Mental math

Math Field Day

Math Field Day is an individual mathematics competition ranging from grades 4-12 held in West Virginia. In 4th-9th grade, students compete within their own grade. In 10th, 11th, and 12th grades, students must compete within all of the grades mentioned. The West Virginia Council of Teachers of Mathematics are avid supporters of Math Field Day, and created it to spur students' curiosity in mathematics.

There are 8 regions created from the 55 counties of the state. The counties of each region are...

  • Region I- Raleigh, Wyoming, Mcdowell, Mercer, Summers, Monroe
  • Region II- Cabell, Lincoln, Logan, Mason, Mingo, Wayne
  • Region III- Boone, Clay, Kanawha, Putnam
  • Region IV- Pocahontas, Webster, Fayette, Braxton, Nicholas, Greenbrier
  • Region V- Wood, Pleasants, Calhoun, Jackson, Ritchie, Roane, Tyler, Wirt
  • Region VI- Hancock, Brooke, Ohio, Marshall, Wetzel
  • Region VII- Barbour, Doddridge, Gilmer, Harrison, Lewis, Marion, Monongolia, Preston, Randolph, Taylor, Tucker, Upshur
  • Region VIII- Berkeley, Grant, Hampshire, Hardy, Jefferson, Mineral, Morgan, Pendleton

Levels of competition

School-Math Field Day begins at the school level. In 4th, 5th, and 6th grades, each school is allowed to send one student from each grade to the next level, county. In 7th, 8th, and 9th grades, each school is allowed to send a "team"(these students do not actually work together) of four students from each grade to the county competition. In 10th, 11th, and 12th grades, the top ten students proceed to county.

County-The county competition is sometimes said to be harder than the regional competition itself, for some, depending on the county they live in. From the county competition, the top three students from each grade 4th-9th are eligible to attend their region's Math Field Day. In 10th, 11th and 12th grades, the top ten students proceed to their region's Math Field Day. The top scoring sophomore, regardless if they placed in the top 10, will receive an award recognizing their achievement.

Region-The regional competition, for some, is said to be easier than the previous county competition, yet for others much harder. Like the county level, the top three students from each grade 4-9 will proceed to the state competition. Also, just like county, the top ten students from grade 10-12 will proceed to the state Math Field Day, and, again, the highest scoring sophomore shall be awarded.

State-Regardless of where you live, students from around the state find the tests and competition at this level much more intense than previous levels. Twenty-four students from each grade 4-9 compete at the state competition, and eighty students from grade 10-12. The top three placing students from each grade 4-9 will receive an award, and here the competition ends for them. In grades 10-12, though, it continues. The top fifteen students will make up West Virginia's American Regions Mathematics League(ARML) team. The next top 15 scoring individuals will be the alternates for the team.

Nationals (for 10th-12th only)-The ARML test is administered at three locations. West Virginia takes the test at Pennsylvania State University. Here, students compete in both individual and team rounds, though there are significantly more team-oriented rounds than individual ones. Last year, West Virginia competed in Division B, and placed 66th of the 79 teams who competed in this competition.

Math Field day also occurs in PUSD of Pasadena California.

Competition structure for 4th-9th


Written Test- This first section of the test counts for the majority of a competitor's points. Each student is given 30 minutes to complete 25 multiple choice questions with a calculator. Each question is worth 8 points, so the maximum a student can get is 200 points. Usually, students get at least near perfect scores on these tests.

Mental Math Computation- The second section of the test is mental math, so it must be done without a calculator. It comprises two sections: mental math estimation and mental math exact. For the mental math estimation portion, students are shown a problem on a projector screen. They are then given 20 seconds to answer the question. Students are not allowed any scrap paper, and are also not allowed any mark outs on the answer sheet. As long as students are within 10% of the actual answer, they get the points for the answer. There are 10 questions on this section, each worth 4 points. The second part of the mental math portion is mental math exact. Students are read a question two times, and must answer the question in 20 seconds. Again, no mark outs are allowed on the answer sheet and no scrap paper is allowed. Like the mental estimation portion, there are 10 questions, each worth 4 points. The mental math section usually can be counted on to break up ties.


The format of the county competition is almost exactly a duplicate of the school competition, except that in addition to these the Written Test and Mental Math Computation, students in grades 4-9 take part in a Quantity Estimation portion as well.

Quantity Estimation- This additional section does not add to the total score of a competitor. Students are allowed to see and hold a bag of candy for around 20 seconds, and must guess the weight in grams of the bag. Previously, students had to guess how many pieces of candy were in the bag, but since scores were so close on this section, it was changed to grams. This section is used to break a tie if scores in both the Written Test and Mental Math Computation are equal.


At the regional level, Quantity Estimation is dropped, but the Written Test and Mental Math Computation portions are still used. In grades 4-8, students take part in a Physical Estimation section, and students in 9th grade are administered a Short Answer section. Also, a difference here is that the Written Test is now comprising 50 questions, with students being allotted 1 hour to complete the test.

Physical Estimation- This section is said to be the hardest portion of all the tests administered. Students in grade 4-8 are allowed to look and touch an object for around 20 seconds. They will have then have to guess one physical property of the object, such as length, width, circumference, area, etc. Students are not allowed a calculator during this portion.

Short Answer- This section is identical to the Target Round in MathCounts. Students in grade 9 are administered 4 rounds of 2 questions, and are allotted 5 minutes to complete each round of questions. The difficulty level of the questions varies from an easy question that might have been on the Written Test to questions that take the vast majority of the time to solve.


Again, the Written Test and Mental Math Computation portions are administered, as are Physical Estimation and Short Answer. In addition to the portions mentioned, a Math Relay section is added.

Math Relay- The top 3 students representing each region work together as a team, though this portion is not scored. First, a student will solve a problem and then hand the answer to the next student. Using this answer, the second student will plug it in the question to solve it, and pass his or her answer on to the last student. This competition is to lower the tension at the state competition and to promote amiability between students.

Competition Structure for 10th-12th

The top 10 students from the county level proceed to regions. The top 10 students from the region represent the region at the State Math Field Day. The top 15 students at the state competition represent West Virginia at the American Regions Math League.

Differing County Formats

The following counties have formats that differ from those aforementioned at their own Math Field Day.

Braxton County- 4th through 8th consist of the written test as well as the estimation/mental math. A mathematical game referred to as "combo" is played for fun but not added to the score of the contestants (Please contribute to the official rules of combo or the citation there of). A separate reward is given to the highest scorer in a grade for combo. 9th consists of two written parts. One being the complete written test, the other being a portion given two questions at a time with a total of 8 questions.

2008 State Math Field Day Results

This year, the state Math Field Day was held at Shepherd University.

Name Place Region Grade
Allen Chen Champion RESA VII 10th-12th
Tommy Liu Champion RESA VII 9th
Pranav Jain Champion RESA VII 8th
Matthias Naill Champion RESA VI 7th
Yashan Thakkar Champion RESA III 6th
Jamie Rose Champion RESA I 5th
Charles Newfeld Champion RESA II 4th
Sam Shideler Runner-up RESA II 10th-12th
Henry Wang Runner-up RESA V 9th
Andy Maloney Runner-up RESA VII 8th
Mathias Naill Runner-up RESA VI 7th
Samantha Garretson Runner-up RESA III 6th
Sneha Patnaik Runner-up RESA III 5th
Emily Hageboeck Runner-up RESA III 4th
Sandeep Patnaik 3rd RESA III 10th-12th
Rocky Diegmiller 3rd RESA VI 9th
David Mayer 3rd RESA V 8th
Levi Spickler 3rd RESA VIII 7th
Shelby Richards 3rd RESA VI 6th
Stephen Chen 3rd RESA VIII 5th
Britt Dolly 3rd RESA VII 4th

See also


1., West Virginia Department of Education, Retrieved February 22nd, 2006

2., West Virginia Council of Teachers of Mathematics Newsletter, Volume 25, Number 2, Retrieved February 22nd, 2006

3., American Regions Math League, ARML Contest Results page, Retrieved February 22nd, 2006

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