Does this bit of common knowledge hold water? Sort of. When the body is depleted of energy, it begins to feed off of itself, first by devouring stored fat. So it would seem to make sense that the less energy you take in before exercise, the more fat your body burns. And this is true, to a point. But the amount of extra fat burned when you don't eat before exercise is pretty small. Plus, without eating, the body has less energy to keep going, which can lead to a shorter workout.
Finally, depending upon the intensity of the activity, exercising on an empty stomach can make you feel pretty famished afterwards. In fact, you might feel so depleted that after working out you end up eating more than you otherwise would. So, theoretically, not eating before exercise could actually lead to weight gain.
Having something to eat before working out, on the other hand, can be a good thing. It gives the body enough energy to sustain a decent workout and leaves you feeling less hungry afterwards. Eating a calorie-rich, lavish breakfast before exercise isn't a good idea, of course, since it will leave you sluggish and overly full. But having a little something before your morning run seems to be the way to go. While scientists have discovered that a kid's working memory holds on average one less item than an adult's, the jury is still out on why this is the case. Is there a difference between the capacity of the adult brain and the child's brain? Or do adults have better-developed strategies for remembering?
Regardless of the correct answer, this suggests that your kids are probably not just making excuses when they tell you they forgot. To make things easier on them, try breaking lists down into small chunks. But if that doesn't help, don't worry. They'll grow up eventually. And then, although they still won't do what they're told, it won't be because they don't remember.