Unit 3 WebQuest - Internet Project

Earthquake

Introduction | Task | Process | Guidance | Conclusion | Questions

Introduction
Have you ever felt an earthquake? Earthquakes are very frightening and can cause great destruction. An earthquake occurs when the tectonic plates of the Earth split or travel by each other. Some areas of the Earth seem to have Have you ever felt an earthquake? Earthquakes are very frightening and can cause great destruction. An earthquake occurs when the tectonic plates of the Earth split or travel by each other. Some areas of the Earth seem to have more earthquakes than others. The table below shows the top ten states in the United States for the number of earthquakes recorded from 1974 to 2003. It also shows the percent of total earthquakes in the U.S. represented by each state's total.

      In this project, you will explore how functions and relations are related to locating, measuring, and classifying earthquakes.

The Task
You plan to enter a science contest that requires you to submit a research report on some type of natural disaster. You have chosen to write a report on earthquakes. If you prefer, the report can be published as a Web page and displayed on the Internet for the judges to review. You must choose one important earthquake on which data is available. Your report (Web page) needs to contain the following information:

• the name, epicenter, and date for the earthquake you have chosen;
• a map of the location of your earthquake relative to other countries, states, or areas of the world;
• an explanation of how the epicenter of an earthquake is located. Be sure to include any tables, graphs, diagrams, or other information that is needed to explain this process;
• an explanation of two measurement scales used to classify earthquakes. You should also give the measure of your chosen earthquake using at least one of the scales.

You will get some ideas about how to complete your project from the Exercises in the textbook in Lessons 8-3, 9-3, and 10-1.

• Find the name, epicenter, and date of an important earthquake upon which you plan to base your research report. For help, try these Web sites.
  wwwneic.cr.usgs.gov
  www.infoplease.com and search for earthquakes
  www.iris.edu
  www.yahoo.com and search for earthquakes
• Find a map that shows the location of the earthquake that you chose. For help, try these Web sites.
  dir.yahoo.com/Science/Geography/Cartography/Maps/
  www.iris.washington.edu/EandO
• Find an explanation of how the epicenter of an earthquake is located. For help, try these Web sites.
  www.seismo.unr.edu
  www.usatoday.com/news/science/geology/understanding-earthquakes.htm
  dir.yahoo.com/Science/Earth_Sciences/Geology_and_Geophysics/ and search for earthquakes
• Find an explanation for at least two measurement scales used to classify earthquakes. For help, try these Web sites.
  www.usatoday.com/news/science/geology/understanding-earthquakes.htm
  www.infoplease.com/ipa/A0763386.html
• Be creative. Add some additional data, information, or even pictures to your research paper or Web page.

1. What is a tsunami? How is it related to earthquakes? What are the dangers of tsunamis?
2. What was the economic impact of the earthquake that you chose to study?
3. How do people prepare for a possible earthquake?
4. Where in the U.S. are earthquakes most likely to occur? Make a map graph showing the most likely locations.
5. How are cities changing building standards to address the possibility of earthquakes?
6. Can earthquakes be predicted and/or prevented? What are researchers doing in the field of earthquakes?

• Present your project to your class or at a family night.
• Present the information on a Web page. Have other students critique your project and help you to make improvements to your project.
• Interview a person who works in researching or recording information about earthquakes. Find out what mathematics this person needs to use in this career.

Lesson 8–3
To pinpoint the epicenter of an earthquake, information is often obtained from three different seismograph stations. Circles are drawn with each station as a center. The point where the three circles intersect is most likely the epicenter of the quake.

1. On grid paper, carefully draw these three circles where each center is the location of a station on a coordinate grid.
   Circle 1: center at (0, 0); radius 3 units
   Circle 2: center at (-6, 0); radius 4 units
   Circle 3: center at (-2, -6); radius 4.25 units
   What are the approximate coordinates of the intersection of the three circles?
2. Write an equation for each of the three circles.
3. Show that the intersection point found in Exercise 1 satisfies the three equations you wrote in Exercise 2. (Your results probably will not be exact since your measurements may have been slightly inaccurate, but they should be close.)

1. On the same coordinate plane, make two scatter plots of the data from the table.
2. What type of function do you think would best model the scatter plots? Find an equation to model each function.
3. Find the difference between the arrival of the secondary wave and the primary wave. Make a scatter plot of distance (x-axis) and difference in time (y-axis). What type of function do you think would best model the scatter plot? Find an equation to model the function.
4. Compare the equations you wrote for the scatter plots. Describe similarities and differences between the three equations.

1. Use a graphing calculator to make a scatter plot for the data in the table.
2. Find an equation for an exponential equation to fit the data.

In this project, students will research earthquakes by using the Internet. In the exercises in the three chapters, students are given a brief glimpse of some of the information that they will need to research for their final project. For example, they learn something about primary and secondary seismic waves in the exercise in Lesson 9-3. Students can access several of the Web sites to learn in more depth about the waves. This project can be completed on several levels depending upon the maturity of the student and his or her interest in science. Web sites can be found that give much more in-depth explanations of earthquakes and the mathematics that are involved. Some students may seek only the simplest explanations for completion of this project, while others may study the more complicated information. You may want to consider collaborating with the earth science teacher at your school for this project.

The Guidance section of the WebQuest contains questions that would be good for a whole-class discussion and for providing interdisciplinary connections, especially to science. If you prefer, have each student research one of the questions and add the information they find to the final presentation of their WebQuest.

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

Students will work on this project in Unit 3.

Lesson	8–3	9–5	10–1
Page	459	539	564

ANSWERS
Lesson 8–3

1. 
   The approximate coordinates are (–2.5, –1.75).
2. Circle 1: x² + y² = 9
   Circle 2: (x + 6)² + y² = 16
   Circle 3: (x + 2)² + (y + 6)² = 18.0625
3. Circle 1: x² + y² = 9; (–2.5)² + (–1.75)² = 6.25 + 3.0625 = 9.3125 ˜ 9;
   Circle 2: (x + 6)² + y² = 16; (–2.5 + 6)² + (–1.75)² = 12.25 + 3.0625 = 15.3125 ˜ 16;
   Circle 3: (x + 2)² + (y + 6)² = 18.6025; (–2.5 + 2)² + (–1.75 + 6)² = 0.25 + 18.0625 = 18.3125 ˜ 18.0625

1. 
2. Sample answer: The data could be fit by a slight curve, but it appears that linear functions can be used to approximate the data. Primary Wave: y = 0.0014x + 0.9364; Secondary Wave: y = 0.0024x + 2.1136
3. 
   Sample answer: The data could be fit by a slight curve, but it appears that a linear function can be used to approximate the data. y = 0.001x + 1.1773
4. Sample answer: It seems like all three equations for the linear functions would be direct variations since (0, 0) is a data point in each. However, each function has a y–intercept, although they are small, ranging from 0.9364 to 2.1136. The slopes of the functions are also small but the secondary wave function is slightly steeper and the slope of the difference function is between the slopes of the other two functions.

1. 
   *This is a graphical representation of the first 4 points of this scatterplot. A graphical representation of the equation from question 2 is also included to help emphasize the pattern of the graph.
2. y = 0.1(10)^x