It's ok to have kids on smaller boards so that they gain mobility for learning tricks. However, a board that board may be too small, meaning too squirrelly. Basically, it will make it harder because your child will not have any stability.

you can go a lil' smaller but the Burton Boards are so easy to ride because of the rockered / convex base that there is no need to go smaller.

And, you will not have to worry about it breaking (plus it comes with a warranty)

The other two answerers pretty much said it, I just wanted to add something about boards breaking. One time I took out one of my old burton boards that was a good 20 or so centimeters short and I was waaaaay out of the weight range and I actually tried to break it by doing really leaned back tail presses and stuff and I couldn't snap the thing. Most boards are a lot tougher than they seem.

k dude your kid is thirteen and he is ridin a 110 my sister thats five and she rides a 105 and she one of the shortest kids in her class and that is a little small for her and im eleven and i ride a 126 and i can do three sixties on that thing and stuff like that and its small for me and im four foot three and ive ridin one thats a 110 and i could not ride it it was to small and im eleven your kids thirteen try like a 120 or a 130 that will be alot better