The topic you touch upon is vast, but I wanted to comment on this phrase: "problem/solution patterns which is very different from showing them the underlying conceptual tapestry".
If for some reason you have to use this format (department restrictions or whatnot) choosing your problems well will simulataneously introduce some of the conceptial conceptual tapestry. Rather than introducing a mathematical tool and then the problem that goes with it, you introduce the problem first (just out of range of the student ability) and bring it to the point where things get stuck, where something new is needed to go further. Then the motivation is clear for the new tool.
