That age - It's your call. I'm an NRA certified instructor and have, recently, taught 100+ boy scouts between the ages of 11 and 17 how to shoot.
Couple things I teach;
Never shoot any animals; no birds, no squirrels, no turtles, no snakes, not even poisonous snakes (unless they're messing with YOU - not vice versa). Learning to hunt is different and I don't want them 'learning to shoot' by blasting animals. There will be no vigilante-nature-witch hunts on my range.
I prefer to teach with bolt action rifles because it teaches aim and trigger control vs. just blasting away. Also, when the side of a .22 shell erupts it doesn't blow out the side of the action on a bolt action gun.
In any regard, it's your call and, as always, be safe.
Edit: If you want to teach your kids how to shoot without waiting until they are 18; sign them up for Boy Scouts! Summer camp is right around the corner and the VAST majority of them have .22 and Shotgun ranges! (though they may not let them shoot the shotguns until they're older) They aslo teach black powder shooting, tomahawk throwing and more! Check it out!