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UNIT I: EARTH SCIENCE MATH SKILLS, GRAPHING, AND MEASUREMENTS

Many students that have taken Earth Science have shown the ability to be accurate.

Accuracy is the ability to hit the target you are aiming for, in this class that could be a correct answer on a test that asks you to perform a set task.

What only a few students have shown is the ability to be precise. Precision requires that you are able to reproduce results time after time. This unit focuses on honing your ability to be both accurate and precise throughout the course.

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Let’s begin with some basic mathematical equations you could be counted on to use during the year. These are found on the front page of your Earth Science Reference Tables.

These will be known as your ESRTs or just Reference Tables

The ESRTs are the single most important document you will receive this year

There are 4 essential equations you will need to be familiar with in order to be successful in the course:

Eccentricity: This equation helps determine the “roundness” of an orbital path (for example, the Earth’s path around the Sun)

Gradient: This equation helps show the change of measurements over a distance (for example, the change in elevation over a distance on a mountain)

Additional Equations

Rate of Change: This equation helps show how quickly or slowly a change happens (for example, a change in air pressure over 24 hours)

Density: Describes the mass within a given volume of an object (for example, the density of a basalt sample)

Ensuring Accuracy

In order to ensure that your responses are accurate throughout the course, there are some fundamental concepts you need to understand.

Rounding: When asked to round a number, round up only if the number to the right is 5 or higher. There is no “rounding down”

Know how to extend an answer or shorten it to the tenths, hundredths, or thousandths places

Accuracy Beyond Whole Numbers

Often we want to know measurements that are more accurate than simply a whole number.

0.0 To the tenths place 0.00 To the hundredths

place 0.000 To the

thousandths place

Units

Almost all measurements in Earth Science must be coupled with units. One exception is when eccentricity is calculated.

All answers must include units unless they are already printed

Lines As Equations

You may be familiar with how you can graphically represent an equation in math. The same is possible in Earth Science, but in a much more simplified way.

The lines you draw in Earth Science will be equal to a value. They are called isolines.

Isolines

Isolines ISOLATE differing values in Earth Science

These values can measure a number of things, such as: Temperature Pressure Elevation Pollution Concentration

Properties of Isolines

Think of isolines like fences that separate neighbors. The neighbors live at different addresses and the isolines keep those properties separate.

Rules for Isolines: Isolines cannot cross

(they are never equal in value)

Isolines must be drawn in smooth arcing lines

All isolines are a part of a closed loop, whether or not you can see the whole loop. All loops must continue off the page unless they close on the page.

Isoline Rhyme

Remember: If true, go through (with your line)

If your line is in between the two values it must continue between those two points.

This is the 50 ft. contour line (contour lines measure elevation), notice how it passes in-between 49 and 51.

Practice

The following are temperature measurements for a classroom in degrees Celsius. Draw isotherms for every 2 degrees Celsius.

Determining the Value of an Isoline

How is an isoline’s value determined if it isn’t labeled? Only some isolines are labeled.

These are known as index isolines

Steps can be taken in order to determine the value of all unlabeled lines

Steps to determining isoline intervals:

Determine the difference in value between 2 close index isolines (lines that are labeled)

600-500 = 100

54

32

1

Step #2:

Count the number of lines from one index isoline to the next

1, 2, 3, 4, 5

Step #3:

Divide: (Difference between

index isolines)/ # of isolines

100 / 5 = 20

Each line increases or decreases by 20

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520

In Earth Science we sometimes would like to know how quickly values change on a field map. We can actually assign a number to this change by using the equation for gradient:

Gradient = change in field value / distance

Determining Gradient

Find the difference in value between points

Divide by the distance between those points

In this example, let’s assume the distance between points is 2 miles and the measurements on the map are in feet.

600 – 500 = 100 100 / 2 miles

Graphing in Earth Science

You will often be asked to use graphs to display data on in-class tests, the midterm, and the final. There are 3 common graphs found in Earth Science:

Line Graphs Bar Graphs Relationships Graphs

General Rules

Be accurate: all points/bars must be correct for the graph to be considered accurate.

Label axes where appropriate and recheck all points/bars

Line Graphs

Line graphs typically show a change in value over time

All points must be connected with a continuous line

Bar Graphs

Bar graphs usually show values of different entities

Example: Rotational periods of planets

All bars must be flat across the top and NOT angled

Relationships Graphs

Show relationships between two things

Negative: As X increases, Y decreases or as X decreases, Y increases

Positive: As X increases, Y increases or as Y increases, X increases

In Earth Science we will often be dealing with very large numbers. Since this is the case, it becomes necessary in some instances to use scientific notation to represent numbers. Scientific notation will look something like this:

1 x 103

or1.0 x 103

The exponent dictates the direction the decimal must move in order to express the number in standard form.

If the exponent is positive: The decimal moves to the right, equal to the

number of the exponent Example: 1 x 103 1000

If the exponent is negative (1 x 10-3): The decimal moves to the left, equal to the

number of the exponent Example: 1 x 10-3 0.001

Converting Standard Form Numbers to Scientific Notation

The number being written must begin with a number higher than zero and only a single digit before the decimal point.

For example: 0.00093 will become 9.3

If the decimal moved to the right, the exponent is equal to the number of spaces it moved with a preceding (-)

For the example above: 0.00093 will ultimately become 9.3 x 10-4

If the decimal moved to the left, the exponent is positive.

867,000 will become 8.67 x 105