Mathcounts

Competition levels

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.

Structure

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. 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 2010–2011 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 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.

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. 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.

Target Round

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. Calculators are permitted, and contestants work individually.

Team Round

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.

Countdown Round

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.

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. 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.

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.

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.

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, and is now regularly webcast online.

Masters Round

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.

Ciphering Round

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.

Scholarships

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. 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 usually awarded to the top ten individuals and the top three state teams at the national level. As Mathcounts promotes itself as a math coaching program, Raytheon offers scholarships to undergraduate students who volunteer as coaches for Mathcounts teams.

Individual score

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.

Team score

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.

History

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. 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. The rules gradually evolved throughout its history, especially in the Countdown round. It spread quickly in middle schools, and is the most well-known middle school mathematics competition.

Awards

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.

Winners

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. This format was first used in 1984. 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. They also may receive scholarships from Mathcounts' sponsors. Trophies are given out at the state level, and occasionally at the national level.

2005

The champion of the 2005 Mathcounts National Competition was Neal Wu of Louisiana, a seventh-grader at the time, and he was ranked ninth in the written round. The runner-up was Mark Zhang from the Texas team. Sergei Bernstein from Massachusetts won the written round as well as the Master's Round. Texas won first place in the team competition, though Indiana had three participants in the Countdown Round. Despite having the national champion, the Louisiana team placed 13th. The award for Most Improved team, comparing the current year's rank to the average of rankings from the past ten years, was Oklahoma, which placed 6th in the national competition under coach Dan Beaty. Two of the top four students were girls (Patricia Li of California and Karlanna Lewis of Florida) for the first time in the history of the national competition.

2006

The champion of the 2006 Mathcounts National Competition was Daesun Yim of New Jersey, and the runner up was Andrew Ardito of New York, respectively ranking 5th and 10th in the written round. The nationals team winner was Virginia (seventeenth last year), and second and third place went to Washington (fifteenth) and Indiana (second) respectively. The winning team from last year, Texas, got fourth, and California (third last year) got tenth. The Most Improved team was South Carolina, which went from 56th place to 16th place under coach John Rushman. The winner of the Spirit award was Wyoming. The Spirit Stick was presented to the Wyoming team by the New Hampshire team (last year's Spirit award winner). The written round winner was last year's champion, Neal Wu. The written round runner-up was Daniel Li of VA, who also won the Masters Round. The highest placing seventh grader was Kevin Chen, from Texas, who placed third after the written round and made it to the semi-finals in the Countdown Round.

2007

The champion of the Masters Round and the 2007 Mathcounts National Champion, was Kevin Y. Chen of Sugar Land, Texas. He was seeded 3rd in the written round. Ben Kraft of Pennsylvania (seeded 5th) was the runner-up. Justin Ahmann from Indiana was the top 7th grader and was 1st in the written round, followed by Allen Yuan of Michigan, while Bobby Shen of Sugar Land, Texas was the top 6th grader (13th). Texas won the team competition as well. The most improved team went to Nevada and the Spirit Award went to Pennsylvania, whose team cheer was a parody of "Weird Al" Yankovic's "White and Nerdy."

Kevin Chen appeared on Live with Regis & Kelly on the May 30, 2007, show. After visiting the "Live with Regis and Kelly" show in May, Kevin was nominated for an annual Relly award. On Friday, September 21, Kevin took home the Relly award for Best Junior Achiever after receiving the most votes from viewers.

2008

6th grader Darryl Wu of Washington won the 2008 national championship, seeded third in the Written Round. He appeared on the talk show "Live with Regis and Kelly" on May 16, 2008. He currently attends Lakeside School in Seattle, Washington. Bobby Shen of Sugar Land, Texas won second place (Bobby was also the 2008 written round champion and master's round champion). The written round runner-up was Jason Hyun, a seventh grader from Maryland. Anderson Wang of Pennsylvania and Evan Miller of Kentucky were the semifinalists in the countdown round. Although Maryland had three students in the top five in the Written Round, they were only placed third in the team round because of their poor team round score. Once again, Texas won team national championship. This is the third title for Texas during last four years; the team was led by Coach Jeff Boyd of Sugar Land, Texas all three years. The most improved team was South Dakota, and the Spirit Award went to New York, whose cheer was a variation of Frank Sinatra's New York, New York.

2009

The 2009 national Mathcounts champion was 8th grader Bobby Shen of First Colony Middle School in Sugar Land, Texas; Bobby appeared on the NBC Today Show on May 11, 2009. David Yang from California was runner-up and winner of the written competition. In the final Countdown round, which was 1st-seeded David Yang against 3rd-seeded Bobby Shen, a controversy arose. The score was tied 3–3, with 4 being necessary to win, when the final question started. David Yang pressed his buzzer quickly, but his answer (which was correct) was disqualified as he overstepped the 3-second time limit for answering. Bobby Shen then gave the same answer (within the time limit), and won the National competition. Alan Zhou of Massachusetts and Maximilian Schindler of Missouri were the semifinalists in the countdown round. The team title went to Texas for the third consecutive year. The winner of the Master's Round was Maximilian Schindler from Missouri, who was second in the written competition. The top 6th grader was Scott Wu of Louisiana, placing 13th. The most improved team was New Mexico, and the Spirit Award went to the Virgin Islands. The top two teams visited the White House on July 20, 2009, where they crossed paths with the Apollo 11 astronauts, Neil Armstrong, Buzz Aldrin, and Michael Collins.

2010

The 2010 National Competition was won by Mark Sellke of Indiana, who also won the written round. Second place in both written and overall was Shyam Narayanan of Kansas, who was also the top 7th grader. The Masters Round winner was Alex Song from Michigan. The other semifinalist was Darryl Wu from Washington, who won the competition in 2008 as a 6th grader. The winning team was California for the 6th time in Mathcounts history. Illinois and Washington won 2nd and 3rd place, respectively. Massachusetts placed 4th and Texas was 6th. The Team Spirit award went to Kentucky, and the most improved award went to New Mexico for the second time in a row. The top 6th grader was Allen Liu from New York. He was 9th place in the written round. The California team, consisting of team members Douglas Chen, Eugene Chen, Lewis Chen, and Aaron Lin along with coach Donna Phair, Sellke, and Narayanan visited the White House on June 29, 2010, where they met President Obama.

2011

In 2011 the National Competition was won by Scott Wu of Louisiana. The runner-up, Yang Liu of Missouri, was also the Masters Round champion. The written champion was Shyam Narayanan of Kansas. Alec Sun of Massachusetts was the top 6th grader and Kevin Sun of Illinois was the top 7th grader. The winning state was California for the 7th time in history. Second and third place went to Michigan and Texas, respectively.

2012

The 2012 National Competition was held at Orlando, Florida. The 2012 champion was Chad Qian from Indiana. Ashwin Sah from Oregon was the runner-up. Sean Shi from California was the Written Round Champion, and Alec Sun of Massachusetts was the Written Round runner-up. Ashwin Sah was the top 7th grader and Michael Ma from Texas was the top scoring 6th grader. The winning state was Massachusetts, whose team members all received $2,000 dollars and a trip to space camp. Illinois and Washington were the 2nd and 3rd place teams, respectively.

2013

The 2013 National Competition was held in Washington, DC. The 2013 champion was Alec Sun from Massachusetts, with Ashwin Sah claiming the runner-up position for a second time. The winning team was Massachusetts. The Mathcounts competitors set a Guinness World Record for the fastest human formation of the Pascal Triangle.

National champions table

Because Canadians are not allowed to participate in the Mathcounts competition at the state level or the national level, a U.S.-Canada competition was started in 1993, called the Pacific Northwest Intramurals. In 2013, Oregon won all 3 categories, and defeated Washington, which later won second place at the U.S. Mathcounts National Competition, while the Oregon team won fourth place at the National Competition.