First, lob both ends off the potato with the knife.
Fourth, instruct the child to run the peeler down the side of the potato until all the skin is removed and hopefully in the grocery bag which can be tossed for easy clean up.
Isn't that brillant?? I might just use the method myself as it totally cuts down on accidental slicing with the potato peeler by 34%.
Now if you want to help the willing child to get some chopping practice in, quarter the potatoes and then then slice about half way through the quarter to give yourself cubes and then let them have at it with a butter knife to finish up the job.
Alright, that's my good deed and brilliant idea for the day. I don't know how much longer I can keep coming up with things that are so amazing, but as long as I do, I promise I'll share them with you. Who am I kidding, I'd share my ideas with you even if they were lousy :D