Abstract: A supplementary teaching instrument based on mathematical basic theories and principles as well as child psychology. The invention employs a number of rectangular blocks of a prescribed shape which occupy a predetermined area when assembled together, and a corresponding area of triangular shaped blocks of various sizes and shapes. In addition to creating artistic designs by different arrangements of the blocks which may be of different colors, the rectangular blocks can be used in the fashion of a domino game, and the dimensional relationship between the triangular blocks and the rectangular blocks teach the basic concepts of mathematics including addition, substraction, multiplication, fractions, areas, and the like.

Abstract: A multiplication facts learning aid kit comprises a model amenable to computerization, teachers manual, set flash cards, and student materials to enable the learner to know the multiplication facts without rote memory.The model comprises a base and a plurality of square prismatic blocks with impressions of cubical units being proportionally-graduated squares up to the square of each numeral through twelve with the first cubic block being 1 cubed while the remaining plies represent integral multiples of the dimensions of said first block. Each composite multiple segmented ply represents multiplication facts in which multipliers are consistently the smaller numeral or are of the same value as the multiplicand. The width and height of the plies increase proportionally as the numeral affixed to the frontal surface corresponds to the value of that multiplication fact.Plies may be positioned to identify pattern relationships between sets of multiplication facts.

Abstract: An educational game system consisting of three or more individual decks of cards, and, in some embodiments, an extra set of cards used for special situations to be described hereinafter, and consisting of at least two individual games. The first of the two games is for developing a working knowledge of a set of mathematical (e.g. arithmetic, propositional, lingual) relations, and can be played by two to a given number n of players using one deck, up to 2n players using two decks, up to 3n players using three decks, etc. The second game is a game of skill and chance, played using all of the decks, which is also a means of separating the decks from each other.

Abstract: A two-stage training device for statistical studies permits the demonstration of advanced statistical principles. Balls are dropped from an upper reservoir through a maze of pins which scatters the balls into a histogram having that shape of a normal curve. The balls from individual cells of the histograms are dropped through a second maze of pins into a second set of vertical cells to form a series of histograms. Dropping subsequent sets of balls from many of the upper cells, visually demonstrates, that: "The Sum Of Normal Independent Sets Of Events Is Normal".

Abstract: A metric block toy comprising ten blocks of varying colors, each block being a one tenth of a meter cube, and having indicia designating ten centimeter increments along one edge of each block, together with other legends designating the length of the edge invarying metric terms. The blocks, when placed in aligned relation, indicate the total length of one meter.

Abstract: A teaching apparatus for Mathematics, specifically algebraic concepts for very young children, enables 3rd and 4th grade level students to solve simple linear algebraic equations. The apparatus includes easily manipulated elements which serve as cognitive reinforcement during the learning process. These physical elements are used in conjunction with a set of rules or "legal moves". The apparatus and corresponding legal moves determine a physical model and physical process to represent both an algebraic linear equation and its algebraic solution. A simple physical element, such as a pawn, is used to denote the unknown quantity. Numbered cubes are used to represent numerical values. These elements are color coded to represent both positive and negative values of the quantities represented. By the use of this apparatus and associated legal moves, students learn to simplify a given linear algebraic equation to the point where the solution or value of the unknown quantity is intuitively obvious.

Abstract: Disclosed are methods for structurally differentiating polynomial functions using parallelogrammic elements. The methods include representing a first ordered pair defined by the polynomial function as a construction of such structural elements. Second or sequent sets are also similarly constructed for an ordered pair defined by a different variable value. The resulting structural sets are compared to determine differences and the differential is expressed either directly or after dividing by the associated change in the variable of the polynomial function used to construct the two or more sets of elements.

Abstract: Methods for structurally differentiating functional relationships between two ordered sets of numbers related as x and one or more functions of x. The methods employ constructing sets of structural elements into parallelograms and any remainder portions. The parallelograms are constructed with at least one side of each having the same lengths or number of units. The structural elements of the sets are also arranged so that any remainder portions of both sets are also equal. The difference in total number of parallelogrammic units is then computed and divided by the difference in the variable x to produce the derivative value sought.

Abstract: A math teaching device comprising an elongate frame utilizing edge guides disposed along each of its long edges, and a plurality of closely similar counting pieces slidably mounted in an upper portion of the frame. The counting pieces are independently movable, and retained in an operative relationship to each other and to the frame by means of the edge guides. The frame has a recessed lower portion configured to receive an elongate display member, with the display member residing in the frame at a location below the counting pieces. The display member has indicia thereon, with such indicia being placed at a spacing that is consonant with the number and size of the counting pieces utilized. The display member may either be a fixed, integral portion of the elongate frame, or in the form of a slider, such that it can be readily removed, and replaced by another display member containing different indicia.

Abstract: A game apparatus for challenging the mental dexterity of two or more players and teaching children readily how to recognize, add and remember monetary sums is disclosed, which uses three cubical members, two main members, one of which has indicia on its faces corresponding primarily to common coins, e.g., 1.cent., 5.cent., 10.cent., 25.cent., 50.cent., and $1; and the other of which has indicia on its faces corresponding to common monetary notes, e.g., $2, $5, $10, $20, $50 and $100; and a lead member which has indicia of instructions on its face, e.g., score, no score, and second chance. The members are housed in a box-like container with a transparent top and thrown by the players in sequencial innings, with the individual player's score in each inning being determined by the upper face amount and the instruction. Each player accumulates his score from his innings and the first to reach a specific amount, such as one grand ($1,000), is declared the winner.

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 toy device for multiplication computation formed by a string of cuboid blocks having an interconnecting elastic string permitting equal segments of multiple blocks to be folded in a back and forth arrangement of aligned rows, the blocks each being individually marked with a number progressing in an ordinary arithmetic series of increasing units from an end block marked 1 to an end block marked with the number of the total blocks in the string, a multiplication computation being represented by a selected number equalling the number of blocks in a segment and a multiple equalling the number of rows, the product of which is the numerical marking of the last block in the segment of the last row.

Abstract: An apparatus for generating arithmetic expressions is disclosed. It comprises sets of number dice and of operator dice. The number dice are provided in two different colors, in order to remove ambiguity arising from the non-cumulative operations of subtraction and division, and to provide a means of designating negative numbers if so desired.

Abstract: A mathematical teaching/learning aid includes a set of thin mathematical cards or blocks, the set including six different types of blocks that represent the numbers +1, -1, +X, -X, +X.sup.2, and -X.sup.2, respectively. A plurality of blocks of each type are included in the set. The numbers +1, -1, +X, -X, +X.sup.2 and -X.sup.2 are referred to as "block type" indicia, and are printed in the center of the two opposed major faces of each corresponding type block. Four edge indicia or dimensions are printed adjacent to each of the respective edges of each face of each block. The product of the edge indicia at adjacent edges of each face is equal to the "block type" indicia of that block. Mating edge alignment tabs and notches or mating edge alignment indicia are provided at or adjacent to each edge of each block to allow edge-to-edge mating of each block with another block in only one configuration.

Abstract: A multiplication-division game containing chips (16) representing multiplication products and playing cards (14) representing multiplier-multiplicand combinations which equal the products of said chips. Each player has a placemat (10) for holding dealt and drawn cards. The chips are arranged in three piles (16) and the players take turns trying to capture the chips by combining pairs of cards whose products equal those of any one of the three top chips. The player who captures the most chips is declared winner; successful multiplier-multiplication cards being discarded. The players alternate play; with each turn a player draws a new card from a stack and matches pairs of cards against the chips until such player can no longer capture any more chips.

Abstract: A two dimensional educational game device (10) in accordance with a first embodiment of the invention includes a plurality of flat rectangular members (15, 30) having arcuate front and rear ends (21, 25) and non-parallel opposite sides (23, 23a) such that said members, when properly interfitted, form a circular pattern. Each member (15) has a number of arithmetic operator printed thereon to establish an array of radially and circumferentially correct mathematical equations. A three dimensional educational device (40) in accordance with a second embodiment of the invention includes a plurality of stackable trays (45) having a circumferential flange (51) extending around each tray (45). Rectangular block shaped members (60) are circumferentially positioned in each tray. Each member (60) includes an outwardly extending surface portion (64) having upper and lower inclined surfaces (66, 68).

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: An educational puzzle that teaches mathematics; the puzzle including a gameboard in the form of a tray, and a plurality of blocks placeable therein, each block being printed with a single numerical digit, and the blocks being arranged in horizontal and vertical rows so as to form a table from "1" to "9" in each direction, and the tray being divided by a central partition having a central gate.

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.).

Abstract: An educational device for teaching place values in a base N number system, and regrouping between places. The device has a plurality of workpieces, a support base, partitions on the base to form a plurality of parallel chambers of a length to stack at least N workpieces, and a storage container. Each chamber has a transfer element and an inlet and outlet to transfer workpieces from one chamber to an adjacent chamber and to the storage container.

Abstract: An educational and recreational mathematical kit comprises a set of n square sticks and a plurality of individual digits imprinted on each of the four sides of each of the sticks. The digits on one side of one of the sticks constitute a number which is a quotient obtained by dividing a number constituted of (P-1)/n nines, in which P is a prime number greater than 11 and n is an integer at least 2, by P, n being so selected that (P-1)/n nines is the minimum number of nines divisible by P so that the quotient is an integral number.

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.