Suppose 1
We often use  'suppose' to mean 'imagine' or 'guess'

I suppose you'll be meeting Danielle when you go to Paris?
When you weren't there, I supposed you must have been held up.
I suppose you two know each other?
Notice that 'suppose' is not normally used in the continuous form. We do not usually say 'I am supposing'.

Now I suppose we'll have to do something else.
We're waiting for John and I suppose he must be stuck in traffic.
At this moment I suppose it doesn't matter.
Notice that for 'imagine not' or 'guess not' that we make 'suppose' negative, not the other verb.

I don't suppose you know where Mary is?
I don't suppose he'll do anything.
I don't suppose you  have a Nokia phone charger here?
When responding to an idea with 'suppose', you can use 'so' to avoid repeating the idea that has already been expressed.

Is Susan coming to this meeting? ~ I suppose so.


Suppose 2
'Supposed to be' can be used to mean 'it is said/believed'.

The new James Bond movie is supposed to be excellent.
He is supposed to have been rude to Mark but I don't believe it.
It is supposed to be the best restaurant in town.
'Supposed to be' can also be used to talk about what is arranged, intended or expected. It is a bit like 'should'.

I'm supposed to get to work by 8.
John is supposed to turn off all the lights when he leaves.
I'm supposed to pay my rent on the first of the month.
It's not supposed to be here.
Often there is a suggestion that the action 'supposed to' happen does not actually happen.

I'm supposed to be there before 8 but I'm often late.
You were supposed to phone me.
I'm supposed to be getting on a plane to Tokyo at this very minute.
'Not supposed to' often suggests that something is not allowed or prohibited.

You're not supposed to smoke in here.
I'm not supposed to tell you.
We're not supposed to use the Internet for personal reasons at work.
'Suppose' can also be used as a conjunction to mean 'what if'. Notice that the verb which follows it is sometimes, but not always, put 'more in the past'.

Suppose we take the earlier train to Munich? It would give us more time there.
Suppose we took the plane instead? That would give us even more time.
There's nobody in reception to let our visitors in. Suppose I sit there until somebody comes?
I'm going to ask him for a pay increase. ~ Suppose he said 'no'? What would you do?