As the Fellowship departed from the Rivendell, all the seasoned adventurers knew they will not follow Frodo to Mount Doom. So, the optimistic version is Frodo, Sam, Merry and Pippin going to the Mount Doom, far away from the Shire they have never left before. The reasonable thing to do is to teach Frodo how to use a map and give him a good map (or at least teach him about the way to Orodruin.) Despite that, in the book we can see that the last time Frodo has seen a map was in Rivendell (before the council, when he had no idea he was going to Mordor.)
The further Frodo and Sam go, the more lost they get, and don't even know how much they can eat, as written in Book 6, Chapter 2, "The Land of Shadow":
‘Begging your pardon, Mr. Frodo,’ he said, ‘but have you any notion how far there is still to go?’
‘No, not any clear notion, Sam,’ Frodo answered. ‘In Rivendell before I set out I was shown a map of Mordor that was made before the Enemy came back here; but I only remember it vaguely. I remember clearest that there was a place in the north where the western range and the northern range send out spurs that nearly meet. That must be twenty leagues at least from the bridge back by the Tower. It might be a good point at which to cross. But of course, if we get there, we shall be further than we were from the Mountain, sixty miles from it, I should think. I guess that we have gone about twelve leagues north from the bridge now. Even if all goes well, I could hardly reach the Mountain in a week. I am afraid, Sam, that the burden will get very heavy, and I shall go still slower as we get nearer.’
Sam sighed. ‘That’s just as I feared,’ he said. ‘Well, to say nothing of water, we’ve got to eat less, Mr. Frodo, or else move a bit quicker, at any rate while we’re still in this valley. One more bite and all the food’s ended, save the Elves’ waybread.’
We can see that the Fellowship had no maps with them when they departed from the Rivendell (I assume that, if he had one, Gandalf would show Pippin a map instead of telling him 'you could have seen some maps few days ago'):
‘We have reached the borders of the country that Men call Hollin; (...)
‘But the mountains are ahead of us,’ said Pippin. ‘We must have turned eastwards in the night.’
‘No,’ said Gandalf. ‘But you see further ahead in the clear light. Beyond those peaks the range bends round south-west. There are many maps in Elrond’s house, but I suppose you never thought to look at them?’
Why was Frodo not given a map and told in more detail about the way to Mordor, despite the fact that he told the Council that he does not know the way?
EDIT: Note, that he had no idea whether he will have any company at the gates of Mordor.