# 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.

## Classroom Activities - Lesson Plans

### Lesson Number 1 - Functions as Mathematical Models of Natural Phenomena

*
Objective(s) - students will be able
*

- 1) To discuss and provide examples of how mathematics is used to describe nature, and natural disasters in particular
- 2) To define and provide an example of a function and a mathematical model
- 3) To provide examples of dimensions and the units used to measure them
- 4) To apply the concepts of function, independent and dependent variable to describe relationships between natural phenomena using multiple representations of functions.
- 5) To classify the relationship between pairs of variables associated with natural disasters as linear, quadratic, or exponential
- 6) To pose questions about natural disasters that may be answered by using a mathematical model
- 7) Describe the difference between a natural hazard and a natural disaster
- 8) Define tsunami, volcano, earthquake, and tornado

*
Prerequisite skills
*

graphing two-variable data, evaluating expressions, translating verbal phrases and sentences to algebraic expressions and equations, solving equations, creating and interpreting tables and graphs on coordinate plane

*
Materials
*

Ruler or tape measure, thermometer, clock, scale

Worksheet or text with tables of different types of function, without the equations

*
Vocabulary - Terms & Symbols
*

function, domain, range, independent variable, dependent variable, f(x) = y, vertical line test, mapping diagram, earthquake, volcano, water wave, tornado, tsunami, dimension, unit

*
Strategy
*

Students should be prompted to discuss different types of phenomena that are measured. They should also discuss what types of instruments are used for the measurements. This discussion should result in defining
*
dimension
*
as in (Banks, 1998). As a class, we list different units that are used to measure the dimensions of mass, force, length, time and temperature. Review the definition of function. Use the student as function input metaphor - can't go to two places at once. Encourage students to come up with measureable quantities and measurement units. Prepare a measurement activity that involves a simple linear function. Prepare tables of different types of functions related to natural disaster for review of function types. Prompt students to classify each table as a type of function. Describe natural hazards and disasters, the different types of natural disasters, and their characteristics. Use the case studies to provide an example of each type of disaster to be studied. An overhead slide show would nicely show the results of the disasters. Ask questions about the characteristics of natural disasters, i.e. "are these two related? How so?" Provide encouragement and feedback.

*
Student tasks
*

Form small groups

List examples of quantities that we measure in the environment

Classify each type of quantity by its dimension, and give an example of units

Discuss how some pairs of quantities may be related

Find two quantities that have a functional relationship

Describe the functional relationship in words using "is a function of" and in symbols using a = f(b)

Present one of your functions to the class, with both verbal and symbolic representations

Engage in measurement activity involving length, time, and force, using ruler, clock, and scale A distance, rate, and time problem would suffice.

Classify a function represented with a table as linear, quadratic or exponential.

Answer elementary questions about the natural disasters discussed, define terms.

*
Questions
*

For each of the following pairs of natural phenomena, determine the dimension and possible units of each variable, and determine if there may be a functional relationship between the two. Then identify the independent and dependent variables, and write a sentence that describes the relationship.

time of day & temperature

month & temperature

location & weather

seismic wave (moment) amplitude & Richter scale magnitude

number of deaths & earthquake magnitude

number of deaths & building materials

Give examples of dimensions and units

What is the difference between a natural hazard and a natural disaster?

What questions can we ask about these natural disasters?

What type of mathematics would help us answer these questions?

### Lesson Number 2 - Modeling Tsunami Height, Tornado Wind Speed, and Safe Distance from Volcanic Bombs with Quadratic and Root Functions

*
Objective(s) - students will be able
*

- 1) To use mathematical models to describe observed relationships between characteristics of natural disasters when values of some variables are known
- 2) To derive mathematical models from existing equations and relations (solve multivariate equations for one of the variables)
- 3) To provide examples of the application of a quadratic or square root function to natural disasters
- 4) To represent functions as equations, tables, graphs, and verbal descriptions
- 5) To describe the domain and range of functions used to model natural disasters
- 6) To draw and label a simple pictoral representation of a wave
- 7) To calculate wavelengths, periods, depths, and velocities of near-shore ocean waves
- 8) To describe the relationship between water depth and wave velocity of shallow water waves in at least two different ways

*
Prerequisite skills
*

Vertex form of quadratic function, translations of parabolas, solving equations using square roots

*
Materials
*

graphing calculator, graph paper, worksheets with student tasks, questions, and a place to write answers

*
Vocabulary - Terms & Symbols
*

Parabola, vertex, axis of symmetry, x-intercepts, maximum, minimum, Wave, water depth, wave velocity, run up, velocity

*
Strategy
*

A wave can be modeled by having two students hold a piece of rope in front of the class. One student propagates a wave, and the other students can be prompted to estimate the height of the wave. Another student propagates a larger wave, and again the students can estimate the height of the second wave. A discussion explaining the definition of amplitude follows. The amplitude here can be related to water depth instead of wave height. Provide one form each of the equations for tsunami and tornado. Prompt students to derive the other form of the relation. Provide students with specific calculation questions that can be solved using the presented equations. Provide encouragement and feedback

*
Student tasks
*

Describe a wave, and its characteristics.

Give examples of waves

Give examples of waves involved with natural disasters

Take notes on tsunami and tornado equations

Attempt to solve equations for the independent variable

Answer questions using either form of the given relations

*
Questions
*

Define a wave, tsunami, volcano and tornado

Find the wavelength of a tsunami with given velocity and period

Find the period of a tsunami with given velocity and wavelength

Find the velocity of a tsunami with given wavelength and period

Find the height of a tsunami with given velocity

Find the velocity of a tsunami with given water depth

Find the energy of a tsunami with given water depth and wavelength

Find the wavelength of a tsunami with given water depth and energy

Find the height of a tsunami with given wavelength and energy

What is a shallow water wave?

Find the safe distance from a volcano that shot a pyroclasic bomb with a given initial velocity

Find the initial velocity of a bomb that lands a given distance from the chute of a volcano

What is the difference between a tornado and a hurricane?

What scale is used to measure tornadoes?

Find the magnitude of a tornado with given wind speed

Find the wind speed of a tornado with a given magnitude

Compare the energies in two shallow water waves with two given sets wavelength and height

What is the relationship between these energies compared to their heights?

Which natural phenomena have quadratic relationships?

Write a sentence describing the relationship between tsunami height, wavelength and velocity

Write a sentence describing the relationship between initial velocity of volcanic bomb and the safe distance from the volcano

Write a sentence describing the relationship between tornado wind speed and magnitude