1. If you miscalculate in math, do you make a mistake or an error?
2. As you work on an assignment, do you complete a part of it or a portion of it?
3. Do you wash your hands in a basin or a bowl?
4. If you are waiting outside the school building, are you waiting on the steps or the stairs?
5. Is the hallway between classrooms a corridor or a passageway?
ANSWERS (1) An error. An error is any incorrect act or calculation, like a spelling error. A mistake is caused by poor judgment or understanding, usually because of oversight or thoughtlessness. A mistake might be failing to buy land when it was cheap. An error would be miscalculating the taxes on it.
(2) If you were allotted one part of the assignment to read, that would be your portion. It would also be your share. A part generally means a section or division, anything less than the whole. A piece can be a complete unit on its own, like a piece of cake or a piece of advice. If it's allotted to you, however, it is your portion.
(3) Both are round dishes for liquids or solids. A bowl is deep and wide, like a cereal or fruit bowl. A basin, by contrast, is wider than it is deep, as in a wash basin.
(4) Steps, though both are treads for one's feet. Steps, however, are external. Stairs are almost always indoor steps, like a staircase.
(5) A corridor is the main passageway in a building linking rooms that are off to the side. It is usually long and straight. Most classrooms open onto corridors. A passageway is a hall or alley that gives access to other areas beyond the rooms off the corridor.
SOURCES: Room's Dictionary of Distinguishables, by Adrian Room; Concise Oxford Dictionary; 'Cassell Guide to Related Words,' by Eugene Ehrlick and S.I. Hayakawa; Webster's Dictionary.