EarthquakesUnit.pdf

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B

Revised 12/18/12 1

Mathematics Senior Level Capstone Course Unit Overview

Title of Unit: Earthquake! Unit Designers:

Erin Hopple Meredith Zirkle Joe Hamaker Judy Cain

Frederick County Public Schools

Edited by Diane Leighty, UVA – SCPS Office of Mathematics Outreach Context:

Summary of the issue, challenge, investigation, or problem.

Students will explore finding the epicenter of an earthquake by two methods (The culminating project will be to assess the earthquake risk in their geographic area and make a recommendation for an increase in insurance cost. Risk assessment will require research of past earthquakes in whatever factors students feel would impact insurance costs.

Number of Class Hours:

9-10 hours Unit

Design: ___Task Based _X__Project Based

Other Subject Areas/Disciplines Addressed:

Earth science, insurance industry

Driving Question: What factors should be used to determine earthquake risk and corresponding insurance coverage and cost?

Mathematics Content Addressed:

Center of circles, amplitude of a wave, graph reading, mean and standard deviation, data collection, mathematical modeling

MPE Addressed:

Problem solving, decision making and integration

Assumption of Prior Knowledge:

Ability to construct a circle, ability to interpret a graph, ability to calculate a mean and standard deviation, ability to enter data into a calculator, ability to select an appropriate mathematical model, basic knowledge of earthquakes

College and Career Readiness/21st Century

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Revised 12/18/12 2

Skills to be taught (T) during this unit or expectation (E) for student use during this unit and assessed (A): BIE Page 35-37

Communication (Oral and/or Written) A Technology E

Critical Thinking/Decision Making A Other: (Describe)

Major Products and/or Performances:

Group: Written report and Oral presentation with appropriate visuals

Presentation Audience:

X Class

School

Individual: Mathematicians journal Expert

Community Other:

Launch: Event or experience used to engage the students interest and inquiry:

If everyone jumps up and down at the same time could it create an earthquake large enough to destroy the world?

Evaluation: Formative Assessments (During the Unit)

Interview Practice Presentations

Mathematicians Journal X Notes

Preliminary

Plans/Outlines/Prototypes X

Checklists

X

Rough Drafts Concept maps

Field Tests Other:

Summative Assessment (End of Project)

Written Products, with a rubric

X Peer Evaluation, with a

rubric X

Oral Presentation with a rubric

X Self Evaluation, with a rubric

Other Product(s) or

Performance(s), with a rubric

Other:

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Revised 12/18/12 3

Equipment/Technology: Internet access, computers with presentation software Materials: Compass, ruler, colored pencils.

Community Resources:

Reflection Methods: Individual, Group, and/or Whole Class

Mathematicians Journal X Small/Focus Groups Whole Class Discussions Fishbowl Discussions

Survey Other:

Material Adapted From:

http://www.sciencecourseware.com/VirtualEarthquake/VQuakeExecute.html

“The Scientific Method in Physical Geology” by Margaret Woyski

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science

Partnership Grant Program NCLB Title II Part B Revised 12/18/12 4 Virginia’s Senior Level Capstone Course

Instructional Plan Unit Title: Earthquakes!

Driving Question: What factors should be used to determine earthquake risk and corresponding insurance coverage and cost?

Task/Project/Problem: Project

ENGAGE How will student’s interested be piqued so they want to engage in the inquiry in this unit? Number of hours: 15 minutes

If everyone jumps up and down at the same time would it destroy the world? Directions for Instructor:

Lead a discussion on student responses; have students discuss methods they might use to try and create an experiment to test their theories.

Anticipated products and artifacts if any: journal prompt

Mathematician Journal Prompts If everyone jumps up and down at the same time would it destroy the world? Justify your answer. EXPLORE Teacher provides guidance for the explorations to prepare students with the knowledge and skills to engage in the task. Students will self-assess on the prior knowledge and skills assumed for the unit

Number of hours: 2

Explore Task 1: Finding an epicenter and magnitude of a virtual earthquake

Please note that use of a computer with Internet access (one per student) is necessary for this activity. An alternative would be to complete the task as a class, as long as the teacher had Internet access available.

Goal of activity

 To find an epicenter of a virtual earthquake.  To find the magnitude of the virtual earthquake.

Description of activity

 Use secondary and primary waves from a seismogram to calculate three S-P intervals.

 Use the S-P graph generated to estimate three epicentral distances.  Find the epicenter by constructing three circles, one from each center.  Measure amplitude of three secondary waves.

 Use the amplitudes to determine the magnitude on a Richter scale.

Materials/Equipment/Resources Needed: HO#1

HO#2 (Teacher Guide and Grading Checklist for HO #1) Ruler, Compass, and colored pencils.

http://www.sciencecourseware.com/VirtualEarthquake/VQuakeExecute.html

Student self-assessment of skills required for unit and recommendations for tutorial and/or practice:

Mathematician Journal Prompts 1. Explain how to find an epicenter of an earthquake. Include the minimum number of locations needed and what information you need about that location. 2. Explain what the amplitude from the seismogram is and how it helps

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Partnership Grant Program NCLB Title II Part B Revised 12/18/12 5 The following websites are good resources for information on earthquakes, s/p

waves and seismology:

http://www.geo.mtu.edu/UPSeis/waves.html http://earthquake.usgs.gov/learn/kids/eqscience.php

http://cse.ssl.berkeley.edu/lessons/indiv/davis/inprogress/QuakesEng3.html

For remediation on math topics utilized in this task, see HO#9 Directions for Instructor

 Students should be able complete the online portion of activity with no instruction.

 When the online activity is finished, students should email the certificate of completion to instructor.

 Students can then work on offline portion using what they learned online.

 Students should complete the first three journal prompts.  Teacher Guide for task: HO#2

Teachers questions and anticipated reactions and results:

 Students should have few difficulties with the online activity, but have class discussion after the journal prompts to make sure students understood the activity.

Student Direction(s): none

Anticipated products and artifacts:  Certificate of completion

 Completed worksheet with information from online activity filled-in  Completed map with epicenter location shaded.

Rubrics: Grading Checklist on HO#2

*************************************************************** Explore Task 2: Finding epicenter from observed intensity using a

Mercalli scale Goal of activity:

 To find an epicenter from incident reports using a Mercalli scale

Description of activity

 Use newspaper headlines to determine earthquake intensity in different cities.

 Mark intensities on a map to create an isoseismal map.  Use map to locate epicenter of earthquake.

Materials/Equipment/Resources Needed: HO#3

HO#4 (Teacher Guide and Grading Checklist for HO#3)

Richter value.

3. What kind of errors exist in finding your epicenter? 4. Compare and contrast the Richter and Mercalli scales.

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Partnership Grant Program NCLB Title II Part B Revised 12/18/12 6 Student self-assessment of skills required for unit and recommendations for

tutorial and/or practice:

Before beginning activity, discuss creating an isoseismal map with students. If information is needed, the following website is a good resource and provides an example of creating an isoseismal map using the Mercalli scale: http://www.data.scec.org/Module/s3act01.html

For remediation on math topics utilized in this task, see HO#9 Directions for Instructor

 Students should follow steps of activity.  If needed show example isoseismal map.

http://www.data.scec.org/Module/Pics/s3a1map.gif  When done complete journal entries 4 and 5.  Teacher guide for task: HO#4

Teacher questions and anticipated reactions and results.

 Students will sometimes have difficulty choosing between two

numbers that seem to fit the headline. Students should be instructed to make the choice they think is best.

Student Direction(s): None Anticipated products and artifacts:

 Completed isoseismal map  Journal entries

Rubric:

Grading Checklist in HO #4

EXPLAIN Teacher introduces the main task of the unit and prepares students to in small group independent work... Number of Hours: 30 minutes

What factors should be used to determine earthquake risk and corresponding insurance coverage and cost?

Students will work in groups. First they will take an earthquake of a given magnitude and create seismograms and headlines to make up their own earthquake. Students will the need to research probability of an earthquake in a particular location (given by the teacher) and the mean and standard

deviation for the probable magnitude. Students will collect data on damages from various earthquake magnitudes and use the data to create a mathematical model for predicting the average cost of damages. Students will research homeowner’s insurance coverage and costs for their location. Based on all research, students will make a recommendation on whether homeowner’s insurance in their location should cover earthquake damage and at what additional insurance cost. Recommendations will be presented orally with appropriate visual aids.

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Partnership Grant Program NCLB Title II Part B Revised 12/18/12 7 Task/Project/Problem:

Student Guide and Project Information: HO#5 Teacher Guide: HO#6

Skills or knowledge needed:

 How to research on the Internet

 How to create a mathematical model from real-life data

Materials/Equipment/Resources Needed:  Copies of the handout

 Internet access

Directions for Instructor:

Assign each group a different city in Virginia. HO#6- Teacher Guide for Project

For remediation on math topics utilized in this task, see HO#9

ELABORATE The student groups are working independently with teacher consultations. Number of Hours: 4

Describe what the teacher will be doing during this time.  Monitor group progress

 Troubleshoot if groups are having difficulty finding the needed information (see HO#6)

Formative Assessments: none

Anticipated Products and Artifacts Described: Written report

Oral Presentation of findings

Rubric(s) for self-evaluation of product and/or presentation, etc.: HO#8 Peer and Self Evaluation Rubric

Tools for Students to Use in Planning: HO#5

Tools for Self-Monitoring the Groups Working Together: none

Mathematician Journal Prompts At this point in your project, what difficulties have you encountered? What could I, as your teacher, or you, as the student, have done to ease these difficulties? EVALUATE Working groups submit products or make presentations Number of Hours: 1.5

Directions for Instructor regarding final evaluation:

Each group will create a written report on the intensity and seismograms for a made up earthquake in Virginia.

Each group will prepare an oral presentation with visual aids. Rubric(s) for teacher and/or audience for presentation: HO#7- Project Rubric

HO#8- Peer and Self Evaluation Rubric

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Partnership Grant Program NCLB Title II Part B Revised 12/18/12 8 Map the Unit

What do students need to know and be able to do to complete the task/project/problem

successfully? How and when will they assess their own necessary knowledge and skills? How will they remediate their own gaps or weaknesses in knowledge and skills? Look at each major task for the unit and analyze the tasks necessary to produce a high-quality product.

Task: Determine what factors should be used to determine earthquake risk and corresponding insurance coverage and cost.

KNOWLEDGE AND SKILLS NEEDED Assumed

already learned

Students will self-assess

Will be taught during the unit

1. Read a graph X

2. Conduct research on the Internet X

3. Calculate mean and standard deviation X

4. Create an appropriate mathematical model X

5. Prepare an oral presentation with visual aids X

6. S and P graphs and intervals X

7. Isoseismal maps X

8. Constructing circles using knowledge of diameter and circumference.

X

9.

10.

11.

What project tools will student’s use?  Know/need to know lists  Daily goal sheet

 Mathematician’s Journals  Briefs/Memos

 Task lists

 Planning Calendar

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Partnership Grant Program NCLB Title II Part B Revised 12/18/12 9 HO #1 Determining an Earthquake Epicenter from Seismograms

Name:______________________________

Part 1: Go to www.sciencecourseware.com/VirtualEarthquake/VQuakeExecute.html

Make sure you read all the information on the page about earthquakes and how they are

measured, when you are ready you will choice one of the four regions where an earthquake has occurred and follow the steps to finding its epicenter. Record your answers from the website below. Press SUBMIT to begin.

Which region did you choose?:_________________________

Read the information on finding the (S-P) interval before viewing the seismograms.

Put the values you choose for the (S – P) intervals of the three stations below:

_______________ ______________ _____________

After using the S and P curves to find the Epicentral distance, record your answers:

_______________ ______________ _____________

After reviewing your epicenter, record the actual data given in the right side of the table here.

Actual Data

Recording station S – P interval Epicentral Distance

How close were you to the actual results?

Next you are finding the magnitude for the Richter scale; enter your amplitudes for the three seismograms and record your answers below.

______________ ____________ _____________

What is the magnitude of your earthquake?: _______________

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Partnership Grant Program NCLB Title II Part B Revised 12/18/12 10

Print out the Richter Magnitude Confirmation Sheet and turn in.

Part 2: Use the given seismograms, S & P wave Travel time graph and map to find the epicenter of an earthquake.

Materials needed: Ruler, 4 different color pencils and a compass.

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Use the seismograms and the attached S & P wave travel time graph to complete the table below.

Recording Station S – P interval Epicentral distance Pittsburgh

Minneapolis Pasadena

Using 3 of the colored pencils create the circles for each distance using a different color on the map below.

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Earthquake Wave Time – Distance Graph

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Partnership Grant Program NCLB Title II Part B Revised 12/18/12 13 HO #2 Determining an Earthquake Epicenter from Seismograms

Name:__Teacher Guide______________

* Answers will vary based off of the region students choose. This is a guide to follow using the San Francisco area region. The other regions can also be completed for guides, if needed.

Part 1: Go to www.sciencecourseware.com/VirtualEarthquake/VQuakeExecute.html

Make sure you read all the information on the page about earthquakes and how they are

measured. When you are ready you are to choice one of the four regions where an earthquake has occurred and follow the steps to finding its epicenter. Record your answers from the website below. Press SUBMIT to begin.

Which region did you choose?:_San Francisco area___

Read the information on finding the (S-P) interval before viewing the seismograms.

Main Points: P-waves have less amplitude than S-waves. When measuring the S-P interval, you are measuring the time (in seconds) from the arrival time of the P-wave to the arrival time of the S-wave.

Put the values you choose for the (S – P) intervals of the three stations below:

___50 sec______ ____72 sec_____ __64 sec______

After using the S and P curves to find the Epicentral distance, record your answers:

___485 km_____ __695 km____ __605 km_____

After reviewing your epicenter, record the actual data given in the right side of the table here.

Actual Data

Recording station S – P interval Epicentral Distance

Eureka, CA 49 sec 478 km

Elko, NV 72 sec 703 km

Las Vegas, NV 64 sec 623 km

How close where you to the actual results?

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Next you are finding the magnitude for the Richter scale; enter your amplitudes for the three seismograms and record your answers below.

___285___ __60____ ___100___

What is the magnitude of your earthquake?: __7.1______

How close were you to the actual magnitude?

The magnitude I found was exactly the same as the actual magnitude. The earthquake we measured was an actual earthquake that occurred in 1989, south of San Francisco. It’s estimated magnitude was a 7.1.

Print out the Richter Magnitude Confirmation Sheet and turn in.

Grading Checklist for Part 1

Part 1: 20 points

The following should be evident on HO #1 Part 1 and Confirmation Sheet to receive full credit:

5 points: Chosen values for S-P intervals and Epicentral distance should be within an acceptable range (+/- 5 seconds/km)

5 points: Actual data is accurately recorded (This data is the given data; there should be no variation from one student to the other, as long as they chose the same region)

2.5 points: Reasonable answer for “How close were you to the actual results?”

5 points: Chosen values for amplitudes should be within an acceptable range (+/- 5 amps) and the found magnitude is within an acceptable range (+/- 0.5 on the Richter scale)

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Part 2: Use the given seismograms, S & P wave Travel time graph and map to find the epicenter of an earthquake.

Materials needed: Ruler, 4 different color pencils and a compass.

The seismograms for a recent earth quake are given below.

Measure (in minutes/seconds) from the start of the wave to the start of the S-wave. The P-wave is the beginning of any noticeable tremors and the S-P-wave is the beginning of the larger amplitude tremors.

Use the seismograms and the attached S & P wave travel time graph (on next page) to complete the table below.

Recording Station S – P interval Epicentral distance Pittsburgh 2 minutes 42 seconds 1000 miles

Minneapolis 1 minute 36 seconds 500 miles

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Using 3 of the colored pencils create the circles for each distance using a different color on the map below.

To do this, use the scale given on the map and the epicentral distance found to draw a circle around each recording station using a ruler and compass showing the distance from the epicenter.

Shade in the area where the epicenter will be located using the last colored pencil. This shaded region is the area of error and the epicenter will be in the center of this area.

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Partnership Grant Program NCLB Title II Part B Revised 12/18/12 17 Grading Checklist for Part 2

Part 1: 30 points

The following should be evident on HO #1 Part 2 to receive full credit:

5 points: S-P intervals found are within an acceptable range (+/- 30 seconds)

5 points: Epicentral distances found are within an acceptable range (+/- 100 miles)

10 points: Circles drawn on map are within a range of +/- 100 miles (using the given scale). The use of a ruler and protractor is evident. A legend should also be included matching each circle with a location.

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Partnership Grant Program NCLB Title II Part B Revised 12/18/12 18 HO #3 Locating an Earthquake Epicenter from Intensity

Name:________________________

Data on earthquakes has been increasing greatly as more and more tools for monitoring

earthquakes becomes available. However, most towns or cities do not have seismograms

available to monitor earthquakes. Another way we can measure an earthquake and finds its

epicenter is to look at the intensity or strength of the earthquake.

The effect of an earthquake on the Earth's surface is called the intensity. The intensity scale

consists of a series of certain key responses such as people awakening, movement of furniture,

damage to chimneys, and finally - total destruction. Although numerous intensity scales have

been developed over the last several hundred years to evaluate the effects of earthquakes, the one

currently used in the United States is the Modified Mercalli (MM) Intensity Scale. It was

developed in 1931 by the American seismologists Harry Wood and Frank Neumann. This scale,

composed of 12 increasing levels of intensity that range from imperceptible shaking to

catastrophic destruction, is designated by Roman numerals. It does not have a mathematical

basis; instead it is an arbitrary ranking based on observed effects.

The Modified Mercalli Intensity value assigned to a specific site after an earthquake has a more

meaningful measure of severity to the nonscientist than the magnitude because intensity refers to

the effects actually experienced at that place.

The lower numbers of the intensity scale generally deal with the manner in which the earthquake

is felt by people. The higher numbers of the scale are based on observed structural damage. Structural engineers usually contribute information for assigning intensity values of VIII or

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The following is an abbreviated description of the 12 levels of Modified Mercalli intensity.

I. Not felt except by a very few under especially favorable conditions.

II. Felt only by a few persons at rest, especially on upper floors of buildings. Swinging of some suspended objects

III. Felt quite noticeably by persons indoors, especially on upper floors of buildings. Many people do not recognize it as an earthquake. Standing motor cars may rock slightly. Vibrations are similar to the passing of a truck.

IV. Felt indoors by many, outdoors by few during the day. At night, some awakened. Dishes, windows, doors disturbed; walls make cracking sound. Sensation is like a heavy truck striking building. Standing motor cars rocked noticeably.

V. Felt by nearly everyone; many awakened. Some dishes, windows broken. A little cracked plaster. Unstable objects overturned. Pendulum clocks may stop.

VI. Felt by all, many frightened. Some heavy furniture moved; a few instances of fallen plaster. Damage is slight.

VII. Damage negligible in buildings of good design and construction; slight to moderate in well-built ordinary structures; considerable damage in poorly built or badly designed structures; some chimneys broken.

VIII. Damage slight in specially designed structures; considerable damage in ordinary substantial buildings with partial collapse. Damage is great in poorly built structures. Fall of chimneys, factory stacks, columns, monuments, walls. Heavy furniture overturned.

IX. Damage considerable in specially designed structures; well-designed frame structures thrown out of plumb. Damage is great in substantial buildings, with partial collapse. Buildings shifted off foundations. Conspicouous ground cracks; underground pipes broken

X. Some well-built wooden structures destroyed; most masonry and frame structures destroyed with foundations. Train rails bent. The ground is cracked, landslides on steep slopes and river banks.

XI. Few, if any (masonry) structures remain standing. Bridges destroyed. Rails bent greatly. Earth slumps and there are landslides in soft ground.

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Partnership Grant Program NCLB Title II Part B Revised 12/18/12 20 Activity: Find the epicenter of an earthquake using intensity data.

When an earthquake happens, newspaper reports tell of the effects and damage in different cities. The epicenter of the earthquake can be found using this intensity data.

1. Using the newspaper headlines below, assign a Mercalli intensity value to each city.

2. Place a number on the attached map to show the intensity at each locality.

3. Draw contour lines separating the areas which report one intensity from those reporting another. (This is called an isoseismal map)

4. Use the isoseismal map to estimate the epicenter of the earthquake.

Newspaper Headlines:

Detroit: “Did you feel the earthquake? Last night a slight earth tremor was felt in this area.”

Pittsburgh: “Items broken by earthquake. Earth tremor awakens many.”

Syracuse: “Mayor’s 10th

floor office chandelier sways in the earthquake.”

Baltimore: “Citizens dash outside as earthquake brings down plaster in many homes.”

Philadelphia: “Doors and windows rattle as tremor strikes.”

Cleveland: “Earth tremor felt on top of new 23-story department store.”

Roanoke: “Pedestrians report parked autos rocked back and forth by earthquake.”

Charlestown: “Almost no one here notices earthquake.”

New York City: “Skyscraper offices sway in earthquake.”

Washington: “Chimneys tumble, new prefabricated buildings collapse in violent earthquake felt here.”

Richmond: “Furniture moved about by earth tremors, but no major damage reported.”

Winston-Salem: “Patients in hospital report that building shakes in earthquake.”

Atlanta: “Earthquake tremors reported north of here apparently miss Atlanta.”

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Partnership Grant Program NCLB Title II Part B Revised 12/18/12 22 HO #4 Teacher Guide to Locating an Earthquake Epicenter from Intensity