NCSS EDUCATION FOUNDATION, INC. NCSS Education Foundation Classroom Instruction Aides for Teachers

The Foundation has published the first edition of the booklet Land Surveying Problems - Trigonometry and Geometry Applied in Real Life Situations. This 104 page booklet presents eight problems representing situations that occur in land surveying. Each problem has several subproblems, sketches of the problem, and sketches and explanations of the concepts involved. The Teacher's Version has complete step-by-step solutions. The following is taken from the Note to Teachers in the Teacher's Version:

• The solutions to these problems have more steps than many in standard high school math textbooks because we want to portray a sense of how trigonometry and geometry are really used by professionals in the real world. This booklet is designed so you can use a whole problem, or just part of the problem if you have less time. These problems would also make excellent class projects if you choose to team with a local Professional Land Surveyor.
• The first problem, Working with Angles, Bearings, and Azimuths, introduces concepts the students will need to complete the other problems. It also explains concepts often used in problems in high school math textbooks, but rarely explained. You may find this information useful in explaining problems in your Geometry or Trigonometry textbook.
• The second problem, Designing a Street, uses right triangle geometry, bearing and angle calculations, and curve calculations to solve a simplified street design problem. Your students can find examples of such streets on campus, or just about anywhere.
• The third problem, Calculating a Subdivision Lot and House Location, uses coordinate geometry and the Law of Sines to solve a problem that land surveyors deal with every day. Students usually are familiar with the concepts of houses on streets, so they will probably relate to this problem. In these problems, the students are prompted by subproblems and illustrations through each step they need to take to arrive at the final solution. Complete and detailed answers illustrating each step are provided in italics in the Teacher's Version.
• The fourth problem, Trigonometric Leveling, illustrates the practical use of vertical angles. These kinds of problems are commonly found in textbooks, but this problem shows that surveyors actually use the principle.
• The fifth problem, Intersecting Distances (GPS Principle), uses the GPS technology many students (and adults) are excited about to illustrate the Law of Cosines. Surveyors who use GPS do not actually perform these calculations. Each GPS unit, or software used in conjunction with the unit, performs somewhat similar but far more complicated calculations. The technology illustrates the principle, however, and we think the students will be interested.
• The sixth, seventh, and eighth problems are progressively more advanced. In these problems, the student must analyze the situation, and decide what geometry and trigonometry principles to apply. As with the other problems, detailed answers are given in the teacher's version of the booklet.
• After the problems, there is contact information about land surveying, degrees, scholarships, and competitions that you and your students may want to pursue, and in the teacher's version, a feed back form, and a request form for other information you may find helpful..

The Foundation is planning other booklets or instruction aides. If you have an idea of something we can provide to help you, please contact us.

NCSS Education Foundation, Inc.    331 S. White Street, PO Box 2101,  Wake Forest, NC 27588  - 
919-556-9848

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