Abstract: An arithmetical teaching aid includes a display board B comprising a rectangular array of display areas A arranged in rows R and columns C. Adjacent display areas A are marked (1, 10, 100 etc.) to represent successive powers of an arithmetic base number so that display areas A (where there are more than one) representing a given power of the base number (e.g. 1,000) are arranged diagonally across the board. Means (for example slides S) are provided for relatively moving the various rows R of display areas so that displays (e.g. 1,000) in the different rows R corresponding to the same power of the base number can be brought into columnar registration. All display areas A corresponding to a given power of the base number have a common tonal and/or textural characteristic which is different from the characteristic of each neighboring display area corresponding to a different power of the base number. Such characteristics are preferably provided by three different colors.

Abstract: A mathematics teaching apparatus comprises at least one set of rectanguloid elements of different shapes and of dimensions equal to 1, 3, 5 and 7 times a common unit or module. The set comprises a plurality of cubic blocks having an edge length equal to 1 unit, bars of unit width and thickness and lengths equal to 3, 5 and 7 units, square slabs of unit thickness and side lengths equal to 3, 5 and 7 units and rectangular slabs of unit thickness and side length combinations 3.times.5 units, 3.times.7 units and 5.times.7 units. Preferably the apparatus comprises two or more such sets which differ in color. The apparatus is useful for demonstrating and explaining various fundamental algebraic formulations and processes, including the algebra of 3-dimensional figures, and mathematical expressions comprising algebraic and whole number terms.