In the world we deal with concrete 'unit' quantities, the 'units' are very concrete, ten pencils, for example we can tell the difference between one pencil and another and we can also trace and identify one of them and see where it goes and differentiate it from other pencils.
If we measure '10 meters' can we do the same? A meter is a certain measurement on a ruler, it does not exist like a pencil, we cannot differentiate a meter unit from another, only a two things that are a meter in length, the same for any 'measured' quantities. If I have 5 pencils and then get more, such that I have '10 pencils' I can trace which pencil is which, if I have an object of mass 2kg and gain 3kg to have mass 5kg I can trace each kg worth of matter, but not the 'kilograms' themselves.
Is this part of how we should view 'units of measurement' or simply as values we would expect to find on measurement, can an object 'possess' units at one time and have two objects each with 'one unit' of length have two different 'units', with one each? What is the best way to deal with these abstract 'objects'?