Arrowheads

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Arrowheads
Native American Mathematic Integrative Lesson
By Roberto Wheaton
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• GOALS OF THE SESSION
• Students who complete this lesson will be
  able to
• 1. Develop an appreciation for geometric shapes
  used in Native American arrowheads.
• 2. Identify and describe how culture and
  materials play a role in geometric shapes used in
  arrowhead designs.
• 3. Investigate the mathematical content required
  for constructing an arrowhead and arrow.
• 4. Calculate the angle and symmetry of different
  arrowheads.
• 5. Calculate the angle of a partial arrowhead to
  identify its cultural group.
• 6. Students will understand the importance of
  the straight line, symmetry and geometric shapes
  for successful arrowhead design.

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Narrative

• Looking at Native American art, buildings, and
  weapons, the influence of geometric shapes can
  greatly be seen from coastal, woodland, plains,
  plateau, southwest and south west cultures.
• Pre Contact Native Americans used bone, shells,
  stone for arrowheads and spears used to hunt game
  or against enemy tribes.
• To become a great warrior, young Native American
  men had to prove great hunting and war skills.
  These skills included physical strength,
  spiritual connection to mother earth and insight
  to nature and animals. A great warrior also had
  the ability to identify materials to make
  effective tools and weapons for effective
  hunting.
• The knowledge and understanding of symmetry,
  balance and geometric shapes was necessary for
  all Native Americans for successful hunting and
  survival.

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Warm Up
Break 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.
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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
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Historical for Activity

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

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

• Adapted from Carnegie Learning-Algebra and
  Geometry Tours
• A team of archaeologists on the
  Texas-Louisiana boarder excavated several broken
  arrowheads and wanted to decipher which tribe the
  arrows belonged to. Given the location, they know
  that they are either Choctaw or Cherokee arrows.
• History notes that the Choctaws were
  primarily an agricultural tribe, unaccustomed to
  making weapons aside from those to hunt, and
  therefore had arrowheads with wider points. The
  Cherokee, on the other hand, had many great
  warriors, and were skilled at making
  fine-pointed, fast arrows. (An angle sharper than
  20 degrees is usually Cherokee.) However, the tip
  of the arrow was broken off? Help the
  archeologists solve the mystery.
• Points A is where the missing tip would be
  located.
• ARW is given to be 78
• Angle ARW3D_____ Reason_________________________
  _
• Angle RWA3D_____ Reason________________
• Angle WAR3D_____ Reason_________________________
  _

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w
R
A
Explain how you calculated the angle of point A
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Can you find the pont and angle of the following
arrowheads?If the angle is less than 20 degrees
it is probably a Cherokee.
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Questions

• 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

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Tessellation Assignment Can you create a
tessellation using arrowhead shapes?
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Pontiac