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.

Explain derivatives using the speedometer ! Ask her how one could find the speed of something , and if she goes saying the average speed , ask her how one could calculate the instantaneous speed. And boom , there comes your derivatives. 
