Abstract: An educational and building toy including a set of blocks of different lengths, having spaced-apart holes the number of which is determined by the proportional length of the block relative to a unit length. A plurality of discs and wafers are also provided, having holes and also indicia opposed thereon for the arithmetical operations of addition, subtraction, multiplication and division, and the cardinal numerals from one to ten, respectively. A plurality of flexible rods having axially-extending and circumferentially spaced ridges are provided. The peaks of the ridges define an outer diameter slightly larger than the diameter of holes in the blocks, discs and wafers, whereby a friction fit is obtained between the rods and perforated pieces to build different objects. The discs have a peripheral flange and a hub. The flange of some of the discs has inner gear teeth for meshing with the rod ridges. The hub hole of some of the discs have indentations for making a spline connection with the rod ridges.

Abstract: A multi-purpose instructing block comprising one hundred blocks divided into ten sets and a calculating frame having two grooves which are designed so that the blocks therein may be moved along the grooves. The blocks of the same set are of a size and color but the blocks of different sets differ in color and length. The multi-purpose instructing block is useful to interest the children in calculating, distinguishing between colors, learning alphabets in addition to making toy houses.

Abstract: An educational toy and method is disclosed for teaching young children arithmetic using pattern recognition. The toy comprises unit size (square) indicia representing `ones` and multiple size indicia (rectangles) representing a multiple of the one digit. The indicia are placed in an organizer which allows the unit indicia to enter in one direction and the multiple indicia to enter the organizer from the opposite direction so as to aid in creating the desired recognizable patterns representing different numbers.

Abstract: An aid for learning roots includes a flat surface with a number of unit squares inscribed inside a larger square surrounded by a border. The board surface contains loops for mating engagement with rectangular patches having hooks for being detachably secured to the loops. There are 25 square patches of a number of colors, each corresponding substantially to a unit square and 25 rectangular strips each of width 1/5 a square side dimension. A perfect cube with unit squares inscribed on its face nests inside three intersecting orthogonal planar surfaces each having unit squares inscribed in a square of the same size as a cube face and a rectangular edge strip.

Abstract: An instructional aid consisting of a plurality of objects useful in teaching and understanding basic concepts of number, addition, subtraction, multiplication and division. Each of the objects in the plurality corresponds to some integer number between one and ten and has a thickness representing the number to which it corresponds. Moreover, each object has a surface having a color or combination of colors representing the prime number or composite number to which it corresponds. The surface having such color or combination of colors has the shape of the Arabic numeral representing the number to which the object corresponds. Alternatively, this surface has the shape of a symmetrical figure with a number of sides equal to the value of the number to which the object corresponds. As a further alternative, this surface consists of a linear composite of unit surfaces, the number of such unit surfaces being equal to the value of the number to which the object corresponds.

Abstract: A base member has a plurality of upwardly facing openings for receiving arithmetic value blocks such as addition or subtraction blocks, a first upwardly facing end opening for receiving positive answer blocks and a second upwardly facing opposite end opening for receiving negative answer blocks. A summing rack including transverse gear teeth is slidably mounted in a longitudinal slot in the base member communicating with each of the recesses. One end of the summing rack has an encoded pattern of holes defining the numerical values of possible positive answers; and the other end of the summing rack has a similar series of holes defining the numerical values of possible negative answers. Each of the recesses which receives an arithmetic value block has a sector gear therein which engages the summing rack teeth and moves the rack a proportionate distance when an addition or subtraction block is inserted into the corresponding recess.

Abstract: The apparatus is used as a teaching aid for arithmetic, metric and analytical geometry and elementary algebra, and is formed by a cubic block array comprising a plurality of different size blocks arranged in rows and columns. The cubic block array has a base array of ten-by-ten blocks commencing with a one centimeter block and progressing in x and y rows with increasing length blocks (1 cm., 2 cm., 3 cm., etc.), and overlying arrays of the same pattern but progressively increasing in height (1 cm., 2 cm., 3 cm., 4 cm., etc.).