Consider is used when talking about a judgement. The judgement is made for something actual. "What do you consider to be the best system of government?" - real It can also mean to think carefully about something. "He considered his options as far as college." 'Suppose' is used to refer to a hypothetical, or made up situation. "What do you suppose would happen if we left a day late?" It can also refer to a guess. "What do you suppose he is doing?" In general, 'consider' usually is used when we have more information, 'suppose' when we have less information and we must guess.