How to explain integrals and derivatives to a 10 years old kid? I have a sister that is interested in learning "what I do". I'm a 17 years old math loving person, but I don't know how to explain integrals and derivatives with some type of analogies.
I just want to explain it well so that in the future she could remember what I say to her.

This is a question for a long car journey - both speed and distance travelled are available, and the relationship between the two can be explored and sampled, and later plotted and examined. And the questions as to why both speed and distance are important can be asked etc
