In our math circles, we often engage our students in mathematical games and contests. There
are several reasons for using these activities:
 Mathematical contests are engaging and entertaining. Students
really love them.
 Mathematical contests are educational. Students learn to present
their solutions and analyze the solutions of their peers.
 Mathematical contests are a team activity — they build up
relationships between students.
In our circles, we have a few favorite team competitions. These are Mathematical Auction, Mathematical Hockey,
Mathematical Domino. All these games have been tested by the years of practice in the mathematical circles
in Russia and in the U.S. We also play various short games, such as Black Box, Jotto, KenKen and others.
Below you can find more about some of our favorite contests.
Mathematical Hockey
Mathematical hockey is a fastpaced and easytolearn twoteam mathematical competition.
The contest is very dynamic, and every member of a team has a chance to participate.
This competition is intended for students ages 8 and up. Our math circles students,
ranging from the 3rd grade to the 10th grade, equally enjoy the game.
Mathematical hockey is played by two teams of 3 to 8 players each.
The rules of the game and several sample games can be found here.
Also, the book Math Circle Diaries contains several
readytoplay games
Mathematical Auction
• Math auction is one of the most engaging math contests
with the rules that are easy to grasp.
An element of excitement is added to the game by the fact
that the problems are auctioned and reauctioned and that play money change hands.
• Math auction problems are not traditional math problems
that can be either solved or not solved.
Rather, they are openended problems with intermediate
solutions that can be further improved.
The intermediate solutions are easy to find; therefore,
the students are always able to find a solution to an auction problem.
• Math auction problems are constructive. They don’t require
a proof and their answers are easily verifiable. Therefore, a math auction
can be organized even in a brand new circle –
a circle where students do not have too much experience with
math reasoning knowledge of math circle subjects and
are not yet familiar with the idea of mathematical proofs.
• The structure of a math auction stimulates students
to keep solving problems even during the stage
when the solutions are already being presented.
Because a good auction problem has several intermediate solutions,
a team could improve its solution by combining its original
idea with the idea that was presented by another team.
After coming up with an improved solution, the team can place a new bid on the same problem.
• Math auction is a game that works best for grades 5 and up.
The rules of the game and several sample games can be found at this link.
Also, the book Math Circle Diaries contains several readytoplay
math auctions.
Mathematical Dominoes

The game of Mathematical Dominoes is the most recent addition to
the Prime Factor Math Circle games collection. It quickly became
the favorite with our students.
 • It’s rules and format are as interesting and exciting for a 3rdgrader as for a 9thgrader
 • It engages each and every student in active problem solving
 • It can be played for as long as it is needed and can be stopped at any moment
 • It requires very few helpers
 • It allows all students to work at their pace and their level
The rules of the game and several sample games can be found at this
link.
Prime Factor Math Circle is a nonprofit organization. The
goal of Prime Factor is to engage school children in the world of
extracurricular mathematics with the purpose of developing their math
knowledge, problem solving skills and creative thinking abilities. We have a
lot of plans and ideas how to grow and expand. We welcome donations and we will put
them to a good use.