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Native American Mathematic Integrative Lesson

By Roberto Wheaton

GOALS OF THE SESSIONGOALS OF THE SESSION Students who complete this lesson will be able Students who complete this lesson will be able

to:to: 1. Develop an appreciation for geometric 1. Develop an appreciation for geometric

shapes used in Native American arrowheads.shapes used in Native American arrowheads. 2. Identify and describe how culture and 2. Identify and describe how culture and

materials play a role in geometric shapes used materials play a role in geometric shapes used in arrowhead designs.in arrowhead designs.

3. Investigate the mathematical content 3. Investigate the mathematical content required for constructing an arrowhead and required for constructing an arrowhead and arrow.arrow.

4. Calculate the angle and symmetry of 4. Calculate the angle and symmetry of different arrowheads.different arrowheads.

5. Calculate the angle of a partial arrowhead to 5. Calculate the angle of a partial arrowhead to identify its cultural group. identify its cultural group.

6. Students will understand the importance of 6. Students will understand the importance of the straight line, symmetry and geometric the straight line, symmetry and geometric shapes for successful arrowhead design.shapes for successful arrowhead design.

Narrative Narrative Looking at Native American art, buildings, and Looking at Native American art, buildings, and

weapons, the influence of geometric shapes can weapons, the influence of geometric shapes can greatly be seen from coastal, woodland, plains, greatly be seen from coastal, woodland, plains, plateau, southwest and south west cultures. plateau, southwest and south west cultures.

Pre Contact Native Americans used bone, shells, stone Pre Contact Native Americans used bone, shells, stone for arrowheads and spears used to hunt game or for arrowheads and spears used to hunt game or against enemy tribes. against enemy tribes.

To become a great warrior, young Native American men To become a great warrior, young Native American men had to prove great hunting and war skills. These skills had to prove great hunting and war skills. These skills included physical strength, spiritual connection to included physical strength, spiritual connection to mother earth and insight to nature and animals. A mother earth and insight to nature and animals. A great warrior also had the ability to identify materials great warrior also had the ability to identify materials to make effective tools and weapons for effective to make effective tools and weapons for effective hunting. hunting.

The knowledge and understanding of symmetry, The knowledge and understanding of symmetry, balance and geometric shapes was necessary for all balance and geometric shapes was necessary for all Native Americans for successful hunting and survival.Native Americans for successful hunting and survival.

Warm UpBreak into teams of two. Imagine you are living in North America 400 years ago and have no current knowledge of technology, science or history. Your major goal is to survive and that means you will need to design a tools and weapons to hunt large and small game.

Activity Triangle and Angles

Place an overhead transparency over the arrowhead worksheet.

Using a ruler and overhead pen, draw a triangle and label the points over the main shape of the arrowheads.

A

B C

Historical for ActivityHistorical for Activity Though the Cherokee were by nature a peaceful Though the Cherokee were by nature a peaceful people, they became expert weapon-makers. people, they became expert weapon-makers. Arrows crafted from heads of flint, and eagle Arrows crafted from heads of flint, and eagle feathers were secured to cane shafts and shot by feathers were secured to cane shafts and shot by bows made of sycamore and hickory.bows made of sycamore and hickory.

The Choctaw were preeminently the agriculturists of The Choctaw were preeminently the agriculturists of the southern Indians. Though brave, their wars in the southern Indians. Though brave, their wars in most instances were defensive and they spent much most instances were defensive and they spent much of their time creating an agrarian society.of their time creating an agrarian society.In the mid 1800’s both tribes were relocated to the In the mid 1800’s both tribes were relocated to the Okalahoma territory. In this forced migration, many Okalahoma territory. In this forced migration, many fell ill and died leaving artifacts scattered throughout fell ill and died leaving artifacts scattered throughout the southern part of the U.S. the southern part of the U.S. The following activity is designed to identify The following activity is designed to identify arrowheads that might belong to the Cherokee arrowheads that might belong to the Cherokee people. people.

Activity Broken ArrowheadActivity Broken Arrowhead

Adapted from Carnegie Learning-Algebra and Geometry Adapted from Carnegie Learning-Algebra and Geometry ToursTours

A team of archaeologists on the Texas-Louisiana boarder A team of archaeologists on the Texas-Louisiana boarder excavated several broken arrowheads and wanted to excavated several broken arrowheads and wanted to decipher which tribe the arrows belonged to. Given the decipher which tribe the arrows belonged to. Given the location, they know that they are either Choctaw or location, they know that they are either Choctaw or Cherokee arrows.Cherokee arrows.

History notes that the Choctaws were primarily an History notes that the Choctaws were primarily an agricultural tribe, unaccustomed to making weapons aside agricultural tribe, unaccustomed to making weapons aside from those to hunt, and therefore had arrowheads with from those to hunt, and therefore had arrowheads with wider points. The Cherokee, on the other hand, had many wider points. The Cherokee, on the other hand, had many great warriors, and were skilled at making fine-pointed, fast great warriors, and were skilled at making fine-pointed, fast arrows. (An angle sharper than 20 degrees is usually arrows. (An angle sharper than 20 degrees is usually Cherokee.) However, the tip of the arrow was broken off? Cherokee.) However, the tip of the arrow was broken off? Help the archeologists solve the mystery.Help the archeologists solve the mystery.

Points A is where the missing tip would be located. Points A is where the missing tip would be located. ARW is given to be 78ARW is given to be 78Angle ARW=3D_____ Reason:__________________________Angle ARW=3D_____ Reason:__________________________Angle RWA=3D_____ Reason:________________Angle RWA=3D_____ Reason:________________Angle WAR=3D_____ Reason:__________________________Angle WAR=3D_____ Reason:__________________________

A

wR

Explain how you calculated the angle of point A

Can you find the pont and angle Can you find the pont and angle of the following arrowheads?of the following arrowheads?

If the angle is less than 20 degrees it is probably a CherokeeIf the angle is less than 20 degrees it is probably a Cherokee..

•What math concepts did Native American need to construct an arrowhead? Arrow?

• How did intended use play a role in the arrowhead angle?

• What changes do you think occurred to arrowhead shape when metal was introduced?

•How does symmetry play a part in arrow and arrowheads?

•What other math concepts can applied to bow and arrow construction?

•Trivia: Which US auto company still uses an arrowhead as a symbol? See last slide

Questions

Tessellation Assignment

Can you create a tessellation using arrowhead shapes?

Pontiac Pontiac