GLOBE
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2014 Relative and Absolute Directions Learning Activity - 1 GPS
Appendix
Welcome Introduction
Protocols
Learning Activities
Relative and Absolute
Directions
Time
From one to ve class periods depending on
which steps you choose to do
Level
All levels with some exceptions noted
Materials and Tools
Paper and pencil
Graph paper
Magnetic compasses
Drawing compasses (for drawing
circles)
Globes
Metric rulers and meter sticks
Bar magnet
Preparation
None
Prerequisites
Beginning levels: Students should be at
the appropriate developmental level to be
able to learn about the use of latitude and
longitude to nd a location.
Intermediate and advanced levels: Basic
understanding of degrees, angles and
coordinate systems.
!
?
Purpose
Learning about latitude and longitude
Developing math skills
Overview
Students begin by asking the simple
question: “Where Am I?” Then they learn
about the magnetic Earth and the use of
compasses and angles. Students also
learn about the difference between relative
and absolute locations.
Throughout this activity, students practice
using a variety of math skills.
Student Outcomes
Learn how to locate a position.
Science Concepts
Latitude and longitude determine
location.
A compass may be used the Earth’s
magnetic eld to give direction.
Physical Science
The position of an object can be
described by locating it relative to
another object.
Geography
Location is used to display information
on maps.
Science Inquiry Abilities
Use a magnetic compass to accurately
determine angular direction.
Identify answerable questions.
Design and conduct scientic
investigations.
Develop descriptions and explanations
using evidence.
Communicate procedures and
explanations.
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2014 Relative and Absolute Directions Learning Activity - 2 GPS
for students to ask are: How can you describe
your location to another student: in your
classroom? in another classroom? in another
school in town? in another town? in another
country? Did students describe their location
using relative or absolute references?
Emphasize their reference frames.
Step 2. Attempting to Impose a Reference
Frame: The Magnetic Earth (For all levels)
Our planet projects a gigantic magnetic eld
as if it contained a large bar magnet. See
Figure GPS-RE-1. Another magnet (like a
magnetized needle) will be attracted to our
planet’s magnetic poles. A magnetic compass
contains a magnet which can spin freely and
be observed. Thus, magnetic compasses
are useful navigational instruments because
they allow one to see the direction of Earth’s
magnetic eld, which almost lines up with
Earth’s north and south poles.
Suspend a bar magnet on a string away from
large metal objects and allow the magnet to
stop any rotation or spin. Attach the string to
Background
The GLOBE program uses GPS receivers
to determine the latitude and longitude of
GLOBE study sites. However, the ideas of
latitude and longitude, coordinates attached
to absolute reference systems, or angles
from north may be new to many students.
This set of activities introduces these
concepts.
When you ask students, “Where are you?”,
they may respond, “At home” or “At school.”
The answers are in their own local reference
frame. If you use a magnetic compass to
determine the direction to a tree that is north
of you, you will probably conclude that the
tree is to your north. However, if you move
east or west by any substantial amount and
use the same compass to determine your
direction to the same tree, you will nd the
tree to be to your northeast or your northwest.
Neither the tree nor Earth’s magnetic poles
have moved, but your compass indicates
a different direction to the tree. There is
something absolute about the positions of
the tree and the poles, but there is something
relative about your measurement technique.
The starting point moved.
If we impose a gridded coordinate system
upon our geographic area of interest or
the entire world and number the various
lines on the grid, we now have a reference
frame in which we can uniquely determine
any location independent of the relationship
between your location and that of another
individual. Latitude and longitude are the
names of the values for the coordinate
system in which we shall be working for
geographic determination of locations with
the Global Positioning System.
What To Do and How To Do It
Step 1. Relative Positions: Where am I?
(For all levels)
Have students ask themselves the question,
“Where am I?” and have them list words or
draw a rough picture of where they are. Lead
a class discussion on what denes “where
are we?”
Encourage questions and time for reection
on where a person is and how one might
explain where anyone was. Good questions
Figure GPS-RE-1: The Earth as a Giant Magnet
Figure GPS-RE-2: Suspended Bar Magnet
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2014 Relative and Absolute Directions Learning Activity - 3 GPS
Appendix
Welcome Introduction
Protocols
Learning Activities
the ends of the magnet as shown in Figure
GPS-RE-2.
Ask students what will happen. The magnet
will eventually stop spinning so that its poles
are aligned with north and south directions.
Students can test the north-south direction
by comparing the magnet with a magnetic
compass.
To use the compass, hold the compass on
your ngers of your outstretched hand and
arm. Hold the compass at relative to the
ground so that the needle can move freely,
and keep it away from all metal objects.
Position yourself so that you can look across
the compass through north while waiting for
the needle to stop moving. Do not place the
compass near the magnet; it will lessen the
effectiveness of the compass.
Step 3. Introductory Compass Angles
(For beginning levels)
On a blank sheet of paper, record the following
observations, using a magnetic compass for
direction.
• Record your specic location (e.g.,
on the big rock outside our classroom
window) and the date.
• List all things that are directly to your
north (use the compass to nd your
direction), east, south, and west, then
write a descriptive paragraph on each
direction.
Tip. Be specic about what is seen and the
direction it is from you. Also record only
permanent objects. In areas where there are
many things that look similar, try to pick out
specic differences.
Remember that good scientists are specic
in their descriptions and their drawings. They
compare and contrast in their observations.
Examples would include the following
descriptions at two different schools. See
Figures GPS-RE-3, GPS-RE-4a and 4b.
1. The red-brown brick building with the
green window frames is due west. To
the north of that building is the factory
with the tall smoke stack.
2. The area to the east has a single oak
tree with a fence extending away from
the observer.
Ask questions about the observations to
encourage students to compare and contrast.
Step 4. Intermediate and Advanced
Compass Angles (For intermediate and
advanced levels)
Figures GPS-RE-4a and GPS-RE-4b: View from a school site facing west, view from a school site facing east
Figure GPS-RE-3: A panoramic view
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2014 Relative and Absolute Directions Learning Activity - 4 GPS
N W S E N
You can divide a circle around you into 360
degrees. This is also written as 360˚. See the
GPS Learning Activity Working with Angles.
Navigational directions from some location
are given as angles around such a circle, with
north at the starting place, or 0˚. East is 90˚.
south is 180˚; and west is 270˚.
Angular Directions from North
Your hand can be used to measure directional
angles effectively. As illustrated in Figure
GPS-RE-5, if you extend your arm, make a
st, and then extend your thumb, the width of
your hand (with thumb extended) is about 15˚
(you may need to extend the little nger as
well). That means that six of your hands with
extended thumbs would t between north and
east. (Each st with extended thumb equals
15˚, because there are 90˚ between north
and east, and 90˚ divided by six sts is 15˚
for each st.) Figure GPS-RE-5: Using your
hand to measure 15˚
Because the angular relationships of each
individual’s hand will differ slightly, you may
nd that you have to extend your nger slightly
so that six “sts” t into 90 degrees. You may
need to try to measure six “sts” between
north and east several times before you
consistently get the same number of “sts” on
repeated trials. Hold your hand as steadily as
possible. Focus on what is at the tip of your
thumb, and then move your hand so that the
back of your hand is now where your thumb tip
was. Because you always take your hand with
you, remember how you extended your arm
and hand so that you can make future angle
measurements. Practice positioning your
hand and thumb so that you get a consistent
number of “hands” between north and east
or north and west. Now record what you see
at the end of each hand width. After you feel
condent with your measurements go on to the
panorama observations below.
Step 5. Panorama Observations (For all
levels)
Take a sheet of paper and fold it in half
lengthwise. Cut along the fold, so that you have
two long halves of the paper. Tape two of the
ends together and mark the four directions on
the paper, as indicated in Figure GPS-RE-6,
so that north is on the two far ends and south
is in the middle. Record all observations as
drawings on the long narrow strip of paper.
Now that you have had experience with the
magnetic compass and with the compass
directions, position yourself in the same spot
as you did for the compass activity. Draw a
panoramic view of what the landscape looks
like all around you by making multiple individual
drawings for each of the four north, south, east,
and west directions. Students can mark all
the other directions that fall in between (south
southeast, northwest by north), by measuring
the angles with their sts.
Step 6. Telling Time with the Sun
To extend this step further, use your st to
measure time. Because the sun moves 15˚ per
hour through the sky, one can estimate the time
in hours until sunset by measuring the number
of hand-widths from the sun to the western
horizon. Knowing your local time of sunset,
you can then work backward and estimate your
local time without a clock!
Step 7. Are the North, South, East, and West
Directions Relative or Absolute? (For all
levels)
Figure GPS-RE-5: Using your hand to measure 15°
Figure GPS-RE-6: Preparing the strip for drawing a
panorama
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2014 Relative and Absolute Directions Learning Activity - 5 GPS
Appendix
Welcome Introduction
Protocols
Learning Activities
Go outdoors and mark a point about two
meters above the ground (for example,
crossed strips of tape on a school window),
so that you can have the students stand along
an east-west line south of the mark. Have the
students form a line with the person on the
far east due south of the mark. The students
should be spaced at arms’ length. See Figure
GPS-RE-7.
In Figure GPS-RE-8, the boxes represent
individual students. With compass in hand,
the rst student takes a bearing on the mark
and nds that the direction is north and the
angle is 0˚. The students will then record “0˚”
in the box, marked “1.” Have each student, in
numerical order, make an angle measurement
between north and the mark. Because all
results will be between north and east for the
scenario illustrated, all measurement results
should be between 0˚ (north) and 90˚ (east).
Why did each student get a slightly different
measurement? Were they all not looking
at the same point? Their compass angles
are relative to their individual and different
locations.
Step 8. Compass Directions Are Relative to
Your Location (For all levels)
For practical purposes, Earth’s north and
south magnetic poles are fixed close to
our planet’s north and south spin axes. In
the absence of other magnets, a magnetic
compass needle aligns itself with Earth’s
magnetic eld. Thus, its needle will point to
Earth’s magnetic poles. (The Earth’s magnetic
poles will not move much during our lifetimes.)
Earth’s magnetic poles appear xed. However,
an observer on the equator will claim the
direction to the north as being along a line
tangent to the equator. Another observer who
is half way from the equator to the north pole
will also claim that the direction north is a line
tangent to the globe at his location. However,
these two lines are not parallel. See Figure
GPS-RE-9. Therefore, they are not pointing
in the same direction. Get a globe and try
this for a variety of different locations around
the world. You can see that the direction
you call north depends on your location.
Therefore, north, south, east, and west are
relative directions. These directions are angle
measurements in the direction of the magnetic
north pole relative to the location from which
the measurement is taken.
Figure GPS-RE-7: Students lined facing a mark to
the North
Figure GPS-RE-8: Overhead diagram of students
facing a particular mark
Figure GPS-RE-9: The direction North as perceived at
different points on Earth
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2014 Relative and Absolute Directions Learning Activity - 6 GPS
Further background: Directions are not
necessarily unique. What problems does
this cause? Navigation between arbitrary
locations requires a known point as a xed
reference. Giving directions to listeners who
are located at different positions means that
they must agree to some point in common
before directions can be given. Unique
starting and ending points (like trade routes),
provide an absolute or xed reference frame
such as a coordinate system placed on a
map. Latitude and longitude provide a similar
reference frame for our spherical planet. Use
the drawing and map in Figure GPS-RE-10
to help students understand relative and
absolute directions and positions. A full page
version of Figure GPS-RE-10 is included at
the end of this Learning Activity for you to
make duplicates for student use. Describe
how to go from your school to your house.
Then describe how to go from another school
to another house. Then ask, what is the
difference? A riddle about absolute directions:
Someone builds a house. All of the outside
walls of the house face south. A bear walks up
to the house. What color is the bear? (Answer:
White - if all sides of the house face south,
then the house must be at the North Pole. The
only bears in the Arctic Circle are polar bears.)
Step 9. Describing a Location (for all levels)
We wish to introduce absolute reference
frames for describing locations. Students
will expand upon past activities to answer
the question “Where am I?” or “Where is
something?” and will learn that they must
specify the “where” with sufficient clarity
so they can communicate their position
unambiguously to someone else. We ask
students to provide directions relative to some
agreed-upon reference or some coordinate
system instead of relative to themselves.
Cartesian coordinates (x,y axes in geometry
and algebra) and latitude and longitude on
the globe provide such a system.
Place two students back to back, each with
checker boards, so that each cannot see
the other’s board. Give them two checkers
(tokens) and have one place the tokens
anywhere upon the board. Without imposing
further rules, have that student describe to
the other student where to place the token,
so that each token is in the same position on
each board. Repeat the process beginning
with the second student. Lead a discussion
on the communication between the two
students. How did the students choose to
communicate the locations of their tokens?
What determined the clarity and difculty of
their communications?
Figure GPS-RE-11: Describing checker locations
YOUR
SCHOOL
ANOTHER
SCHOOL
ANOTHER
HOUSE
YOUR
HOUSE
North
0
180
South
East
90
West
270
North
0
180
South
East
90
West
270
Figure GPS-RE-10: Directions from home to school are
different for everyone
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2014 Relative and Absolute Directions Learning Activity - 7 GPS
Appendix
Welcome Introduction
Protocols
Learning Activities
Step 10. Numerically Describing a Location
(for intermediate and advanced levels)
Label a piece of graph paper or a drawn grid as
shown in Figure GPS-RE-12, Have students
nd positions communicated as follows: (1,2),
where the rst number describes the distance
to move to the right from zero on the horizontal
axis and the second number describes the
distance to move up along the vertical axis.
Then, have students draw a simple picture
from the following lines between the given
sets of positions. See Figure GPS-RE-13.
(4,1) to (4,4) (4,1) to (5,2) (5,2) to (5,5)
(1,4) to (1,1) (1,1) to (4,1) (1,4) to (4,4)
(1,4) to (2,5) (2,5) to (5,5) (4,4) to (5,5)
Discuss what information is needed to
communicate points and drawings. For
example, each line required information about
a starting point and an end point.
On a new piece of gridded paper, go to
position (7,4), and draw an arc with a drawing
compass that has a radius of two units. With
position (1,1) as the center, draw an arc with a
radius of ve units that intersects the rst arc.
Finally, draw a third arc, with a radius of ve
units and which has a center at (8.0). Where
do they intersect? How many arcs are needed
to determine a point.
Suppose that the Cartesian coordinates in
Table GPS-RE-1 were mapping a portion of
ocean and that the side of each square was
the distance it takes a radio signal to travel
in one millisecond. There are three ships at
sea, the Alexandria is at (0,0), the Corsica
is at (1,5), and the Hsuchou at (6,3). Each
ship receives a distress signal from a fourth
ship, the Bainbridge. The time that it took
the Bainbridge’s distress signal to travel to
the three potential rescue ships will help the
ships locate Bainbridge’s position. Can you
nd the distressed ship? (Measurement of
signal travel times forms the basis of radar
and GPS.)
Figure GPS-RE-13: The resulting simple picture
Figure GPS-RE-12: Label a sheet of graph paper
Figure GPS-RE-14: Cartesian coordinates dening
arcs
Table GPS-RE-1: Ship location and time for
Bainbridge’s signal to travel to each ship
Signal travel time
Ship Location Milliseconds
Alexandria (0,0) 4.0
Corsica (1,5) 2.0
Hsuchou (6,3) 3.5
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2014 Relative and Absolute Directions Learning Activity - 8 GPS
Step 11. Describing Geographical Locations
(for intermediate and advanced levels)
On a globe, the east-west lines are lines of
constant latitude and the north-south lines
are lines of constant longitude. Have students
discuss how they are similar to and how they
are different from the lines they found on
the Cartesian coordinate system. Find the
locations listed in Table GPS-RE-2.
Take a globe and nd your location. Estimate
values for your latitude and longitude from the
globe. Now nd the point on the globe opposite
your location and estimate its latitude and
longitude. What are the relationships between
the latitude and longitude coordinates for
these two opposite locations?
Note: Steps 9, 10, and 11 present concepts
similar to those in Odyssey of the Eyes
Learning Activity in the Land Cover/Biology
Investigation.
Adaptations for Younger and Older
Students
Qualitative descriptions of measurements
may be more appropriate for younger
students. For example, describing a compass
direction as being “northeast” may be clearer
than “45˚ from north.” More quantitative and
analytic techniques may be appropriate for
older students. For example, they can use the
Pythagorean Theorem to determine distances
between locations in a at, gridded coordinate
system.
Student Assessment
Have students identify various cities or
geographical features using latitude and
longitude. Give them a list of cities and have
them determine latitude and longitude for
each. Also have them nd distances between
geographical locations.
Table GPS-RE-2: Places on the Globe
Latitude Longitude Name
36
o
N 139
o
E
60
o
N 30
o
W
27
o
S 109
o
W
90
o
S 0
o
E
90
o
S 180
o
W
- - Your location
- - Your opporsite location
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2014 Relative and Absolute Directions Learning Activity - 9 GPS
YOUR
SCHOOL
ANOTHER
SCHOOL
ANOTHER
HOUSE
YOUR
HOUSE
North
0
180
South
East
90
West
270
North
0
180
South
East
90
West
270
GPS Investigation
School Site Location Map Graphic
