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Beyond Crossroads: Summer Workshop

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Beyond Crossroads: Summer Workshop

Where

in the World

Am I?

Integrating Mathematics

with Geology

- Problem Solving
- Modeling (real world situations)
- Reasoning as they develop convincing mathematical arguments
- Connecting with other disciplines
- Communicating mathematics
- Using Technology to enhance mathematical thinking & reasoning

- Developing mathematical power. Students will engage in rich experiences that encourage independent exploration in mathematics, develop and reinforce tenacity and confidence in their abilities to use mathematics, and be inspired (them)* to pursue the study of mathematics and related disciplines.
- Linking multiple representations. Students will select, use, and translate among mathematical representations-numerical, graphical, symbolic, and verbal-to organize information and solve problems using a variety of techniques.

- How to use a compass
- How to read UTM’s from a Quad
using grid overlays

- How to use a GPS

- Kinesthetic approach to degree measurement
- Brunton Baseplate Compass

Direction of Travel Arrow

Read Bearing Here

Orienting Needle

Azimuth Ring

Magnetic Needle

Base Plate

- Hold compass parallel to ground with Direction of Travel Arrow pointing away from you.
- Be sure to avoid metal jewelry or belt buckles.
- Suppose you want to walk in the direction of 270 degrees. (We are inside, so your direction will not be accurate…pretend we’re outside.)

- First, make sure the hollow orienting needle is pointed North.
- If it is not, stop now and adjust the azimuth ring with the 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.

Finally, walk following the Direction of Travel Arrow.

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

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

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

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

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

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

For this reason many scientists object to using it.

- You may be familiar the Mercator projection as appears on the left.
- A Transverse Mercator projection appears on the right.
- The Transverse Mercator projection is very accurate in narrow zones.

The globe is subdivided into narrow longitude zones, which are projected onto a Transverse Mercator projection.

A grid is constructed on the projection, and used to locate points.

Universal Transverse

Mercator projection

A cylinder touching the globe at the central meridian of a longitude zone lies entirely outside the earth.

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

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

UTM grid coordinates are expressed as a distance in meters:

to the east, "easting",

to the north, "northing".

There are no negative numbers

Minimum and maximum easting values are:

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

465,000 mE and 515,000 mE at 84° N

- Here’s Why:

At the equator

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

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.

42 90 155 N

13 5 20 685 E

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

42 90 155 N

13 5 20 685 E

- Look at the bottom of your map.
- The number 715000mE is read as, “715,000 meters East.”
- 715 is short-hand for 715,000, and is 1000 meters West of 716000mE.

- The number 4763000mN is read, “4,763,000 meters north” of the equator.
- The next UTM number above is 4764,
and is 1000 meters north.

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

- If you want to find your location with more precision than is available from the grid lines on the map,
you will need a tool that is

marked in finer divisions.

One such tool is a

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.

- Your map has a UTM grid drawn for you.
- Many quadrangle maps show only the blue tick marks on the edges, so use a straight edge to create a grid by connecting the marks with a pencil.

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

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

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

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

- The 5945 and 8163 locate the 1000 meter square containing the star.

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

- The 5945 and 8163 locate the 1000 meter square containing the star.