That's one main reason for this thread. Out of the really long list of possible US math competitons, what are the really worthwhile ones?
Math homework typically has many problems based on the same concept. Math competitions can be viewed sources of non-routine problems, even if you do not officially participate. Sometimes my middle child wants math problems, so I can have him do a Continental Math League contest from the book "Math Contests, Grades 4, 5 & 6, Vol. 5" by Steven R. Conrad and Daniel Flegler. There are other books in this series, and they cost less than $10.