Math Geocaching with GPS

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Math Geocaching with GPS
Teacher Guide
Students have the opportunity to go outside the
classroom to gain hands-on experience with Global
Positioning Systems (GPS) through a geocaching
activity on their campus, but with a twisteach
waypoint coordinate is missing some digits that
can be completed by solving math problems.
Overview
Process Standards 3-1, 4-1, 4-2, 4-3, and lesson
can be tailored to incorporate any Algebra I,
Geometry, or Algebra II Standards.
PASS Objectives
Algebra, Geometry, Geography.
Subjects
GPS Skills
Coordinate Geometry, Measurement of Elevation,
Navigation Between Waypoints, Bearings,
Distances, Accuracy Issues with GPS.
High School, but math problems can easily
becustomized to any subject or grade level.
Grade Level
Beginning to Intermediate.
GPS Skill Level
If more time is available, students can learn
more about GPS capabilities, such as tracking
routes and assessing accuracy of waypoints. Once
back in the classroom, students can either graph
the waypoints by hand or use a GIS to plot
waypoints and tracks atop an aerial photo.
Other Skills
Class set of GPS units (Recommend 1-2 students
per GPS).
Materials
Time
Should be completed in one 50-minute class.
Teachers can personalize this activity to the
locationsand math concepts of their choice.
Please contact William Flynn if you would like
some help in adaptingthis activity for your
purposes.
Lesson Preparation
Math Geocaching with GPS
Teacher Guide
2
Math Geocaching with GPS
Splitting the class into multiple groups may be
effective if the campus is large with enough
features that make good candidates for waypoint
stops. This way, the students are going in
different directions and it keeps them honest
since only some waypoints and signs will be
relevant to their routes.
ConsiderRouting
First, select optimal starting and finishing
points. Be creative and try to develop a
storyline or theme that will unify all of the
points. This serves as a form of clue and makes
the activity more enjoyable for the students.
Then select the locations for waypoints between
the start and finish. Keep in mind the length of
the class period and the distances students will
need to traverse. Keep the routes as uniform in
possible in terms of distance. Once you have
selected the waypoint locations, use a GPS to log
the coordinates in decimal degrees. Give the
students the coordinates through three decimal
places and create a math problem that will
compute an integer solution of two digits (01 to
99) that will represent the fourth and fifth
digits of the decimal degree coordinate.
Suggestionsfor Design
On the day of the activity, post small signs at
each of the waypoints (see the examples that
follow) to help direct the students. The signs
should be easy enough to be spotted at close
range but should not be visible from across the
campus. Position the geocache in similar fashion
and fill it with inexpensive prizes and trinkets
to reward the students. Include a log book for
the students to sign so that they can receive
credit and be proud of their accomplishments. Be
sure to recommend www.geocaching.com if the
students want more fun!
Execution
Math Geocaching with GPS
Teacher Guide p. 2
3
Math Geocaching with GPS
We started outside at Waypoint 1 and had an
overview and orientation over GPS. To make sure
the students had a basic grasp and were
comfortable with the GPS units, we navigated to
Waypoint 2 as a group. From the Fork in the
Road (the PTHS Demons pitchfork), the class
split into two groups. Group 1 was sent by the
devious demon to a Wrong Way sign and the gate to
the sports complex. The demons foul play sent
Group 2 to left field of the baseball diamond and
to the gymnasium. Then, each group had the same
clue to lead them back to the parking lot, where
the geocache was waiting for the students in the
bed of the instructors truck.
Example fromPerkins-Tryon HS
PTHS Geocaching Waypoints START (1) Back Door
35.98627 North 97.02385 West 950 feet (2) Fork
in the Road 35.98569 North 97.02187 West 926
feet Group 1 (3a) Wrong Way Sign 35.98638
North 97.02280 West 927 feet (4a) Sports Complex
35.98651 North 97.02184 West 921 feet Group
2 (3b) Left Field Foul Pole 35.98775
North 97.02141 West 936 feet (4b) Gymnasium Hill
35.98673 North 97.02296 West 963
feet FINISH (5) Truck Bed in Lot 35.98711
North 97.02249 West 922 feet
Developed by William R. Flynn william_at_musicgeograp
her.com
Math Geocaching with GPS
Teacher Guide p. 3
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Math Geocaching with GPS
The Global Positioning System (GPS) is used
commonly in our daily lives, whether through
in-dash navigational systems in cars, atomic
clocks that synchronize the school bells with the
correct time, or in handheld GPS units that we
might take along for hikes because bread crumbs
are now obsolete.
A popular recreational activity these days is
called geocaching, which is basically a treasure
hunt for the 21st Century, where people stash
prizes all over the world and give coordinates
and clues to challenge GPS users to find these
locations.
Tonight is the big game for the Perkins-Tryon
High School football team, but the Demon mascot
has stolen the school spirit and thought it would
be fun to hide it in a geocache somewhere on the
campus. The good news is that the Demon has
given you several clues in the form of GPS
coordinates in Latitude and Longitude. The bad
news is that the latitudes and longitudes are
incomplete, with the last two digits of each
coordinate missing. In order to determine where
you need to go, you will have to solve a math
problem, which answer yields the missing digits
for the coordinates.
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Math Geocaching with GPS
Math Geocaching with GPS
The following table shows how important it is to
report location coordinates to several decimal
places. The demon has given you the first three
decimal places, but that only puts you within
111.2 meters, about the length of a football
field. If you solve your problems correctly, you
will have the fourth and fifth decimal places and
should be able to get to within a few feet of the
waypoint. Accuracy of GPS (Decimal
Degrees) Reported Coordinates Accuracy
(metric) Accuracy (imperial) 1 Degree __ __
. 111.2 km 69.17 miles 1/10 Degree __ __ . __
11.1 km 6.91 miles 1/100 Degree __ __ . __ __
1.1 km 0.69 miles 1/1000 Degree __ __ . __ __
__ 111.2 meters 364.83 feet 1/10,000 Degree __
__ . __ __ __ __ 11.1 meters 36.48
feet 1/100,000 Degree __ __ . __ __ __ __ __
1.1 meters 3.64 feet Alright, now lets get
out there and find the school spirit! Go Demons!
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Eureka!
Congratulations, you have found the
geocache. The demon has been foiled again. Now
hurry and open the lid to release the school
spirit!
Sign the log for3 pts (Field Goal)and reward
yourselfby taking a prize!
Fork in the Road
The demon has hidden the school spirit
somewhere on our campus. We only have forty
minutes to find it so we will break up into two
groups. The demon thought it would be a fun game
to give you some math and GPS puzzles. Good luck!
35.98569 North 97.02187 West
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A Devious Demon
Youre getting warmer! Dont let the demons
foul play make you quit.
Solve this equation x 67 17 There are
two possible answers.Use the smaller result to
completethe North latitude coordinate. Usethe
larger result to complete theWest longitude
coordinate.
35.986 _ _ North 97.022 _ _ West
A Devious Demon
Youre getting warmer! Dont let the demons
tricks make you quit.
Solve this equation x 84 12 There are
two possible answers.Use the smaller result to
completethe North latitude coordinate. Usethe
larger result to complete theWest longitude
coordinate.
35.987 _ _ North 97.021 _ _ West
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Play Ball!
Nice rally! The demon has one last test for you.
Complete the pattern 2, 3, 5, 7, ?? 35.986 _
_ North Complete the pattern 1, 4, 9, 16, 25,
36, ?? 97.021 _ _ West
The Tip Off
Nice shot! The demon has one last test for you.
Complete the pattern 2, 3, 5, 7, ?? 35.986 _
_ North Complete the pattern 1, 4, 9, 16, 25,
36, ?? 97.021 _ _ West
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NAMES _________________ PERIOD
___ _________________ GPS UNIT ______
ROUTE 1 GEOCACHING ACTIVITY
Perkins-Tryon High School What are the
coordinates in decimal degrees for the portable
building? (1) __ __ . __ __ __ __ __ North
Latitude (3) Is this a or Latitude?
____ (2) __ __ . __ __ __ __ __ West
Longitude (4) Is this a or
Longitude? ____ (5) What is your accuracy in
feet? _______ FEET (6) How many satellites
are you connected to? _______ SATELLITES (the
BLACK circles)
WAYPOINT 1 35.98569 North Latitude Fork in
the Road 97.02187 West Longitude (7)
Describe this location. __________________________
________________________
WAYPOINT 2 Complete the missing digits for your
next set of coordinates using the Devious
Demon answers from the following math
problems. (8) 35.986 __ __ North
Latitude Solve the equation 3x - 16 7(x
24) (9) 97.022 __ __ West Longitude
Evaluate the expression 2(11 5 4
72) (10) Describe this location. _______________
___________________________________
WAYPOINT 3 Complete the missing digits for your
next set of coordinates. Play Ball! The math
problem below has two answers. Use the smaller
answer for (11) and the larger answer for
(12). Once you have done this, go to this
location. (11) 35.986 __ __ North
Latitude Solve the equation x 67
17 (12) 97.021 __ __ West Longitude (13
) Now where are you? ____________________________
______________________
WAYPOINT 4 Complete the missing digits for your
next set of coordinates using the
Eureka! answers from the following math
problems. (14) 35.987 __ __ North
Latitude Complete the pattern 2, 3, 5, 7,
____ (15) 97.022 __ __ West
Longitude Complete the pattern 1, 4, 9, 16, 25,
36, ____ (16) What is your elevation?
_________ FEET (17) Describe this
location. ________________________________________
_________
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NAMES _________________ PERIOD
___ _________________ GPS UNIT ______
ROUTE 2 GEOCACHING ACTIVITY
Perkins-Tryon High School What are the
coordinates in decimal degrees for the portable
building? (1) __ __ . __ __ __ __ __ North
Latitude (3) Is this a or Latitude?
____ (2) __ __ . __ __ __ __ __ West
Longitude (4) Is this a or
Longitude? ____ (5) What is your accuracy in
feet? _______ FEET (6) How many satellites
are you connected to? _______ SATELLITES (the
BLACK circles)
WAYPOINT 1 35.98569 North Latitude Fork in
the Road 97.02187 West Longitude (7)
Describe this location. __________________________
________________________
WAYPOINT 2 Complete the missing digits for your
next set of coordinates using the Devious
Demon answers from the following math
problems. (8) 35.987 __ __ North
Latitude Solve the equation 5x - 54 3(x
32) (9) 97.021 __ __ West Longitude
Evaluate the expression 9(17 4 12 62) -
4 (10) Describe this location. _________________
_________________________________
WAYPOINT 3 Complete the missing digits for your
next set of coordinates. The Tip Off The math
problem below has two answers. Use the smaller
answer for (11) and the larger answer for
(12). Once you have done this, go to this
location. (11) 35.986 __ __ North
Latitude Solve the equation x 84
12 (12) 97.022 __ __ West Longitude (13
) Now where are you? ____________________________
______________________
WAYPOINT 4 Complete the missing digits for your
next set of coordinates using the
Eureka! answers from the following math
problems. (14) 35.987 __ __ North
Latitude Complete the pattern 2, 3, 5, 7,
____ (15) 97.022 __ __ West
Longitude Complete the pattern 1, 4, 9, 16, 25,
36, ____ (16) What is your elevation?
_________ FEET (17) Describe this
location. ________________________________________
_________