A 633Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking **HERE**

On a sunny day in the middle of May, two survey colleagues and I spent the day in Muskego Park along with five advanced high school math students. This was the second year the program was presented to a group of students. Our goal was to show them that there are every day practical applications for math. We had a fun day that proved to be very successful.

**Public Relations Opportunity**

The idea for a field trip of this sort started with Muskego High School math teacher Julie Kraft. In mid-April, she contacted the Wisconsin Society of Land Surveyors (WSLS) Executive Director Frank Thousand about a potential program. As the Chapter representative from the Milwaukee area, I was asked to contact Ms. Kraft. She indicated to me that she knew very little about land surveying, but she read recently that surveyors are ranked very high in terms of their job satisfaction and also that surveyors "use math". Based on her enthusiastic approach, I set out to prepare a program for her students.

I decided to prepare a day of surveying centered on the students running a closed traverse. The program would require the students use a conventional total station, as well as robotic survey equipment to gather angular and distance data. This data would be used to calculate coordinates for the ultimate purpose of finding a number of "mystery points".

I met with Ms. Kraft in her classroom to present my program for her approval. She provided very positive feedback and indicated that she thought the program would be well received by her students. It was decided that I would prepare sample math problems and provide a presentation to her students the day before the field trip to give them an introduction to land surveying and surveying terms.

**Program Development**

With the program idea approved, I set out to provide myself a refresher course on traverse calculations. The traverse work sheet to calculate latitudes and departures would need to be dusted off after 20-plus years of computeraided calculations. The trigonometry knowledge and formulas necessary for traverse calculations would be provided to the students in the form of example problems that included:

• Azimuth to Bearing Conversions

• Summation of Angles

• Balancing Traverse Angles

• Azimuth Calculations

• Latitude and Departure Calculations

• Misclosure and Precision Calculations

• Angle and Distance Calculations from Coordinates

I prepared a Power Point presentation that detailed the math calculations the students would be required to complete. The presentation also included some general background on land surveying, its associated terms, and the equipment the students would be introduced to. I also covered coordinate systems and the Public Land Survey System.

**Classroom Presentation**

I presented an introduction to surveying and survey math to 20 pre-calculus students. They listened intently and asked a number of good questions. One young lady asked, "Do these monuments get vandalized or are they damaged often?" Ms. Kraft wondered, why, if they are placed every half mile, we never see them? We discussed terminology that was new to them. Even though they were hit with a lot of information rather quickly, I trusted that the introduction would be beneficial to the success of the upcoming field trip.

**Field Trip in Muskego Park**

Prior to the field trip, Bonestroo, Inc. Crew Chief Jim Fritz and I spent a part of a day at the park establishing the eight control points and their corresponding coordinate values. We decided to simplify the students’ calculations by using an assumed coordinate base of 5000, 5000. Jim and I also collected side shots and determined the coordinates of the four "mystery" points. We would ultimately provide these coordinates to the students and ask them to determine the identity of the four "mystery" points.

Licensed surveyors Gary Smith and Kevin Slottke assisted me in preparation for meeting the students first thing in the morning to get started on our traverse work. It was a breezy and cool spring day with ample sunshine when we met Ms. Kraft and five of her students at our base, Picnic Area 5. After introductions, we provided the students a drawing of the traverse overlaid on an aerial photo of the park. We also reviewed the traverse calculation spreadsheet and our goals for the day.

We set out with two student survey crews to collect the traverse angles and distances. Each student had the opportunity to:

• Set-up and level the backsight

• Operate a conventional and robotic total station

• Provide a back sight with a prism pole

• Keep notes

Our traversing time allowed for conversations with the students that were very engaging and interesting. These students are very driven, involved in extracurricular activities and after school jobs, and thinking a lot about life after high school. My survey crew had a future dentist, doctor, artist, teacher, and biochemist. They worked together and helped each other as they started to understand our task at hand.

We collected at set of three angles at each traverse point, along with multiple foresight and backsight distances. As we traversed close to the southwest corner of the park, the students were given the opportunity to search for a section corner hidden in a tree line. With the aid of an aerial photo and a tie sheet, the students were able to find the monument and also learn what poison ivy looks like.

After a couple hours of traverse work, the class met back at Picnic Area 5 to dive into the necessary calculations. Although it was only 10:30 a.m., the students were hungry after all of their hard work and decided to start a "working" lunch. Each survey crew worked together to average their angles and distances. The students from each crew shared their results with each other. The summation of angles and subsequent balancing was completed next. All of this data was used to populate the angles and distances on the traverse worksheet. We finished our traverse calculations by computing azimuths, latitudes and departures, and coordinates for each of the eight control points. By the time our calculations were complete, the students had a very good understanding of the importance of trigonometry to the land surveyor. They also had some fun trying to add angles on their calculators faster than a certain surveyor could do on paper, while writing upside down.

After a much deserved break, the students undertook the task of calculating the angles and distances necessary to locate the four "mystery" points. They determined which control points were closest to the objects they were searching for and then used them to calculate the angle to turn and distance to go in their search. They completed coordinate subtractions to determine changes in latitude and departure, as well as, using the Pythagorean Theorem to arrive at the necessary distance. Using the basic trig function of tangent and an angle addition, they had the angle they needed to turn. A deal was made with the students. If they found all four "mystery" points, they would be rewarded. With much excitement, the students headed back into the field to see if their calculations were accurate enough to win the bet. As a part of this exercise, we navigated to the first hidden point using coordinates and GPS survey equipment. The students were given an opportunity to see a demonstration of GPS and the time that can be saved by using this technology. They

located a hydrant, trash bin, and horseshoe pin with relative ease, as they turned an angle, paced to the approximate location, and shot distances with a conventional total station. A picnic grill was a bit more of a challenge as a 90-degree error in calculation had them looking in the wrong location. After a not-so-quick recalculation, the students found their last hidden object.

After their successful point search, the students headed back to Picnic Area 5 where they were treated to ice cream and brownies to acknowledge their accomplishments. As the day wrapped up, we took the opportunity to field many questions and even to share some survey stories with the group. Based on the feedback we received, it was obvious that the students walked away with an understanding of what surveyors do and how mathematics is an integral part of their everyday work. Not every day as a surveyor is "a walk in the park", but this day certainly was.

*Al Schneider is a Senior Project Manager at Bonestroo, Inc., and a licensed surveyor in Wisconsin and Illinois. He is a board member of the Wisconsin Society of Land Surveyors and state coordinator for the Trig-Star program.*

A 633Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking **HERE**