Beyond Crossroads: Beyond Crossroads: Summer WorkshopSummer Workshop

Where Where

in the World in the World

Am I?Am I?

MACMAC33 2006 Project2006 Project

Integrating Mathematics Integrating Mathematics

with Geologywith Geology

CWC Students & GPSCWC Students & GPS

7 + 1 Standards 7 + 1 Standards for Intellectual Developmentfor Intellectual Development

from Crossroads and Beyond Crossroadsfrom Crossroads and Beyond Crossroads Problem SolvingProblem Solving Modeling (real world situations)Modeling (real world situations) Reasoning as they develop Reasoning as they develop

convincing mathematical argumentsconvincing mathematical arguments Connecting with other disciplinesConnecting with other disciplines Communicating mathematicsCommunicating mathematics Using Technology to enhance Using Technology to enhance

mathematical thinking & reasoningmathematical thinking & reasoning

7 + 1 Standards 7 + 1 Standards for Intellectual Developmentfor Intellectual Development

from Crossroads and Beyond Crossroadsfrom Crossroads and Beyond Crossroads

Developing mathematical power. Developing mathematical power. Students will engage in rich experiences that encourage independent Students will engage in rich experiences that encourage independent exploration in mathematics, develop and reinforce tenacity and confidence exploration in mathematics, develop and reinforce tenacity and confidence in their abilities to use mathematics, and be inspired (them)in their abilities to use mathematics, and be inspired (them)** to pursue the to pursue the study of mathematics and related disciplines.study of mathematics and related disciplines.

Linking multiple representations. Linking multiple representations. Students will select, use, and translate among mathematical Students will select, use, and translate among mathematical representations-numerical, graphical, symbolic, and verbal-to organize representations-numerical, graphical, symbolic, and verbal-to organize information and solve problems using a variety of techniques.information and solve problems using a variety of techniques.

Topics CoveredTopics Covered

How to use a compassHow to use a compass How to read UTM’s from a QuadHow to read UTM’s from a Quad

using grid overlaysusing grid overlays How to use a GPSHow to use a GPS

Using a compassUsing a compass

Kinesthetic approach to degree Kinesthetic approach to degree measurementmeasurement

Brunton Baseplate CompassBrunton Baseplate Compass

PartsParts

Direction of Travel Arrow

Azimuth Ring

Base PlateMagnetic Needle

Orienting Needle

Read Bearing Here

Compass InstructionsCompass Instructions

Hold compass parallel to ground with Hold compass parallel to ground with Direction of Travel Arrow pointing Direction of Travel Arrow pointing away from you.away from you.

Be sure to avoid metal jewelry or belt Be sure to avoid metal jewelry or belt buckles.buckles.

Suppose you want to walk in the Suppose you want to walk in the direction of 270 degrees. (We are direction of 270 degrees. (We are inside, so your direction will not be inside, so your direction will not be accurate…pretend we’re outsideaccurate…pretend we’re outside.).)

First, make sure First, make sure the hollow the hollow orientingorienting needle needle is pointed North. is pointed North.

If it is not, stop If it is not, stop now and adjust now and adjust the azimuth ring the azimuth ring with the with the orienting needle.orienting needle.

Next, rotate the Azimuth Ring so that 270º is at the Direction of Travel Arrow

Now, rotate your body and the entire compass until the Magnetic Needle aligns North with the Orienting Needle.

Put “Fred to Bed”Put “Fred to Bed”

Using a Using a CompassCompass

Finally, walk Finally, walk following the following the Direction of Direction of Travel Travel Arrow. Arrow.

Your next direction is 120º. Set your compass and orient it.

Suppose you would like to identify the Suppose you would like to identify the bearing from where you are standing to the bearing from where you are standing to the nearest doorway.nearest doorway.

Face the doorway so that the direction of Face the doorway so that the direction of travel arrow is pointing in the direction of travel arrow is pointing in the direction of the doorway.the doorway.

Rotate the magnetic needle until it is in the Rotate the magnetic needle until it is in the orienting needle.orienting needle.

Read the bearing at the direction of travel Read the bearing at the direction of travel arrow. Remember, each tick mark arrow. Remember, each tick mark represents 2 degrees.represents 2 degrees.

Understanding UTM’s

Understanding UTM’sUnderstanding UTM’s

Unlike latitude and longitude, the Unlike latitude and longitude, the UTM system is man-made. (It was UTM system is man-made. (It was developed by the U.S. Army Corps of developed by the U.S. Army Corps of Engineers in the 1940’s.)Engineers in the 1940’s.)

For this reason many scientists For this reason many scientists object to using it.object to using it.

Understanding UTM’sUnderstanding UTM’s

You may be familiar the Mercator You may be familiar the Mercator projection as appears on the left.projection as appears on the left.

A A TransverseTransverse Mercator projection appears Mercator projection appears on the right.on the right.

The Transverse Mercator projection is very The Transverse Mercator projection is very accurate in narrow zones.accurate in narrow zones.

The world has 60 zones, each 6The world has 60 zones, each 6oo..

Understanding UTMUnderstanding UTM The globe is subdivided The globe is subdivided

into narrow longitude into narrow longitude zones, which are zones, which are projected onto a projected onto a Transverse Mercator Transverse Mercator projection.projection.

A grid is constructed on A grid is constructed on

the projection, and used the projection, and used to locate points. to locate points.

UTM’sUTM’s Universal Universal TransverseTransverse

Mercator projectionMercator projectiona.a. A cylinder touching the A cylinder touching the

globe at the central globe at the central meridian of a longitude meridian of a longitude zone lies entirely outside zone lies entirely outside the earththe earth..

b.b. A cylinder that touches the A cylinder that touches the outer edges of the zone outer edges of the zone lies entirely inside the lies entirely inside the earth within the zone.earth within the zone.

c.c. A cylinder that touches the A cylinder that touches the globe at two points is the globe at two points is the best compromise.best compromise. The The scale along the central scale along the central meridian of each zone is meridian of each zone is 0.9996 of true scale. True 0.9996 of true scale. True scale occurs about 180 scale occurs about 180 kilometers east and west kilometers east and west of the central meridian.of the central meridian.

The upside of the grid system is that, since the grid is rectangular and decimal, it is far easier to use than latitude and longitude.

The downside is that, unlike latitude and longitude, there is no way to determine grid locations independently.

Understanding UTM’sUnderstanding UTM’s

Understanding UTMUnderstanding UTM

UTM grid coordinates UTM grid coordinates are expressed as a are expressed as a distance in meters:distance in meters:

to the east, "easting", to the east, "easting",

to the north, "northing".to the north, "northing".

There are no negative There are no negative numbersnumbers

Understanding UTMUnderstanding UTM

Minimum and Minimum and maximum easting maximum easting values are:values are:

167,000 mE and 167,000 mE and 833,000 mE (at 833,000 mE (at equator)equator)

465,000 mE and 465,000 mE and 515,000 mE at 84° 515,000 mE at 84° NN

Understanding UTMUnderstanding UTM

Here’s Why:Here’s Why:

1 111

6 666 666,000

1666,000 333,000

2

500,000 333,000 167,000

500,000 333,000 833,000

km

km m

At the equator

Understanding UTM’s

The GRID OVERLAY is accurate to a precision of 100m.

13 5 20 685 E

42 90 155 N

Using a UTM grid overlay

The grid overlay is placed on the map with its edge aligned with the grid lines.

The example shown here locates the star to a precision of 100m.

Understanding UTM’s

The CORNER TOOL is accurate to a precision of 10m.

13 5 20 685 E

42 90 155 N

Reading UTM’sReading UTM’s Look at the bottom of your map.Look at the bottom of your map.

The number The number 771515000m000mEE is read as, is read as, “715,000 meters East.” “715,000 meters East.”

7715 is short-hand for 715,000, and is 15 is short-hand for 715,000, and is 1000 meters West of 1000 meters West of 771616000m000mE.E.

Reading UTM’sReading UTM’s The number The number 47476363000m000mNN is read, is read,

“4,763,000 meters north” of the “4,763,000 meters north” of the equator.equator.

The next UTM number above is The next UTM number above is 474764, 64, and is 1000 meters north.and is 1000 meters north.

A UTM measuring tool is used for A UTM measuring tool is used for measuring in between.measuring in between.

Using a UTM grid overlayUsing a UTM grid overlay

If you want to find your location with If you want to find your location with more precision than is available from more precision than is available from the grid lines on the map, the grid lines on the map,

you will need a tool that is you will need a tool that is

marked in finer divisions. marked in finer divisions.

One such tool is a One such tool is a

grid overlay. grid overlay.

Using a UTM grid overlayUsing a UTM grid overlay The grid overlay The grid overlay is is

placed on the placed on the map with its edge map with its edge aligned with the grid aligned with the grid lines.lines.

The example The example shown here shown here locates the star locates the star to a precision to a precision of 100m. of 100m.

Using a UTM Grid OverlayUsing a UTM Grid Overlay

Your map has a UTM grid drawn for Your map has a UTM grid drawn for you.you.

Many quadrangle maps show only Many quadrangle maps show only the blue tick marks on the edges, so the blue tick marks on the edges, so use a straight edge to create a grid use a straight edge to create a grid by connecting the marks with a by connecting the marks with a pencil.pencil.

Using a UTM grid overlayUsing a UTM grid overlay

The position of The position of the mark can be the mark can be determined determined more precisely more precisely using a corner using a corner tool. tool.

Using a UTM Corner RulerUsing a UTM Corner Ruler

A UTM Corner Ruler consists of two A UTM Corner Ruler consists of two scales at right angles to each other. scales at right angles to each other. On a 1:24,000 scale map you will be On a 1:24,000 scale map you will be able to determine a position to within able to determine a position to within a 10m square. a 10m square.

Using a UTM Corner RulerUsing a UTM Corner Ruler

Start by placing the top right corner Start by placing the top right corner of the Corner Ruler on the SW corner of the Corner Ruler on the SW corner of the UTM grid that contains the of the UTM grid that contains the feature. (The ruler edges should feature. (The ruler edges should extend to the West and South.)extend to the West and South.)

Using a UTM Corner ToolUsing a UTM Corner Tool

In 10m abbreviated format In 10m abbreviated format the coordinates of the star the coordinates of the star are:are:•5945 5945 (159,450(159,450 m E),m E), andand •8163 8163 (4,781,630(4,781,630 m N)m N)..

The The 5945 5945 and and 81638163 locate locate the 1000 meter square the 1000 meter square containing the star.containing the star.

Using a UTM Corner ToolUsing a UTM Corner Tool

In 10m abbreviated format In 10m abbreviated format the coordinates of the star the coordinates of the star are:are:•5945 5945 (159,450(159,450 m E),m E), andand •8163 8163 (4,781,630(4,781,630 m N)m N)..

The The 5945 5945 and and 81638163 locate locate the 1000 meter square the 1000 meter square containing the star.containing the star.

Atlas GPSAtlas GPS

Find the UTM coordinates and Find the UTM coordinates and distances between each. distances between each.