If you are supposed to do something, it means that this is what is expected of you. eg I'm supposed to be home at midnight : my parents have said that I need to be home at midnight. I'm supposed to hand in my essay by Friday : the essay is due/ the deadline for handing in the essay is Friday.

いい質問ですね！ One application of 'supposed' is like ～はず～ in Japanese. 例えば： １．I am supposed to go to the bank tomorrow. ⇒　私は明日銀行へ行くはずです。 ２．Aren't the children supposed to return home by 8pm? ⇒　子どもたちが夜8時までに帰ってくるはずじゃないんですか。 Also, as of Brianさんの答え、'suppose' can also be used like this=> Suppose we get lost. (What if we get lost.) - "Suppose" is used in place of "What if." 日本語で：　「もし、私たちが迷子になってしまったら?どうする？」みたいな感じ。。。 It actually pretty easy and also convenient once you get the hang of this word! もし、わからないところがあったら、聞いてくださいね！ 頑張ってください！ (=^・^=)

"Suppose" is used to introduce a suggestion: Suppose we get lost. (What if we get lost.) - "Suppose" is used in place of "What if." "Supposed to" is used to talk about what someone generally believes is true. These chemicals are supposed to kill cockroaches. You're supposed to be at work right now. - "be" + supposed + infinitive You "are" + supposed + to be........ The difference between your two sentences: I suppose that It is supposed to be -The first sentence, "I suppose that," introduces a suggestion. The speaker is speculating. -The second sentence, "It is supposed to be," comments on what the speaker or the public generally believe is true. I suppose that this explanation might be wrong, but it is supposed to be true, according to Michael Swan's book Practical English Usage. I hope that helped some. The other answers above were also good, fyi.

Saying "I suppose that..." is like saying "I think that..." or "I'm guessing that... or "I would imagine that...""

well,i am willing to explain their difference to u,i hope u can get it it was supposed to be ...means what one thing should have been,i can set an example to u in order that u can know it better:You're supposed to buy a ticket, but not many people do.I thought we were supposed to be paid today.u can get it easily with these sentences i suppose that means the same as "i think that..."