Equations

What do players learn?

Equations is the Game of Creative Mathematics. Equations involves authentic learning experiences and problem solving at the highest levels.

All grade levels play with the same set of procedural rules. However, each division level of competition introduces increasingly more difficult mathematical concepts for the players to use. Players are challenged to use their mathematical knowledge and ability and to develop new skills in progressively more competitive ways. Players usually learn more from applying their knowledge in the competition than they do in their normal classroom studies.

Elementary Division (grades 4-6) players concentrate on the six basic mathematical operations (+ – x ÷ ^). At the Adventurous level, which introduces variations to the basic game, such concepts as factorials, greatest common factor, least common multiple, averaging, fractions, negative numbers, decimals, and percents are made available to the players. Please see the elementary division variation sheet to view all of the challenges our players are encouraged to use in competition.

Middle Division (grades 7-8) players continue to use everything that is available to the Elementary Division as well as new concepts such as working in bases other than base ten, fractional and negative powers and roots, and other challenging middle division variations.

Junior and Senior Division (grades 9-12) players have all that is available from the lower levels and may also choose such new concepts as modular arithmetic, imaginary numbers, and other challenging junior variations or senior variations depending on the division.

How do you play?

Equations was invented by Yale Professor Layman Allen in about 1960. The game consists of a playing mat and 24 cubes. Each cube contains four digits and two operation signs. A numerical Goal is set and players must form a Solution equal to the Goal from the 24 cubes rolled (the Resources). For example, the Goal might be 2^5 (2 to the fifth power, which is 32). A Solution might be: (5×5)+8-1. This would be a simple Elementary Division (grades 4-6) example. As players mature and go up in grade level, the Goals and Solutions become increasingly complex.

Each match involves three players from different schools. Many such matches occur simultaneously and last for 35 minutes. Depending upon the time scheduled, two or three such matches can take place on a given day.

Special rules called variations are available for each Division and reinforce what is taught in the mathematics curriculum for those grade levels. Before the cubes are rolled in a “shake”, each player selects one Variation from the list provided for that Division. In subsequent “shakes,” players may select different Variations. A 35-minute match may involve two to six “shakes,””shakes” allowing many different mathematical concepts to be applied.

Once the Goal is set, players take turns moving cubes from the resources to the Required, Permitted, or Forbidden sections of the mat. Any cube moved to Required must be used in any Solution; any cube in Permitted may be used; any cube in Forbidden may not be used. These moves from the players themselves shape the game. The moves force players to adjust their Solution or to even create a new Solution in response to their opponents demands. In any one “shake,” a player may create and examine fifteen or twenty different Solutions, depending upon the moves of the other players.

At any point a player may challenge “Now” or “Never” against the person who moved last- the Mover. A “Now” challenge means the player who challenged -the Challenger– can make a Solution using all of the cubes in Required, maybe some from Permitted and at most one more cube from the Resources. “Never” means the Challenger believes the Mover cannot make a Solution using all the cubes in Required, and any other cubes from the Permitted section or the Resources. After a challenge, at least one player must show a correct Solution on paper. If no player can show a correct Solution after a “Never” challenge, the Challenger wins.

The full procedural rules for Equations can be viewed or downloaded here.

Equations competitions encourage students to apply the mathematics they already know and to learn new math concepts sometimes years before they will learn these ideas in school. Complex problem solving is a key component to this game; mathematical knowledge and constantly evolving skills are the characteristics of teams that dominate this game.

How do I get the game Equations?

Check the links here to view and print the Official Tournament Rules and/or to obtain the study materials that have been written by experienced coaches over decades.

The Equations Academic Games may be purchased from Accelerated Learning Foundation.

For competitions, each school must bring one Equations game for every three players that will compete.

Academic Games and study materials remain the property of the purchasing school. If cared for, they will last for decades, for practices and competitions. The Equations Academic Games have not changed for decades, much as the basic materials involved in an athletic competition do not change.

The Official Tournament Rules are modified slightly every year based upon suggestions from member Leagues and the National Committee.