One of the earliest math Trails was by Dudley Blane and Doug Clarke in 1985 for a trail around the city of Melbourne Australia.
Math Trails are an opportunity to imagine, realize, and play with the math that exists in the world around us, but in a particular place or location. Math Trails are guided in some manner, either because of a defined route already in place in the location, or perhaps by fictitious characters who act as guides. Some Math Trails are wound around a story too. The audience for a Math Trail will determine the level and challenge of the mathematics experienced in the Trail.
See https://www.comap.com/highschool/projects/mathtrails/MathTrails.pdf for a nice description of Math Trails, some examples, and details and insight into the creation of a Math Trail. “Math Trails” by Mary Margaret Shoaf, Henry Pollack, and Joel Schneider, 2004, COMAP.
Some other Math Trail examples:
Welland Canal Math Trail, by Dr. Eric Muller (circa 1990s).
Niagara Falls Math Trail, by Dr. Eric Muller (circa 1990s, after the Welland Canal Math Trail was created).
Beal Math Trail, by Dr. Jamie S. Pyper, made for the Western Ontario Mathematics Association (the WOMA conference for math teachers) in 1999, showcasing the newly renovated H. B. Beal Secondary School.
Althouse Math Trail, by Dr. Jamie S. Pyper, made for the Western Ontario Mathematics Association (the WOMA conference for math teachers) in 2003. The asterisk and numbers in a black circle represent particular locations in the building. Participants would pick up a piece of a newspaper article from each location – to be put together to reveal another piece of information about the building. The whole newspaper article a copy of the article printed in the local paper in 1965 when the building first opened. (Some images have lost their credit notation over time, credit being added as I re-find it.)
Welcome to McArthur Hall, by Dr. Jamie S. Pyper, made for elementary school preservice teachers, and secondary school preservice teachers, to give them a sense of intermediate level (grades 7 and 8) mathematics, in 2012. At the time of creating this Math Trail, the Intermediate/Senior teaching and learning mathematics classroom was located in A239, across the hall from A237, which was relatively the centre of the building. Over the years, renovations have moved some of the rooms to new locations… a new version is in the works, but for now, if you follow this version… beware the loss of way and pitfalls! (Image credit notation on the last page.)