# The Science of Natural Disasters

## CONTENTS OF CURRICULUM UNIT 07.04.10

- Introduction
- Purpose
- Goals and Objectives
- Key Concepts
- Students
- Rationale
- Teaching Strategies
- Classroom Activities - Lesson Plans
- Lesson Number 3 - Modeling Earthquake Magnitude and Population Growth using Exponential and Logarithmic Functions
- Resources
- Appendix: Implementing National, State and District Standards

### Unit Guide

## Modeling Natural Disasters with Mathematical Functions

Your feedback is important to us!

After viewing our curriculum units, please take a few minutes to help us understand how the units, which were created by public school teachers, may be useful to others.

## Lesson Number 3 - Modeling Earthquake Magnitude and Population Growth using Exponential and Logarithmic Functions

*
Objective(s) - students will be able
*

- 1) To physically model an earthquake and describe how friction and surface area relate to earthquake magnitude
- 2) To describe the relationship between earthquake magnitude and energy in at least two different ways
- 3) To define seismic moment, Richter magnitude, and moment magnitude
- 4) To describe the relationship between seismic moment and moment magnitude in at least two different ways
- 5) To describe the relationship between earthquake magnitude and frequency of occurrence in at least two different ways
- 6) To apply exponential and logarithmic functions to the relationship between earthquake magnitude and energy released
- 7) To apply exponential and logarithmic functions to the relationship between time and population size

*
Prerequisite skills
*

order of operations, rules of exponents, graphing functions manually and with graphing calculator, solving equations by taking logarithms and exponentiating

*
Materials
*

Sponges of different sizes, all with a flat side, string, weights

graphing calculator, graph paper, worksheets including discussion prompts and calculation exercises

*
Vocabulary - Terms & Symbols
*

friction, acceleration due to gravity, surface area, energy (concept & different units), logarithm, exponent

*
Strategy
*

The cause of an earthquake can be simply modeled using a sponge, a piece of string, and some weights. If only one sponge is available, this exercise can be done as a classroom demonstration of a force overcoming friction. Otherwise, students may be divided into groups, each of which has one type of sponge, a piece of string, and some weights. Each group places a saturated sponge on a table a given distance from the edge. Students then incrementally place weights on the end of the string, which is hanging off the edge of the table. As a class, we estimate the surface areas of the sponges that are in contact with each table. As a class we discuss and record how much weight or force it takes for each sponge of different area to be moved initially. The weight resembles the amount of force required to build up along a fault before it gives way and yields an earthquake. The area of the sponge represents the area of rock that moves during an earthquake. Students should conclude that it takes more force to slide the larger sponge. Students should be prompted to generalize that the larger the area of moving rock, the larger the earthquake. This discussion segues into the discussion of earthquake magnitude. The effects of an earthquake on a building may be shown by shaking a tall rectangular gelatin on a table. The table is bumped from the side, and the "building" should shake considerably. Begin discussion of population by asking students what the local, state, national, and global populations are. These would be good questions for students to research independently. Abbott includes many nice graphical representations of population fluctuations and growth. Provide notes on earthquakes and population growth. Provide one version of each equation that will be used in the exercises. Encourage and provide feedback.

*
Student tasks
*

Participate in sponge and weight exercise

Record data

Participate in concluding discussion

Take notes on earthquakes and population growth, particularly equations

Attempt to solve each equation for the independent variable

Practice calculations on worksheet

Respond to and discuss open-ended questions

*
Questions
*

Define an earthquake, seismic moment

Name two scales used to measure earthquake magnitude

Find the seismic moment of an earthquake with a given moment magnitude

Find the moment magnitude of an earthquake with a given seismic moment

Find the Richter scale magnitude of an earthquake that released a given amount of energy

Find the amount of energy released in an earthquake of a given Richter magnitude

Find the recurrence interval of an earthquake with a given minimum Richter magnitude

What is the current population of the United States?

What is the current population of the earth?

How can the growth rate of a population be found using the birth rate and death rate?

At the current growth rate, in what year will the world population be 10 billion?

At the current growth rate, what will the world population be in 2050?

What effects does the human population have on other species of animals and plant?

on natural resources?

Which natural phenomena have exponential relationships?