This year our Math Club members are really intent on training for the AMC. They want someone in our school to break a score of 100 to move onwards to take the AIME.
Here’s the deal.
I want to help the leaders of math club find a way to do this. I don’t know how. We only meet for 25 minutes a week.
Is anyone out there a leader of a math club, that “trains” students for these types of contests? How do you do it? Literally, I’m asking for how you structure a meeting, and what kids are doing, and what you are doing during that meeting.
Also, if you as a math club adviser have any websites or books that you find invaluable, that would also be of great help.
I assume one of the important websites is Art of Problem Solving. After a ton of digging, you find that on that site is a list of AMC problems of years past, and solutions. What else ya got?
PS. One of my favorite math competitions from when I was in high school was the USAMTS. It’s a mail in math contest with 4 rounds, and amazingly wonderfully frustratingly challenging problems. So if you don’t know about it, and you have a super talented math star in your school, I’d check it out and (if you like it) share.
Continuous Everywhere but Differentiable Nowhere 
Sent to me by @k8nowak:
AMC Question Database, sorted by topic: http://www.unl.edu/amc/mathclub/5,1-database.shtml
MAA MinuteMath: http://maaminutemath.blogspot.com/
I’d like to second the recommendation of the USAMTS. I definitely feel like that’s where I learned to prove things. This sounds a little strange, because they don’t provide any instruction, but knowing that if I did a good job writing a proof somebody would pay attention was enough motivation. (By that point, , if I recall correctly. I had taken a course through CTY‘s summer programs that was basically an “introduction to proofs” course. They don’t offer that course any more.)
As for sources of more problems, there are books. The Art of Problem Solving books, available from the web site of the same name, have a lot of nice problems of the sort usually seen in competitions.
Michael, I *just* asked my department head if we can order those AoPS books. I’m glad you find them chalk full of nice problems.
Also, I felt *exactly* the same way about USAMTS. The fact that a real person takes the time to go through your work was really important. Plus, as you said, you have to write something that constituted a proper solution, so you needed to be extra careful that you’ve considered all cases. It too was the place I learned to prove things.
Sam,
Are all of the math club students in the same classes? Past AMC questions (that reflect the topic currently being covered) can be used as warm up problems.
We also do a 1 hour session a few weeks prior to the AMC. We go over scoring, talk about test taking strategies and do a half-dozen sample problems in groups. Then we give them a past exam to work on over the next week. Kids stop in on their own to get help/check their answers.
Needless to say, this isn’t the most systematic approach. :-)