Perhaps a math club with an option to enter an elementary competition. My DD13 participates in the local ARML team learning sessions. ARML is for students through High School, so there are topics brand new to her, and with only 15 of the 30 going to the competition, she won't be one (and doesn't want to be). But she goes for the enjoyment of learning and exposure to higher-level topics. Some go for the competition option, but there are kids down to 6th grade just there to discuss math with their high-talent peers. (I must admit, it's interesting seeing a 10 year old discussing arctangents).

Here are some elementary competitions if you want to look into them - http://artofproblemsolving.com/wiki...ementary_school_mathematics_competitions