MathCounts
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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.
The competition is divided into four levels: scholastic, chapter, state, and national. Each school is allowed to send one team of four students, plus four alternates, to the chapter competition. Alternates' scores are not credited towards their teams, even when they score better than first-string teammates. However, they are eligible to win individually.
High-ranking students from each chapter competition, as well as high-ranking teams, progress to the state-level competition. The exact number of qualifiers varies from state to state. 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.
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Structure
The MathCounts competition contains five rounds: Sprint, Target, Team, Countdown, and Masters rounds.
Sprint Round
In the Sprint Round, contestants solve a written exam consisting of 30 problems with a time limit of 40 minutes. Problems are not multiple choice; they require that competitors write down the answers to their questions. In addition, there are no penalties for incorrect answers. Calculators are not permitted during this round, and contestants work individually.
Target Round
The Target Round contains four two-problem mini-examinations, for which 6 minutes are allowed apiece. The problems in the Target Round are significantly more difficult than the problems in the Sprint Round. Calculators are permitted, and contestants work individually.
Team Round
The Team Round is a 10-question exam for which 20 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 contestants 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 10th- and 9th-place finishers (according to the written competition) competed against each other; the winner then became 9th place and competed against the 8th-place finisher, and so on. It is from this pattern of 10th, 9th, 8th, 7th, etc. that the name "Countdown Round" was derived. Note that it was possible for a contestant who placed 10th on the written part of the competition to become 1st through nine consecutive wins, 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 single elimination bracket. The top 12 scorers on the written round advance to the Countdown Round. In the first round, 5th place challenges 12th place, 6th place challenges 11th 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.
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.
For the earlier rounds, each match consists of three problems; if there is a tie (1-1 or 0-0) further problems are used to resolve it. In later rounds, the match ends when either contestant scores 3 problems.
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 is regularly televised on ESPN.
Masters Round
At the national level, there is an additional round known as the Masters Round, open only to the top four contestants. Participants are given a limited amount of time to develop a presentation based upon an advanced mathematical topic, not known to them until immediately before their presentations. While an award is given for the best presentation, the Masters Round does not affect participants' rankings.
Speed Round
In some states (Florida most notably), at both the district and state levels, there is a speed 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 ten points, the second person nine points, etc. After six or seven questions, each school then switches people. 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. Because no calculators are allowed, competitors must be able to do calculations quickly and mentally.
Subject matter
MathCounts is a contest designed for 6th, 7th and 8th 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.
Examples of problems
Sprint
- The number 121 is a palindrome, because it reads the same backwards as forward. How many palindromes are between 100 and 500?
- How many diagonals does a regular seven-sided polygon contain?
- The coordinates of vertices of a parallelogram are (10,1), (7,-2), (4,1) and (x,y). What is the sum of the distinct possible values for x?
Target
- A license plate consists of two letters followed by two digits; for example: MP78. Neither the letters nor the digits may be repeated, and neither the letter “O” nor the number “0” may be used. When reading from left to right, the letters must be in alphabetical order and the digits must be in increasing order. How many different license plate combinations are possible?
- What is the largest integer n such that
- (1+2+3+…+n)2 < 13+23+…+73?
Team
- Coin A is tossed three times and coin B is tossed two times. What is the probability that more heads are tossed using coin A than using coin B? Express your answer as a common fraction.
- Carlos has chosen twelve different compact disks (CDs) he would like to buy. Four are rap music, five are country music, and three are heavy metal music. Carlos then randomly selects five of the 12 CDs to purchase. What is the probability that this purchase includes one CD from each of the three categories? Express your answer as a common fraction.
Countdown
- How many prime numbers are between 30 and 40?
Speed
- Marty has 16 pennies, 12 quarters, 5 dimes, 2 nickels, and one half-dollar. How much more does he need to pay for a five-dollar movie ticket?
Scoring
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 enter the Countdown Round. In the 2005 Nationals, the highest score was a 39, and a score of 30 sufficed to enter the Countdown Round (Top 12).
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.
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 Washington, D.C.
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
- Michael Edwards, 1984
- Timothy Kokesh, 1985
- Brian David Ewald, 1986
- Russell Mann, 1987
- Andrew Shultz, 1988
- Albert Kurz, 1989
- Brian Jenkins, 1990
- Jonathan L. Weinstein, 1991
- Andrei C. Gnepp, 1992
- Charleton Bosley, 1993
- William O. Engel, 1994
- Richard Reifsnyder, 1995
- Alexander Schwartz, 1996
- Zhihao Liu, 1997
- Ricky Liu, 1998
- Po-Ru Loh, 1999
- Ruozhou Jia, 2000
- Ryan Ko, 2001
- Albert Ni, 2002
- Adam Hesterberg, 2003
- Gregory Gauthier, 2004
- Neal Wu, 2005
Results of Recent Competitions
The champion of the 2004 MathCounts National Competition was Gregory Gauthier, from Wheaton, Illinois. 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. The runner-up was Mark Zhang from the Texas team, which won. 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.
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
- Quizbowl
- Academic games
- Reach For The Top
- List of mathematics competitions
- American Mathematics Competitions
External links
- MathCounts Home Page (http://www.mathcounts.org/)