The first mathematical competition open to young scholars is the Math Olympiads (MOEMS Mathematical Olympiads for Elementary and Middle Schools). Beginning with the fourth grade, division E (grades 4-6) and division M (grades 6-8), students are given a set of five problems administered monthly for five consecutive months (November to March) with each nonroutine problem requiring careful thinking under time pressure. Each correct answer scores 1 point, and at the end of the competition, accumulated scores from all five exams are added up for a maximum possible total of 25 points per individual. Individual awards are given based off the number of points accumulated: the Olympiad patch (each of the top 50% of all participants in each division), the silver or gold pin (each of the top 10% of all participants in each division), and bronze medallion- Dr. George Lenchner Award (each student who achieves a perfect score of 25 points). Team awards are given, for each division, each team in the top 10% of all teams receives a plaque.
After the Math Olympiads, MATHCOUNTS is exclusively a competition aimed at middle school students and promotes competition against peers, as opposed to a threshold. The competition begins in the school to determine who will be participants in the Chapter (local) competitions. Chapter competitions are held in February consisting of the Sprint (40 minutes consisting of 30 problems worked on individually), Target (30 minutes consisting of 8 problems presented to competitors in pairs), and Team Rounds (20 minutes consisting of 10 problems that team members work on together). The conclusion of the Chapter competitions features a Countdown Round, a fast-paced, oral competition for top-scoring individuals. The winning team will advance to the State Competition which takes place in March. Additionally, the two highest-ranking competitors not on the winning team (who may be registered as individuals or as members of a team) will advance to the State Competition. Top four individual competitors from each State competition go on to all-expenses-paid trip to the National competition which takes place in May. All national competitors will receive a plaque and other items in recognition of their achievements. The national champion is determined during the countdown round. This individual receives the $20,000 Donald G. Weinert College Scholarship.
The other popular Math competitions are The Math League (Math Contests) for grades 4 to 12; MAA American Mathematics Competition 8 (AMC8) for middle school level; Math Kangaroo in USA for grades 1 to 12; Continental Mathematics League for grades 2 to 9 and in Massachusetts, Intermediate Math Leagues of Eastern Massachusetts (IMLEM) for grades 7 to 9; An annual Mathematics competition for middle school (MOAA) at Andover MA; Harvard-MIT Mathematics Tournament (HMMT) for high school students etc.
The competitions do not end at middle school. Upon entering high school, many students join their high school Math League team to compete against area high schools. Generally, most mathematically adept students will take the MAA American Mathematics Competition 10/12 (AMC10/12). For students who perform exceptionally well on the AMC 10/12, they are invited to continue participating in the AMC series of examinations that culminate with the International Mathematical Olympiad (IMO). The first in this series is the American Invitational Mathematics Exam (AIME), followed by the USA Mathematical Olympiad and Junior Mathematical Olympiad (USAMO and USAJMO). The top students from the USA(J)MO are invited to the Mathematical Olympiad Program in the summer after the exam. Students from the Mathematical Olympiad Program are then eligible to be selected for the following summer’s six-member team that will represent the United States of America at the IMO.