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* [[2004]]: Gregory Gauthier, Illinois
* [[2004]]: Gregory Gauthier, Illinois
* [[2005]]: Neal Wu, [[Louisiana]]
* [[2005]]: Neal Wu, [[Louisiana]]


== National Team Winners ==

* [[1984]]: [[Virginia]]
* [[1985]]: [[Florida]]
* [[1986]]: [[California]]
* [[1987]]: [[New York]]
* [[1988]]: New York
* [[1989]]: [[North Carolina]]
* [[1990]]: [[Ohio]]
* [[1991]]: [[Alabama]]
* [[1992]]: California
* [[1993]]: [[Kansas]]
* [[1994]]: [[Pennsylvania]]
* [[1995]]: [[Indiana]]
* [[1996]]: Pennsylvania
* [[1997]]: [[Massachusetts]]
* [[1998]]: [[Wisconsin]]
* [[1999]]: Massachusetts
* [[2000]]: California
* [[2001]]: Virginia
* [[2002]]: California
* [[2003]]: California
* [[2004]]: [[Illinois]]
* [[2005]]: [[Texas]]



== Results of Recent Competitions ==
== Results of Recent Competitions ==

Revision as of 03:01, 24 April 2006

File:Mathcounts logo.gif

MathCounts is a middle school math competition held in the United States. Its founding sponsors include the CNA Foundation, National Society of Professional Engineers, and the National Council of Teachers of Mathematics.

File:MathCounts trophy.jpg
A trophy from a State MathCounts competition

Subject matter

MathCounts is a contest designed for sixth, seventh and eighth graders. Therefore, the subject matter of the contest does not contain mathematical topics beyond geometry. For example, complex numbers, calculus, and trigonometric identities are not featured in the contest. Instead, the contest places an emphasis on advanced problem solving skill within traditional middle-school mathematics.

Competition levels

The competition is divided into four levels: school, chapter, state, and national. However, the school round is optional and does not have to be used to determine the team sent from each school. Each school is allowed to send one team of four students, plus four individuals, to the chapter competition. Individuals' scores are not credited towards their teams, even if they score better than first-string teammates. However, they are eligible to win individually.

High-ranking students and teams from each chapter competition progress to the state-level competition. The exact number of qualifiers varies from chapter to chapter. At the state level, the top four individuals progress to nationals as a single team representing the state. As a result, a state team is typically comprised of students from different schools. Every student and coach who participates in the national competition receives a free graphing calculator, donated by sponsor Texas Instruments; in 2004, the prize was a TI-83 Plus Silver Edition. In the past, TI-85s, TI-89s, and TI-92s have been distributed. The 2005 prize was a TI-84 Plus Silver Edition. The 2006 prize is also a TI-84 Plus Silver Edition.

Structure

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 competitions add extra rounds, such as the Speed 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 of all of the problems in the written individual contests due to the fact that the Sprint Round tests contestants' abilities to solve problems within a tight time constraint.

Target Round

The Target Round contains four two-problem mini-examinations, for which 6 minutes are allowed per pair. The problems in the Target Round are significantly more difficult than most of the problems in the Sprint Round. 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 teammates take the examination as a group. These problems are typically more difficult than the individual round problems, so that it would be virtually impossible for a single contestant to solve all of them alone within the available time.

Countdown Round

The Countdown Round is a fast-paced head-to-head competition, and is the final round used in determining individual rankings. Calculators are not allowed in the Countdown Round.

At the national level, prior to 2004, 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 ninth place and competed against the eight finisher, and so on. It is from this pattern of tenth, ninth, eighth, seventh, etc. that the name "Countdown Round" 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 fifth place to face off against twelveth place, sixth place to face off against 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, as opposed to previous years when a student could potentially win the championship after defeating a single opponent.

Fourty-five seconds are allotted per problem and no calculator may be used. 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.

For the earlier rounds, each match consists of three problems; if there is a tie (1-1 or 0-0) further problems are given and a sudden death victory rule is imposed to resolve it. In later rounds, the match ends when either contestant answers three problems correctly.

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. The National Countdown Round has been regularly televised on ESPN since 2003.

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.

Ciphering Round

In some states (Florida most notably), 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.

Scoring and ranking

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. For example, in the 1996 National competition, the highest score was a 38, and a score of 33 sufficed to place you into the top ten, allowing you to enter the Countdown Round. In the 2005 Nationals, the highest score was a 39, and a score of 30 sufficed to place you into the top twelve, allowing you to enter the Countdown Round.

At Chapter and State levels, ranking is determined by raw individual score. Ties are broken by comparing performance on the last ten questions on the Sprint Round. If contestants are still tied, individual pre-selected problems used to break ties.

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) plus twice the number of questions it answered correctly on the team round. A perfect team score is 46.0 + (2 * 10) = 66.0.

Examples of problems

Sprint

  • Chapter: What is the arithmetic mean of all of the positive two-digit integers with the property that the integer is equal to the sum of its first digit plus its second digit plus the product of its two digits?
  • State: Yesterday, 28 students took a test. The arithmetic mean of those 28 scores was 72 points. Two students who were absent yesterday took the test this morning, and the arithmetic mean of all 30 test scores is 73 points. If the difference of the two scores from this morning is 22 points, what is the lower score from this morning?
  • Nationals: A fair, standard six-faced die is tossed eight times. The sequence of eight results is recorded to form an eight-digit number. What is the probability that the number formed is a multiple of eight? Express your answer as a common fraction.

Target

  • Chapter: Jamie has a jar of coins containing the same number of nickels, dimes and quarters. The total value of the coins in the jar is $13.20. How many nickels does Jamie have?
  • State: In 1960, there were 450,000 cases of measles reported in the U.S. In 1996, there were 500 cases reported. How many cases of measles would have been reported in 1987 if the number of cases reported from 1960 to 1996 decreased linearly?
  • Nationals: Gunther's average on ten quizzes is 7.8. Each score is a positive whole number less than or equal to 10. He remembers that he scored at least one 5, at least three 7's, at least two 9's and at least one 10. What is the sum of all the distinct possible values for Gunther's median quiz score? Express your answer as a decimal to the nearest tenth.

Team

  • Chapter: If Ella rolls a standard six-sided die until she rolls the same number on consecutive rolls, what is the probability that her 10th roll is her last roll? Express your answer as a decimal to the nearest thousandth.
  • State: The sum of Angie’s age and John’s age equals Michael’s age. Angie’s age is a prime number, but John’s age and Michael’s age are not prime numbers. The sum of John’s age and Michael’s age is a prime number, and Angie’s age minus John’s age is a prime number. One more than half of John’s age is a prime number. Angie is the only teenager, and she is older than John. How many years old is John?
  • Nationals: The 9-digit number abb,aba,ba3 is a multiple of 99 for some pair of digits a and b. What is b - a ?

Countdown

  • Chapter: If y − x = 7, what is the value of x − y ?
  • State: What is the sum of all the integers between –12.1 and 3.3?
  • Nationals: A volleyball coach has three setters and eight other players on her team. Without assigning any of the positions, in how many ways can she choose six starters if exactly one of the three setter is selected as a starter?

Timeline

Most schools begin preparing for the MathCounts competition in September or October. The team is often selected via an optional school-level competition provided by MathCounts.

The local-level competitions (officially called the "Chapter" competitions) occur throughout the month of February, and the state-levels occur in March. The national contest, a four-day event, occurs in May. The actual contest occurs on the second day of the event, which is usually a Friday.

In 2006, the National MathCounts competition is to be held in Arlington, VA, between May 11 and May 14.

In 2005, the National MathCounts competition was held in Detroit, Michigan, between May 5 and May 8.

In 2004, the National MathCounts competition was held in Washington, D.C. between May 6 and May 9, with the actual contest on May 7.

In 2002 and 2003 the national competition was held in Chicago, Illinois, while prior to 2002 every national competition was held in Washington, D.C.

National champions


National Team Winners


Results of Recent Competitions

The champion of the 2004 MathCounts National Competition was Gregory Gauthier, from Wheaton, Illinois, who also had the highest individual score on the written portion, won the Masters Round, and whose team also won. Jeffrey Chen of College Station, Texas finished second. On May 18, 2004, the 2004 national champions made a visit to the White House.

The champion of the 2005 MathCounts National Competition was Neal Wu of Louisiana, which was remarkable, since he was a seventh-grader at the time as well as being seeded ninth. The runner-up was Mark Zhang from the Texas team. Sergei Bernstein won the written round as well as the Master's Round. Texas won first place in the team competition, although Indiana had three participants in the Countdown Round. Despite having the national champion, the Louisiana team placed 13th. The Most Improved team was South Carolina, which went from 56th place to 16th place under coach John Rushman. 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.

History

MathCounts started in 1984. Since then, many schools registered to this program. As of March 18, 2004, 6093 schools have been registered.

See also

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