Anyone who has seen these strange circles from an airplane can see how easily they can be incorporated into a Google Earth math lesson. These crops take this shape from a watering system called central pivot irrigation. Central pivot irrigation uses a series of pipes, trusses, and wheel towers to suspend water sprinklers above the crops. The system rotates around a center point where the water is pumped into from a well or other source.
I’ve assembled a collection of placemarks where these and other circles appear in Google Earth. My goal was to create something more engaging than the circle geometry page in a math textbook. In Crop Circles, the students are presented with twenty problems that start off with basic area and circumference computation and then evolve into multi-step problems involving rates, cost, and comparison. In each problem, students are tasked with measuring the radius of the circle using Google Earth’s ruler tool and then solving the problem. Some of the problems involve fractional parts of circles and others are complex area problems where students must find the difference of two areas. Metric and customary units are used with the measurements.
I’ve included a Teacher Reference Sheet, but you should encourage your students to complete the work on loose-leaf paper. (If these problems were presented on a worksheet then the role Google Earth plays would be diminished.) Students should use calculators and show their work in steps to a final answer with correct units. I did not dictate what value to use for pi, so be sure to convey your expectations.
Google is constantly updating the imagery in Google Earth. Consequently, some of the crop circle images may not seem to match the problems. Show the students how to use the Historical Imagery tool to view earlier dates of the landscapes. I've made references to particular dates in the placemarks for several critical problems.
The grade level I’ve given is 5-8, but, as usual, it depends on your students ability level. Try the problems yourself and see if you want to pick a set for them to complete. Real World Math’s copyright encourages you to make changes or adaptions to its content. Add your own problems or ask students to devise one to share with the class.
Note: I’ve composed these problems to the best of my ability from my home in Guam. The types of crops at each placemark, or the cost of seed and fertilizer, are my best guesses. I scoured the Internet for information, so I don’t think I’m too far off the mark. Which brings us to the circles. They aren’t completely circular and it was difficult to determine their centers without marking up my computer screen with a compass. You’re going to have to allow some wiggle room with the students’ answers and my efforts. Please email me at 4RealWorldMath@gmail.com to offer suggestions, corrections, or submit a problem of your own.