Advanced math club intake assessment

I have an elementary aged child who is advanced in math and bored in math class unfortunately.  My kid's school has PTA clubs led by parents and supports parents in leading clubs of their choice.  So to help him and kids in his position, I'll be leading a math club targeted toward advanced students to provide a place for my child and some of the other kids in his situation an avenue to dive into more advanced math to finally be challenged by math.  Since demand for a place in clubs usually exceeds supply and I'm expecting a lot of interest, I asked for permission to limit the club registration to kids who are advanced in math so I can cover advanced topics and could skip the basics in my instruction, and received permission to do so since it is appropriate based on the curriculum I plan to cover.  I was hoping for advice as to how to make the determination for purposes of registration?  I thought about asking parents to evaluate their own child when they are signing their kids up for clubs and tell them to be honest about their child's ability as I'll have to ask kids to leave who cannot keep up and offer their spots to kids on wait list, or doing a written test and accept kids scoring over a certain score.  But both seem complicated and I'm wondering if there is an easier way.  The club is after-school and completely voluntary for both students and parent volunteers leading it and designed for a deeper dive into more complicated math problems.  Since we will only have 2 parent-volunteer-teachers for the whole group of kids, we will not be set up to help kids who are not keeping up or have behavioral issues (at least not without more parental help) and so it is important for the success of the club to keep the level of the kids in the club roughly the same and advanced enough to keep up with challenging math word problems, but I'm a bit at a loss as to how to ensure that.  Anyone's school has a similar club and how are kids evaluated for purpose of that club? 

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I encourage you to be less stringent about not allowing kids who can’t “keep up”; to be honest, it sounds kind of snobby. You can do whatever exclusive club you want outside of school (private math olympiad team or first lego league, for example), but my parental expectation is that a school sponsored club at least should try to be welcoming to all who express interest. Also be aware there is a huge gender difference in expressed math interest so please make a big effort to get girls involved and keep them involved. Finally, as a reluctant answer to your actual question, use SBAC scores as the optional screening. Phrase it  something like, “students with a score of x or more on the x grade SBAC test are likely to get the most out of this club.” (You can look up the sbac consortium online to get percentiles, which the state of CA only provides upon request.)

as a parent of a boy with very high math scores (98th percentile), I would not be interested in signing him up for your club as you describe it so I suspect you may not have a wait list.

Ask teachers to recommend students. 

I agree with the comment to be less stringent. Years ago I worked with some parents who wanted to start a school spelling bee club; they also only wanted the top kids. If you want to basically hand-pick participants, you should do that privately and hold the class outside of school.

I appreciate that you want to do something for your child that will also benefit other children; however, what if you were a kid who really loved math and were not picked? How would you feel?

A PTA-supported program should not have competitive participation standards. It should be first-come or a lottery.

If you use math circle problems, you can do them with a mixed-level group, as long as everyone wants to engage in problem solving. In any case, unless you only have one grade level, you'll have a variety of skills. You can check out https://nrich.maths.org/ which is a UK website that has good problems. I've used Nrich, and Math Circle problems with mixed groups, including a math fair that I used to organize for my daughter's school. 

http://www.msri.org/web/msri/education/for-k-12-educators/math-circles