# Measuring the Shaking of the Earth

 Author: Jim Schad Unit Title: Measuring the Shaking of the Earth Grade: 10/11th Subject: Algebra II Estimated Duration: 6 days (5 – 51 minute bells and 1 – 102 minute bell) Unit Activities: Activity 1:  Introduction of the Big Idea, Essential Question and Generating Driving Questions Activity 3:  Exponential Equations Activity 4:  Logarithms - The Inverse Functions of Exponential Equations Activity 5:  Logarithms - Table, Graph and Chart Activity 6:  Building a Seismograph (EDP) Building a Seismograph, Handout Background Knowledge:  The students need to understand before this unit how to compute and manipulate linear and non-linear functions. They also need to have a basic understanding of trigonometry. Date: July 2013
##### The Big Idea (including global relevance)

Measuring earthquakes accurately is important historically, economically, politically and socially throughout the world.  Where a person lives, the amount of investment and aid and the grave political decisions made in the light of a seismological event are just a few of the global and personal decisions that depend on measuring such phenomena.  The 1812 earthquake caused by the New Madrid fault was one of the most destructive earthquakes in the continental United States.  This fact shows that no one can be assured that they are immune to the possibility of experiencing such a disaster in the future.  How we detect and measure such events not only affect the lives of others, but may directly influence our own personal lives.

##### The Essential Question

Possible essential questions:

• How do we measure an earthquake?
• What are the different ways of measuring an earthquake?
• What does it mean when it is reported “the earthquake was a magnitude of…..”?
• How do we compare earthquakes?
• How does one find out what the magnitude of an earthquake is?
##### Justification for Selection of Content

Exponential and logarithmic functions have always been difficult for students.  The Algebra II Semester Exam for second semester will be used as the final summative assessment of the students.  Past results of this assessment are not available.  However testing Alg. II students at Clark using curriculum based instruments has shown up to a 38% failure rate in this area.  A pre-test and post-test using problems similar to the ones that will be found on the district semester exam will be used to evaluate the effectiveness of this unit.

##### The Challenge

Possible challenges:

• Make a working seismograph with the given materials.
• Create a tool that can be used to generate the Richter scale magnitude from a reading on a seismograph
##### The Hook

Teacher shows videos of the 1989 San Francisco earthquake and a map of the intensity of the quake.  Then shows a PowerPoint presentation on the New Madrid earthquake of 1812.

The Interruption of a World Series Game

San Francisco Earthquake 1989

##### Teacher's Guiding Questions
1. How are earthquakes measured and monitored?
2. What does math have to do with earthquakes?
3. How does a seismograph work?
4. How does a seismograph measure?
5. What is the difference between magnitude and intensity?
6. What does the Richter Scale look like on a graph?
7. Why is the Richter Scale exponential and not linear?
8. How is the magnitude of an earthquake computed from the seismograph?

##### ACS (Real world applications; career connections; societal impact)

Applications:  By doing the math related to a seismograph the student will apply their knowledge of logarithms to a real-world situation.  This a math application to society in determining how strong was an earthquake and its comparison to other earthquakes.

Career Connections: This material is directly related to careers such as a geological engineer, geophysicists, soil technician, structural engineer, geologist and seismologist.

Society:  Society in the Mid-West would be greatly impacted by an earthquake in the New Madrid region.  The impact has the potential to be amplified due to the lack of knowledge and preparation in this region. Cincinnati would be included in the region at risk.

##### Engineering Design Process (EDP)

The students will design and build a working seismograph to experience how scientists monitor earthquakes and measure them.

Algebra II Standards – Ohio Common Core Standards

9-12.F.TF.5 Model periodic phenomena with trigonometric functions. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*

9-12.F.IF.4 Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

9-12.F.IF.5 Interpret functions that arise in applications in terms of the context. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*

9-12.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.*

9-12.F.LE.4 Construct and compare linear, quadratic, and exponential models and solve problems. For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.*

##### Where the CBL and EDP appear in the Unit

The Challenge Based Learning (CBL) is Lesson 4, activity 6 which entails both the building of the seismograph and the creation of the tool used to convert the readings into Richter.  The Engineering Design Process (EDP) will be embedded in the activity with the creation of a working seismograph.

##### Misconceptions

Understanding the Richter Scale:  It is not linear.  There is the misconception for example that a magnitude of 8 is twice the energy than a magnitude of 4.  Because its exponential a magnitude 8 is many more times a magnitude 4.

Obsessing on the structure of buildings only:  The structure of buildings are very important in the prevention of injuries and the minimizing of disasters.  But it is not the only important consideration.  Another very important consideration is soil compaction.  An epicenter of an earthquake could be many miles away, but its intensity will be felt greatest at those locations that have lose and unstable earth.  Fills which are not properly compacted (and natural unbalanced locations) are the most dangerous places during an earthquake.

##### How to Make This a Hierarchical Unit

For example in an 8th grade math class this unit could be re-designed to meet the Common Core Standards below:

8.F.3  Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.  For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1),(2,4) and (3,9), which are not on a straight line.

8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Some possible activities could be comparing the graphs of a linear function and of an exponential function to illustrate and discuss the differences.  Students could use graphing calculators to see the different characteristics of the functions.  A simple function that generates a parabola could be used to simulate the logarithmic function of the Richter Scale so students could understand the different increases in magnitude.

Students could construct pattern sensitive tables from the simple linear and non-linear functions, for example and to see how they act differently.

In building the seismograph students could just construct the simple machine itself and use a “shake table” to see how it works.  The students could also measure the amplitude of the curve without converting it to the Richter Scale.