Abstract: A mathematics teaching system for visually and physically teaching a student how to perform multiplication and division calculations in a simple to understand format. The mathematics teaching system includes a housing having a plurality of apertures aligned in vertical and horizontal rows, an upper opening within the housing for inserting tokens into, a lower opening for allowing tokens to escape, a vertical slot and a horizontal slot within the housing for receiving slider members, a plurality of vertical reference numerals and a plurality of horizontal reference numerals, and a stopper member slidably positioned within a lower portion of the housing for retaining the tokens in a desired location for allowing calculation by a student.

Abstract: A teaching device comprising a group of balls, a first counter, a second counter and a tray interconnecting the first counter to the second. The first counter represents the problem to be solved, and the second counter indicates the solution to the problem. Both counters include several parallel columns for holding several of the balls in a line, and a stop for at least one of the columns to limit the number of balls that can be held by that column. The tray is placed below the first counter so that balls placed in the first counter may be dumped into the tray by removing the stops from the columns of the first counter, and then pushed or allowed to fall from the tray into the second counter.

Abstract: A number wheel counter has a worm wheel connected with the least significant number wheel. A worm gear engaged with the worm wheel is mounted for both rotational and translational movement about a spindle. Cam means are provided such that as the worm gear is rotated, it is also displaced bodily by the cam means so that the worm wheel remains unmoved. At the end of a defined travel of the cam means, the worm gear is returned rapidly to a rest position driving the worm wheel in the manner of a rack and pinion. In this way the number wheels are driven intermittently with the time interval during which the number wheels are between discreet number positions being minimized.

Abstract: A mechanical calculator employs a register consisting of gears. Each register gear has two sets of teeth. One set has teeth all around the circumference of the wheel while the other set consists of a single carry-over tooth. The register gears are spaced widely enough apart that they do not engage one another. An intermittent carry-over motion is transmitted from one register gear to an adjacent register gear by a selectively insertable and removable carry-over gear, which is mechanically unconnected to the remainder of the calculator. The operations of multiplication and division are enabled by a set of individually selectively insertable and removable multiplying gears. The number of teeth on these gears, and their diameters, are integral multiples of those on the register gears. The multiplying gears are mechanically unconnected to the remainder of the calculator.