Play with them. Children between 3-5 or so need to see that playing by the rules and taking turns can be fun even if they don't think so. Introduce a variety of opportunities. At school age, if you think the child just isn't trying, there probably is too much pressure being put on too many difficult achievements. The ambitions of the adults may be too much for the child.
Success breeds success.
The basis of a good primary education is having the opportuniity to solve problems by trial and error. Listen and be open minded. Preadolescents, ages 9 and 10, is a great age and my favorite. These kids like to be off with their friends and busy in activities, but allowed to do so, they are great at home. You can talk about ideas with them and not just about things.