1. A rrowheads Native American Mathematic Integrative Lesson By Roberto Wheaton

2. GOALS OF THE SESSION GOALS OF THE SESSION Students who complete this lesson will be able to: Students who complete this lesson will be able to: 1. Develop an appreciation for geometric shapes used in Native American arrowheads. 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. 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. 3. Investigate the mathematical content required for constructing an arrowhead and arrow. 4. Calculate the angle and symmetry of different arrowheads. 4. Calculate the angle and symmetry of different arrowheads. 5. Calculate the angle of a partial arrowhead to identify its cultural group. 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. 6. Students will understand the importance of the straight line, symmetry and geometric shapes for successful arrowhead design.

3. 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.

4. 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.

5. 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 BC

6. 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 1800’s 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.

7. Activity Broken Arrowhead Adapted from Carnegie Learning-Algebra and Geometry Tours 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. 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. 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 ARW=3D_____ Reason:__________________________ Angle RWA=3D_____ Reason:________________ Angle WAR=3D_____ Reason:__________________________

8. A w R Explain how you calculated the angle of point A

9. Can you find the pont and angle of the following arrowheads? If the angle is less than 20 degrees it is probably a Cherokee.

10. 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

11. Tessellation Assignment Can you create a tessellation using arrowhead shapes?

12. Pontiac