Equations: The Game of Creative Mathematics

This set of games and puzzles taught the operations of arithmetic in an entertaining setting and was sold from about 1963. Equations was developed by Layman E. Allen at Yale University Law School as the director of the ALL (Accelerated Learning of Logic) Project that developed mathematical games under a grant from the Carnegie Corporation of New York. Allen applied for a trademark for Equations in September 1963; it was registered in July 1965 but that trademark expired. In December 2013 Autotelic Instructional Materials Corporation applied for another trademark that was approved for publication in April 2014.
The set includes thirty-two wooden cubes—twelve are red, eight are blue, six are green and six are black. Each cube has a different one-digit number or mathematical symbol imprinted on each of its six faces. These symbols include the four basic symbols of arithmetic (addition, subtraction, multiplication, and division) as well as symbols for exponentiation and taking square roots
The set also includes a timer, a playing mat, a leaflet listing “GAMES for THINKERS” that were available from WFF ‘N PROOF, and an instruction book written in 1969 by Allen, EQUATIONS: The Game of Creative Mathematics. All these materials are stored in a green plastic case that is marked on the cover: EQUATIONS (/) THE GAME OF (/) CREATIVE MATHEMATICS.
In 1968 Allen moved from Yale to the University of Michigan with a joint appointment in the Law School and the Mental Health Research Institute, where he continued his work on instructional games. Over the years the name and location of the distributor of Equations changed, although the phrase “Games For Thinkers” has been associated with it from before Allen’s move to Ann Arbor. Price lists in the WFF ‘N PROOF Newsletters (part of the documentation in accession 317891) indicate that at first the game was distributed by WFF ‘N PROOF in New Haven, Connecticut, and sold for $3.50, including postage. In 1970 the price was raised to $5.50 and the game was distributed by WFF ‘N PROOF through Maple Packers in Turtle Creek, Pennsylvania. A firm called Learning Games Associates of Ann Arbor later took over distribution of the game and donated this, and another (MA*335304), example to the Smithsonian in 1975. Later Fairfield, Iowa, became the location of Autotelic Instructional Materials as well of as the next distributor of the games, the Accelerated Learning Foundation.
Games For Thinkers Website.
Currently not on view
Object Name
date made
ca 1969
Allen, Layman E.
Learning Games Associates
Physical Description
plastic (overall material)
wood (overall material)
paper (overall material)
overall: 2.5 cm x 15.25 cm x 12.5 cm; 31/32 in x 6 in x 4 29/32 in
place made
United States: Michigan, Ann Arbor
ID Number
accession number
catalog number
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Mathematical Recreations
Data Source
National Museum of American History, Kenneth E. Behring Center


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