Hi Katie! First of all, your son did well; you’re not as far off as it may seem.
“in terram” must be translated as “into the land” because when the preposition “in” is followed by its object in the Accusative case (here, terrAM), “in/on” changes to “into/onto.” “Sennaar” is then an appositive renaming the “terram”. Technically, “into the land Shinar”, which sounds like the KJV or Elizabethan English, right?
“in campo”, then, follows the other side of that rule: when “in” is followed by its object in the Ablative case (here, campO), “in/on” is the correct translation. Your son only forgot to translate field as a singular noun (it would have been campIS for plural). Field/plain are interchangeable translations at this stage of the game.
Hope that helps!