MOEMS past tests.
I received several past problem sets from the Math Olympiad when I signed us up. I tend to use these as take home problems that we discuss the next week. There's also a problem of the month on the site. I've found these to be hit or miss in terms of interest.
I've picked up a ton of past tests and books from a friend who runs the local version of this contest. These I've also been using selectively to find a challenge problem for the week.
Art of Problem Solving Pre-Algebra.I occasionally steal one of the challenge problems that seemed to work well for my son when he tried them out.
Purple Comet Math Meet.
A fairly challenging online math contest aimed at Middle School and High School. The old problem sets are a great resource even if you don't do the contest.
UW Math Hour Olympiad.
There are not a lot of problems here but they're all really good. Look about half way down on the page.
Park City Mathematics Institute:
I liked the tiling problem sets I found in the beginning. I haven't fully decided if they are at the right skill level.
2 more of the sets
6 Problem/Posters that are all really fun:
Project Gutenberg's Amusements in Mathematics, by Henry Ernest Dudeney
This was published in 1916 but the puzzles are still fun.
http://nrich.maths.org/frontpage - British site with a lot of interesting pre-canned lesson ideas across multiple grade levels.
https://www.exeter.edu/mathproblems - Exeter Phillips complete set of Math 1 - Math 3 problems. These are an actual curriculum built solely out of a problem chain.
http://www.cemc.uwaterloo.ca/resources/potw.php Problem of the week from U Waterloo. I find these a bit dry / too close to homework but I may take advantage of them in the future.
http://www.mathteacherscircle.org/ Expii's problems of the week. Po-Shen Loh the author is the coach for the national team.
http://areamaze.com Its only one type of problem as the name suggests but they're fun.
This has a great document showing sample sessions and topics used by various math circles. This was one of my favorite initial reads.
This is a fun site and occasionally it has a topic that translates really well into the afterschool setting.
Large collection of material aimed originally at inquiry based learning at the college level. But its
My favorite collection of challenge problems. Its updated fairly frequently but currently closed. Your best bet is to follow five triangles on twitter and save all the problems he posts there.
My selected saved problems are here: http://mymathclub.blogspot.com/p/collected-problems-2.html
Another set of interesting puzzles and problems.
Another interesting but fairly difficult set of geometry problems. I haven't fully reviewed yet to
see if any are usable at this level.
Brand new site from AoPS with MathCounts style problems to solve online.
A large set of interesting mathematical curiousities. These look great for starting off a session.
* graph theory for kids http://jdh.hamkins.org/math-for-eight-year-olds/
* http://www.mathteacherscircle.org Math Circle Teacher's Network. Some very interesting videos and general advice on getting started.
* https://www.facebook.com/groups/1001mathcircles/ The natural math facebook page. This is very active.
* https://undergroundmathematics.org/ Ok this is really a high school site out of Cambridge aimed at GCSE exams. But the underground map is so charming I'm including it anyway.
* http://www.mathandmischief.com/ A homeschooler who appears to have similar mathematical taste to me. I like her recent video lists.
A blogger I'm liking recently.
http://www.kutasoftware.com/ A set of standard worksheets on various topics. Possibly useful as warm-up material in small doses.
I liked this one because it had a week by week description of what this circle did. Especially initally it was interesting for leveling and ideas about how long various activities took. Its also continues to be helpful as a source of ideas for topics.
This one is more straight problem sets. I haven't used it much yet but I'm thinking about doing a solve-a-thon at some point and reusing their sets.
- Knights of Pi
- Math is Cool
- Blaine Washington State Math Competition
- Julia Robinson Math Festival
- Washington Math Olympiad