### Summary

In this unit, students learn the very basics of navigation, including the different kinds of navigation and their purposes. The concepts of relative and absolute location, latitude, longitude and cardinal directions are explored, as well as the use and principles of maps and a compass. Students discover the history of navigation and learn the importance of math and how it ties into navigational techniques. Understanding how trilateration can determine one's location leads to a lesson on the global positioning system and how to use a GPS receiver. The unit concludes with an overview of orbits and spacecraft trajectories from Earth to other planets.### Engineering Connection

Many types of engineering are important to the development of navigational equipment used for travel on sea, in space and on land. Understanding the science of natural phenomena enables engineers to design and create structures and systems for a variety of navigational purposes. Mathematics is also essential to the development of navigational equipment. Satellites designed and tested by engineers use equations that take into account the relative effects of space and time.

Engineering is built upon a network of knowledge extending back in time. Even though celestial navigation is for the most part historical, the best engineers understand how things used to be done, building on the same mathematics concepts—such as geometry and trigonometry—used by engineers every day. Engineers make predictions and analyze circumstances related to motion; they must understand the relationships between speed, time and distance. They use many techniques that often involve computers to help process the many calculations required to make good estimations.

Engineers design systems that require precise and known locations, and often use triangulation calculations. They use triangulation with ground data to determine where in space satellites are located. Accurately determining a satellite's location is important to adjusting its position to keep it on course. The global positioning system (GPS) uses the same concept of triangulation; the development of this now-ubiquitous system was made possible by the contributions from many engineering disciplines. Mechanical engineers created satellite and other GPS equipment that performs reliably in the unique environment of space. Electrical engineers designed computers, circuit boards, power systems and wiring. Aerospace engineers determined satellite arrangement and orbit around the planet. Programming by software engineers enabled the satellites to operate on their own and transmit useful data to Earth receivers.

Engineering is vitally important to the creation of technology used in space, on water and on land. Without engineers, our ability to navigate our world and beyond would be much more difficult. The possibilities for future developments are only limited by our imaginations.

###
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*.

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*.

###### Next Generation Science Standards: Science

- Conduct an investigation and evaluate the experimental design to provide evidence that fields exist between objects exerting forces on each other even though the objects are not in contact. (Grades 6 - 8) Details... View more aligned curriculum... Give feedback on this alignment...
- Develop and use a model to describe the role of gravity in the motions within galaxies and the solar system. (Grades 6 - 8) Details... View more aligned curriculum... Give feedback on this alignment...

###### Common Core State Standards: Math

- Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. (Grade 6) Details... View more aligned curriculum... Give feedback on 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... Give feedback on this alignment...
- Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. (Grade 7) Details... View more aligned curriculum... Give feedback on this alignment...
- Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. (Grades 9 - 12) Details... View more aligned curriculum... Give feedback on this alignment...
- Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. (Grades 9 - 12) Details... View more aligned curriculum... Give feedback on this alignment...

### Unit Schedule

- Day 1: Where Is Here? lesson
- Day 2: Nidy-Gridy activity
- Day 3: Northward Ho! activity
- Day 4: Find Your Own Direction activity
- Day 5: How to be a Great Navigator! lesson
- Day 6: Vector Voyage! activity
- Day 7: The North (Wall) Star activity
- Day 8: Navigating by the Numbers lesson
- Day 9: Stay in Shape activity
- Day 10: Trig River activity
- Day 11: Getting it Right! lesson
- Day 12: Close Enough? activity
- Day 13: Computer Accuracy activity
- Day 14: Sextant Solutions activity
- Day 15: Topo Map Mania! lesson
- Day 16: Where Is Your Teacher? activity
- Day 17: The Trouble with Topos activity
- Day 18: Getting to the Point lesson
- Day 19: Classroom Triangles activity
- Day 20: Topo Triangulation activity
- Day 21: Topos, Compasses, and Triangles, Oh My! activity
- Day 22: By Land, Sea or Air lesson
- Day 23: Nautical Navigation activity
- Day 24: Navigating at the Speed of Satellites lesson
- Day 25: State Your Position activity
- Day 26: It's About Time activity
- Day 27: GPS on the Move lesson
- Day 28: GPS Receiver Basics activity
- Day 29: GPS Art activity
- Day 30: GPS Scavenger Hunt activity
- Day 31: Not So Lost in Space lesson
- Day 32: A Roundabout Way to Mars activity
- Day 33: Satellite Tracker activity

### Contributors

See individual lessons and activities.### Copyright

© 2009 by Regents of the University of Colorado### Supporting Program

Integrated Teaching and Learning Program, College of Engineering and Applied Science, University of Colorado Boulder### Acknowledgements

The contents of this digital library curriculum were developed under grants from the Satellite Division of the Institute of Navigation (www.ion.org) and the National Science Foundation (GK-12 grant no. 0338326). However, these contents do not necessarily represent the policies of the National Science Foundation and you should not assume endorsement by the federal government..

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