A math trail is an activity that gets students out of the classroom so they can (re)discover the math all around us. Whether out on a field trip or on school grounds, students on a math trail are asked to solve or create problems about objects and landmarks they see; name shapes and composite solids; calculate areas and volumes; recognize properties, similarity, congruence, and symmetry; use number sense and estimation to evaluate large quantities and assess assumptions; and so on. This is one of those creative, yet authentic activities that stimulate engagement and foster enthusiasm for mathematics—and so it can be particularly useful for students in middle and high school, when classroom math becomes more abstract.

A math trail can be tailored to engage students of any age and of all levels of ability and learning styles. Its scope and goals can be varied, and it can include specific topics or more general content. And best of all, it can make use of any locale—from shopping malls to neighborhood streets, from parks, museums, and zoos to city centers, to name a few. Any space that can be walked around safely can work. A Day of Exploration My school has used a ready-made math trail designed by the Mathematics Association of America. Although it’s designed for Washington, DC, its general ideas can be applied in any city or town. It could be particularly appealing for teachers because it’s open-ended and can be tailored to the curricular and educational needs of the students. In addition, as schools from all over the country visit the nation’s capital, it provides a math activity that can be easily added to the many history, art, and civics lessons elicited by such a field trip. Our math trail is loosely structured on purpose: As the whole Grade 7 takes part in this trail and as many chaperones are not math teachers, we make it clear that the purpose of the day is for the students to explore, discover, enjoy, and celebrate the beauty of math and its presence all around us. Using the MAA’s Field Guide and a map of the National Mall, each group spends the first hour of the day planning their route. How they spend their time is up to each group—this freedom is what the students like the best about the day. Some students want to visit the newly renovated East Building of the National Gallery of Art—a treasure trove of 2D and 3D geometric ideas, patterns, and artifacts. Can we calculate or estimate the volume of its octagonal elevators or triangle-base stairwells? Even without measuring tape? Others can’t wait to ride the Mall carousel while thinking of the trigonometric function the ride’s motion describes. Other students look at a more pressing problem: Considering the scale of the map, what is the shortest route to Shake Shack from the Sculpture Garden? Is that path unique? Is the distance the same in Euclidean geometry? Walking at a fast pace—say 4 mph—how long will it take to get there? Can we get our food and make it back to the bus on time? Another group might estimate how many people visit the Air and Space Museum in a day. And how do we go about solving this problem?