# 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

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## Goals and Objectives

By completing this unit, students will be able to perform the flowing tasks:

### Mathematical Topics

- 1) Discuss and provide examples of how mathematics is used to describe nature, and natural disasters in particular.
- 2) Define the following: variable, algebraic expression, equation, function, and mathematical model.
- 3) Use mathematical models to describe observed relationships between characteristics of natural disasters when values of some of the variables are known.
- 4) Derive mathematical models from existing equations and relations (solve multivariate equations for one of the variables).
- 5) Compare different classes of mathematical models and functions.
- 6) Provide examples of applications of each type of function to the study of natural disasters
- 7) Provide examples of dimensions and the units used to measure them
- 8) Represent functions as equation, tables, graphs, and verbal descriptions
- 9) Describe the domain and range of a function used to model a natural disaster
- 10) Draw a picture of a wave, and label the associated quantities or characteristics

### Natural Science Topics

- 1) Describe the relationship between earthquake magnitude and energy in at least two different ways (multiple representations of functions)
- 2) Define seismic moment, local magnitude, moment magnitude
- 3) Describe the relationship between seismic moment and moment magnitude in at least two different ways
- 4) Describe the relationship between earthquake magnitude and frequency of occurrence in at least two different ways
- 5) Calculate wavelengths, periods, and velocities of near-shore ocean waves
- 6) Describe the relationship between water depth and velocity of near-shore (shallow) ocean waves in at least two different ways
- 7) Make calculations using mathematical models of natural disasters phenomena
- 8) Classify the relationship between pairs of variables associated with various natural phenomena as one of the following: linear, direct variation, inverse variation, quadratic, or exponential.
- 9) Pose questions about natural disasters that could be answered by using a mathematical model
- 10) Describe the difference between a natural hazard and a natural disaster
- 11) Define tsunami, volcano, earthquake, and tornado