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Mathematics Competitions

Mathematics competitions are a good way to encourage problem solving among mathematically able students who usually enjoy participating. Sets of old problems are a good resource for competition practice or classroom activities. The three contests listed here are among the most well-known.

American Mathematics Competitions (AMC)
The purpose of the AMC is to increase interest in mathematics and to develop problem-solving ability through a friendly competition. The questions range in difficulty from easy to very difficult in order to appeal to a broad range of students. The exam covers material normally associated with the seventh- and eighth-grade mathematics curriculum, including, but not limited to, the arithmetic of integers, fractions and decimals, percent and proportion, number theory, informal geometry, perimeter, area, volume, probability and statistics, and logical reasoning. Copies of prior year exams are available for purchase.

MATHCOUNTS is a national program for competition in mathematics for seventh and eighth graders. School teams use materials provided by MATHCOUNTS to practice throughout the fall. Four students are selected to compete as a team and as individuals in written and oral competitions at a local meet held in February. Winners progress to state and national competitions.

Mathematics Olympiads for Elementary and Middle Schools
These are contest problems that are administered five times during the school year within the school. The top few scores are sent as the "team score" as part of the competition. The problems are challenging and engaging. The elementary section is challenging for grades 46 but precocious third graders have been known to participate. The middle school level is geared to grades 7 and 8. The most benefit can be obtained from this program if the problems are debriefed in a classroom workshop where strategies are shared. There is a fee for participating in the competition. Previous problems are available and are an excellent source of rigorous problems for upper elementary students who need a challenge.

Here is a sample Olympiad problem for elementary grades:

A H + A = H E E

In the addition problem above, different letters stand for different digits. A H represents a two digit number and H E E represents a three digit number. What number does H E E represent?

Here is a sample problem from the Middle School contest problems: Of all the mathletes at Smith Middle School, 80% own computers and 40% are in the band. However, 10% of all mathletes neither own their own computers nor are in the band. What percent of the mathletes both own their own computers and are in the band?