Rodney Huddleston and Geoffrey K. Pullum, A STUDENT'S INTRODUCTION TO ENGLISH GRAMMAR (Cambridge University Press, 2005)
Those using this book to teach a course of only 8 or 10 weeks may want to skip these exercises. If a bit more time is available, some of them may be useful.
1. We actually don't see any grounds for doubting that just three possible orders of {the, dog, ran, away} are grammatical, but perhaps some students might query this, and come up with ideas that are worth discussing. The exercise is not very important, but it provides a reminder that out of any list of words, if the list length is n, then there will be n! different orders of arrangement that they can be put in (with be some duplications if some words occur twice in the list). What n! means is the factorial of n; that is, n times n - 1 times n - 2 times n - 3... and so on down to 1. As an example, 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800. Yet out of the n! arrangements of n words, almost all are ungrammatical. The strings of English words that comply with all the requirements of English grammar are actually very few in number relative to all the possible strings that could be constructed. The lesson is that someone who wants to learn a language has only just begun the task when they have learned its words.
2. We've noticed that a remarkable number of students slip up on iv. Yet looking words up in a dictionary is all that's needed.
3. In iv there is a use of but that is not common any more in English, but don't ignore it; a good dictionary should enable you to see which (much more familiar) word you could use instead that would sound more informal.
4. Keep in mind that if it's about the internal makeup of words, the answer is that it is morphological; if it's about the way words (regardless of their meanings) combine into sentences, it's syntactic; and if it's about meaning — what the sentence would be literally saying if it were uttered in some context — then it's semantic.
5. This is open-ended — an essay question that can be done either briefly or at considerable length. Suggestions from the instructor concerning target length would be useful. The issues raised are actually quite subtle. Some people seem to think that the descriptive approach amounts to saying that absolutely anything is grammatical if people say it, and that's not true at all (look back at exercise 1). Others seem to think that all prescriptive grammarians are benighted fools, and that isn't true either.
6. This is a research exercise. We won't hide what we believe will turn out to be the case: we think it would be extraordinarily hard to guess the country of origin of a piece of written English just from the syntax.