I'm going to participate in a course (as a teacher) where I'm suppose to teach high school math to high school students in about 15 days during the year. Each class has about 1 hour long. Now, I think it is quite impossible to really get deep into the concepts in so little time, and so I got the following idea: I could gather some texts/articles discussing advanced high school subjects and try to discuss them together with the class. My intention is to provide different experiences and to develope critical thinking. The problem is that I know very little material on this matter, so I'm looking for some references and tips on where to find appropriate material. Can someone help me, please?
EDIT: Let me add more information to my post. This course is not a regular one. It is actually a voluntary set of lectures taking place at the university and aimed to help high school students to pass the 'vestibular', which is a brazilian test (similar to the american SAT's) students have to do in order to get accepted in public universities. The (math) content of the test is basically all high school math taught in Brazil. This includes basic set theory, basic notions of functions, trigonometry, plane and analytic geometry, algebra of matrices and so on. Thus, our course is aimed to help these students with a set of prep lectures. Each teacher can choose the topics he wants to present. In my case, I'll probably teach about functions and first and second order degree equations but these topics are really demanding and 15 one-hour classes are not sufficient to cover all material, so I'm thinking about alternative ways to approach it. Because students often like class discussions, I thought about providing some discussions based on alternative material (not regular books, which are too long to get at any point in 15 days).