I belong to a Yahoo Group for people using the homeschool curriculum that I use, and one of the moderators is wise and often funny too. Her solution for dealing with kids who say they're bored is priceless:
In the medical field, we ask patients to rate their pain on a scale of 1 to 10. When my kids complain of boredom, I ask them to rate it on the same scale. If they are approaching a 10, this is a true emergency! No amount of mindless entertainment can save them now. Only rigorous work can maintain the heart rate above asystole.
I have never had a child become so bored that I had to start CPR, but anything is possible once boredom reaches life threatening levels.
Once the patient says, "stop it mom, you are not funny", then you know you have successfully converted a code W (W stands for whining) to a normal rhythm.