Using investigations in teaching mathematics has for many years become an established feature of most curricula around the world. Investigations can be a vehicle for enabling children to experience the genuine excitement that comes from mathematical discovery. The true spirit of inquiry and investigation lies in the mind-set that continually asks questions about a given situation. The author relates that he was brought back to earth by some of his students when they were discussing these ideas. One of the students commented that topics like Pascal's Triangle, the Fibonacci Sequence, Golden Ratio, etc. must be among the most explored topics in mathematics and are often used for investigations in teaching. How is it possible to come up with any new questions on such topics? An Internet search using Google, for example, gives thousands of hits for each of these phrases. So, what can possibly be left to investigate? In this article, the author provides several examples of modifying Pascal's Triangle and Fibonacci sequence, and illustrates the point that it does not matter how many previous investigations have been conducted, as long as the information that students are investigating is new to them.