Mathcounts
Mathcounts, stylized as MATHCOUNTS, is a nationwide middle school mathematics competition held in various places in the United States. Its founding sponsors include the CNA Foundation, the National Society of Professional Engineers, and the National Council of Teachers of Mathematics.
The subject matter includes geometry, counting, probability, number theory, and algebra.
Competition Levels
The competition is divided into four stages: school, chapter, state, and national. The problems increase in difficulty between levels—perfect scores are relatively common at the school-level, while winners of the written round at the national-level do not often achieve a perfect score. Each school is allowed to register ten students, including a group of four designated as the school team.The top teams and individuals from each Chapter competition advance to States. The exact number of qualifiers varies from region to region, depending on multiple factors including the number of competitors in the region. At the State competition, only the top 4 individuals qualify for Nationals. The coach of the first place team at States becomes the coach for that state at Nationals. At the National competition, all the competitors compete individually in the Sprint and Target Rounds, and the four individuals from each state compete in the Team Round to represent their state.
Structure
The Mathcounts program is open to sixth, seventh, and eighth-grade students in 57 U.S. states and territories. Students can participate through the Competition Program, the Club Program, and the Real Math Challenge. Prior to 2010, homeschools and virtual schools were allowed to compete in all aspects of the program. In the 2010–2011 program year, such schools were limited to individual participation with one exception: homeschool clubs that participated as a team in 2009–2010 were grandfathered into the 2010–2011 competition. Starting with the 2011–2012 program year, the Board of Directors established new guidelines that again allowed home and virtual schools to participate both as individuals and as members of a team.The standard Mathcounts competition contains four rounds: Sprint, Target, Team, and Countdown. At some state competitions, the top four contestants, determined by the Countdown Round, participate in the Masters Round. Some state and regional competitions add extra rounds, such as the Ciphering round.
Sprint Round
In the Sprint Round, contestants solve a written exam consisting of 30 problems with a time limit of 40 minutes. There are no penalties for incorrect answers. Calculators are not permitted, and contestants work individually.Questions in the Sprint Round are usually the easiest problems in the written individual contests because the Sprint Round is intended to test contestants' ability to solve problems within a tight time constraint. The problems generally increase in difficulty so that nearly all students can solve the first few problems while few to none correctly answer the last few. Sprint round questions are worth one point each.
Target Round
The Target Round contains eight problems, presented in four pairs of two. Students have six minutes to work on each pair of problems. Calculators may be used during this round. The problems in the Target Round are usually more difficult than most of the problems in the Sprint Round. Each correctly answered problem is worth two points. The problems generally increase in difficulty as the round progresses. Contestants work individually.Team Round
The Team Round is a ten question exam which teams of four have twenty minutes to complete. Calculators are allowed, and up to four teammates take the examination as a group. Contestants are allowed to discuss the problems with their teammates. Team round problems are typically more difficult than those on the individual rounds. Each question is worth two points.Countdown Round
The Countdown Round is a fast-paced head-to-head competition. It is the only oral round, and it is the final round in most competitions. It is an optional round at State and Chapter competitions. At some competitions, including Nationals, the winner of the Countdown Round is considered the overall champion or is used to determine qualification for later rounds. However, at most Chapter and State competitions, the round doesn't have any effect on qualification for later rounds or final standings. Calculators are not allowed in the Countdown Round. The National Countdown Round was shown on ESPN from 2003 to 2005, and now it is presented in a webcast every year.From 1988 to 2003, the National Countdown Round was a head-to-head ladder-style competition. The tenth and ninth-place finishers on the written portion played a match; the loser was ranked tenth while the winner played against the eighth-place competitor. The loser of this match ranked ninth while the winner moved on to play against the seventh-place student. This continued until a challenger reached the first-place student; the loser of this final match ranked second while the winner was declared the champion. It is from this pattern of the tenth, ninth, eighth, seventh, etc. that the name "Countdown" was derived. This format is still used in many Chapter and State competitions, in part because Mathcounts requires that this structure be used if the Countdown Round will determine the final individual rankings.
Beginning in 2004, the format of the Countdown Round at the national competition changed to a weighted single elimination bracket. The top twelve scorers on the written portion advance to the Countdown Round. In the first round, the top four scorers on the written portion received a bye into the second round leaving the fifth place to face off against the twelfth place, and the sixth place to face off against the eleventh place, etc. This change was presumably made to ensure that the final round would be more exciting and more suspenseful, since now the champion must win at least three consecutive matches, while previously a student could potentially win the championship after defeating a single opponent.
Masters Round
This round has been replaced by the Math Video Challenge in current years. At the national level and in some states, there is an additional round known as the Masters Round, open only to the top four contestants. Participants are given thirty minutes to develop a fifteen-minute oral presentation based upon an advanced mathematical topic, not known to them before their preparation time begins. While an award is given for the best presentation as determined by a panel of judges, the Masters Round does not affect participants' rankings.Ciphering Round
In some states, at both the chapter and state levels, there is an extra Ciphering Round. In this round, which does not count for overall individual or team scores, each school sends one representative to a stage. A problem is then flashed up on a projector screen, and competitors, working individually, have one minute to answer. No calculators are allowed. Using a buzzer system, the judges then determine the order in which the students determined their answers. The first person to answer correctly earns his/her school five points, the second person four points, etc. After four questions, each school switches their representative. The process is repeated four times so that each team member has a chance to compete in a round. The winner of this round is the school that accumulates the most points. Because no calculators are allowed, competitors must be able to do calculations quickly and mentally.Scholarships
Scholarships are awarded to high-ranking students at the national competition, and many universities give scholarships to the top finishers at the state level. Some math summer programs, such as MathPath, give out scholarships to top Mathcounts students. Some of Mathcounts' other sponsors, such as Texas Instruments, General Motors, and Lockheed Martin, also provide scholarships.Qualification for Mathcounts scholarships usually vary by state, but scholarships and prizes are often awarded to the top ten individuals and the top three state teams at the national level. Raytheon offers scholarships to undergraduate students who volunteer as coaches for Mathcounts teams.
Scoring and ranking
Individual score
Each contestant's individual score is equal to his or her Sprint Round score plus twice his or her Target Round score. A perfect score is 46.At the Chapter and State levels, ranking is determined by either raw individual score or by the results of the Countdown Round, depending on the state/chapter. Ties are broken by comparing performance on the Sprint Round. If contestants are still tied, the last five problems of the Sprint Round are compared. If contestants are still tied, pairs of Target problems are used to break ties. Occasionally, a tie-breaker round may be needed if the contestants have answered exactly the same questions correctly and incorrectly.
At the National Competition, ranking on the written portion is used to determine seeding in the Countdown round. The final place is determined by performance in the countdown round.
Team score
A team's score is equal the average of the sum of its members' individual scores plus twice the number of questions answered correctly on the team round. With the individual scores of a maximum of 46 each and team-round scores a maximum of 20, a perfect team score is 66.History
Mathcounts was started in 1983 by the National Society of Professional Engineers, National Council of Teachers of Mathematics and CNA Foundation to increase middle school interest in mathematics. The first national-level competition in the modern format was held in 1984. Since then, a national Mathcounts competition has been held annually, but will not be held in 2020 due to the COVID-19 pandemic. A replacement has been made on AOPS.Before 2002, every national Mathcounts competition was held in Washington, D.C. The competition spread quickly in middle schools, and today it is the best-known middle school mathematics competition.