With the Mars 115 being an air rifle and therefore for the Deutsches Jungvolk this unit could be either:
Jungbann 3/113 or Fähnlein 3/113. I have no records showing that there was ever a Jungbann 3/113 so this unit designation must be for Fähnlein 3/113. I don't yet have an exact location for that Fähnlein in my list but it will have covered a part of Freiburg (im Breisgau). I don't think this will be a school.
Another option could be that this was rifle number 3 within the stocks of Jungbann 113. I doubt that but I'll look into the regulations and see if I can find how these items were marked.
No probs. I see from an older post of mine that the regulations do not specify a method of marking rifles. Yours however will mean "Fähnlein 3 of Jungbann 113".
In France, I often see hj training weapons with markings like this on the stock. But nothing regulatory I think, often engraved at the bottom of the stock or on the metal ring for dismantling the breech.
The 111 and 412, would the proper term be Gefolgschaft 111 and Bann 412? Also I see the 111 is termed often with the HJ group from Berlin in The Handbook of the HJ, so would this be a group from Berlin sent to Aschersleben ?