- Math Circle Diaries, Year 1: A Complete Curriculum
- by Anna Burago
In our math circles, we often engage our students in mathematical games and contests. There are several reasons for using these activities:
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 is a fast-paced and easy-to-learn two-team 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 ready-to-play games
• 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 re-auctioned 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 open-ended 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 ready-to-play math auctions.