The most important thing you need to teach your kids when they are bored is to figure out for themselves what they are going to do. They should not immediately come to you for their entertainment or to tell them what to do.
If we are going to have a generation that will invent things, create solutions, solve problems, etc. we just not instill in them that they the ability to do great things.
The next time your child tells you he is bored, ask, "What are you going to do? I can't wait to hear what you come up with! I wonder if you are going to design something, create something, learn something new, hmmm..."
If they respond with, "I don't know" or "I can't think of anything" then tell them to go think about it for a while because you know they are incredibly smart and talented.
Lose the jar, if you ask me.