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Mathematics Help Reference

This is a help resource for 4th through 8th grades. We have just redesigned and reformatted these pages to enable faster loading and display times, but some pages still load slowly. Different browsers display graphics differently, so some math symbols may not appear to line up perfectly in some sentences. Our educational CD-ROMs contain the complete, searchable, indexed help facility shown below, along with the helpful problem-solving tips section. We hope you find this a helpful resource.

Whole numbers and their basic properties
Decimals, whole numbers, and exponents
Using data and statistics
Ratio and proportion
Percent and probability
Metric units and measurement
Introduction to algebra
Positive and negative numbers




QUESTIONS (TIME LIMITS AND TOPICS) Each contest is a 30-minute multiple-choice test. Questions may involve any topic appropriate to the grade level of the contest. If, for any reason, a question must be dropped, no replacement will be made.

CONTEST COPIES Each school will receive 30 copies of each contest in which they are participating. Schools requiring additional copies of any contest are permitted, on the day of the contest, to make as many additional copies as are required. A separate registration form should be submitted from each participating school.

CONTEST MATERIALS PACKAGE You should receive materials for Algebra Course 1 and Grades 4 & 5 by April 1; for Grade 6 by the last Tuesday in February; for Grades 7 & 8 by the next to the last Tuesday in January. If any contest materials have not been received by these dates, the League should be phoned immediately at 1-201-568-6328. Each contest materials package includes 30 copies of the contest and a solution key for the contest. A school needing additional copies of any contest is permitted, on the day of the contest, to make as many additional copies of the contest as are required. Special arrangements for blind or other handicapped students, or for non-English-speaking students, may be made by any school.


GRADES 4 AND 5 and ALGEBRA COURSE 1 In each school, the highest scoring student on each contest receives a book award. Other high scoring students in each school receive certificates of merit.

GRADES 6, 7, AND 8 In each school, a certificate of merit is awarded to the highest scoring student on each contest. For each contest, awards are given to the two schools with the highest total scores in the League and also to the two students with the highest total scores in the League. For each contest, additional regional awards are given to the highest scoring school in each region (which may be a county, province, state or other grouping as determined by the League). Counties/Provinces/States with fewer than fifteen participating schools are grouped together into regions for the purposes of awards. No school may win both a regional award and an overall League award on any one grade level in the same school year. The League reserves the right to break ties based upon performance on selected questions, or, at its option, to issue duplicate awards.

CONTEST LOCATION Each school may administer the contests on its own premises or any other suitable site.


(The 4th and 5th Grade and Algebra Course 1 Contests are non-competitive; these procedures do not apply.)

Except in unusual circumstances, the contests must be held on the scheduled date. In the event of school closings, special testing days, school trips or other administrative functions, severely inclement weather, or similar disruptions of the normal school day, permission is granted to conduct the contest on a proximate school day.

STARTING TIME Each contest may be held, on the scheduled date, at any time convenient for the school. All students officially participating in a contest within the same school should take that contest at the same time. Scores of students taking the contest at any later time should not be included on the score report filed with the League.

Each contest must be actively proctored at all times by a teacher. Neither the proctor nor anyone else may interpret any question to any student during the contest.

Only students officially registered in the same accredited school of record may participate on that school's team. A student may take only a contest designed for a grade the student has not completed or a higher grade (regardless of the math course in which the student is enrolled.) Students taking the 4th or 5th grade contest may also take the 6th, 7th, or 8th grade contest. Students taking the 6th, 7th, or 8th grade contest may take only one such contest (but they may take the Algebra Course 1 Contest). On each contest, all official participants must take the contest in school at the exact same time. A student taking the contest at a later time or period or on a later day must not be included on the score report. Students absent on the contest day may take the contest but must not be listed on the score report.

MATERIALS ALLOWED Only plain paper, pencil or pen, and any calculator without a QWERTY keyboard, may be used by the participants. No graph paper, compasses, straight edges, rulers, printed mathematical tables, or other devices shall be allowed, except where special arrangements have been made for handicapped students or when dictionaries are made accessible to non-English-speaking students.

Each contestant should be given a copy of the contest and should complete the information requested on the cover page of the contest. Answers submitted for each question must appear in the appropriate space in the answer column. Answers written elsewhere will receive no credit. After the signal to begin is given by the proctor, the timing of the contest will begin.

Warnings that "fifteen minutes remain," that "five minutes remain," and that "one minute remains" should be given at the appropriate times. No other warnings or announcements (relative to the contest) should be made to any contestant during the contest.

MARKING THE ANSWERS At the end of the contest, the question papers should be collected by the advisor. The advisor should then open the sealed envelope containing the solution key and should mark each paper, awarding 1 point for each correct answer. All papers should be marked exactly according to the solution key. If you wish to appeal an answer, please follow the appeals procedure, but score your students' papers according to the official answer key. The League has the option to disqualify any school that submits a mismarked paper.

SUBMITTING CONTEST RESULTS ONLINE The advisor should score the contests. For each contest, the advisor should submit the scores of the school's participants to the League's Internet Score Report Center. The school score for each contest will be the sum of the scores of the five highest scoring participants from the same school of record. The score report must be submitted to our Internet Score Report Center by Friday of the contest week.Student papers may be returned to the students, except that papers with scores above 30 must be held until June 1.

APPEALS PROCEDURE Appeals will be awarded only on the basis of an incorrect official answer or a correct alternative interpretation of a question. Detailed explanations of alternative interpretations should be made in the comments section when filing the score reports. Appeals filed with the League must include the names of all students listed on the score report for whom an appeal is being filed. If you disagree with an official answer, file an appeal. You must use only the official solution key in grading student papers.

AUTHENTICATION OF RESULTS League policy is to authenticate scores and eligibility of participants from schools winning major awards. The League reserves the right to authenticate scores and/or to reexamine students or validate student solutions before granting official status to any score. Schools must keep all papers with scores above 30 until June 1. The League has the option to disqualify any school that submits a mismarked paper. A school disqualified for cause on any contest is ineligible for awards in any League contest.

Dan Flegler / Phone: 1-201-568-6328, Fax: 1-201-816-0125
Steve Conrad / Phone: 1-516-365-5656, Fax: 1-516-365-5657

Get Involved!

How to get your school involved in Math League Contests

Check the Math League Registration Center for the Math League Contests in your state to see if your school is participating, and in which contests. Schools are listed by County in the U.S., and by Province in Canada.

If your school is not yet registered, and you would like to see them compete in Math League Contests, you can encourage them to participate. Here's how:

Thanks for your interest and good luck!


About The Math League

The Math League was formed in 1977 by Steven R. Conrad and Daniel Flegler.

In October 1985, Steven R. Conrad and Daniel Flegler were both honored by President Ronald Reagan as recipients of Presidential awards for "Excellence in Mathematics Teaching." Mr. Conrad was the winner from New York, and Mr. Flegler the winner from New Jersey. Mr. Flegler was the 1977 recipient of Princeton University's award for "Distinguished Secondary School Teaching." Mr. Conrad and Mr. Flegler have been preparing contests for math students across North America since 1977. They have co-authored 18 books.

Steven R. Conrad taught at Roslyn High School, Roslyn, New York, from 1980 to 1998. Prior to that, he taught at Benjamin Cardozo High School in Bayside, New York and Francis Lewis High School in Flushing, New York.

He began his undergraduate education at Washington University, St. Louis. He received a B.S. from Queens College and an M.S. from Yeshiva University. He has done additional graduate study at the University of San Francisco, Fordham University, and St. John's University, where he earned a certificate in School Administration.

More than 60 of Mr. Conrad's students have been named to the honors group of the Intel National Science Talent Search for mathematics papers they have written. Six of them have finished in the top 10 nationwide. His sons are both math professors.

He was Problem Editor for The Mathematics Student Journal (an official journal of the National Council of Teachers of Mathematics) from 1972 to 1978 and was an associate editor of The New York State Mathematics Teachers' Journal for 3 years. He has contributed problems to many journals, and has had articles published in Mathematics Magazine, The Mathematics Teacher, , American Mathematical Monthly, and Crux Mathematicorum. He is a reviewer for The Mathematics Teacher. For 4 years, Mr. Conrad was the author for the American Regions Mathematics League. He has also been the contest author for the Association of Mathematics Teachers of New Jersey, and director of contests for New York City. Currently, he is the author for contests sponsored by Bergen County, New Jersey, Suffolk County, New York, and Fairfax County, Virginia. He has also authored contests for Montgomery County, Maryland and Nassau County, New York. County, New York. Mr. Conrad served for six years as a member of the committee which developed the SAT II for the College Board.

Daniel Flegler taught at Waldwick High School, Waldwick, New Jersey, from 1965 to 1991, where he served as department chairman for 11 years. Mr. Flegler received his B.A. from Brown University and his M.A. from Columbia University. He has done additional graduate work at Fairleigh Dickinson University, the University of Iowa, and Rutgers University, from which he received his certificate in educational administration.

More than 15 of Mr. Flegler's students have been named to the honors group of the Intel National Science Talent Search for mathematics papers they have written. Three of them have finished in the top 40 nationwide.

From 1972-78, Mr. Flegler served on the Executive Committee of the Association of Mathematics Teachers of New Jersey, and was assistant editor of the New Jersey Mathematics Teacher. In addition, he has written contest problems for both New York City and Nassau County, New York. He has also directed the contests for Bergen County, New Jersey.


Frequently Asked Questions

Books and Copying



Math Help



Fees & Billing







Answers to Questions

Books and Copying

May I make copies of pages from your books of past contests to use with my students?

If you have registered for this year's contest, you may duplicate pages from our books for use with your class. If you are not registered for this year's contest, then you may not duplicate pages from the books.

Do the Volume 6 books contain the contests that appeared in previous volumes?

Later book volumes do not contain the contests published in previous contest problem books. You can view a complete listing of the contests published in each volume here.

Math Help

I have a math question. Can I e-mail you for help on my math homework from Math League?

We are happy to answer letters regarding questions that appear on our contests.

You are also welcome to browse our online Help Reference, which contains math reference information, with sample questions and solutions for grades 4-8.

We do not respond to math questions that do not appear on our contests. If you need help with homework or another question, visit "Ask Dr. Math" (K-12 grades only).

Can you mail or e-mail me the solutions for contest xxx?

Sorry, we do not have solutions for our contests in a suitable format for sending by e-mail. Our contest problem books have complete solutions, and can be ordered online. Just use any of the links on the left marked 'Shopping" to browse our list of contest books.

Fees and Billing

I received an invoice for my order but I haven't received the materials yet. Do I have to pay in advance?

As indicated on your invoice, payment is due upon receipt of all materials ordered. It is not necessary to pay any part of your order until you have received the complete order, although payment is certainly accepted (and welcomed) at the time you receive the invoice.

How much does the High School League cost for the school year?

The cost of entering the High School League for a school year is $90. There are no other fees associated with it.

I didn't order the high school contests but I received a set anyway. Must I pay for these?

Since the first high school contest occurs early in the school year, the League mails a set of contests to any advisor whose school was enrolled in the League last year. If you wish to participate in the League, please complete the registration form that was included with the contest package. The cost of participation is $90. If you do not wish to participate, please discard the materials in a secure manner.


How many contests are in a set?

High school contests come with 6 sets of 30 contest copies each: one set for each of the year's six contests.

All other contests consist of 30 contest copies per set. You may make additional copies of any contest on the day of the contest.

How do I check if my school is registered for contests?

A new contest registration index page has been added for teachers, administrators, and parents to check thier school's registration status. The web page is best viewed with a Javascript-enabled browser. The list is updated frequently. School registration listings will appear about 2 weeks after contest registration is mailed to us; about 1 week for schools using our online registration form.

I received an invoice for my order but I haven't received the materials yet. Do I have to pay in advance?

Payment is due upon receipt of all materials ordered, as indicated on your invoice. It is not necessary to pay any part of your order until you have received the complete order, although payment is certainly accepted (and welcomed) at the time you receive the invoice.

How do I obtain additional Certificates of Merit for my top students?

If your school needs more Certificates of Merit, send your name, school, and school mailing address to our mailer at:

Math League Certificates
P.O. Box 17
Tenafly, NJ 07670-0017

Include a self-addressed, stamped envelope (two stamps required) large enough to hold certificates.

My school is closed or on a special schedule the day of the contest. May we still participate?

You may reschedule the contest for either the alternate testing date listed or, with the permission of the League, for another date close to the official testing date.

My package for 4th Grade Contests (or 5th Grade or Algebra Course 1) did not include a score report form. How do I report the scores?

Our contests for 4th Grade, 5th Grade, and Algebra Course 1 are intramural contests that do not require the submission of scores to the League. Instead of giving plaques to the top two schools and top two students in the League as we do on all our other contests, we provide each school with a book prize to award to the top student in the school. We also include certificates of merit for other high-scoring students.

One of my best students was absent from school on the day of the contest. May this student take the contest later?

Although you may administer the contest to this student and award this student a certificate of merit if this student is the highest scoring student in your school, you may not submit the student's score to the League. Only students who take the test during the first testing are eligible for official recognition by the League.

I'm scheduled for the 6th, 7th and 8th grade contest. Must all grades take the test at the same time or on the same day? Must all my students take the contest at the same time?

For 4th grade, 5th grade, and Algebra Course 1, students may take the contest whenever it is convenient. You may give the 6th, 7th, and 8th grade contests on different dates. For each of these contests, students whose scores are reported to the League must all take the contest at the same time. If you give the 6th (or 7th or 8th) grade contest at several different times and on several different days, only the scores of the students who were present for the first testing session may be reported to the League.

I'm a new high school advisor this year, although my school was in the League last year. I have not yet received my high school package. What should I do?

Your school package was sent in September to last year's adviser. Please check and see if the package can be located. If not, e-mail us at (or call 1-201-568-6328) and we will ship another package immediately.

Some of my 8th grade students are studying algebra (or other high school math classes). Are they permitted to participate in the 8th grade contest?

Any student who has not yet completed the 8th grade may participate in the 8th grade contest, regardless of the math course in which they may be enrolled.

Should my 8th grade students enroll in the Algebra Course 1 contest or the 8th grade contest?

Students who take the algebra course 1 contest may also take any other contest the League sponsors.

I teach a 6th grade student who is doing 7th grade math. In which contest should this student participate?

A student may participate officially in only one of the contests for grades 6, 7, and 8. A 6th grade student taking 7th grade math may participate officially in either the 6th Grade Contest or the 7th Grade Contest, but not both. In this case, the choice of contest is not made by us: it's made by you and/or your student.

We only have 1 or 2 students in our school interested in these contests. May we participate?

There is no minimum number of students required to participate in any of these contests.

Our school wants to participate but we do not want our scores listed. May we participate on an unofficial basis?

Any school may choose to be an unofficial participant in the contests. Unofficial schools receive the same materials as official schools, but are not eligible for plaques. For grades 6, 7, and 8, only high scoring schools and students are listed on the score report summary published by the League. For high schools, the scores of all schools are listed in the score report summary unless a school requests not to be listed.

My child is being home-schooled. May my child participate in the contest?

Your child can participate on either an official or an unofficial basis. To participate unofficially, order our contest subscription package for homeschoolers, which will be sent to you in May for testing at home. You can compare your child's unofficial performance on the contest to scores of official participants by viewing the contest results at our Web site. If you want your child to be an official participant, you need to arrange with an accredited local school to order the official contest package, and proctor the contest for your child on the official contest date. All test materials would be mailed to your local school. 

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