Mathematica can be taught on quite a few different levels, depending on the background of who is learning it and why. If the problem is to use existing functions (as if Mathematica were a more powerful replacement for a TI calculator) in a limited domain, the best approach would be to walk the user through several typical examples. Even there it is possible to fail by covering too many options, and not having enough laboratory work. Think of this approach as lumping: easy to learn, limited domain of applicability.
The opposite approach would be splitting, and that is the approach used by Maeder in his various Mathematica books. As with most splitting approaches, it has a broad domain of applicability, but is not easy to learn unless you like abstract mathematics. Maeder presented the basic Mathematica language first, then showed a few general applications (integration, differentiation, numerical calculations) as example. Very good, but apparently few actually read his books and the current tutorial approach is not splitting.
The current approach seems to be demonstrations of features of particular features or modules. Good, but is a lumping approach that leaves the student with the ability to do specific things but not generalize.
So:
Recommend that you pick some small subset of Mathematica, say basic arithmetic, maybe basic arithmetic using 2D matrices (an Excel subset). Decide who will be learning from it (first year Accounting students, perhaps). Then, write a short manual teaching the specific subject to the specific audience. As an extension, you might try showing how to make histograms, make plots, or how to include dates.
Remember, this is just an English paper. Youre showing off the English, and you have to get a subject complex enough to show off your ability to teach, but simple enough to fit into available work hours. Mathematica is a lot like reality however well you describe it, your description will be incomplete, so draw lines and dont cross them.