Hands-on Activity: Geometry and Geocaching Using GIS & GPS

Contributed by: University of Wyoming

This image is a label for an official geocache artifact. It is a green label with the official geocache emblem, which shows a cartoon of a person tracking towards a waypoint flag searching for a hidden treasure. The background is green with black lettering. Users are required to submit the cache name, contact name, and info.
An official geocache label. Users affix the label to the container they have hidden and provide contact information for the cache.
copyright
Copyright © 2012 Lee Cannon, CC BY-SA 2.0, Flickr https://www.flickr.com/photos/leecannon/6924688841

Summary

Students take on the role of geographers and civil engineers and use a device enabled with the Global Positioning System (GPS) to locate geocache locations via a number of waypoints. Students save their data points, upload them to geographic information systems (GIS) software, such as Google Earth, and create scale drawings of their explorations while solving problems of area, perimeter, and rates. The activity is unique in its integration of technology for solving mathematical problems and asks students to relate GPS and GIS to engineering.

Engineering Connection

Students assume the role of a civil engineer as they model public works project. By working with GPS technology, students learn how engineers can mark locations with data and map that information using GIS software. Engineers use satellite imaging and GIS principals, and the activity demonstrates the broader use of these tools in engineering applications. Students will also make connections to specific elements of mathematics that an engineer may use, such as applying unit rates to determine how much material an engineer would need to complete a project.

Pre-Req Knowledge

Students need to be able to calculate area of various polygons, both regular and irregular. Students also need to be able to use a protractor and have a basic understanding of how a compass works.

Learning Objectives

After this activity, students should be able to:

  • Use GPS technology to locate points given a latitude and longitude to determine locations on Earth and store those points digitally by transferring latitude and longitude data from a GPS to GIS (Google Earth).
  • Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and using appropriate tools such as a protractor.
  • Explain how GPS and GIS relate to engineering.
  • Solve problems related to angle measurements and angle relationships, such as complementary, supplementary and triangle and quadrilateral angle relations.

More Curriculum Like This

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Educational Standards

Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.

  • Use appropriate tools strategically. (Grades K - 12) Details... View more aligned curriculum... Do you agree with this alignment?
  • Draw, construct, and describe geometrical figures and describe the relationships between them. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
  • Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
  • Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
  • Solve real-world and mathematical problems involving the four operations with rational numbers. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
  • Students will develop an understanding of the core concepts of technology. (Grades K - 12) Details... View more aligned curriculum... Do you agree with this alignment?
  • Students will develop an understanding of the relationships among technologies and the connections between technology and other fields of study. (Grades K - 12) Details... View more aligned curriculum... Do you agree with this alignment?
  • Students will develop an understanding of the role of society in the development and use of technology. (Grades K - 12) Details... View more aligned curriculum... Do you agree with this alignment?
  • Technological systems can be connected to one another. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
  • Use appropriate tools strategically. (Grades K - 12) Details... View more aligned curriculum... Do you agree with this alignment?
  • Draw, construct, and describe geometrical figures and describe the relationships between them. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
  • Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
  • Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
  • Solve real-world and mathematical problems involving the four operations with rational numbers. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
Suggest an alignment not listed above

Materials List

Each group needs:

  • GPS-enabled device (most smartphones are equipped with GPS receivers)
  • GPS app such as Free GPS (for Apple iOS) or Maverick: GPS Navigation or Handy GPS (for Android)   
  • Computer or other device with an internet connection and Google Earth software installed (or the ability to install the software)
  • Appendix A: Student Activity Handout
  • protractor
  • ruler

For the class to share:

Introduction/Motivation

[This activity is associated with the Integrating GIS, Mathematics, and Engineering lesson.]

This is a word cloud which shows a variety of words related to GIS. Larger words include “information,” “Geoinformatics,” and “science.”
A word cloud that connects similar terms relating to GIS and GPS.
copyright
Copyright © 2012 Environmental Informatics Marburg, CC BY-NC-SA 2.0, Flickr https://www.flickr.com/photos/environmentalinformatics-marburg/8839279513

In the associated lesson, Integrating GIS, Mathematics, and Engineering, you became familiar with GIS and GPS as well as some of the more practical mathematical and engineering applications associated with those systems. For this activity, you are going to explore these technologies further by playing the hybrid role of a civil engineer and geographer. You will be using GIS and GPS devices to participate in a geocache hunt! These caches are located within a predefined space outside and your job will be to navigate between them using GPS and math. Be prepared to do your own mapping while tracking your movements and viewing satellite images of your journey into geocaching! In this activity, you will find a latitude and longitude on your GPS, mark waypoints, solve geometry and unit rate problems, upload GPS data to a GIS, and take on the role of an engineer!

Civil engineering is primarily about designing infrastructure and making it sustainable for public use. Because engineers use an immense amount of information in planning infrastructure, GIS technologies provides them with tools to analyze and visualize these data. By playing the role of a civil engineer, your task, on a smaller scale, is to help improve access to an area of public land. You will analyze information in order to design the perimeter of a new green space that will be surrounded a fence, which will enclose part or all of the defined property.

Additionally, you will design a brick pathway within the fenced-in area and calculate the number of bricks necessary to complete this task. You will receive more information as we go over the instructions.

By the time you finish this activity, you will: have transferred data from a GPS device to GIS software; tracked and located geocaches; created scale drawings of your journey; calculated the area within the boundaries of your exploration; and designed sidewalks and fences, all while taking into account materials through an engineering lens.

Vocabulary/Definitions

coordinate: The combination of longitude and latitude, along with elevation, make a GPS coordinate which defines a single point on the surface of the earth.

geographic information system: A way to store, edit, and manipulate data or information, usually using maps; commonly referred to as GIS.

Global Positioning System: A satellite based navigation system that allows users to determine their position on the earth, among other uses; commonly referred to as GPS. More broadly, GPS can refer to any device used to locate a given position.

latitude: This represents an angle north or south of the equator, but is more easily understood as the y-coordinate of a location on the surface of the earth.

longitude: This represents an angle east or west of the prime meridian, but is more easily understood as the x-coordinate of a location on the surface of the earth.

waypoint: In the case of navigation, a fixed longitudinal and latitudinal coordinate or GPS point that identify a physical point.

Procedure

Background

The associated lesson, Integrating GIS, Mathematics, and Engineering, provides key contextual background and instruction on GPS, GIS, and waypoints.

Before the Activity

Note: this activity requires a substantial amount of set-up; however, you can modify the procedure to fit your needs.

  • Locate a large area (suggested minimum of a hectare, or 10,000m2) to set up the GPS activity. Soccer, baseball, or football fields should suffice for those who do not have easy access to green space near their school, but a slightly larger area is required to follow the exact relative locations of waypoints laid out in the example provided here. You can modify the example to fit your constraints.
  • Create your geocaches and label them with a name. Each geocache will contain math problems, located in Appendix C: Problems for Geocaches, where students solve for unknown angle values. After solving each problem, they can follow the “solution” angle to find the next geocache and make a waypoint. Use a small receptacle (plastic tub, folder, etc.) for each geocache. The waypoints from each geocache, when put into Google Earth, will form the shape of an irregular pentagon, with each geocache representing a vertex.
  • The geocache problems in Appendix C: Problems for Geocaches match the recommended irregular pentagon seen in Figure 1 below. Placing the geocaches in a slightly more irregular shape will assist in making the activity more challenging; however, depending on the angle from which one geocache is located relative to another, you may have to make modifications to your math problems. To make the activity more realistic, choose an area with trees, taller grass, rocks, or other cover within which to conceal the geocaches. See below for more information about the geocaches.
  • Plot your course using your GPS-enabled device and place your geocaches in the confines of your hectare area. Make sure the angle solutions located within each geocache correspond to the location of the next geocache (or geocaches). Also, choose a waypoint near geocaches from which each group can start. You can later upload these waypoints from the GPS device into Google Earth.   
  • Most smartphone-based GPS devices will not guarantee accuracy higher than 5 meters. With this in mind, try to keep each geocache location far from one another as is reasonable, ideally no closer than 40 meters apart at a minimum. There is a margin for error in this activity necessitated by the accuracy of the equipment as well as with Google Earth.
  • Be sure that there are sufficient GPS-enabled devices and corresponding computers to access the Google Earth program per group. (Download a free copy of Google Earth for your classroom computers.) You can alter the group sizes to accommodate different numbers of GPS devices in each class. Students may use either smartphones or dedicated GPS units, but the teacher will need to be able to troubleshoot and plan for each type of technology. Ideally, you can find enough Apple and/or Android smartphones to use in the classroom. Because this is the most likely scenario, the following tutorial uses those platforms.
  • Each group will receive a waypoint (latitude/longitude) to input into their GPS to start the activity. For this reason, a larger polygon of five sides or more should help with group distribution around the activity zone. Try to spread the groups out amongst the geocaches as evenly as possible. To create a waypoint (or “placemark”) in Google Earth, simply click on the thumbtack icon in the top navigation bar, click and drag the tack to the desired location, and type in a name and notes. See Figure 1.

This image is a satellite photo that shows several fields with a track as seen from the software program Google Earth. Additionally, there are portions of the interactive parts of the software highlighted with hints drawn in.
Figure 1. How to use waypoints in Google Earth.
copyright
Copyright © 2017 Jake Schell, University of Wyoming

  • Share the latitude and longitude waypoint that each group will use for them to start the GPS activity at that location. Students will complete Appendix D: Group Members Latitude and Longitude Log with each group member’s name and starting latitude and longitude. In Google Earth, waypoints show up in the “Places” bar on the left-hand side of the screen. To edit, right click on the waypoint name in the map (or in the “Places” bar) and click on “Get Info.” See Figures 1, 2 and 3.

This image is a satellite photo that shows several fields with a track as seen from the software program Google Earth. The image shows a dialogue box which appears when right clicking on waypoints, allowing users to access various commands, such as “Get Info”.
Figure 2. How to get data from Waypoints in Google Earth.
copyright
Copyright © 2017 Jake Schell, University of Wyoming

This image shows the “Get Info” dialogue box for waypoints in Google Earth. Data seen includes the name, latitude and longitude, and notes for the waypoint.
Figure 3. The “Get Info” dialogue box in Google Earth
copyright
Copyright © 2017 Jake Schell, University of Wyoming

  • Remember, if you do not set up your geocaches from this example, you must create word problems that result in angle measurements and distances for students to follow in order to move from geocache to geocache. For this reason, consider using the pentagon above and associated problems from Appendix C: Problems for Geocaches. An example of the activity’s flow by solving math problems and moving from location to location is as follows: Assume that a group is starting at the waypoint “Geo 1”, and you want them to proceed to the waypoint “Geo 2”. The problem provided at “Geo 1” needs to result in a solution of 90 degrees, because the students need to move at a compass bearing of 90 degrees (or due east) to arrive at the next waypoint (assuming they were being asked to go in order). As an example, the question could read:
    1. Two angles are complementary. What is the sum of their angle measures?
    2. The area of a rectangle is 405 meters. The width of the rectangle is 3 meters. What is its length?

The answers to these questions (90 degrees and 135 meters, respectively) tell the students how far and in what direction to walk to the next geocache. 

  • Following the geocache activity, the students focus will shift from one of GPS and GIS expert to that of a civil engineer. The engineer is designing some walkways that will be made of brick and a fence for part of the perimeter. The designs will be limited to the shapes formed by the locations of each geocache locations; however, following the example above, imagine the brick walkway will form a border around the perimeter of the rectangular section of the pentagon, with two paths crossing going east-west and north-south through the middle of the rectangle (see Appendix B Civil Engineering Calculation). The walkway needs to be two meters wide and each brick covers 1/9 square meters. The students will calculate how many bricks would be required for the engineer to complete the project. Based on the shape you create, you can alter the size and shape of the path to suit your needs. See Appendix B Answer Key for sketch of this scenario. You may want to create a shape for the fence or allow students to design a fence, which is a nice way to scaffold the activity. You may also alter the constraints of the fence and pathway if you so choose. For the example provided, the engineer is only fencing off the triangular portion to the east and is placing fence posts every 1 5/6 meters.

With the Students

Day 1

Part 1. Introduction:

  1. Hand out the Appendix A: Student Activity Handout, considering any necessary changes to fit your class, and arrange students in their groups for the activity. Students should continue to refer to the activity handout through the duration of this activity.
  2. Read the Introduction/Motivation section above with the students and provide background for the geocache activity.
  3. Go over the instructions for the activity with the students.

Part 2. Navigating the Geocaches

  1. Refer students toward the latitude and longitude for their first geocache and navigate to new geocaches and GPS coordinates by solving math problems. Each student will need a pencil to work out the problems with in the field. Each group will start at different locations, which will be Geocache 1 in their handouts.
  2. Handout papers (from Appendix D Group Members Latitude and Longitude Log) with the latitude and longitude of the geocaches to individual groups.
  3. Direct students to copy down the latitude and longitude Geocache 1 in their student handout sheets. Instruct students to look at the geocache locations in the handout and solve the two geometry problems located within each geocache. Note that there is room to work each problem. One of the answers will tell students what direction, as an angle or compass bearing, to walk to find the next geocache, and the other answer will result in a distance to travel in meters. Remind students that if they end up making errors, they will not find the next geocache, so be careful!
  4. Once the group finds the next hidden geocache location, they will make a new waypoint in their GPS device and copy the name of the geocache as well as its latitude and longitude into their worksheet. Students will know they have finished when they arrive back at the location where they started. Once they find all of the geocaches, students can return to class to work on Appendix A: Student Activity Handout.

Day 2

Part 3: Scaling Down

  1. In the second part of the activity, students will assume the role of a civil engineer. In this role, their “supervisor” wants to know the area that is contained by the geocaches so they can make improvements upon a parcel of public land. They also want to see a sketch of the area to scale. The students’ job is to calculate how much material they will need for a few projects associated with this improvement project.
  2. Instruct students to export the waypoints from your GPS device into Google Earth, just as they did in their lesson.
  3. Draw a scale representation of the shape on graph paper. This is included in the section of the student activity handout titled Scaling Down. Students should calculate the area of the shape they created as well as include scale and the actual distances represented by their drawing, as the objective is to make an accurate scale drawing of the perimeter created by their geocaches. Students can then break up the area into polygons to calculate their areas. Note that they are calculating the true area represented on the surface of the earth, not the area on the paper.
  4. Explain how to construct the sidewalk and fence areas. If you followed the example provided in the teacher preparation portion of this activity along with the Appendix B Answer Key, this will be relatively simple. Again, this is a great place to provide extensions or scaffolding. Will students create their own fences and pathways, or will they follow a set design such as the one provided with the activity? Some students will benefit from a set, guided pathway, while others can extend the lesson by designing their own. You may want to wait until you get back in from the field to convey this information.

Part 4: Activity Summary

To summarize, here is the outline of what you will be doing:

  • We will go into the field and mark our geocaches with waypoints on the GPS. We will navigate between geocaches by answering the geometry questions contained within them, which will provide us with a distance and direction to walk to the next location.
  • We will use the information above and our GPS units to find all of the geocaches.
  • Taking on the role of an engineer, we will upload our waypoints into Google Earth, a GIS platform.
  • We will draw a scale version of the track we made on graph paper in the student handout.
  • We will then calculate the area of earth contained within our track.
  • We will design or draw a pathway through the area and a fence for all or part of the perimeter, calculating the necessary amount of materials that would be required to build such features.

Attachments

Troubleshooting Tips

  • You need to familiarize yourself with all technology ahead of time.
  • In the event that the GPS does not send the information to the email account, you could provide students with your own Google Earth Data, or they could work with another group’s data. Alternatively, they can manually input the latitude and longitude data into the waypoint through the “Get Info” tab after right clicking a waypoint (Figures 2 and 3).
  • If upon opening the KML file from the email Google Earth does not open the file, try to click and drag the file directly into Google Earth. Release the mouse pointer over the map and the waypoints should load.
  • If the app freezes or aborts, try resetting the device. On Apple devices, a hard reset may be required.

Assessment

Pre-Activity Assessment

Formative Assessment from Discussion: During the lesson and activity introductions, you should be able to assess the level of familiarity students have with the technology at hand. This informal assessment may generate data that helps you establish groups. A group of students who have no GPS or little map experience could be at a significant disadvantage; heterogeneous groupings based on familiarity with the topic may be advisable.

Activity Embedded Assessment

Waypoint Check: Groups proceed through the geocache by correctly answering geometry problems. Therefore, a check of their geocache GPS coordinates should tell the teacher whether they were correctly solving the problems during the GPS activity. However, teachers could also take up student or group work from the geocaching portion to grade separately.

Have students take a screen shot of their group’s Google Earth screen after all GPS waypoints have been uploaded and prior to moving on to step 2 of “Scaling Down.” Students can submit these images or you can check them off.

Post-Activity Assessment

Activity Handout: The teacher should grade Part 2 (“Scaling Down”) from the Appendix A: Student Activity Handout. Grading Part 1 (“Navigating the Geocaches”) is optional. This will let you know if students understood the technical and problem-solving portions of the activity.

Activity Extensions

Any variety of extensions are possible from creating different polygons to construction of different pathways or varying the engineering scope of the activity.
Have students research how civil, environmental, geophysical, and other engineers use GPS to monitor the motion of the earth. Possible applications for research include monitoring glacial growth and recession, plate tectonics, and landslides. Have students create a digital slide show to present to the class.

Students can create their own shapes, fences, and walkway designs to solve for themselves or in groups.

Activity Scaling

  • For lower grades, consider teaching the activity by providing students with directions and distances to travel between geocaches, or remove calculations for materials and eliminating some of the higher-level math.
  • For higher grades, you could provide higher-level math content questions at each geocache or model curved or traced paths from which students can build their paths.  

Additional Multimedia Support

Geographic Information Systems (GIS): Dan Scollon at TEDxRedding - TEDx Talks

How Does GPS Work? - sciBRIGHT

What Is GIS? - Esri

Using Your iPhone & Google Earth for Plot Mapping

References

Patton, K. The Fundamentals of GIS and Real World Application (PDF). Western Wyoming Community College. No date.

Using Your iPhone & Google Earth for Plot Mapping (PDF). IR-4 Project, Department of Environmental

Toxicology, UC-Davis.

http://wrir4.ucdavis.edu/Resources/Tricks/docs/GPSGoogleEarth%20Plot%20Mapping-iPhone.pdf.

Accessed September 25, 2018

GIS Solutions for Civil Engineering (PDF). ESRI. Accessed September 25, 2018.

http://www.esri.com/library/brochures/pdfs/gis-sols-for-civil-engineering.pdf

Contributors

Jake Schell; Andrea Burrows

Copyright

© 2018 by Regents of the University of Colorado; original © 2017 University of Wyoming

Supporting Program

University of Wyoming

Acknowledgements

This digital library curriculum was developed under the guidance of Andrea Burrows, Linda Hutchinson, and Michele Chamberlin at the University of Wyoming.

Last modified: October 6, 2018

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