Yes kids can outgrow ADHD - it is now believed that the part of the brain that controls impulses doesn't fully developed until the late teens - thus why it appears that kids "outgrow" ADHD, but it's more like their brains finally grow"in" completing this section, providing them the impulse control they lacked previously. The book "Spark" by John Ratey, explains this very well.
And yes, younger children, tend to be more hyper"active" because they are just that - kids - that need to move and jump and run because that is how they are built and their bodies physically grow at such a rapid pace when they are little, they need all that energy to keep things growing. Once they reach "full size" essentially, the hyperactivity disappears and might often be replaced with inattentiveness.
If you want a great read, get "Spark" it's a fantastic book.
Children do not outgrow ADHD. As they enter puberty the symptoms of hyperactivity start to fade or simmer down but inattentiveness may become more problematic. The brain doesnt fully mature until age 25 but again, with the right interventions and treatment plan over time, symptoms are managed bettter and potential can be met in a very positive way :). The course of ADHD is moving in a normal direction williemom. Some symptoms tone down as the child matures but inattentiveness does persist but again, managed properly, having ADHD can be a non issue or even a gift if used to bring out the child's personal best as they get older
They can outgrow many symptoms, esp hyperactivity. Other symptoms tone down. They develop coping mechanisms, for example my spouse gets a lot of aerobic exercise, eats plenty or protein and takes a magnesium/calcium supplement and a large omega-3 supplement. All of these things keep the residual symptoms manageable. Basically, I think it no longer plays a predominant role in their lives (for many).