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# MATHCOUNTS

**MathCounts** is a large national mathematics competition and mathematics coaching program that has served millions of middle school students since 1984. Sponsored by the CNA Foundation, National Society of Professional Engineers, the National Council of Teachers of Mathematics, and others, the focus of MathCounts is on mathematical problem solving. Students are eligible for up to three years, but cannot compete beyond their eighth grade year.

## Contents

## MathCounts Curriculum

MathCounts curriculum includes arithmetic, algebra, counting, geometry, number theory, probability, and statistics. The focus of MathCounts curriculum is in developing mathematical problem solving skills. In general, MathCounts problems encourage creative thinking while discouraging brute forcing.

Before 1990, MathCounts chose particular areas of mathematics to highlight each year before changing the focus of the competition more broadly to problem solving.

## MathCounts Competition Structure

### Sprint Round

30 problems in 40 minutes. This round is generally made up questions ranging from (relatively) extremely easy to extremely difficult. Some of the difficult problems are only difficult because calculators are not allowed in this round. Like all of the other rounds, it gets progressively harder from the School-level competition to the National-level competition.

### Target Round

8 problems given 2 at a time. Each set of two problems is given six minutes, students may not go back to previous rounds even if they finish before time is called. Unlike the Sprint and Countdown rounds, use of calculators is permitted, but like all of the other rounds, it gets progressively harder from the School-level competition to the National-level competition.

### Team Round

10 problems in 20 minutes for a team of 4 students. These problems typically include some of the most difficult problems of the competition. Use of a calculator is allowed (and required for some questions). Like all of the other rounds, it gets progressively harder from the School-level competition to the National-level competition.

### Countdown Round

High scoring individuals compete head-to-head until a champion is crowned. The Countdown round is facilitated differently in the Chapter, State, and National competitions.

### Ciphering Round

In some states, (most notably, Florida) there is an optional Ciperhing Round. Much simila to countdown, a team sends up a representative to go against all representatives from the other teams. A problem is shown on a screen and students work fast to answer the problem. The students give their answer and after 45 seconds the answer is shown and the answers are checked to see if they arfe right. The fastest correct answer gets five points, the next fastest gets 4 etc. There are 4 questions per individual and teams send up 4 people. A perfect score is then 80.

#### Chapter and State Competitions

In the Chapter and State competitions, the Countdown round is not mandantory. However, if it is deemed official by the chapter/state, the following format is used:

The 10th place written finisher competes against the 9th place written finisher. A problem is displayed, and both competitors have 45 seconds to answer the question, and the first competitor to correctly answer the question receives one point. The person who gets the most correct out of three questions (not necessarily two out of three) winner.

The winner of the first round goes up against the 8th place finisher.

The winner of the second round goes up against the 7th place finisher.

This process is continued until the Countdown Round reaches the top four written competitors. Starting then, the first person to get three question correct wins (as opposed to the best-out-of-three rule).

#### National Competition

At the National competition, there are a couple structural changes to the Countdown Round. The top 12 (not the top 10) written finishers make it to the Countdown Round, and the format is changed from a ladder competition to a single elimination tournament where the top four written competitors get a bye. This setup makes it far more likely for a 12th place finisher to become champion, and it makes it less likely for a first place written finisher to become champion, equalizing the field.

At the first round and the second round, the first person to correctly answer three questions wins. However, at the semifinals, the rules slightly change - the first person to correctly answer four questions wins.

### Masters Round

Top students give in-depth explanations to highly challenging problems. This round is optional at the state level competition and is mandatory at the national competition.

### Scoring and Ranking

An individual's score is their total number of correct sprint round answers plus 2 times their total number of correct target round answers. This total is out of a maximum of 30 + 2(8) = 46 points.

A team's score is the average of the individual scores of its four members plus 2 points for every correct team round answer, making a team's maximum possible score 66 points. Therefore, it is possible to win with a relatively low team score and a phenomenal individual score, as the team score is only roughly 30% of the total team score.

## MathCounts Competition Levels

### School Competition

Students vie for the chance to make their school teams. Problems at this level require the least depth of curriculum.

### Chapter Competition

Chapter competitions serve as a selection filter for state competitions. A few states don't need to host chapter competitions due to population size.

### State Competition

The top 4 students in each state form the state team for the national competition. The coach of the top school team at the state level is invited to coach the state team at the national competition. Interestingly, the coach of a state team is not necessarily the coach of any of the state's team members.

### National Competition

#### Nation Competition Sites

For many years, the National MathCounts competition was held in Washington, D.C. More recently, the competition has changed venues often.

- The 2007 competition will be held in Fort Worth, Texas.
- The 2006 competition was held in Arlington, Virginia.
- The 2005 competition was held in Detroit, Michigan.
- The 2004 competition was held in Washington, D.C.
- The 2002 and 2003 competitions were held in Chicago, Illinois.

#### Rewards

Every competitor at the National competition receives a graphing calculator that varies by year - for example, in 2006 it was a TI-84 Plus Silver Edition with the MathCounts logo on the back.

## MathCounts Resources

### MathCounts Books

- MathCounts books at the AoPS Bookstore
- Art of Problem Solving's Introductory subject textbooks are ideal for students preparing for MathCounts.

### MathCounts Classes

- Art of Problem Solving hosts MathCounts preparation classes.
- Art of Problem Solving hosts many free MathCounts Math Jams. Math Jam Schedule. Math Jam Transcript Archive.

### MathCounts Online

- MathCounts Homepage
- Art of Problem Solving hosts a large MathCounts Forum as well as a private MathCounts Coaches Forum.
- Elias Saab's MathCounts Preparation Homepage
- The MathCounts Bible According to Mr. Diaz
- Building a Successful MathCounts Program by Jeff Boyd, who coached the 2005 National Champion Texas MathCounts team.

## What comes after MathCounts?

Give the following competitions a try and take a look at the List of United States high school mathematics competitions.

- American Mathematics Competitions (AMC)
- American Regions Math League (ARML)
- Mandelbrot Competition
- Mu Alpha Theta