We've done a number of 2- and 3-night BPing trips with our kids, now 8 and 12. Versus adults, they are at about 35% and 50% of the calorie intake. In about 18 months, with a teenager growing 5 inches in a year, he'll probably exceed our intake. Perhaps exceed BOTH our intakes. I certainly did at that age.
General advice: keep it fun. Take your time. Be flexible. DON'T be saying, "We need to keep moving to get to camp." Don't plan any itineray that requires you to be so highly scheduled. If they want to build a dam across a creek, catch fireflies, or eat berries, hopefully you can dance with that.
We serve pretty healthy food at home, but we let it slide on trip. Mac&Cheese is a big hit and, frankly, after a day on the trail, the carbs taste good to you, too. On winter camping trips, we rent a USFS cabin (this is Alaska after all!) with a wood stove, and bring frozen pizza. Okay, a little fast foody, but after skiing in 4 miles at 0 to 10F, we (again) lean towards keeping it fun. An aluminum foil tent over the wood stove and it's hot and good to go.
You have to bring s'mores if you're allowed to have a camp fire. Freeze a pack of hot dogs (and/or gourmet sausages for the adults) with sturdy buns and ketchup packets. Packed inside a jacket or sleeping bag, they will last 24-36 hours that way.
Take the fun parts of scouting - fire lighting contests, compass course, knot tying, whittling - and make time to do those things.
Let them help set up the tent. Yes, it will take longer, but they will feel like THEY did it. And, hey, after a few trip, they CAN set it up on their own.
Some kids need to veg out and we have a reasonably strong no electronics rule. But a iTouch as an ebook? Okay with us. Light and multi-purpose.
I've had a different experience and found different info about altitude than Bob did:
We took the kids to 13,000 feet, the NPS raises a total stink about it, and we knew in advance. My MD wife is board-certified in several fields but not Peds so as adjugant facility at UWash, she contacted pediatric pneumenologists regarding HAPE, HACE and AMS. Their answer: No difference in the susceptibility nor in the progress of the disorders. HOWEVER it can be harder to detect it in kids. If they doze off, you lose any feedback. But if they are walking, talking, and in a good mood, they're fine. Just like an adult.
Under about 5 feet and a hike is a lot more work for them. You need to keep their packs light - pretty much only give them volume, not mass (sleeping bags and pads). Over 5 feet and my experience has been they function as small, inexperienced adults.
You need to train them on several points during training hikes in advance:
Drink till you pee.
Wash your hands before eating.
Fix any sore spots on your feet IMMEDIATELY.
Stay on the trail.
Wash your hands before snacking
Do NOT pass a trail junction, ever, without waiting for the group.
Watch your sun exposure.
Wash your hands after tioleting.
Keep the alcohol hand sanitizer at the ready.
All of which applies to any hiker, but if you want them to have fun, you have to avoid the painful learning curve many adult newbies inflict on themselves.