If you didn't already know, when making mashed potatoes, it's a good idea to cut potatoes into smaller, but equal in size, pieces to help them cook faster.
If you are going to make boiled potatoes (but I also do this when I'm making mashed potatoes anyways), start them in cold water. Potatoes are very dense. When you start cooking them from cold water, this will allow them to cook more evenly from the outside in.
-The Littlest Chef