Lesson: GIS, Mathematics, and Engineering Integration

Contributed by: University of Wyoming

This image shows the amount of energy the United States receives from the sun on average. Higher amounts of energy are displayed in red and generally include the south and west while lower energy areas are displayed in yellows and greens and tend to be in the north and east. The image was formed using GIS technology.
A map created with GIS technology that shows the amount of energy that different parts on the US obtain from the sun. Engineer can use maps like this one to determine a location for a solar cell array for generating electricity.
copyright
Copyright © 2008 National Renewable Energy Laboratory, Public Domain, U.S. Department of Energy https://www.eia.gov/energyexplained/index.php?page=solar_where

Summary

This lesson introduces the concept of geocaching as a way for students to explore using a Global Positioning System (GPS) device and basic geographic information (GIS) skills. Students familiarize themselves with GPS, GIS, and geocaching as well as the concepts of latitude and longitude. They develop the skills and concepts needed to complete the associated activity while considering how these technologies relate to engineering. Students discuss images associated with GPS, watch a video on how GPS is used, and review a slide show of GIS basics. They estimate their location using latitude and longitude on a world map and watch a video that introduces the geocaching phenomenon. Finally, students practice using a GPS to get an understanding of the technology and how location and direction features work while sending and receiving data to a GIS such as Google Earth.
This engineering curriculum meets Next Generation Science Standards (NGSS).

Engineering Connection

Civil engineers, petroleum engineers, environmental engineers and many others use GPS and GIS to analyze data and make informed decisions. A civil engineer may use GPS and GIS in a large-scale urban planning project. A petroleum engineer may want to map the extent of a rock outcropping known to contain oil or gas deposits. They could map the surface of the outcropping using a GPS and integrate other data into the map using GIS. An environmental engineer may use these tools to map water resources or study climate change. This lesson demonstrates another important connection between engineering and math, which is problem solving: students must break up larger composite shapes into smaller shapes in order to simplify their calculations.

Pre-Req Knowledge

Students need to be familiar with calculating area of regular and irregular shapes, finding missing angle measures, and understanding complementary and supplementary angles.

Learning Objectives

After this lesson, and activity students should be able to:

  • Determine a latitude and longitude from a map
  • Operate a GPS
  • Identify location (latitude and longitude)
  • Create a waypoint
  • Use compass and distance features

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Geometry and Geocaching Using GIS & GPS

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What Is GIS?

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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.

  • Construct an explanation based on evidence for how geoscience processes have changed Earth's surface at varying time and spatial scales. (Grades 6 - 8) 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?
Suggest an alignment not listed above

Introduction/Motivation

At any given moment, there are thousands of satellites orbiting our Earth. In fact on any clear, cloudless night where you’re a good distance away from the lights of a town or city, you may be able to look up and spot a satellite or two passing overhead! There are a variety of satellites overhead; some used for military purposes, observation, communication, or weather. One of the most famous satellites, the Hubble Space Telescope, is a vital research tool that doesn’t look at the Earth, but instead scans the darkness of space to study our universe. However, one of the most important satellites, or group of satellites, make up a navigation system called the Global Positioning System, which is more commonly known as GPS. This satellite-based system—developed by the U.S. Government for military use in the 1970s, and later for civilian use in the 1980s—provides information about position and location to users around the globe, including you!

This image shows a GPS satellite in orbit as rendered by an artists’ representation. The satellite is adorned with solar panels for generating electricity and has a metallic core with various instruments surrounding the main body.
An artist’s rendering of a GPS satellite in orbit.
copyright
Copyright © 2012 US Government, Public Domain, Wikimedia Commons https://commons.wikimedia.org/wiki/File:GPS-IIRM.jpg

We can use GPS through GPS-enabled devices, such as a navigation system in a car or even on a smartphone. Usually, apps like Google Maps or Apple Maps use GPS to help everyday users with directions or location. However, GPS has a wide range of commercial and business applications, particularly in engineering. Civil engineers use GPS to help survey and plan infrastructure projects. Aerospace engineers install GPS in aircraft or even rockets to assist with navigation. Environmental engineers may employ GPS to gather data on geographic locations or the wildlife contained within them.

Before we dive deeper into other applications of GPS, let’s take a look at the following questions and see if we can answer them.

What is GPS? What does it do?

  • GPS stands for Global Positioning System.
  • It helps you pinpoint your location, usually on a map.

What would you used GPS for?

  • GPS is used a GPS for directions, to plot a course, or to find a waypoint on a map.

Why would engineers put a GPS on a rocket? (Present Image 3 here.)

  • To make sure it doesn’t land somewhere dangerous and goes where it was intended to fly.

This image depicts a rocket equipped with a GPS satellite as it propels through the air, showing a stream of flame and smoke from the engines. The rocket is red on top and white on bottom with a red stripe in the middle. The text on the photo reads “IN POSITION. Air Force launches newest GPS satellite”.
A rocket launch into space with a GPS satellite in its payload.
copyright
Copyright © 2012 Robin Meredith, Public Domain, U.S. Air Force, 45th Space Wing Public Affairs http://www.af.mil/News/Article-Display/Article/110340/air-force-launches-new-gps-satellite/

What kind of engineers would be needed to develop and launch a rocket?

  • Aerospace engineers, mechanical engineers, materials engineers or chemical engineers.

Why do you think people/engineers would want to monitor the location of animals, such as a wolf? (Present Image 4 here.)

  • To monitor their migration habits, check up on health of animals released after medical treatment, or track endangered species.

This image shows a grey wolf (canis lupus) facing the camera and wearing a tracking collar. The wolf is on snowy ground with branches seen in the foreground and background. His coat is mostly grey, white, black, with a patch of red near his shoulder.
A grey wolf in the wild wearing a tracking collar.
copyright
Copyright © 2003 U.S. Fish and Wildlife Service, Public Domain, Wikimedia Commons https://commons.wikimedia.org/wiki/File:Canis_lupus_with_radio_collar.jpg

Why do you think an engineer would need to know locations on earth? How about locations in space?

  • To study a given area and help humans utilize the resources.
  • To collect data.
  • To help improve the world.
  • To navigate effectively and to avoid other space objects.

[As either an introduction or supplement to the lesson, consider showing students one of the following videos: from TEDx Talks, Geographic Information Systems (GIS): Dan Scollon at TEDxRedding; from sciBRIGHT, How Does GPS Work?; or from Esri, What is GIS? Also, introduce students to the PDF titled The Fundamentals of GIS and Real-World Applications Handout and go over it throughout the lesson.]

Introducing GIS

If any of you have used a navigation app such as Google Maps, then you have actually used a GIS, even if you were aware of it!

In order to understand GIS and GPS, we must first understand how we mark locations on the earth. People use a GPS-enabled device to determine their location using latitude and longitude. Latitude and longitude are like the x- and y-axes on the coordinate plane. To picture this, imagine that you could unroll the earth and make it flat, like a map. Then, you could put axes over the map as in Figure 1 below. Those lines are called latitudes (which represent your location from north to south) and longitude (which represent your location from east to west). The equator—a horizontal line that passes through South America, sub-Saharan Africa, and much of Indonesia—represents the x-axis: 0° north and south, while the prime meridian—a vertical line passing through the United Kingdom—represents the y-axis: 0° east and west.

This image shows an ovular map of the world, with a light brown color showing the land masses and blue showing the oceans. Only continents and oceans are labeled. There are parallel straight lines going east to west and curved lines running north and south, each of which is labeled with an angle measure.
Figure 1. This map of the world shows lines of latitude and longitude, including red segments denoting the prime meridian (longitude 0°), equator (latitude 0°), Arctic Circle, Antarctic Circle, Tropic of Cancer, and Tropic of Capricorn.
copyright
Copyright © 2008 Dbachmann, OpenGL, Wikimedia Commons https://commons.wikimedia.org/wiki/File:Earthmap720x360_grid.jpg

One example using latitude and longitude is to determine the approximate center of the lower 48 United States, located at (latitude) 39.8° north and (longitude) 98.6° west near Lebanon, KS.

Now, estimate the location of your school using this latitude and longitude map. During the next part of the lesson, we will check our estimates with real GPS coordinates. You can also estimate coordinates on a physical map in the classroom, such as one from National Geographic. Just remember, for latitude, remember to include the degree symbol ° and “north” or “south”. For longitude, remember to include the degree symbol ° and “east” or “west”.

Geocaching

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.
A label for an official geocache. 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 This image has not been modified in any way from its original form.

One fascinating way that GPS and GIS are used is in a hobby called “geocaching”. This is basically a treasure hunting activity that takes place literally worldwide, and can be taken on by anybody with a sense of adventure and a GPS or smartphone! This short video, “What is Geocaching,” helps explain this real-world adventure happening right now all around you.

We are going to work with geocaches using our own GPS devices during a future activity, all while exploring what it would be like to be an engineer using GIS and GPS!

GPS Hardware and GIS Software

In preparation for the activity, we will practice:

  • Creating and sending a waypoint to Google Earth
  • Determining your distance from a waypoint
  • Navigating to and from the waypoint
  • Following a compass bearing

Below are screenshots based on the Apple iOS software. For the purposes of this tutorial, the following instructions are for the “Free GPS” app, available on the iOS platform. There are alternate GPS apps for Android operating systems, such as “Maverick: GPS Navigation” or “Handy GPS.” Google Earth is available for both iOS and Android, and is available in the App Store and on Google Play. You can also use a desktop version of Google Earth to export or email waypoint data from a smartphone.

Example of how to create and send waypoints to Google Earth:

The main screen in the Free GPS app will show your compass bearing and the distance from a chosen waypoint as shown in Figure 2.

This image is a screenshot of an iPad running the Free GPS app. It shows the user’s heading, speed, and distance from the selected waypoint. It also shows three buttons for input: “Settings,” “Map,” and ‘Waypoints.”
Figure 2. The home screen for the Free GPS app.
copyright
Copyright © 2018 Jake Schell, University of Wyoming
Open the Free GPS app. To create a waypoint, simply click on “Waypoints” and then “Add Waypoint.” If you are in the location you want to use, click on “Add Current Position” to use your current position for the new waypoint. This will enable you to see the latitude and longitude of your location, and change the name of the waypoint. See Figure 3.

This image is a screenshot of an iPad running the app Free GPS. It shows the waypoint’s latitude and longitude, name, and has three buttons for user input. They are “Help,” “Cancel,” and “Add”.
Figure 3. The waypoint screen for the app Free GPS.
copyright
Copyright © 2018 Jake Schell, University of Wyoming

Take note of your location in latitude and longitude of the classroom as an example. Again, for latitude remember to include the degree symbol ° and “north” or “south.” For longitude, include the degree symbol ° and “east” or “west.”   

To send a waypoint from this app to Google Earth, simply go to “Settings” and click “Email Waypoints." See Figure 4.

This image is a screenshot of an iPad running the app Free GPS. It shows the settings screen, which allows users to adjust units for latitude and longitude and distance, as well as contact the application’s developer and send files to email addresses.
Figure 4. The settings screen for the Free GPS app.
copyright
Copyright © 2018 Jake Schell, University of Wyoming

Open Google Earth on a computer, and then open the file from the email on your computer and it should appear in Google Earth.

Next, we will walk around the room to experience how the distance and compass functions work. On the main screen, the app shows how far you have walked from the waypoint you created originally. You will use a feature like this in the activity. Be sure you hold the device flat, parallel to the ground. Notice as you move, so does the compass, showing you your heading facing straight in front of the device. You will also need to use this compass bearing during the activity. Here is a helpful chart to familiarize yourself with compass headings and how they relate to north, south, east, and west.

[Once students are familiar with the app, you should be ready to move on to the activity, Geometry and Geocaching Using GIS and GPS.]

Lesson Background and Concepts for Teachers

Geographic information systems (GIS) integrate data from a wide variety of fields—natural sciences, social sciences, and engineering—and can display data in map form. The Global Positioning System (GPS) is a global satellite-based navigation array that provides location and time information to a GPS receiver anywhere on or near the earth, provided the device has a line of sight to four or more GPS satellites. GIS and GPS go hand-in-hand as much of the data used in GIS is obtained with GPS coordinates to pinpoint a location based on the data.

Geocaching is a hobby in which people hide items around the world and post instructions on how to find them. Other geocache hunters then use a GPS-enabled device to find the hidden cache, or treasure. GPS devices display a user’s location on a map, where they can save their locations and upload the data to a computer. Many devices now have GPS receivers embedded within them, such as smartphones as well as technology used in engineering like surveying equipment. Students take the role of a geocache hunter, using a GPS-enabled device to locate a certain point on the Earth’s surface. They use hints at each waypoint to find other locations. When mapped out on Google Earth, they can visualize the length and direction of where they traveled.  

Engineers of all types use GPS and GIS to acquire, compile, and view data so they may make informed decisions throughout their problem-solving process. This lesson introduces students to GIS and GPS through the lens of geocaching while practicing other concepts like geometry and scale. Students need to be familiar with calculating area of regular and irregular shapes, finding missing angle measures and understanding complementary and supplementary angles. The lesson can also be used in conjunction with rate and unit rate concepts.

Most free GPS apps are quite user friendly and can be used by an individual with limited knowledge of GPS and GIS. This lesson uses one example of a free GPS app available for iOS. If you decide to use another application (for example, on an Android device) you must know how to send waypoints to Google Earth via email in the form of a KML file (also known as Keyhole Markup Language; a computer text language that expresses geographic annotation and visualization.) If the KML file does not load in Google Earth, you can click and drag the file from its folder wherever you chose to save it directly into Google Earth. Release the mouse pointer over the map portion of Google Earth to achieve this.

Most GPS software should allow the user to send waypoints to Google Earth as a KML file. The class is responsible for making sure they understand the GPS software of the devices used in the classroom.

Before undertaking this lesson and its associated activities, it is the teacher’s responsibility to be familiar with the technologies—both GPS and GIS (Google Earth). For more information on teacher preparation, please see the activity, Geometry and Geocaching Using GIS and GPS.

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.

Associated Activities

  • Geometry and Geocaching Using GIS & GPS - Students use GPS devices to find and mark geocaches as well as to travel from location to location. Each geocache provides a geometry problem, and the answer indicates the direction and distance to travel to the next geocache. This lesson has students taking on the role of a civil engineer who is working to build some new features in the area, including a pathway and a fence. Students work with unit rates to find how much material will be required and draw the area as a scale model on graph paper.
  • Topographic Maps and Ratios: A Study of Denali - Students overlay topographic maps onto Google Earth satellite imagery. By analyzing Denali, the tallest mountain in North American, students discover how to use map scales as ratios to navigate a map. Students also use rates to make sense of contour lines and elevation changes in an integrated GIS software program, Google Earth. Students problem-solve to find potential pathways up a mountain by calculating gradients.

Lesson Closure

What is GIS? What is GPS? How are they related? How does geocaching use these technologies? Why might various engineers want to use GIS and GPS in their jobs? When do you use GIS in your daily activities? What are latitude and longitude?

Attachments

Assessment

Pre-Lesson Assessment

Turn and Talk: Conduct a class discussion surrounding the following questions:

  • What is GPS?
  • What is GIS?
  • Have you ever used either?
  • Can you think of any type of engineer who might use either?

Post-Introduction Assessment

Re-Visit Turn and Talk: [By asking the same questions before and after for discussion, you can gauge how much information your students learned during the lesson.]

What is GPS? What is GIS? Have you ever used either? Can you think of any type of engineer who might use either?

Lesson Summary Assessment

Researching Engineers: Based on their knowledge of GPS, GIS, and geocaching, discuss as a class the types of engineers that may use these geographic information tools. Prompt students with the following career paths:

  • Civil Engineer
  • Mechanical Engineer
  • Energy Systems Engineer
  • Medical Engineer
  • Geologic Engineer
  • Another engineer of your choice (check with teacher first).

Homework

Preparing for the activity: Have students prepare for the activity by either downloading a free GPS app and creating at least three waypoints on their way home from school (if they have access to their own smartphone). Or, create an assignment using the The Fundamentals of GIS and Real-World Applications Handout such as exploring Google Earth or finding a particular set of latitudes and longitudes on a traditional map. 

Lesson Extension Activities

Give students time to research different types of engineers. Students can either be assigned to research and write about these career types individually or present their findings in small groups.

References

Katrina Patton. The Fundamentals of GIS and Real World Application (PDF). University of Western Wyoming.

Using Your iPhone & Google Earth for Plot Mapping (PDF). UC-Davis. http://wrir4.ucdavis.edu/Resources/Tricks/docs/GPS-GoogleEarth%20Plot%20Mapping-iPhone.pdf

Other Related Information

There are other interesting lessons on TeachEngineering with GIS as a keyword. Most of these lessons and associated activities involve data, maps, and projections, and could be great activities to try on in association with this lesson (see list below). However, this lesson and activity deals with a different niche that is not available in other lessons: the hands-on use of a GPS device and its integration with GIS is unique.

Other relevant teachengineering.org activities and lessons:

What Is GIS?

Projections and Coordinates: Turning a 3D Earth into Flatlands

What’s Wrong with the Coordinates at the North Pole?

Who Can Make the Best Coordinate System?

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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