Unit 3 Cross Curricular - Internet Project

Hidden Treasure

Introduction | Task | Process | Guidance | Conclusion | Questions

Introduction
Are you intrigued by the idea of hidden treasure? Did you know that a trove of silver could be hidden near San Antonio? A colorful historic figure was Jim Bowie, most commonly known for his Bowie knife. Legend has it that in the 1700s he mined silver and gold in Texas and then buried his treasure in some still unknown location. In 1836, Jim Bowie was killed at the battle of the Alamo, taking with him the secret location of his silver. Since then, many people have tried unsuccessfully to find the treasure. The table below shows how the value of silver, based on the value of the U.S. dollar, has changed over the years.

     In this project, you will use quadrilaterals, circles, and geometric transformations to give clues for a treasure hunt.

The Task
You work for a national company that plans to market treasure hunts to radio stations, television stations, and other organizations in various cities. Your company will profit by selling these hunts to the organizations. You need to present a sample treasure hunt to your boss. You may select any city in the U.S., or the world, if you prefer. After your hunt has been designed, you need to prepare a portfolio including the map to be used, clues, questions, and answers. If you prefer, you can prepare a Web page with this information that others can view. Then customers for this product could view a sample treasure hunt. Be sure that your portfolio or Web page contains the following information:

• the name of the city to be used for the treasure hunt and a map that participants will use;
• at least five clues that will help treasure hunters find the location. One of the clues must be based upon a quadrilateral, one must involve a transformation, and one must include a circle. (See the Questions for sample clues.);
• at least five questions that the participants must answer correctly in addition to finding the location of the treasure. The questions must relate to geometry. (See the Questions for sample geometry questions.).

• Select a city and find a map for the city. For help, try these Web sites.
  www.yahoo.com and search for the city you want to use
  www.embassyworld.com/maps
  www.maps.com
  www.expedia.com/pub/agent.dll?qscr=mmfn
• Write at least five clues that will lead hunters to the location of the hidden treasure. See the Questions for examples of clues.
• Write at least five questions that require a knowledge of geometry to answer. See the Questions for examples of geometry questions.
• Be creative. Add some additional data, information, or even pictures to your portfolio or Web page.

1. Use geometric figures other than quadrilaterals or circles for your clues.
2. Design a treasure hunt for a U.S. state, a several-state region, or for an entire country or continent.
3. Include the names of tourist attractions in your clues.
4. Trade your project with one of your classmates. Have your classmate try to locate the treasure using your clues and answer your questions. Have your classmate critique your clues and questions.
5. Make a brochure of your map, clues, and questions. Add the names and locations of tourist attractions to your brochure.
6. Make a treasure hunt for your own city or state.
7. Write a different set of clues that will lead to the same location for the treasure.

• Present your project to your class or at a family night. At the family night, give parents and students maps of the city you have chosen. Have them work together to find the location of your hidden treasure.
• Present the information on a Web page. Have other students critique your project and help you to make improvements to your project.
• Write a one-page summary of your project, including what you have learned from creating the clues for the treasure hunt.

Lesson 7–2
Maryn is creating a treasure hunt for San Antonio. Print a copy of the map of San Antonio at www.sanantoniocvb.com/visitors/com_samaps.asp. Select “maps,” select the PDF form of “Downtown Street Map,” and print it. (You may want to make several photocopies of the map to use for the exercises in this project.) Follow the directions that Maryn gives as clues for her treasure hunt. Answer any questions and keep your work for this exercise to use in the project exercises in Chapters 8 and 9.

1. Clue:
   Connect the following four locations with line segments. Try to locate the four points at approximately the center of each intersection.
   Point A: the intersection of Quincy Street and Lexington
   Point B: the intersection of Quincy Street and Baltimore
   Point C: the intersection of Brooklyn and Dallas
   Point D: the intersection of Richmond and Dallas
2. Question:
   Classify the quadrilateral in Exercise 1. Justify your reasoning using features on the map.
3. Question:
   How does the distance along the portion of the street located between Quincy and Dallas inside the quadrilateral compare to the lengths of the sides of the quadrilateral lying on Quincy and Dallas?

Lesson 8–4
Refer to quadrilateral ABCD in Lesson 7-2. Maryn gives the following directions for her next clue to the location of the hidden treasure. Follow the directions on your map of San Antonio. Answer the questions and keep your work for this exercise to use in the project exercise in Chapter 9.

1. Clue:
   Use quadrilateral ABCD. Reflect quadrilateral ABCD over the line represented by N St. Mary’s street. Label the new quadrilateral A´B´C´D´.
2. Question:
   E is a point on . Where will E´ be on quadrilateral A´B´C´D´? Explain.
3. Question:
   How will the angle and side measures of quadrilateral ABCD compare to the angle and side measures of quadrilateral A´B´C´D´? Explain.

Lesson 9–1
Refer to quadrilateral ABCD and its reflection quadrilateral A´B´C´D´ in Lesson 8-4. Maryn gives the next clue to the location of the treasure. Follow the directions on your map of San Antonio and answer any questions about the locations.

1. Clue:
   Label Point F as the center of the star marking the location of the Alamo. With radius FB', draw a circle with center F. Mark the point where the circle intersects S Alamo as T.
2. Location of the Treasure:
   The treasure is located near T. Describe the location of the treasure in relationship to other locations on the map of San Antonio.

Hidden Treasure

TEACHER NOTES

In this project, students will use the Internet to research the history of a geometry topic. They need to find two people who contributed knowledge to this topic and write a summary of this contribution. They also need to find a problem proposed or solved by one of these people relating to the topic they are studying.

The Guidance section of the Cross Curricular Project contains questions that would be good for extending the project. If you prefer, have each student research one of the questions and add the information they find to the final presentation of their project.

Several Web sites are included in to help students in completing the project. Encourage students to find additional sites and to share those sites with other students.

Students will work on this project in Unit 3.

Lesson	7–2	8–4	9–1
Page	393	459	499

ANSWERS
Lesson 7–2

1. See students maps
2. The figure appears to be a trapezoid. One pair of sides is parallel because Quincy Street and Dallas should be parallel streets. The trapezoid is not isosceles because the other two sides are not equal in length.
3. The distance on that street is one-half the sum of the measures of the distances on Quincy and Dallas.

Lesson 8–4

1. See students’ maps
2. It will be on between A' and B' since reflections preserve betweenness of points.
3. They will be the same since reflections preserve angle and distance measures.

Lesson 9–1

1. See students’ maps.
2. Sample answer: The location of the treasure appears to be near the west end of the Convention Center in Hemis Fair Park.