Did You Feel That?

DID YOU FEEL THAT?

Jennifer Cleiland

Beauregard High School

Algebra 2

Introduction / Task / Process / Evaluation / Conclusion / Resources

Earthquakes are one of the deadliest and most destructive natural disasters known to mankind. Earthquakes can happen at any place and at any time on the earth – even in Alabama. Most of the earthquakes happen along fault lines throughout the world. The picture above is from the destructive earthquake that occurred on April 18, 1906 in San Francisco along the well-known San Andreas Fault line. 2006 was the 100th anniversary of this quake which cost 3,000 people their lives and over $400 million “1906” dollars in property damage. The Richter scale had not yet been developed, but recent studies show that the earthquake was between a 7.7 to an 8.3. This earthquake helped scientists understand earthquakes better and what they can do to life and property. It also launched the first integrated, government – commissioned scientific organization in the U.S. on earthquakes.

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Introduction / Task / Process / Evaluation / Conclusion / Resources

Your task will be to choose one of the largest and deadliest earthquakes in history around the world. You will make a power point presentation on this earthquake and present your findings to the class. You will try and answer the question: “Can we determine where and when an earthquake will occur?” and “How big will the next one be?”

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Introduction / Task / Process / Evaluation / Conclusion / Resources

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You will be working in a small group of 2 or 3 people. You will be working together to do the following:

1.  Pick a major earthquake

2.  Find information on that earthquake

3.  Find how to determine the magnitude of an earthquake

4.  Make a scatter plot using the magnitudes of earthquakes

5.  Find the epicenter given a quadratic (conic) system

1.  Pick a major earthquake

Your group will find an earthquake that is at least a 7.0 on the Richter scale. After you have chosen an earthquake, your group must tell me which one you have chosen. No two groups may choose the same earthquake. You can find one using the following websites:

http://earthquake.usgs.gov/regional/world/byyear.php

http://earthquake.usgs.gov/eqcenter/top10.php

http://www.infoplease.com/ipa/A0763403.html http://www.livescience.com/forcesofnature/deadliest_earthquakes.html http://library.thinkquest.org/03oct/00544/english/earthquakes_facts.htm

2.  Find information on the earthquake that you have chosen

a.  Where it happened

b.  Date and time that it happened

c.  Magnitude on the Richter Scale

d.  Exact location of the epicenter (if possible)

e.  Destruction – casualties and property damage

f.  Any indirect disaster (fire, tsunami, landslides …)

g.  Do they expect another one in this area of the same magnitude any time soon?

h.  How many earthquakes have occurred in this area before or after the one you have chosen that was significant (at least a 5.0 on the Richter Scale)?

You can find this information through the websites above or use the following search engines:

http://www.google.com

http://www.yahoo.com/

http://www.dogpile.com

http://www.bing.com

If you cannot find much information on the earthquake you have chosen, you may need to pick another earthquake. There are many to choose from.

3.  Find how to determine the magnitude of an earthquake

Go to the following website: Richter Scale This explains how logarithms and base 10 are used in determining how to find the magnitude of an earthquake. The website doesn’t give the exact formula of how they find the magnitude. So, here is how they did it

The Magnitude formula is:

M = log A – D

where M is the magnitude, A is the amplitude and D is the distance factor.

In the first example, they gave that the earthquake was 100 km away with an amplitude of 1mm. Using the table below, an earthquake that is 100 km away has a distance factor of -3. Use this information in the formula:

M = log (1) – (-3)

M = 3.0

In the second example, they gave that the earthquake was still 100 km away, but the amplitude was 10mm.

M = log (10) – (-3)

M = 4.0

Distance Distance factor Distance Distance factor

0 -1.4 55 -2.7

5 -1.4 60 -2.8

10 -1.5 65 -2.8

15 -1.6 70 -2.8

20 -1.7 75 -2.85

25 -1.9 80 -2.9

30 -2.1 85 -2.9

35 -2.3 90 -3.0

40 -2.4 95 -3.0

45 -2.5 100 -3.0

50 -2.6 110 -3.1

Since it is probably difficult to find the epicenter and amplitude of the earthquake that you have chosen, let’s do some problems of other earthquakes given the information to find the magnitude. Use the table and equation below (Round your answers to the nearest tenth).

a.  An earthquake that has distance 100 km away and has amplitude 25 mm.

b.  An earthquake that has distance 25 km away and has amplitude 100 mm

c.  An earthquake that has distance 85 km away and has amplitude 190 mm

d.  An earthquake that has distance 60 km away and has amplitude 80 mm

e.  An earthquake that has distance 45 km away and has amplitude 120 mm

f.  How much larger is the intensity in the earthquake in question c than in question b?

4.  Make a scatter plot using the magnitudes of earthquakes

The table below shows the number of earthquakes that occur in a year with the given magnitude. Use a scatter plot from the chart insert on the power point using the information. The Richter scale would be your x-axis and the number of earthquakes would be your y-axis. Use the average of each Richter scale (starting at 3.5 - 4.2) as each x-coordinate. For example, the first x-coordinate that you would use is 3.85 because it is the average of 3.5 and 4.2.

a.  What kind of function does the scatter plot appear to make?

b.  Why do you think it made this type of a function?

c.  Interpret what the graph means, as if it is the first time you have seen the graph.

Richter scale no. / No. of earthquakes per year / Typical effects of this magnitude
< 3.4 / 800 000 / Detected only by seismometers
3.5 - 4.2 / 30 000 / Just about noticeable indoors
4.3 - 4.8 / 4 800 / Most people notice them, windows rattle.
4.9 - 5.4 / 1400 / Everyone notices them, dishes may break, open doors swing.
5.5 - 6.1 / 500 / Slight damage to buildings, plaster cracks, bricks fall.
6.2 - 6.9 / 100 / Much damage to buildings: chimneys fall, houses move on foundations.
7.0 - 7.3 / 15 / Serious damage: bridges twist, walls fracture, and buildings may collapse.
7.4 - 7.9 / 4 / Great damage, most buildings collapse.
> 8.0 / One every 5 to 10 years / Total damage, surface waves seen, objects thrown in the air.

5.  Find the epicenter given a quadratic system

Finding the epicenter is essential in finding the magnitude of an earthquake which in turn tells us how much destruction it has made. Below is how to determine the epicenter and exactly what happens in recording earthquakes.

Recording Earthquakes

What happens?

1.  P Waves arrives first, followed by S Waves. P Waves travel about 2.5 times those of S Waves due to differing paths of travel. Travel times vary systematically to a distance of 11,000 km from the focus.

2.  Beyond 11,000 km P Waves are delayed several minutes over predicted arrival time and S Waves do not arrive at all.

Locating Earthquakes

1.  Difference between arrival times of P and S waves is determined. This gives distance to the epicenter from the seismograph.

2.  Three seismographs are triangulated to give actual location of the epicenter (Figure).

3.  Once distance to epicenter is known a correction factor is applied to amplitude of largest wave (usually S) to determine magnitude.

On the geometer’s sketchpad, you are to graph the following quadratic system where the center of each circle is the location of a station, and then answer the questions. Remember to plot the points first.

Circle 1: center is at (0,0) and radius is 3 units

Plot (0,0) and (3,0)

Circle 2: center is at (-6,0) and radius is 4 units

Plot (-6,0) and (-2,0)

Circle 3: center is at (-2,-6) and radius is 4.25 units

Plot (-2,-6) and connect where the other two circles meet

a. What is the solution of this quadratic system?

b. Write an equation for each of the three circles.

c. What does the solution tell you about an earthquake?

Introduction / Task / Process / Evaluation / Conclusion / Resources

You will now use the information that you found in the PROCESS to make a power point presentation and make a 4-5 minute presentation to the class. Each question asked should be answered in a complete sentence so that anyone looking at your power point will understand what you are answering. Your group is required to print a copy of your power point presentation and turn that in. Your power point should include the following slides:

Slide 1: Title Page – Title, the earthquake that you have chosen, group’s names, date of project, and class. (Make the title creative)

Slides 2-5: The information that you found in #2 a-h. You may have more than 5 slides if you want. Include any pictures that you have found on these slides. Make these the most interesting and creative slides possible. You can add any extra info on these slides that you have found that I didn’t ask for specifically.

Slide 6: The answers to questions #3 a-f about finding the magnitude of earthquakes.

Slide 7: Make a scatter plot from #4 onto this slide. Insert a chart and find the scatter plot (I will help you if you cannot find it). You will have to insert the values for each axis. Include the answers to #4 a-c on this slide.

Slide 8: Copy and paste the quadratic system made in geometer’s sketchpad for #5 onto this slide. Include the answers to #5 a-c on this slide.

Slide 9: Answer the ultimate question asked at the beginning of the project under TASK.

Slide 10: Add a slide or slides of anything that you found about your earthquake that was not asked for, but you thought was interesting and would like to share.

Your project will be graded according to the following rubric:

CATEGORY / 4 / 3 / 2 / 1
Power Point Components / All slides are present and complete. Each question is answered in a complete sentence. Each slide is easy to read and understandable. / Most slides are present and are easy to understand. Most of the questions are answered in a complete sentence. / Some slides are present. Not many can be understood easily. Most of the questions are not answered and/or they are not answered in a complete sentence. / Most slides are not present. They are not understandable. Most or none of the questions are answered and not in complete sentences.
Neatness and Organization / The work is presented in a neat, clear, organized fashion that is easy to read / The work is presented in a neat and organized fashion that is usually easy to read. / The work is presented in an organized fashion but may be hard to read at times. / The work appears sloppy and unorganized. It is hard to know what information goes together
Use of Graphics / All graphics are attractive (size and colors) and support the theme/content of the presentation. / A few graphics are not attractive but all support the theme/content of the presentation. / All graphics are attractive but a few do not seem to support the theme/content of the presentation. / Several graphics are unattractive AND detract from the content of the presentation.
Presentation / All group members are actively involved in the 4 to 5 minute presentation. / 2 or more of the 3 members are actively involved in the 3 to 5 minute presentation. / At least one or more of the members makes 3 to 5 minute presentation. / At least one of the members makes a 1 to 3 minute presentation.
Cooperation / Group delegates tasks and shares responsibility effectively all of the time. Group has 100% attention and respect for other groups as they present. / Group delegates tasks and shares responsibility effectively most of the time. Group gives most of their attention and respect to other groups presenting. / Group delegates tasks and shares responsibility effectively some of the time. Group hardly gives any attention and respect for other groups as they are presenting. / Group often is not effective in delegating tasks and/or sharing responsibility. Group gives no attention and respect for other groups as they are presenting.

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Introduction / Task / Process / Evaluation / Conclusion / Resources

We have now discovered how destructive earthquakes can be worldwide. We have also discovered that they are very unpredictable, and it is unknown to us when the next “big” one is going to be and where. All we can do is go by what our history has told us and shown us about earthquakes. We have learned that formulas, logarithms, quadratic systems, and graphs are used in determining where, when, and how big these natural disasters can be.

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Introduction / Task / Process / Evaluation / Conclusion / Resources

Websites:

http://earthquake.usgs.gov/regional/world/byyear.php

http://earthquake.usgs.gov/eqcenter/top10.php

http://www.infoplease.com/ipa/A0763403.html

http://www.livescience.com/forcesofnature/deadliest_earthquakes.html http://library.thinkquest.org/03oct/00544/english/earthquakes_facts.htm http://www.google.com

http://www.yahoo.com/

http://www.dogpile.com

http://www.ldeo.columbia.edu/LCSN/Eq/20030429/20030429_0859.html http://library.thinkquest.org/03oct/00758/en/disaster/earthquake/faultlines.html

http://quake.usgs.gov/info/1906/index.html

Books:

Glencoe Algebra 2

Larson Precalculus

Alabama Course of Study

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