Schoolhouse Rock did a great series of videos on multiplication. I mixed this 32 minute compilation myself, as a means of getting content I can not purchase through iTunes onto my Apple TV.
And here are some great videos from YouTube channels that are either not-entirely-kid-friendly, or otherwise of lesser quality.
Subscriptions are another mechanism by which Apple TV can more easily locate content you like. We have found (generally) that only Sesame Street and KidsTV123 offer exclusively-child-friendly & high-quality videos. Also, you can not subscribe to a channel with Apple TV (you can only add/remove Favorites with Apple TV). So, sooner or later, you'll want to sit down in front of an actual computer and dedicate time to properly configuring your child's YouTube Favorites & Subscriptions. It took me hours to get everything set up satisfactorily (and to find decent content).
Really hope this is of use to other parents. We mostly use YouTube+AppleTV during our bed-time ritual (brush teeth, clean nose). Once you've created a decent YouTube favorites collection and configured Apple TV to support your "normal" TV remote (so volume control and Apple TV control are combined into the same remote) it is pretty simple for a child (and parent) to use.
Apple TV's removal of YouTube advertising makes it so our son isn't presented with a barrage of advertising images, and also no instant linking to unknown videos that are just 1 tap away. It does, still, require constant supervision. At the end of any Apple TV Favorites content, YouTube will then present videos it considers related. These are unknown videos, and often crappy.
So far, our son is fine navigating back to Favorites and picking another video from there. But it is still a too-quick mechanism by which YouTube can be explored. Apple TV's YouTube app isn't 100% kid safe... just "safer".