Activity
Day
1
Begin
by asking the students:
“ How would you tell somebody in England exactly where Bangladesh is in
the world? How do ships know their location out in the middle of the Pacific
Ocean?”
Hopefully somebody will mention navigation and bring up the ideas of
latitude and longitude. If nobody has a clue, then use the following “activity” to
get the idea across of laying out a grid that everybody can agree upon
and use that grid for finding the location of something.
Quickly
have the students arrange the desks in straight rows
and columns and move to a specific desk. Ask the students, “How
would you describe my location in the room?” Have
the students discuss how to do this, and, hopefully,
someone will point out that you need a “starting
point” or “origin” to give distances
and directions to your location. The class will also
need to agree which direction is which (north, south,
east, and west) in order for the coordinates to make
sense. Pick a specific student as the “origin” of
the coordinate plane and have that student give the coordinates
of your location. Do this several times with different
students as the origin until the class understands the
concept of the coordinates. To assess how well the students
understand, pick an origin and wander around asking students
at random, “What are your coordinates?” Insist
that the students give their coordinates in terms of
two directions, such as, “3 desks north and 4 desks
east.”
If
somebody does mention latitude and longitude, ask the
class, “How can we model these concepts using what
we have here in the classroom?” Allow time for
students to discuss ideas. They could use the desks as
described in the paragraph above or ceiling tiles or
floor tiles if applicable. Be open and accept any reasonable
answer that has a rectangular grid connected to it. Again,
insist that the students give their coordinates in terms
of two directions, such as, “3 tiles south and
6 tiles west.”
Tell
the students that there are maps of the world that are
laid out on a similar rectangular grid, just like the
grid they used in the classroom. Pass out the Mercator
Projection maps. (This map can be found at http://alabamamaps.ua.edu/world/world/world2.pdf)
Explain that Mercator Projection is different because
the grid is rectangular and this causes distortion in
the size of the countries as you move closer to the poles.
(See Teacher Background, Mercator Projections.)
Have
the students find and darken the lines representing the
equator and Prime Meridian on the map. Tell the students
that the point of intersection of these two lines is
the origin from which coordinates are calculated. The
darkened lines also divide the projection into four quadrants,
which are labeled quadrants I, II, III, and IV in their
standard positions as if on a coordinate plane. Ask the
students to tell you the quadrant the following coordinates
are in:
1. 
2. 
3. 
Tell
the students that the quadrants also allow us to use
positive and negative Cartesian coordinates to find locations.
Ask them, “Looking at the map, which coordinates
would you expect to be positive?” Which would be
negative? (North latitudes and East longitudes would
be positive while South latitudes and West longitudes
would be negative). Discuss the importance of which direction
comes first in the coordinate pairs. (Degrees of latitude
come first and then degrees of longitude, which are backwards
from the normal ways of plotting points as the first
number gives the location vertically and the second number
gives you the location horizontally) Ask the students
the range of numbers valid for each coordinate. (Degrees
of latitude can vary from  and
degrees of longitude can vary from )
Ask the students to tell you the quadrant the following
coordinates are in:
1. 
2. 
3. 
Give
the students the following coordinates to locate on their
map: (these are just examples; you may choose your own.)
1. (Houston,
Texas)
2.  (Nairobi,
Kenya)
3.  (Site
of Titanic Sinking)
Homework
Since
the students will be approximating the locations of tectonic
plates later in science by plotting the locations of
earthquakes, you may use the following website to select
the coordinates in degrees latitude and longitude of
current earthquakes: http://neic.usgs.gov/neis/bulletin/ .
If you want the coordinates in positive or negative Cartesian coordinates,
use the following website instead: http://earthquake.usgs.gov/recenteqsww/Quakes/quakes_all.html.
Round the degrees to the nearest whole number.
In
social studies the students will be looking at tsunami
and their locations. Below is a list of coordinates for
earthquakes that have caused tsunami in the past. Have
the students plot their locations on their maps and identify
the country as well:
1.  (Alaska)
2.  (Chile)
3.  (Indonesia)
4.  (Aleutian
Islands)
5.  (Kamchatka
Peninsula, USSR)
6.  (USA-California
coast)
Source: http://www.prh.noaa.gov/ptwc/olderhmsg
Day
2
Go
over the students’ maps and locations from the
day before. Discuss any questions the students might
have. Tell the students that there are many different
types of maps, each having both good and bad aspects.
Pass out the Robinson Projection maps, which may be found
at http://alabamamaps.ua.edu/world/world/world3.pdf ,
and ask, “How is this map different from the Mercator
Projections we used yesterday?” Allow time for
students to discover and discuss differences. Pass out
Latitude and Longitude maps as well to help the students
find lines of latitude and longitude on the Robinson
Projection as they are curved this time rather than being
straight lines. (http://alabamamaps.ua.edu/world/world/page006.pdf)
For
practice, have the students find the location of the
following cities given their coordinates:
1.  (Las
Vegas, Nevada)
2.  (Shanghai,
China)
3.  (Melbourne,
Australia)
4.  (Karachi,
Pakistan)
5.  (Jakarta,
Indonesia)
(I
just chose these cities at random. You can get the coordinates
of many cities at http://www.indo.com/distance/)
Ask
the students, “What else are maps used for besides
finding locations?” (finding distance) Now we need
to talk about how distances on maps can be related to
latitude and longitude.” For convenient measurement
of distance, mariners developed the nautical
mile (nm), to fit measures of latitude and longitude.
By definition, 1 minute of longitude at the
equator = 1 nautical mile( ).
Since there are 60 minutes in one degree, this means
at the equator, one degree of longitude = 60 nm =
69.05 miles. To convert nautical miles to miles,
use the website http://www.metric-conversions.org/length/nautical-miles-to-miles.htm or
the conversion .
Have
the students convert the following distances (you could
introduce unit analysis here)
1. 
2. 
3. 
4. 
Ask
the students, “What’s the problem of using
longitude to define 1 nautical mile?” Point out
that the distance covered by one degree of longitude
shrinks as we move away from the equator and towards
the poles, where all the lines of longitude converge
to one point. On the other hand, minutes of latitude
do not shrink which is why even modern mariners use the
following relationship:
one
degree of latitude = 60 nm = 69.05 mile everywhere
on earth, or
one minute of latitude = 1nm everywhere
on earth
Source: http://www-ocean.tamu.edu/~dkobilka/navigation.html
Have
the students calculate the number of nautical miles (and
miles) you travel between the following two locations.
(Keep the meridian the same so only the latitude is changing)
1.  
2. 
Tell the class, “We are now going to calculate the distance between
two locations where only the longitude is different. Looking at the map
you can see that the distance covered by one degree of longitude at 35° N latitude
is different from the distance covered by one degree of longitude at
50° N latitude because the meridians are father apart at
35° N latitude than they are at 50° N latitude.” To
calculate the distance one degree of longitude at any latitude use the
formula
For
example, the distance covered by one degree of longitude
at 35° N latitude is
and
the distance covered by one degree of longitude at 50° N latitude
is
Now
have the students calculate the distance from 
Remind
the students that they must calculate the distance covered
by one degree of longitude at the given latitude before
they can calculate the number of nautical miles traveled
by changing the longitude.
Homework
Do the Distances, Latitude, and Longitude sheet for homework
Day 3
Begin
by going over the homework from Day 2 and allow time
for discussion of the “Thought Question.” Assuming
the world is flat, calculate the number of nautical miles
you travel “vertically” by using the change
in the degrees of latitude and the nautical miles you
travel “horizontally” by using the change
in the degrees of longitude. This gives the students
two sides of a right triangle and they would then use
the Pythagorean Theorem, from geometry, to find the length
of the hypotenuse, which is the distance they are looking
for. (It’s much more complicated if you use a curved
surface.)
Tell
the students, “We needed to use geometry to get
an approximate answer for the thought question”.
Today we are also going to use some more geometry, specifically
circles, to find the coordinates of the location of the
epicenter of an earthquake.” Substantial
parts of this lesson are derived from “Earthquakes” http://mimp.mems.cmu.edu/~ordofmag/earthqua/earqua.htm
I would
recommend putting Figure 6-2, the seismogram from Dallas,
on the same page but above Figure 6-1. This will put
the data from Dallas directly above the graphs and should
make it easier to explain/demonstrate the steps the students
need to follow to complete the example.
Guide
the students through each step, allowing them the time
to complete the step before moving on to the next. The
students may have some trouble making the dots on the
tracing paper. Tell them that it does not matter where
the first dot is placed, but that the second dot must be
placed so there is a 3.3 minute gap between the dots.
Demonstrate sliding the tracing paper across the graph
until the two dots line up with the curves; one dot should
be on the S-wave curve and the other dot should be on
the P-wave curve. Drop a vertical line down to the horizontal
axis, and the value on the horizontal axis will tell
you the distance from Dallas to the epicenter (roughly
1200 miles).
Homework
Have
the students follow the same steps for the data from
the other three seismograms, Figure 6-3. using the location
of one of the cities as the center, draw a circle with
the appropriate length radius (the distance from the
city to the epicenter). Do this for the other two cities
as well. The point of intersection of the three circles
is the epicenter of the earthquake. Have the students
estimate the location of the epicenter in degrees latitude
and longitude or positive and negative Cartesian coordinates.
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