I did exactly this sort of thing in Excel, and it works trivially there.
Design your form in the upper half of the page.
Copy it to the lower half - the lines, borders, spacing, etc., NOT the contents.
Organize it so that, for example, Cell a1 = "Name", and cell A2 can be filled in with (e.g.) John Smith.
Then, in the lower half of the page, starting, perhaps in row M,
Cell M1 contains: =A1
Cell M2 contains: =A2
Then M1 would contain "Name" (you could just type "Name", here, but, doing it this way means that, if you decide to change the form (Name -> Nom to support your Spanish students), you don't have to retype M1, it just automatically "learns" from A1.
And, of course, M2 would be John Smith.
You could do something similar in Word, but it is a LOT more tedious to set up, involves bookmarks and manual updating, etc. Odds are pretty good that, if you have Word, you also have Excel, and it's straightforward in Excel.
By the way, in my case, filling in one form actually filled in additional forms on additional sheets in the same workbook. In my case, one form was used as label for the "thing", and the second form was used by the contest judges for the grading. I just filled it out once, and it automatically flowed to the other four forms. Just an idea.