My first military button

[crosstraining]

I got my first military button today. Is there anyway to date this? I googled, but the pictures and info seems endless. I also found a mystery item near the button. These were both found in a fairly small area on the side and toward the back of a school. The school site has been in use since the early 1900’s. The oldest coins I have found there are in the late 30’s and early 40’s. Any help with dating or a better description that I can google would be appreciated. Thanks