Math Olympiads: Challenge Your Advanced Math Learners

Incorporate this great program into your curriculum to challenge your most advanced mathematicians!

By Barry Nitikman

gold medal

The Math Olympiads are an international program that trains students to develop the ability to solve challenging, high-level math problems. If you choose to participate, your class will study advanced problem-solving techniques, and compete in special tests given one Tuesday per month from November to March. Each test consists of five challenge problems that must be solved within 3-5 minutes, but the participants have the freedom to allocate their time to the various problems as they see fit. At the end of the season, the program presents awards to students with the top scores, as well as the classes who have overall superior performance. The head office in New York will send certificates, pins, trophies, and even a sample press release so that you can call attention to your class’ achievement.


An Internationally-Consistent Program

When I say international, I mean it. There are dozens of countries participating, and tens of thousands of individual schools. Your kids will be asked to solve the exact same problems as kids at international schools in Kenya, Tanzania, Mumbai, or New Zealand. Of course, there will also be mathematicians attempting these problems in Dubuque, Rochester, Fargo, Los Angeles, and Omaha, to name a few.

If you are saying to yourself “Oh geez, this sounds great, but I don’t feel qualified to teach all these techniques,” have no fear! Please trust me on this, get the book Creative Problem Solving in School Mathematics by George Lenchner. Mr. Lencher is the founder of MOEMS, and until his death a few years ago, was still highly involved in the program. This is a wonderful book filled with systematic, solid instruction and practice in these techniques. If you’ve never really taught advanced problem solving, this book will help guide you along. It will lay everything out for you in an organized way, and make it possible for your class to progress in mastering these strategies.

Mathematical Thinking for Your Strong Learners       

I have participated in this very worthwhile and exciting program with my own classes for many years. I will say at the outset, this program requires fairly good ability in math; it is not appropriate for those who struggle, it would only lead to frustration. However, my experience has been that it is ideal for gifted or advanced kids who thrive on working with complex and challenging problems; exactly the kind of material that advanced or gifted children need to stimulate and develop their interest and abilities in math. It does not deal with rapid-fire calculations or number crunching. Rather, it is intended to develop the ability to think mathematically and to solve problems where there is not an obvious approach to solving them.

Steps for Participating in Math Olympiad

  1. Sign up at the beginning of the school year for your class, or a combination of classes. To participate fully as a class, you need at least 10 participants. However, you can combine classes up to a total of 35. (Homeschoolers can also participate, I believe.)
  2. If at all possible, get a parent to be the liaison. At the beginning of the year, you enter in the names of all participants. Then, once a month, November-March, have your liason download and print out enough tests for the class, as well as the answer sheets. For a fun challenge, I take the test along with the class. For full details and information on signing up, see
  3. Train your class in the problem-solving techniques they will use to solve these kinds of problems:
  • Draw a picture or diagram
  • Find a pattern
  • Make an organized list
  • Make a table
  • Solve a simpler problem
  • Guess and check (trial and error)
  • Experimenting/reasoning
  • Act out the problem
  • Work backwards    

There are some variations, but the list of techniques is fairly standard. These are the basic approaches that most will use to attack these kinds of problems. Some problems will require slightly different creative approaches, or a combination of techniques. But a thorough grounding and solid practice in the standard techniques will foster the confidence and ability to solve high-level problems.

Test Day Logistics

You give the test one Tuesday per month, from November through March. I wait until Wednesday to go over the solutions.  I have the students revisit the problems with a partner or small group, and once they’ve done that, we take turns going up to the Elmo and explaining our various approaches. This is almost always a highlight, as kids love to explain their thinking. You know your own class and will have to determine the best method for you.

In my opinion,  the Math Olympiads are not worth doing at all if you don’t spend significant time revisiting and discussing the solutions and approaches they took on each problem. Hearing how others approached the problems, and especially looking at how people went wrong, is where the true growth will occur.

After each Olympiad is finished, your liaison (or you) simply enters in the scores online, which takes about 20 minutes max.  MOEMS headquarters will send you periodic notices and stats, including such things as the exact percentage of kids worldwide.  Sometime during late April or May, you will receive a package containing your awards.   

Sample Olympiad Problems 

From Division E (4th-6th)

  • Dwayne lives in a street with 12 houses. Every day, he gets more letters than any other house. Today 57 letters were delivered to his street. What is the smallest number of letters that Dwayne could have received today?
  • A bus can hold 24 adults or 30 children. 25 children are already on the bus. What is the largest number of adults that can still get on the bus?
  • AB, CD, EF, GH, and JK are five 2-digit numbers. Different letters represent different digits. Find the greatest possible value of the fraction below:

 AB + CD +EF

     GH - JK

From Division M (7th-8th):

  • How many whole numbers between 1 and 150 have exactly three different factors?
  • Jakob has 3 more brothers than sisters. How many more brothers than sisters does his sister Sari have? 
  • How many different 5-digit palindromes are there? (note: a palindrome is any number that reads the same forwards and backwards, such as 151 or 729927.)  


Problem Solving

This lesson on problem solving process is intended for 5th graders, and follows an organized, systematic process in solving a challenging word problem.

Zoom-In: Early 20th Century Original Student Math Problem

This is a really interesting lesson for 7th/8th graders in which they solve an original problem written by a young native American student. It is well thought-through and well-presented.

Apple Logic and Problem Solving

A very interesting two-lesson series on problem solving for grades 4-6.