How much sugar (grams) can a child safely consume a day without harmful side effects?

We are a family going "on the wagon" regarding sugar. We are cutting out the sugary kids drinks and preprocessed "kid's" foods to opt for a more nutritious diet. I think too much sugar content in my 9 year old's lunches could have caused her to be extra sleepy after lunch and feel bad. We also have a 3 year old and would like to see if it calms her down any. What should I aim for? I need a bar to use when actually looking at the sugar gram contents of the food we're about to eat.