I like the idea of offering non-competition options as well as competition. This might make the club more appealing to girls, some of whom may feel turned off by competition. I think it is really important to work on making sure the club is inclusive that way. You could also integrate art activities that are math-oriented. My DD10 is fascinated by Vi Hart's math doodle videos on YouTube. Appealing posters with cool art from those videos could draw in a broader audience. I also like the Lego robotics (although this can be expensive) and the coding idea. I would emphasize that there would be fun, hands-on activities. My DD did not want to do the math league at her school because she perceived it as boring, pencil and paper work, yet she loved the engineering night held by a local university's engineering dept and excelled at the activities.