There are opportunities for interested students to compete. The emphasis at meetings, however, is on working cooperatively. There are no tests or grades. There are a few contests that some of the classes do occasionally during regular meeting times. Everyone in the class will participate, but it does not matter how anyone does individually.
Tournaments - several Saturdays a year we go to competitions where we compete against local school teams. These are fun! The kids enjoy the camaraderie of being with their teammates, and there is a lot of socializing. There are awards for top individual and team performances. Again, our top few kids are very interested in that. But most of the kids are not. We celebrate strong individual performances, but no one cares about weak performances. They do not count against the team in any way, and we basically ignore them. Most kids are never going to win a thing at this, and that's fine. I encourage all the kids to cheer on the few who are trying to win recognition, and for the entire team to feel pride when a team member does well. It takes a strong bench to produce a very small number of stars, and the kids who win nothing are still contributing to the group.
Many kids come in not interested in competing. We encourage kids to at least try it before they rule it out. We have some very low key local elementary contests that are appropriate for young beginners. We will steer individual kids towards or away from various contests to try to ensure a positive experience. There is actually an advantage to young beginners to attend their first competition early, when nothing is expected. Then later, if they want to compete more seriously, they have experience and know what to expect.
For strong kids, one of the benefits of competitions is to find mathematical peers. Most kids will find their peers within the group. But kids who are the top kid in the group for their grade will figure out who their peers are by running into them through competitions. Their peers might be at the city, state, or even national level. Kids will be running into their peers not just at contests, but at summer camps, enrichment programs, and even college and beyond.
Even kids who are relatively weak within our group should consider going to occasional contests once they are gr 6 or so. Our group skews very high. Kids may be pleasantly surprised when they compare themselves against a larger, more typical group. Also, for kids planning to go to college, there will be tests like the SAT that they will not be able to opt out of. The math contests give them a zero-stakes opportunity to learn some mechanics of test taking, and to learn to cope with test anxiety. Particularly if kids experience a competition fairly early (gr 5 for middle school contests, gr 7-8 for high school contests), nothing at all is expected. It's just experience, with nothing riding on it. No one will notice or care how they do.
We have been very successful at this. Since starting in 1998, we have sent eight teams and one individual to the State Mathcounts tournament, and we have sent three individuals to the National Mathcounts competition. Our high schoolers have won various awards at both the state and national level. Four of them have qualified in various years for the USA Mathematics Olympiad and two have participated in free summer camps designed to prepare top US math students for possible international competition.