CATCH ME IF YOU CAN:
Understanding the Global Positioning System
The global positioning system (GPS) is able to determine the location
of anyone or anything which has a receiver. The complete global
positioning system consists of 29 satellites and a GPS receiver which
can decode signals from the satellites. The GPS receiver is what we
can purchase in stores here on Earth. Each GPS satellite transmits
radio signals which contain the current time. The GPS receiver uses
the time stamp to determine how long it takes the signal to travel
between the satellite and the receiver. In this manner the receiver
can determine the distance to each satellite. Once the distance is
known between the receiver and several satellites, the location of the
receiver can be constructed. In addition, the Global Positioning
System can determine the velocity of the receiver by calculating the
distance between two locations, and how long it takes for the receiver
to travel between the two locations.
In this activity students will reconstruct a two dimensional map of
another student's journey with the same reconstruction methods used by
the Global Positioning System. Students will also calculate the
average velocity of the traveller between different positions along
the journey.
Materials
To complete this activity each student (or group) will need the
following materials:
The Journey
In this activity student Travellers will make a journey in several
stages. Travellers will mark their positions along the way, recording
their distance from three different GPS satellites. At each position
along the journey students will roll two dice and will take the
product of the numbers on the dice to indicate the time (in minutes)
it took to travel to that position.
In the second part of the activity, student Mappers will use only the
recorded distances from the GPS satellites to reconstruct the
Travellers' journey. The Mappers will also calculate the average
velocity of the Travellers between positions on the journey.
- Students may work individually or in groups. Each student (or
group) should start with a blank copy of the GPS Coordinate Grid
worksheet and a blank copy of the Advanced GPS Log Sheet. The
students should write their names on the GPS Coordinate Grid and check
the box next to Traveller. The students should write their names
under Travellers' Names on the Advanced GPS Log Sheet.
- Start by marking your starting location (position 1) with a dot
someplace on the grid.
- Measure the distance from your starting location to GPS
satellite \#1 using a ruler. Always use the center of the black
bullseye at the corner of each satellite image as the point you are
measuring to. Record this distance on the Advanced GPS Log Sheet next
to position 1, under GPS satellite \#1.
- Next, measure the distance from your starting location to GPS
satellite \#2 using the ruler. Record this distance on the GPS
Advanced Log Sheet next to position 1, under GPS satellite \#2.
- Now, measure the distance from your starting location to GPS
satellite \#3 using the ruler. Record this distance on the GPS
Advanced Log Sheet next to position 1, under GPS satellite \#3.
- Mark a second point on the GPS Coordinate Grid, this will be
the second position on your journey. Draw a straight line,
with an arrow, from the starting position to the second position to
indicate which direction you traveled.
- Roll two dice and take the product of the numbers on the face of
the dice. Record the product on the Advanced GPS Log Sheet next to
position two. This number indicates the time (in minutes) it took to
travel from the starting position to position two. Do not fill in the
last two columns on the Advanced GPS Log Sheet, they will be filled in
later by the Mappers.
- Measure the distance from the second position to each GPS
satellite as you did before and record these distances on the GPS
Advanced Log Sheet next to position 2, under the appropriate satellite
number.
- Repeat this process for as many positions as you would like to
make on your journey (7 is a nice number). Measure carefully the
distance from each position to each of the GPS satellites and record
the information on your Advanced GPS Log Sheet.
- Roll the dice at each new position and record on the GPS
Advanced Log Sheet the product of the numbers on the dice. This
product represents the time (in minutes) it took to travel to that
position from the previous one.
- Keep the map of your journey hidden from your fellow classmates.
You classmates are going to try and reconstruct your journey next, and
you wouldn't want them to know what it looks like ahead of time.
Which Way Did They Go, and How Fast Are They Running?
The information on the Advanced GPS Log Sheet constructed in Section 2
will be used to reconstruct a map of the journey taken by the those
who made the log. In this portion of the activity the students will
determine the location of the Travellers with the same reconstruction
methods used by the Global Positioning System. Students will also
determine the average velocity of the Travellers between each position
along the journey.
- Each student (or group) should start with a blank copy of
the GPS Coordinate Grid and a Advanced GPS Log Sheet which has
already been completed by another student (or group). The
students should write their names on the GPS Coordinate Grid and
check the box next to Mapper. The students should write their
names under Mappers' Names on the Advanced GPS Log Sheet.
- Using a drawing compass and the GPS Coordinate Grid,
construct a faint arc which is centered on GPS satellite \#1 and
has a radius equal to the distance indicated on the Advanced GPS
Log Sheet from GPS satellite \#1 to the starting position. You
can use a ruler to measure the opening distance of the compass.
If the compass will not open wide enough, use a string instead. Tie one
end of the string to your pencis and use the ruler tomeasure a lenght of
string equal to the distance indicated on the GPS Log Sheet. Use the string
to construct a faint arc which is centered on GPS satellite \#1 and has a
radius equal to the distance indicated on the GPS Log Sheet from GPS satellite
\#1 and the starting position.
- Using a compass (or the string), construct a faint arc which is centered
on
GPS satellite \#2 and has a radius equal to the distance indicated
on the Advanced GPS Log Sheet from GPS satellite \#2 to the
starting position.
- You may notice that if you were to complete the compass
circles around each of the first two satellites, they would cross in
two different locations. This would make it difficult to know which
is the position of the traveller. We can solve this problem, just as
the Global Positioning System does, by using a third satellite.
- Using a compass (or string), construct a faint arc which is centered on
GPS satellite \#3 and has a radius equal to the distance indicated
on the Advanced GPS Log Sheet from GPS satellite \#3 to the
starting position.
- The point where these three arcs cross is the only point on
the grid which satisfies the distance requirements recorded on the
Advanced GPS Log Sheet. Do to reconstruction errors, the three arcs may not
touch exactly in one point. You can approximate the starting point by choosing
the point in the center of the area where the three arcs overlap. This is the
starting position of the
journey you are trying to reconstruct. Mark this crossing point
on the GPS Coordinate Grid with a colored pencil. If you have
drawn the arcs lightly you may leave them in place, or you may
carefully erase them.
- Repeat the process above to locate the second
position on the GPS Coordinate Grid using the distances indicated
on the Advanced GPS Log Sheet.
- Once you have located the second position, use a colored
pencil to draw a straight line with an arrow from the starting
position to the second position to indicate the direction of
travel.
- Let the scale of the grid be 1/4 inch = 1/4 mile. Measure
the distance between the starting position and position two with a
ruler. Record this distance, in miles, on the Advanced GPS Log
Sheet.
- The average velocity of the Traveller between the two
positions you have recorded is the distance travelled divided by the
time it took to travel that distance. Calculate the average velocity
in miles/minute of the traveller between the starting position and
position two and record it on the Advanced GPS Log Sheet.
- Repeat the above steps to locate all positions on the
journey. Make sure to connect each position with a straight line
and an arrow, to indicate the direction traveled. Measure the
distance travelled, and use the recorded time to calculate an
average velocity between each position.
- When you have completed reconstructing the journey from the
information on the Advanced GPS Log Sheet, compare your map with
the original map made by the student (or group) who constructed
the Advanced GPS Log Sheet in the first place. How did you do?
Were you able to figure out the path they took on their journey?
Activity Extensions
There is a less advanced version of this activity which has the
students reconstruct the Travellers journey without calculating the
average velocity between positions along the way. See the CHICOS
website for a copy of this lesson. Other activity extension ideas are
listed below.
- A journey through town. Copy the GPS Coordinate Grid
onto a clear piece of acetate (overhead transparency). Lay the
grid over a map of your town, or any town map. Now, as the
students construct their journey they can mark the position at
specific places in town. The next group, which reconstructs the
journey, can indicate where the Traveller stopped (e.g. toy store,
ice cream shop, local park).
- An interdisciplinary extension. Once this activity is
complete have the students write a short story describing their
adventures along the journey. Or, have them draw a map around the
journey path on the GPS Coordinate Grid indicating where they went
and what they saw along the way.
Using the calculated velocity information, students could
work into their story (or map) explanations as to why the Traveller
was moving at a slow, or quick, pace during different legs of the
journey (e.g. Traveller comes across grizzly bear and has to run,
Traveller sprains ankle and hobbles along).
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