You might like to look at Chapter 11 of this great book, which contains a clear example of the scientific methos being used whilst also presenting us with one of the most hilarious moments in the book, in my opinion. In search of some kind of fuel or explosive that will give the rocket the sufficient power they need to shoot up into the sky, the boys hit upon the idea of creating a liquid to use by heating up saltpeter and other chemicals, including sugar. It is clear that the boys have absolutely no idea what they are doing, as the author's fear that he will be blown up indicates. Also, note the way that they reassure the author's mother:
"We'll write everything down like a recipe," I said, trying to assure her. "Wash the pot, clean up everything before we melt another batch."
When the author's mother asks them if it will make their rockets fly better, the only answer the boys can give her is "Maybe," which captures the scientific method in its essence, as the boys are experimenting with different ideas, with no idea of how they will turn out, but through observation and notetaking, hope to increase their level of knowledge of what will make the best rocket fuel.