This was kind of a thing in Canada? I think it was done by my time. My older brother, in average shape, got a very fancy “Bronze Medal Fitness” patch in grade school. Have no idea if that is good, or what the requirements were. Wasn’t a thing for me. Maybe it was related to ParticipAction - very dated commercials supposed to encourage physical activity.
My school didn’t do it, but I knew about it because I would go to Girl Scout camp and see the patch on other girls’ patch jackets.
My grade school had a formal competitive event around this (mid 70s). Most students thought it was weird and dumb; a bunch of kids got “participant” certificates but nobody earned whatever the thing was for excellence or high performance.
However: years later, when I was working in HR doing recruiting stuff (early 90s), I was very amused to see that one of our applicants had put this on his resume as an achievement, dated from his own childhood.
We interviewed him. He was a doofus. We didn’t hire him.
I always felt left out by never seeing any sign of it. Thought I could have done well. Some kids could use the boost. But maybe others would be left with no medal.
It was all meant to make a pool of good little soldiers.
It was definitely a JFK thing. I remember it from early 60s elementary school; I’m surprised to hear it was still around in the 80s.
As a kid who wasn’t particularly athletic, but hardly a couch potato, the goals were completely unreachable. Rather than encouraging me to get more fit, I think it made me feel like I was in much worse shape than I really was.
I think I was in fourth grade when everyone had to participate. We weren’t given any training or preparation; just take the test. I didn’t pass. 
That’s what I remember, too, except that it was in junior and senior high school (I graduated in '69). I went to a Catholic elementary school, and I don’t remember doing it there.
But I have absolutely zero memory of any patches or awards of any kind. If they gave any out, it must have been in secret.