: Homework assignment. Allow two school days and two weekend days. Ideally, discuss and assign on Thursday, giving students opportunities Friday and Monday to use the computer lab at school if they do not have access to the Internet at home.

1. On Thursday, assign the research project for students by briefly discussing the Mimbres Indians and the pottery they created. Show only one or two examples of the work of the Mimbres. The handout, "Teacher Summary: The Mimbres" provided in the Handouts section provides a brief summary.

2. Distribute the handout, "Mimbres Geometry: Background Summary." to the students. Together, read each portion of the handout, including the grading guide. Answer questions.

Establish the time line for this activity and note due dates.
Be clear about the writing style they should use to submit the answers to the questions on the Background Summary.

NOTE: Collaborating with a language arts teacher may result in a more structured report and a different grading guide. Possibly, this assignment could earn dual credit in both areas of instruction.

ASSESSMENT: See Mimbres Geometry: Background Summary handout for scoring guide.

Part II: Geometry Component

Time Required: In class session for one class period.

On Tuesday, collect the Background Summary assignments and distribute the sheet of typical Mimbres motifs. (You can create your own. Sources are listed in the Source Material section.) You may want to solicit comments from students about the motifs.
Together, choose one of the motifs and discuss the instructions for completing the Geometry Graphics grid, categorizing the chosen motif as you go. When you are certain that the students understand what to do, allow them to work in small groups, but each person should complete his own grid.
At the end of class, briefly solicit comments on the categories. Discuss any items they chose to fit in the "Other" category. Remind students that they will need these sheets tomorrow as well as their protractor, compass, and straight edge.

ASSESSMENT: See Constructed Response form.

Part III: Art Component

Time Required: Second in-class session for one period.

1. In order for students to design their own plate with a Mimbres motif, students will need to practice several construction techniques on plain unlined paper. Use a typical high school geometry book that contains well-illustrated construction techniques.
   Students will need to have command of the following skills:
   Compass
   construct a circle
   construct concentric circles or arcs
   mark six points on a circle
   construct parallel arcs

   Compass and Straight Edge
   bisect a line
   create a perpendicular at a given point
   find the center of a given circle

   Protractor
   measure a given angle
   construct an angle of given size
   Ruler
   measure accurately

2. Students will select a motif and reproduce it on a paper plate, mimicking the technique of the Mimbres as they designed motifs on pottery. Encourage them to use very faint lines and to leave the construction lines in place until you have seen the finished product.
   The actual coloring of the design should be done with very fine black felt tipped pens or black roller ball pens. Whatever implement the students chooses, they should use that implement exclusively because all black ink is not the same color and varying the color will detract from the finished product.

NOTE: Collaborating with an art teacher could result in the students branching out into other media. (See EXTENSIONS for an on-line lesson plan, Mimbres Geometry.)

ASSESSMENT: See Rubric for Mimbres Construction, Part 3.

Suggestions for Extensions

1. Use the Mimbres Pottery unit available from the website www.dhc.net/~artgeek/mimbres (Site written and maintained by Lauren H. Killam).
2. Analyze other motifs typical of other cultures such as molas from South American cultures.
Examine some other aspect of Native American culture for mathematical applicants such as housing structures. For example, tipis are actually examples of conic sections. Hogans are variations on cylinders. Igloos are hemispheres with a variety of sizes and cylindrical connections. Typical arrangements of igloo communities illustrate a form of efficient packing patterns.

Resource Materials

Books

America's Fascinating Indian Heritage. James A. Maxwell, Ed. Readers' Digest Assn, Inc. 1978 ISBN 0-89577-019-9

Giammattei, Victor M. and Nanci Greer Reichart. Art of a Vanished Race: The Mimbres Black-on-White. Dillon-Tyler, Publishers 1975. ISBN 0-916280-00-4

Wesche, Alice. Wild Brothers of the Indians. Treasure Chest Publishers, Inc. Tucson, As. 1977 ISBN 0-918080-21-5

CLIP ART

North American Indian Motifs CD-ROM and Book. Dover Publications Inc. 1996 ISBN 0-486-99945-9

---

Graphic Organizer for Part II

Name:_____________________________________ Due Date:_________________

Instructions: For each motif, check all the geometric terms or procedures necessary to recreate the design.

	1.	2.	3.	4.	5.	6.	7.
1. Point
2. Line
3. Arc
4. Triangle
5. Rectangle
6. Rhombus
7. Parallelogram
8. "n"-sided figure
9. Ellipse
10. Circle
11. Perpendicular lines
12. Concentric circles
13. Parallel lines
14. Measured angle
15. Translational symmetry
16. Reflective symmetry
17. Rotational symmetry
18. Repetition of elements
19. Free form
20. Other
a. __________
b. __________
c. __________

---

Summary handout for Part I

Name:______________________________________ Due Date:___________________

1. RESEARCH
   Using the Internet, research the group of Native Americans known as the Mimbres, a subgroup of the Mogollen Tribes of the southwestern United States.
   KEY WORDS:

   Native American History - Mimbres
   Mimbres Indians
   Mimbres Pottery
   Mogollen - Mimbres

   PRINT three to five of the sites you visit. Be sure you include all the documentation for the website, the author, or the group responsible. I want to be able to retrace your exact route to find the same information.

2. WRITING
   Using the printed research, you will summarize what you have found in your own words when answering the following questions.
   1. Who were the Mimbres Indians?
   2. What living conditions did the Mimbres experience?
   3. What influence the Mimbres' choice of pottery designs?
   4. What significance did the pottery and designs hold for the Mimbres?
   5. What happened to the Mimbres?
   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:
      TITLE (centered)
      (Your name)
      (Due date of summary)
      Skip two lines
      (Paragraph One: Rephrase question one to lead into your first paragraph.) Skip one line
      (Paragraph Two: Rephrase question two to lead into your second paragraph.) Skip one line
      Continue in this format until you have answered all five questions.
      REMEMBER that each paragraph must consist of three to five complete sentences. Check the grading guide at the end of this handout for more information.

   2. On a separate sheet of paper you will list the complete documentation for each of the research pieces you printed. Use this format:
      SOURCES (centered)
      Skip two lines
      1. List the complete website, author, or group.
         Skip one line

      2. (Continue numbering and listing all of your sources.
         Skip one line

   3. Staple your work in this order to hand in:
      Top Sheet: Your written paragraphs
      Second Sheet: Your written Sources page
      Bottom Sheet: All of your printed research in the same order that you listed them on the Sources page

   4. Grading criteria
      1. Three to five printed sources with complete 10 points documentation by first due date
      2. Written answers to questions
         1. Format was followed correctly 5 points
         2. Each answer contains three to five sentences 5 points
         3. Answers are in students own words 5 points
         4. Grammar, spelling, punctuation are correct 5 points
         5. Sentences exhibit a variety of constructions 5 points
      3. Source sheet
         Format was followed correctly 5 points
         TOTAL 40 POINTS

---

---

NOTE: The teacher is encouraged to conduct an Internet search using the key works listed at the beginning of the lesson for a more extensive knowledge base. However, avoid presenting too much information so that the students can investigate the subject on their own.

Around 1000 AD and continuing for about 300 years, a small group of people inhabited the Gila and Mimbres river valleys in southeastern Arizona and southwestern New Mexico. They were descendants of the Mogollon people, but they left no written record of their short span in history. They disappeared from the river valleys by 1300 AD, leaving no real clues about the reason for their disappearance.

What the Mimbres did leave behind was unique black and white pottery decorated in a very distinctive manner with stylaized animal, plant, human, and abstract designs.

The geometric forms were so unique and attractive that the patterns captured the imagination of those who discovered the pieces many years later. Each design uses geometric principles to create a unique piece of art that tells a story about the life of the Mimbres

In addition to the geometric aspect of the designs, the use of positive and negative space on the pottery identified the Mimbres as true artists. They were also skilled creating a feeling of three-dimensional movement on a basically two-dimensional surface.

---

Item

After researching the culture and pottery of the Mimbres Indians and analyzing the geometric designs used on the pottery, you must develop a design for dinnerware for your family. However, the subject matter of your design must be derived from physical objects that represent important influences in the lives of your family. Carefully sketch a design placed in a circle. Then explain in detail the reasons you selected the motif. Identify the construction techniques that you would need to use to actually construct the design accurately.

EXAMPLES OF CORRECT RESPONSES:

Students may choose any motif(s) as long as they can defend with several reasons the cultural significance of the motif to his family.

Construction techniques should be from those discussed in part three. Each technique should be obviously appropriate to the portion of the design described.

SCORING GUIDE

10 points	Design is very neat and balanced; represents two or more aspects of student's culture and each aspect is explained clearly; three construction techniques are employed and identified correctly.
8 points	Design is neat and balanced; two items in the culture are explained; two constructions are employed and identified correctly.
6 points	Design lacks balance and is executed poorly; two items of significance are identified and explained in some way; two construction techniques are employed and identified.
0 points	The design lacks neatness. Significance is poorly identified and explained. Construction techniques are not apparent or identified.

---

  Grade of A Grade of B Grade of C

Incorporates all portions of the plate/bowl in the design	All	All but one	All but two
Construction lines are visible but very faint.	All	Almost	Several not visible
Construction techniques are correctly executed	All	All but one	All but two
All aspects of the design are constructed	All	All but one	All but two
Incorporated three different construction techniques	Yes	Yes	Two techniques

---

Teacher Notes

For teachers who would like to use all three parts of this unit but who may not feel qualified to handle all parts, I suggest pairing with a teacher from another subject area. Generally, Part I is a typical assignment in a sophomore English class. Cooperative teaching could be arranged with the English department, and dual credit could be earned for the same project.

It is difficult for me to find time to complete this unit all in consecutive days as it is described here. I frequently split the parts up so that we do three or four problem sets from the textbook between portions of the unit.

Modifications for Special Needs Students

Enrichment or gifted: Use an activity such as the Mimbres Pottery activity found at this website: www.dhc.net/~artgeek/mimbres.html (Site written and maintained by Lauren H. Killam.) A print-out of this web site is included in my packet of course work.

Basically, students would work with the art department in actually creating coiled pottery and decorating the work with Mimbres designs using the background research and activities from this Mimbres Geometry unit.

At-risk or slow learner: The Mimbres Pottery activity can also be adapted for the at-risk or slow learner by substituting this activity for the Part III portion of the Mimbres Geometry unit. Some students will not be able to master the construction techniques well enough to perform well on Part III, but they may be able to work with a more forgiving material like clay. Also, the at-risk students will have more than one class period and more than one instructor to work with on the project.

IEP students: The IEP students will have a study skills hour to use to come back into my classroom to work on whatever portion gives them trouble. They also have another teacher as a resource for the research and writing portion. Depending on their program, they may be able to make a sound recording reporting what they have researched rather than writing a report.

ESL students: Since out town has a large Hispanic population generally from Mexico and Central American countries, it is easy to modify this project to use cultural motifs from their native lands. Many of them travel back to their homeland during the year, and they can bring materials to substitute for the Mimbres motifs. This will give them an opportunity to speak to the group to explain what they are using, and it will give the non-Hispanic students an opportunity to learn culture and language from another country.

---

Student Samples

---

What do you think of this lesson? SuccessLink needs to know. Click here to tell us.