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Mathcounts logo
Type Foundation
Headquarters Alexandria, Virginia
Honorary Chair
Thomas A. Kennedy[1]
Main organ
Board of Directors

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.[2]

The subject matter includes geometry, combinatorics, counting, probability, number theory, and algebra.[3]

Competition levels[edit]

The competition is divided into four stages: school, chapter, state, and national. In general, the problems become harder as one progresses towards nationals. Each school is allowed to register one team of four students, six individual students and some alternates.

High-ranking students and teams from each chapter competition progress to the state-level competition. At the chapter-level all students are eligible to advance based on their individual score, but members of a team are also eligible to advance based on their team score. The exact number of qualifiers varies from chapter to chapter. At the state level, the top four individuals, which, from state to state, varies between using solely the written results or including the Countdown round results, progress to nationals as a single team representing the state. When a school wins the best team award, the coach of that school is named the coach of the state team.[4]


The Mathcounts program is open to sixth, seventh, and eighth-grade students in every U.S. state and territory. Students can participate through the Competition Program, the Club Program, and the Real Math Challenge.[5] Prior to 2010, homeschools and virtual schools were allowed to compete in all aspects of the program. In the 2010–2011 program year,[contradictory] 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.[6] Starting with the 2010–2011 program year,[contradictory] 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.[7]

The standard Mathcounts competition contains four rounds: Sprint, Target, Team, and Countdown. At the national and 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.[8]

Sprint Round[edit]

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. To break a tie, scorers eliminate the participants who first answer a problem incorrectly, checking backwards from problem 30.

Questions in the Sprint Round are usually the easiest problems in the written individual contests because the Sprint Round tests contestants' ability to solve problems within a tight time constraint. The problems may get harder from the first question to the last, but this is not always true. Sprint round questions are worth one point each.[9]

Target Round[edit]

The Target Round contains four, two-problem mini-examinations, for which six minutes are allowed per pair. 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. In the pairs, one question tends to be a "confidence booster" and another a challenging problem. Each problem is worth two points. The mini-exams are intended to get harder as the round progresses, with the first mini-exam having the easier problems and the last mini-exam having the hardest problems. Contestants work individually.[10]

Team Round[edit]

The Team Round is a ten question exam for which twenty minutes are allotted. Calculators are allowed, and up to four teammates take the examination as a group. In this round, contestants are allowed to discuss the problems within the team. Team round problems are typically more difficult than the individual round problems in the hopes that they would be difficult for a single contestant to solve all of them alone within the available time. Each question is worth 2 points for the team score, and the total score is added to the average of the four individual scores in order to determine the winning team. These estimates are for the school competition. Higher level competitions will likely be different.[10]

Countdown Round[edit]

The Countdown Round is a fast-paced head-to-head competition, and is the final round used in determining individual rankings. It is the only oral round. The Countdown Round is an optional round in states and chapters. At some competitions (i.e. most states and nationals), this round is used for determining the winners. Otherwise, this round is usually for fun, when only trophies are awarded (at most chapter competitions, and some state competitions). Calculators are not allowed in the Countdown Round.[10]

Two contestants compete face to face in the countdown round. A problem is posted on a projector, and the two contestants race to finish the problem (with pencil and paper). Forty-five seconds are allotted per problem. However, the problem will only be scored by the first participant to correctly answer it, and therefore it is essential for participants to work quickly. Upon finishing the problem, a contestant is expected to press his/her buzzer. The first person to buzz in (within 45 seconds) with the correct answer gains a point. If an incorrect answer is given, the contestant will not get a point and is not allowed to buzz in again. For the earlier rounds, each match consists of five problems; if there is a tie (2-2, 1-1, or 0-0) further problems are given and a sudden victory rule is imposed to resolve it. In later rounds, the match ends when either contestant answers four problems correctly. It is not uncommon for a contestant to press their buzzer before actually solving the problem, in some cases well before solving it, intending to make use of the allotted 3 seconds to finish solving the problem. For obvious reasons, this is a risky strategy. It backfired against, among others, David Yang in the finals of the 2009 Countdown round, in which he correctly answered but just outside the 3-second allotment.

At the national level, in 1987, the Countdown Round pitted all ten contestants against each other. The first six to ring in first with a correct answer advanced to the next sub-round, after which the first three to ring in with a correct answer advanced to the final round. The top three contestants then went head-to-head. Written competition trophies were given out separate from Countdown Round medals (the official winners) before the ladder style competition.[11]

From 1988 to 2003, the Countdown Round was a head-to-head ladder-style competition. The tenth and ninth-place finishers on the written portion competed against each other; the winner then became the ninth place and competed against the eight finisher, and so on. It is from this pattern of the tenth, ninth, eighth, seventh, etc. that the name "Countdown" was derived. It was possible for a contestant who placed tenth on the written part of the competition to become first through winning nine consecutive matches, but no contestant could place more than one rank below his or her rank before the Countdown Round.[11]

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 in hopes of making this final round more exciting and more suspenseful, since now the champion must win four consecutive matches (three if they received a first-round bye), as opposed to previous years when a student could potentially win the championship after defeating a single opponent.[12]

At the state and chapter levels, the Countdown Round may or may not be held. If it is held, it may or may not be official; some chapter and state competitions choose to hold a countdown round as a separate competition that does not affect the final rankings of competitors. If a countdown round is official at the state or chapter level, it must be a ladder-style tournament, although there have been instances where improper formats were used officially. Single-elimination tournaments are common, especially at the state level. The National Countdown Round was regularly televised on ESPN from 2003 to 2005,[13] and is now regularly webcast online.

Masters Round[edit]

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 until thirty minutes before their presentations. While an award is given for the best presentation decided by a panel of judges at the Nationals level, the Masters Round does not affect participants' rankings. The Masters Round in national competition consists of the top 2 competitors in the Countdown Round, as well as the top 2 written competitors who were not in the Countdown finals. In the 2012 National Competition there was no masters round due to the Reel Math Challenge (which is now named the Math Video Challenge).

Ciphering Round[edit]

In some states (most notably Florida), and at both the chapter and state levels, there is a ciphering round. In this round, which does not count for overall individual or team scores, each school sends one representative up. 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 of answering. 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 team winner of this round is the school with the most points. This round is mainly a fun, fast-paced round where speed is vital. Due to the fact that no calculators are allowed, competitors must be able to do calculations quickly and mentally.[10]


Cash scholarships are awarded to high-ranking students at the national competition and many universities give scholarships including full tuition to the top finishers at the state level. Some math summer programs, such as MathPath give out scholarships for doing well at MATHCOUNTS.[14] Some of Mathcounts' other sponsors, such as Texas Instruments, General Motors, and Lockheed Martin also provide scholarships.[15]

Qualification for Mathcounts scholarships usually vary by state, but scholarships and prizes are usually awarded to the top ten individuals and the top three state teams at the national level.[16] As Mathcounts promotes itself as a math coaching program, Raytheon offers scholarships to undergraduate students who volunteer as coaches for Mathcounts teams.[14]

Scoring and ranking[edit]

Individual score[edit]

Each contestant's individual score is his or her Sprint Round score (out of 30) plus twice his or her Target Round score (out of 8), so that a perfect score is 46. Many years, perfect scores do not occur due to the varying difficulty of the problems from year to year. For example, in the 1994 National competition, the highest score was a 38, and a score of 35 was needed to qualify for the Countdown Round. In the 1996 National competition, the highest score was a 38, and a score of 33 sufficed for placement in the top ten and qualification for the Countdown Round. In the 2005 Nationals, the highest score was a 39, and a score of 30 sufficed for placement in the top twelve, qualifying for the Countdown Round. At the 2008 National Competition, the highest score was a 43, and a score of 37 sufficed for top twelve placement.

At Chapter and State levels, ranking is determined by either raw individual score or standard countdown placing, depending on the state/chapter. Ties are broken by comparing performance on the Sprint Round. If contestants are still tied, the last ten problems of the Sprint Round are compared. If contestants are still tied, individual pre-selected 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.[17]

Team score[edit]

A team's score is equal to one-fourth the sum of its members' individual scores (even if the team has fewer than four members, a disadvantage to smaller teams) 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 10, a perfect team score is 66.[17]


Mathcounts was started in 1983 by the National Society of Professional Engineers, National Council of Teachers of Mathematics and CNA Foundation as a competitive environment to increase middle school interest in mathematics.[18] The first national-level competition in the modern format was held in 1984. Before 2002, every national Mathcounts competition was held in Washington, D.C.[19] The rules gradually evolved throughout its history, especially in the Countdown round.[11] It spread quickly in middle schools, and is the most well-known middle school mathematics competition.[20]


There are many ways to win an award. At Chapter competitions, four competitors and their coaches get awards for individual scores and about four teams and their coaches get team awards. At State competitions, the awards are the same with one less team award. However, in Nationals competitions, the four highest scorers, the four highest places in the Countdown Round, the three highest teams, the winner of the Masters Round, the team that improved most, and the team with the most spirit get awards.

The award for the most improved state has teams competing against the past. Whichever team has a score most improved from the year before gets this award.

The Spirit Award is different from the other awards. It requires no knowledge of math, but rather rewards the team for supporting each other and their state, and for creating a positive cheer/song/chant to present to all of the other teams before competing.


Six people in red shirts and beige pants standing in a line next to men in black suits all in front of a man wearing a grey suit and a red tie
President Barack Obama meets award recipients of the 2010 Mathcounts National Competition in the Oval Office Monday, June 28, 2010.

Each year, teams of four students per state compete, from which one individual winner and one team winner is chosen; the individual winner is chosen through a written examination and then an oral head-to-head competition (the Countdown round), and the team winner is chosen through a series of written examinations.[21] This format was first used in 1984.[22] The top team as well as the participants in the Countdown round are sometimes allowed a trip to the White House and meet the current President of the United States.[23] They also may receive scholarships from Mathcounts' sponsors.[24] Trophies are given out at the state level, and occasionally at the national level.[10]

See also[edit]

Notes and references[edit]

  1. ^ "Board of Directors | MATHCOUNTS". Retrieved 5 August 2016. 
  2. ^ "Wyoming Society of Professional Engineers". 
  3. ^ "Raytheon Takes on New Assignment: Helping Eva Make out with Thomas". 
  4. ^ "MATHCOUNTS". 
  5. ^ About Mathcounts
  6. ^ "Team Eligibility Rules Changes". 2011. Archived from the original on 2012. 
  7. ^ Mathcounts competition program
  8. ^ "Everything2 – MathCounts". 
  9. ^ "Online Tutoring – Mathcounts description". 
  10. ^ a b c d e "Mathcounts Competition Components". Mathcounts. Archived from the original on November 3, 2007. 
  11. ^ a b c "MATHCOUNTS levels page". 
  12. ^ "University of California – Two schools will represent Orange County in a state math competition to be held in March at UC Irvine" (PDF). 
  13. ^ "MATHCOUNTS Competition Levels – Coaches guide". 
  14. ^ a b "Minnesota MATHCOUNTS". Archived from the original on July 21, 2007. Retrieved 2008-01-01. 
  15. ^ "Sponsors". Archived from the original on December 29, 2007. Retrieved 2008-01-01. 
  16. ^ "Smart Catalog – MATHCOUNTS". 
  17. ^ a b "ND Mathcounts". 
  18. ^ "Piedmont Mathcounts". 
  19. ^ "General Motors Renews as National Sponsor of MATHCOUNTS". 
  20. ^ "Yale MATHCOUNTS". 
  21. ^ "Mathcounts – For Fun and Inspiration". Mathcounts. Archived from the original on December 30, 2007. Retrieved February 8, 2008. 
  22. ^ "About the Mathcounts Foundation". Mathcounts. Archived from the original on December 30, 2007. Retrieved February 8, 2008. 
  23. ^ "President George W. Bush meets award recipients of the 2005 Mathcounts National Competition". United States government. Retrieved February 8, 2008. 
  24. ^ "Sponsors". Mathcounts. Archived from the original on December 29, 2007. Retrieved January 1, 2008. 

External links[edit]