To trudge is to walk slowly and heavily, with effort, because you are tired or because the ground makes it hard — deep snow, mud, sand, a long hill, stairs with heavy bags. The word contains both the difficulty and the feeling. Someone who trudges is not enjoying it; there is weariness in the sound of the word, and a little bit of resignation. Two ingredients, and both matter: heavy steps, and a distance that goes on too long. You trudge *through* snow or mud, *up* a hill, *across* a field, *home*, *back*. It is used just as much about ordinary tiredness — a student trudging home after cram school, a worker trudging up to the office on Monday — as about mountains and snow. English has a small family of walking words that your students will meet together, and *trudge* sits neatly among them: *stroll* is slow and happy, *stride* is fast and confident, *trudge* is slow and heavy, *plod* is almost the same as trudge but suggests steady patience more than tiredness, *shuffle* means barely lifting the feet. There is also a noun — "it was a long trudge home" — meaning a tiring walk. Slightly less common than the verb, but perfectly natural. And a figurative use worth knowing: you can trudge through a boring book or a pile of paperwork, meaning you keep going through something dull and long. Regular verb: trudge, trudged, trudging.