No matter where you were educated, medals may have crossed your path at school by way of participation and recognition in academics or sports.
The High School which I attended, is Brooklyn Technical High School. At my graduation in 1977, I was awarded the Graphic Communications course medal. I sadly have not seen in since 1987 or so (a sad commentary for a collector!)
However, now as Historian for the Alumni Foundation, I have been able to gather medals dated back to the school's founding in 1922, and even from the school from which Brooklyn Tech was created, Manual Training High School.
There are awards for academics - math, science and english; awards for sports - city championships in baseball, football and bowling. Most of the school medals are from special dies with special dies, the school name or logo as part of the design, rather than a generic award. We have several examples of early castings of the Penn Relay Plaques designed by R. Tait MacKenzie.