Math RWLO Template Title Placeholder



Earthquakes! Amplitude and Magnitude Connection

Preface

This RWLO is the first of three separate and sequential RWLOs. Thus, if time permits and prerequisites met, students can continue an extension by completing the following two RWLOs “Earthquakes! Amplitude, Energy and Magnitude Connections” and

“Earthquakes! Intensity and Amplitude Connection”.

Project Overview

Students will understand the differences and the connections between the Amplitude and Magnitude of Earthquakes.

Students will have prior knowledge of logarithms and exponentials.

Students will investigate the fifteen most recent earthquakes in the world. For each of the fifteen earthquakes, the students will

I. Latitude and Longitude Location of Earthquakes

1. Annotate the time, date, latitude, longitude, depth, magnitude and general location of each earthquake.

2. Plot their location on a world map. (Plotting is optional)

II. Amplitude and Magnitude

1. Express the magnitude as a logarithmic function of amplitude.

2. Express the amplitude as an exponential function of magnitude.

III. Summary

1. Write a letter to a fifth grader explaining the above in a clear and succinct fashion.

2. The letter will only include mathematical concepts at or below a fifth grade level.

Student Learning Objectives

For this RWLO, the student will be able to:

1. Plot each earthquake’s location using latitude and longitude coordinates.

2. Define magnitude, energy and amplitude.

3. Express each earthquake’s magnitude as a logarithmic equation of amplitude.

4. Express each earthquake’s amplitude as an exponential equation of magnitude.

5. Make a comparative table of each earthquake’s magnitude values versus the ratio

of its amplitude to the smallest amplitude recorded.

6. Determine the exponential regression function that best models the table above.

7. Graph the above.

8. Summarize numbers 1 through 7 listed above.

Procedure

Time: Inside Class - Time will be approximately two hours.

Outside Class - Time will be approximately two hours.

Materials: Scientific graphing calculator, paper, pencil, eraser, computer with internet access, and a World Map with Latitude and Longitude coordinates ().

Prerequisites: Coordinate plotting skills, knowledge of exponential and logarithmic functions, basic computer skills and scientific graphing calculator skills.

Implementation: Use this RWLO as an assignment following a chapter on logarithmic and exponential functions. Note that that this RWLO works well as an activity both inside the classroom or outside the classroom.

Teacher Steps:

I. Latitude and Longitude Location of Earthquakes

1. Review plotting, latitude and longitude definitions, properties of logarithmic and exponential functions. Note Plotting the earthquakes is optional.

2. Access and discuss the information given on the United States Geological Survey websites listed below.

o

(United States Geological Survey – Earthquake Hazards Program)

o

(USGS – Recent Earthquakes The last 8 – 30 days)

3. Access and review the National Geographic, Xpeditions website.

o

(National Geographic map of the World)

This is a world map with latitude and longitude coordinates.

4. Handout copies of the map to students.

5. Handout the Assessment Worksheet.

6. Entertain questions from the students.

Procedure (continued)

II. Amplitude and Magnitude

1. Review definitions of magnitude and amplitude.

(Visual Glossary)

2. Review the relationships between logarithmic and exponential functions.

3. Review how to express the magnitude as a logarithmic function of amplitude.

Let [pic] be the magnitude of a specific earthquake. Let [pic] be the amplitude of

the same specific earthquake. Note: [pic]

4. Review how to express the amplitude as an exponential function of magnitude.

As before, let [pic] be the magnitude of a specific earthquake. Let [pic] be the

amplitude of the same specific earthquake. Then [pic]

5. Review the ratios of two earthquake amplitudes, for instance the amplitude of

earthquake x to earthquake y. For example, let earthquake[pic] have a magnitude of 5.6 and earthquake[pic] has a magnitude of 5. Then the ratio (let [pic] be the ratio) of the two amplitudes would be[pic].

In other words, earthquake[pic] is about 4 times stronger than earthquake[pic].

6. Review how to determine the exponential regression functions.

7. Review how to graph the scatter plots and regression functions on the same

coordinate plane.

III. Summary

1. Discuss with students how to make a summary paper utilizing

a An opening paragraph discussing what they wish to discuss.

a A body consisting of two paragraphs, one paragraph discussing each of items I. - II. above and

a A concluding paragraph referring back to their opening paragraph.

Content Material

Student Directions:

Students,

• You are to work in groups.

• Your groups should consist of at least 3 students to a maximum of 4 students.

• Each day you will meet as a whole class to share and discuss group questions that may arise.

• You will complete the Evaluation of Individual Contribution to Group Rubric upon the conclusion of this activity. The Group Evaluation Form will allow you to assess the participation of each individual in your group. This evaluation will be included in the rubric (Part 2: Evaluation of Individual Contribution to Group Rubric) determining your grade for this activity.

• You will complete the worksheet

“Earthquakes! Amplitude and Magnitude Connection” located on the following seven pages.

Referenced URLs:

•

(United States Geological Survey – Earthquake Hazards Program)

•

(USGS – Recent Earthquakes The last 8 – 30 days)

• .

(National Geographic Map of the World annotated with Latitude and Longitude)

•

(Visual Glossary)

•

(Measuring earthquakes -energy released in an earthquake)

•

(Magnitude/Intensity)

•

(The Severity of an Earthquake)

Content Material (continued)

Earthquakes! Amplitude and Magnitude Connection

WORKSHEET

Student Name ______________________________ Date ___________________

I. Latitude and Longitude Location of Earthquakes

1. Select the fifteen most recent earthquakes, using the website “Recent Earthquakes - Last 8-30 Days” URL .

2. Complete Table A below.

Table A

|Date |Time |Latitude |Longitude |Depth |Magnitude |General Location |

| | | | | | | |

| | | | | | | |

| | | | | | | |

| | | | | | | |

| | | | | | | |

| | | | | | | |

| | | | | | | |

| | | | | | | |

| | | | | | | |

| | | | | | | |

| | | | | | | |

| | | | | | | |

| | | | | | | |

| | | | | | | |

| | | | | | | |

3. Plot each of the earthquake locations on the National Geographic World map using the latitude and longitude coordinates. Be sure to use the “National Geographic Xpeditions World Map” (). (See following page.)

Content Material (continued)

II. Amplitude and Magnitude

For the following two questions, you may want to refer to the USGA Glossary of Terms

Feel free to use other pertinent USGS websites as well.

Content Material (continued)

3. Complete Table B below using the magnitude of each of the fifteen earthquakes you

listed in Table A, Section I-1.

Table B

|Earthquake |Magnitude |Magnitude as a |Amplitude as an |Amplitude |

| | |logarithmic function of |exponential function | |

| | |Amplitude |of Magnitude | |

|Example |5 | |[pic] |10000 |

| | |[pic] | | |

|Earthquake 1 | | | | |

|Earthquake 2 | | | | |

|Earthquake 3 | | | | |

|Earthquake 4 | | | | |

|Earthquake 5 | | | | |

|Earthquake 6 | | | | |

|Earthquake 7 | | | | |

|Earthquake 8 | | | | |

|Earthquake 9 | | | | |

|Earthquake 10 | | | | |

|Earthquake 11 | | | | |

|Earthquake 12 | | | | |

|Earthquake 13 | | | | |

|Earthquake 14 | | | | |

|Earthquake 15 | | | | |

Content Material (continued)

4. The largest magnitude listed of the fifteen most recent earthquakes was _____________.

5. The smallest magnitude listed of the fifteen most recent earthquakes was ____________.

6. Complete Table C Real Time Comparative Table of the earthquake magnitude values versus the ratio of its amplitude to the smallest amplitude recorded.

Table C Real Time Comparative Table

|Earthquake |Magnitude |[pic] |

|Note #1 In this example case only, |5 |[pic][pic] |

|let Magnitude Smallest be 3.8. | |(Note, this means that an earthquake of |

|Note #2 The letter “i” references the “ith” | |magnitude 5 is about 15.8 times stronger than |

|earthquake. For instance, if i = 6, then we are | |the earthquake with magnitude 3.8.) |

|referring to the 6th earthquake. | | |

|Earthquake 1, i = 1 | | |

|Earthquake 2, i = 2 | | |

|Earthquake 3, i = 3 | | |

|Earthquake 4, i = 4 | | |

|Earthquake 5, i = 5 | | |

|Earthquake 6, i = 6 | | |

|Earthquake 7, i = 7 | | |

|Earthquake 8, i = 8 | | |

|Earthquake 9, i = 9 | | |

|Earthquake 10, i = 10 | | |

|Earthquake 11, i = 11 | | |

|Earthquake 12, i = 12 | | |

|Earthquake 13, i = 13 | | |

|Earthquake 14, i = 14 | | |

|Earthquake 15, i = 15 | | |

|Earthquake Smallest | | |

|(Refer to answer of #5 above.) | | |

Content Material (continued)

7. The Exponential Regression function that best models the ratio of the amplitude as a

function of magnitude (Table C) is

_______________________________________.

8. The [pic] for the Exponential Regression equation that best fits your data is ___________.

10. Use Table C.

a. Make a scatter plot of the magnitude versus amplitude ratio values.

b. Graph the Exponential Regression equation that best fits your scatter plot

values.

Content Material (continued)

III. Summary

1. Write a four-paragraph letter to a fifth grade student explaining the connections you have learned with respect to measuring earthquakes. One main requirement is that your letter will only include mathematical concepts at or below a fifth grade level.

Specifically, you must write the four paragraphs as annotated below.

P1 Write an opening paragraph discussing what you will be explaining.

P2 Explain how to plot earthquakes using latitudes and longitudes.

P3 Explain how to determine amplitude and magnitude.

P4 Write a concluding paragraph referring back to your opening paragraph.

2. Submit your Worksheet.

Assessment - Rubric (See next two pages.)

Part 1: Point Breakdown Worksheet Rubric for: (page 13 and 14)

“Earthquakes! Amplitude and Magnitude Connection”

Part 2: Evaluation of Individual Contribution to Group Rubric for: (page 15)

“Earthquakes! Amplitude and Magnitude Connection”

Part 1: Point Breakdown Worksheet Rubric Student Name: _________________________________________

Part 2: Evaluation of Individual Contribution to Group Rubric

Print Your Name Here _________________________________

1. Describe your specific contribution to the activity completion. Thoroughly describe the parts that you completed and the contributions that you provided to the whole project.

2. Characterize the contribution of each member in your group: How well did your group work together? Discuss each member’s (including yourself) level of preparedness for the group’s meetings, and the depth of thought, completeness, and thoroughness of each member’s contribution. Indicate the group members name and then make your comments for each member of the group.

Print Name ______________________

Comments:

Print Name ______________________

Comments:

Print Name ______________________

Comments:

Print Name ______________________

Comments:

Links to Course Competencies

This RWLO is appropriate for the following courses: College Algebra, Precalculus, Geophysics, Earth Sciences and Physics. Specifically, this RWLO meets the following course competencies:

• Evaluate a function from its graph, formula, or equation.

• Graph the inverse of a logarithmic function.

• Graph the inverse of an exponential function.

• Solve logarithmic and exponential equations.

• Set up and solve applications involving logarithmic and exponential functions.

• Integrate “Lists, Scatter Plots, and Graphs” on a scientific graphing calculator.

• Demonstrate an understanding of seismic and earthquake dynamics.

• Assess real time data using the internet.

Supplementary Resources

• “Earthquakes” by Kaye M. Shedlock & Louis C. Pakiser



• “Earthquake”, an article about the natural seismic phenomenon.



• USGS, Science for a Changing World - Earthquake Hazards Program



Recommendations

Recommendations for Integration:

This RWLO is the first of three separate and sequential RWLOs. Thus, if time permits and prerequisites met, students can continue an extension by completing the following two RWLOs “Earthquakes! Amplitude, Energy and Magnitude Connections” and

“Earthquakes! Intensity and Amplitude Connection”.

Prerequisites: Coordinate plotting skills, knowledge of exponential and logarithmic functions, basic computer skills and scientific graphing calculator skills.

Recommendations for a Back-Up Plan:

A good idea is to make copies of the referenced URLs in the event that the internet is unavailable.

In addition, copies of the websites could be saved to a CD and given for students to use.

Recommendations for Implementation:

Use this RWLO as an assignment following a chapter on logarithmic and exponential functions. Note that that this RWLO works well as an activity both inside the classroom or outside the classroom.

Use the following steps in guiding your students.

I. Latitude and Longitude Location of Earthquakes

1. Review plotting, latitude and longitude definitions, properties of logarithmic and exponential functions.

2. Access and discuss the information given on the United States Geological Survey websites listed below.

o

(United States Geological Survey – Earthquake Hazards Program)

o

(USGS – Recent Earthquakes The last 8 – 30 days)

3. Access and review the National Geographic, Xpeditions website.

o

(National Geographic map of the World)

This is a world map with latitude and longitude coordinates.

4. Handout copies of the map to students.

5. Handout the Assessment Worksheet.

6. Entertain questions from the students.

Recommendations (continued)

II. Amplitude and Magnitude

1. Review definitions of magnitude and amplitude.

(Visual Glossary)

2. Review the relationships between logarithmic and exponential functions.

3. Review how to express the magnitude as a logarithmic function of amplitude.

Let [pic] be the magnitude of a specific earthquake. Let [pic] be the amplitude of

the same specific earthquake. Note: [pic]

4. Review how to express the amplitude as an exponential function of magnitude.

As before, let [pic] be the magnitude of a specific earthquake. Let [pic] be the

amplitude of the same specific earthquake. Then [pic]

5. Review the ratios of two earthquake amplitudes, for instance the amplitude of

earthquake x to earthquake y. For example, let earthquake[pic] has a magnitude of 5.6 and earthquake[pic] has a magnitude of 5. Then the ratio (let [pic] be the ratio) of the two amplitudes would be[pic].

In other words, earthquake[pic] is about 4 times stronger than earthquake[pic].

6. Review how to determine the exponential regression functions.

7. Review how to graph the scatter plots and regression functions on the same

coordinate plane.

III. Summary

1. Discuss with students how to make a summary paper utilizing

a. An opening paragraph discussing what they wish to discuss.

b. A body consisting of two paragraphs, one paragraph discussing each of items I. - II. above and

c. A concluding paragraph referring back to their opening paragraph.

-----------------------

1. Define the Amplitude of an earthquake using your own words and schematics.

2. Define the Magnitude of an earthquake using your own words and schematics.

9. Explain your results of [pic] ________________________________________________

______________________________________________________________________

______________________________________________________________________

0

8

y

0

100

x

[pic]

[pic]

................
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