Abstract: A method and apparatus of teaching mathematical problem solving includes using a series of containers, each consisting of an inherent problem requiring the use of mathematical skills for solution. The series of containers meets all conditions for the teaching of mathematics as recommended by the National Council of Teachers of Mathematics in their 1989 document "The Standards". The complete solution satisfying "The Standards" for each container ordinarily takes a period of days. A kit consisting of such containers is disclosed.

Abstract: A pack of playing cards for an educational game comprises a number of sets of cards exactly equal to the number of faces on a die. Each card has a front and rear face, each rear face being identical to each other. Each card has disposed on the front face at least one question and answer and a depiction of at least one die-face, the number represented by the die-face being credited to a player correctly answering the question on the card during the game. Each card of each set has disposed thereon the depiction of the same die-face, the die-face being different in each set, and there being equal numbers of cards in each set.

Abstract: The method for teaching mathematics to students with disabilities includes an interactive program with a synthesized speech output and voice input, the interactive program being designed with different predetermined modules for different skills (i.e., addition, subtraction, multiplication and division) and for different levels (i.e., beginner, intermediate, expert) and for different modes of learning (i.e., tutorial, testing), the interactive program describing the mechanical process for setting up the problem as if the user had no disabilities and breaking down the problem into smaller and easier problems and querying the user as to the answer to those smaller problems.

Abstract: The present invention is directed to a system for demonstrating mathematic concepts, such as fractions and their equivalents. The system includes at least one device constituted by a pie chart sheet having a slot, and a rotating disk having a slit. The slit in the rotating disk provides a leading edge which is inserted through the slit on the chart page to allow the rotating disk to cover any selected portion of the chart. Because the cuts in both the pie chart on the chart sheet are radial, rotation of the disk about a common center point is facilitated.

Abstract: An instructional system or method for statistics students. Twenty slots are defined into which one hundred data cubes are placed. The number of cubes per slot varies from one to ten, excluding six. The slots with ten cubes are arranged adjacent to a center line, and the number of cubes per slot drops as the distance between a slot and the center line increases. The cubes model a normal distribution curve and can be used to estimate probabilities and other statistics concepts. The system associates statistics computational methods with the fundamental concepts of statistics in a manner that enhances the students understanding of statistics as a whole. The system also enables students with low aptitude for math and quantitative methods to grasp the concepts of statistics and pass the college tests for entering those disciplines which require a standard knowledge of statistics for admission.

Abstract: A self-corrective, reversible device comprising a handled, slotted framework, on each side of which the top frame is imprinted with inverse mathematical symbols, below which is a number line from one through ten in ascending and descending order. Below the number line, nine channeled horizontal rows each contain ten grooved, colored, movable, workpieces. The first four rows on side "A" teach counting, addition, subtraction and place value. These workpieces have the following values: Row one, "1" each; Row two, "1" each; Row three, "10" each and Row four, "100" each. Workpieces in each row are the same color, but each row is a different color. Corresponding with these four rows in both value and color are four boxes imprinted on an erasable surface contained within the framework. The remaining five rows on side "A" teach large and small letters of the alphabet, phonics and consonant blends.

Abstract: An educational jigsaw puzzle (20) in accordance with a first embodiment of the invention including a plurality of substantially flat components (22) having various beginning members (23, 24). Beginning mathematical expressions (26, 27) located on components (24, 25) are directionally combined with same-component expressions (28, 29), and equivalent expressions (30) are located on components (22) with matching edges. These equivalent expressions (30) are then directionally combined with same-component expressions (32), and new equivalent expressions (30) are located on components (22) with matching edges. The process of combining new equivalent expressions with same-component expressions continues until final equivalent expressions (34) are found. Components (22) not containing mathematical expressions are either blank or contain portions of pictures (38). Guidelines (36) and pictorial representations (40) of mathematical expressions may be contained on numerous components (22).

Abstract: A multi-level educational game apparatus and method for teaching children and adults language, mathematical, and other skills. The educational game includes a board and a plurality of cards. The board comprises a plurality of rows and columns, each having a letter, word, or picture imprinted thereon. The cards have letters, words, numbers, symbols, or pictures imprinted thereon that correspond to the participant's boards. The board game includes multi-levels of difficulty corresponding to varying individual language and other ability levels. An instructor will read aloud the card and give a brief explanation of the card's contents. When a participant recognizes the cards contents on his board, he will cover the respective box with a marker. The object of the game is to complete a row or other predetermined sequence of boxes prior to another participant.

Abstract: A learning tree board game is provided which includes a game board having a picture of a tree, a sand box area on a lower left hand corner, a green area on a lower right hand corner and a plurality of identifiable indicia upon the picture of a tree. A plurality of playing tokens are provided, in which one for each of the game players is placed on the sand box area at the beginning of the game and then on one of the identifiable indicia during the play of the game. A deck of cards are used, in which each card has indicia thereon which matches up with one of the identifiable indicia upon the picture of a tree of the game board. The deck of cards is placed on the green area face down at the beginning of the game and then one card is picked by each player taking a turn during the play of the game.

Abstract: A game for enhancing mathematical skills is played in the a classroom with teams of players or individual players. In accordance with one embodiment, the game utilizes a branched lattice having a central starting point and a plurality of terminal points. The lattice is placed on the floor of a classroom. In playing the game, students select three numbers from a location on the classroom wall and factor those three numbers to find the prime factors of the numbers, which prime factors are then recorded in input/output tables. The tables have an output line or column in which the output value "-1" is written if the number of factors is odd; the output value "0" is written if the output value includes repeated primes, indicating raising a prime to a power; and the output value "+1" is written if the number of prime factors is even. The output values are used to locate the input/output tables, which are on slips of paper, at correct terminal points of the lattice.

Abstract: A digital clock display and a math display are disposed on a surface of a math teaching unit. A processing unit is configured to display time including an hour and a minute on the digital clock display based on control signals from a clock circuit and a clock setting apparatus. The processing unit is configured to display math equations on the math display such that a first operand equals the hour and a second operand equals the minute.

Abstract: A system for teaching proofs, including a set of playing cards and a playing field electronically displayed on a computer game screen. The playing field includes two boxes labelled "GIVEN" and "CONCLUSION" for entry of a premise and a conclusion from a theorem (or other problem). By selecting from a certain menu or submenu contained in a window, a card may be reviewed. To set up the playing field, a mathematical statement, displayed on a set-up card of a group of set-up cards containing each statement from the universe of statements known, is entered into the boxes. The statements may be custom labelled. Geometric figures associated with the theorem may also be electronically drawn on the screen by a user to complete the set-up. After set-up is complete, a user then chooses from a set of playing cards, each card displaying a specific mathematical concept from the universe of mathematical concepts such as definitions, postulates, constructions, properties and theorems, and places it on the playing field.

Abstract: A visual teaching aid (10) that allows educators to relate similarities and differences between differing topics and between subtopics within a single topic. The visual teaching aid includes a map (14) and a plurality of labels (16). Contained on the map (14) are a plurality of geographic features (18) such as continents, countries, states, cities, islands, oceans, seas, gulfs, harbors, rivers, lakes, islands, and peninsulas. These geographic features (18) appear as those on a normal map but are preferably not related to actual geographic features (18). Each label (16) associates with a particular geographic feature (18) and also describes an educational topic or subtopic. The labels (16) are logically arranged such that similar topics and subtopics reside in closer proximity to one another than do differing topics and subtopics. Also included with the present invention is a coordinate system (82) for locating geographic features (18) on the map (14).

Abstract: An electronic learning system that utilizes a plurality of coded cards on which sensory-information representations are provided to present pictorial-symbol information and/or language-symbol information, in conjunction with a housing that contains card slots in combination with a visually and functionally distinctive button associated with each individual card slot and a button associated in an equal manner to all card slots, wherein a card may be inserted in each of the card slots. The operator can cause the system to generate unique audible information associated with the sensory-information representation provided on any selected card by pressing the visually and functionally distinctive button associated with the card slot in which the card is inserted.

Abstract: An apparatus for teaching polynomial expressions includes an arrangement of groups of rows and columns that represent the variables of factors of a polynomial expression. Each group of columns or rows has a different width or height, respectively, and represents a different variable in the polynomial expression. The apparatus enables an algebra student to visualize the rules that apply to polynomial expressions. In one embodiment, the rows and columns are defined by a plurality of pegs or nails fixed to a supporting member. Each factor of the polynomial expression is represented by isolating the variables of the factors by extending an elastic member around the appropriate pegs. The intersection of the two isolated factors represents the product of the factors.

Abstract: A visual aid teaching device for translating one or more superimposed picture images in a linear path at different positions with respect to a stationary underlay picture includes as basic components: a pair of edge strip members, each embodying two or more channel tracks; a transparent, or opaque, rectangular flat surface member snugly mounted on the edge strips through their channel tracks to assemble the body device; sets of layers, each including a stationary underlay picture member and one or more superimposed picture image members. Both members may include algebraic graphs or circles divided into sets of sectors. The layer members can be mounted on the other channel tracks. Algebraic problem solving of compound inequalities in one variable can be demonstrated algebraically along with their graphic solution sets simultaneously by means of translating one or more superimposed graphs at different positions with respect to a set of number line graphs.

Abstract: This present invention relates to displaying devices for instructive purposes. One object of this invention is to provide a composition of translations or a combination of rotation and translations in two orthogonal dimensions, to locate superimposed picture images to any selective location with respect to stationary pictures. The devices of this present invention are used to visually compare intelligence or information in the form of pictures, diagrams, or graphs for instructive reasons.Another object is to provide animated motion of pictures, diagrams, or graphs for teaching aid in education and in mathematics in particular. This invention provides animated transformation of geometric diagrams or Algebraic graphs to visually demonstrate the proofs of geometric theorems or to find instantaneous solutions of geometric problems or algebraic problems graphically for curricula in geometry and algebra.

Abstract: A statistical sampling apparatus is formed with a box-like enclosure having transparent top, front and bottom walls. A stationary ledge extends in a plane between the top and bottom wails and stops short of the front wall so that there is a space that communicates between the volume below the ledge and the volume above the ledge. A plurality of identically shaped beads are disposed within the enclosure. The upper surface of the ledge has a patterned array of identical recesses which receive certain of the beads when the enclosure is up-ended and the beads are allowed to wash over the ledge. The beads are of different colors in a known distribution, and the patterned array of recesses is divided into series of a smaller numbers of recesses for statistical sampling purposes.

Abstract: An educational apparatus includes a housing having a front wall with laterally spaced arrays of sensing and positioning holes and sets of letter or number display members each including one or more positioning pins and one or a pair of differently spaced and located positioning pins projecting from the rear faces of the display members, the pins being slidably engageable with respective holes. A switch matrix is located behind each hole array and is connected to the input of a calculator or message enunciating network located in the housing and having an output connected to LCD's on the housing front wall and/or to a transducer speaker in the housing. Calculator function switch buttons are located on the front wall.

Abstract: A matrix of discs each having a first end wall spaced from a second end wall, having a cavity therebetween, including a weighted portion to provide for the discs to sink within a body of water, such as a swimming pool. The first and second end walls include contrasting digital enumerations, wherein individuals are addressed math problems and the solutions to the problems are indicated by a numerical sum to be retrieved from within a swimming pool and the like by participating individuals.

Abstract: A game board includes a plurality of circular areas, each having a circular array of wedge-shaped segments to receive a circular overlay, wherein the segments may have a number indicated thereon or the overlay may be provided to indicate arbitrary numbers, wherein a plurality of dice are employed, with individuals mathematically computing employing addition, subtraction, division, and multiplication to calculate a final summation indicated by the dice to indicate a predetermined number of one of the segments, wherein a token member is positioned over a segment to indicate a correct total thusly derived. Each player is afforded various time intervals to assemble a correct total.

Abstract: A mathematical teaching aid or game comprising a background grid having components and subcomponents each positioned within individual cells of the grid so that many mathematical arrangements and concepts can be displayed. Each component has a face color from a set of colors and contains on its face the outline of a geometric shape from a set of geometric shapes. Each component represents a unique pairing of color and shape outline. Each subcomponent has a shape congruent to the shape outline from the set of shapes and matches exactly one component with respect to color and shape outline. The components are mounted upon the grid cells and the subcomponents can be mounted upon either a grid cell or upon a corresponding shape outline.

Abstract: An electromechanical demonstrator board of one or more of the six trigonometric functions. The board is powered electrically by a battery and mechanically by a hand crank which drives a pointer and contact arm. The circuits include light emitting diodes (LEDs) arranged into three groups. The first group represents a unit circle. The second group is on a vertical segment, and the third group is on the path of the function and the horizontal axis. The first group of LEDs indicates particular angle measures on the unit circle. In the second group, vertically oriented LEDs indicate harmonic motion. The third group of LEDs demonstrates a graph of the trigonometric function and the measure of linear movement related to rotation on the unit circle.

Abstract: A statistics teaching aid of the Quincunx type. The device includes a pinplate which has at least one movable row of pins. Shifting of the movable pinrow effectively increases or decreases the number of pinrows on the pinplate. By shifting the pinrow, an operator can alter the shape of the resulting distribution of balls.

Abstract: A Quincunx type of statistics training device having an improved ball-stop apparatus. The ball-stop comprises a base member having a plurality of forwardly extending pins. The base member is spring biased in a rearward direction and a latch mechanism is used to lock the base member in a forward position. Moving of the latch member allows the ball-stop to move rearwardly and thereby release any balls which had stacked up atop its pins.

Abstract: An educational aid for word and numeral recognition including a baseboard and sets of cards positionable on the baseboard in aligned relation to enable a student to recognize numerals, the value of such numerals and the definitive word for such numerals. Each card is a relatively large, rigid panel having a numeral, the definitive word for the numeral and distinguishable colored dots indicating the value of the numeral on one side with the obverse side of each card eliminating the colored dots to provide a more advanced educational aid. The baseboard includes a pair of stationary symbols indicating the action or manipulation for the numerals indicated onto adjacent cards and the result of such manipulation or action between a second and third card with the first two cards indicating the problem and the third card indicating the solution to the problem.

Abstract: This invention encompasses teaching kits for mathematics and a set of cooperating cards for use with the kits. A single surface displaying manipulable elements arranged on the surface is used to teach concepts of counting denominate units and evaluating expressions. Two surfaces displaying manipulable elements arranged on each surface simulate a linear equation. Four surfaces displaying manipulable elements arranged on each surface simulate a system of two linear equations. The elements are distinguishable by physical features in such a way that typically as many as three distinct denominate units are displayed with both positive and negative representations. The invention can be extended, in general, to a system of n equations, with 2n surfaces. Certain elements mask the occurrence of other elements in such a way as to simulate a variable in an equation. The cards serve to provide information for utilizing the boards and also can be employed by themselves.

Abstract: A flash card type of teaching system includes problem cards that are divided into sets by color coding. A key card that is in view of the student(s) contains answer information that is also color coded to assist the student(s) in choosing the correct response to a particular problem.

Abstract: An operations processor for facilitating memory of the 12 times table. The operations processor comprises two concentric cylinders, the inner cylinder having marked thereon a periodical array of numbers. The outer clinder arranged for indicating one of the operands and the solution to a particular multiplication. A user merely twists and raises or lowers the inner cylinder with respect to the outer cylinder thereby displaying any sum of the 12 times table.

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: An educational game includes a substrate having a plurality of separate sets of indicia thereon and structure for exhibiting the indicia of one of the sets of the substrate. A random symbol is generated from a plurality of possible symbols and an initial exhibition of a number fewer than all of the indicia in the set is carried out such that the number of indicia exhibited corresponds in value to the generated symbol. During the initial exhibition, the remaining indicia of the set which are not revealed are concealed by the structure. A player playing the game is provided with a way to indicate his or her prediction of a designated indicia to be subsequently revealed in the set so that upon subsequent exhibition of the indicia of the set, a comparison with the player's choice may be made.

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: Blocks of three different shapes can be detachably secured to a supporting surface such as a board and can form numbers from 0 to 9 inclusive in digital format.

Abstract: A soft-sculptured, game board doll (10) includes a three-dimensional body portion (12) and removable hair (14), feet (16) and nose (18). A plurality of color markers (54) are selectively registrable over corresponding color areas (52) disposed about body (12). A plurality of different game boards (60), (62), (64), (68) and (69) are detachably securable to the back surface (70) of body portion (12).

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 method and apparatus for teaching physical principles of fluid flow and the mathematical principles of integration by concrete, measurable examples comprised the use of a plurality of teaching funnels each capable of being supported by a mounting mechanism in a stable position over a receptacle. Each funnel has perimetric sidewalls with interior surfaces that conform to equations that will provide an integrable function when plugged into the equation for computing the time it takes for the funnel to empty of liquid. The funnels can have a base covering the lower end of the funnel with an outlet orifice formed in the base. The orifice is spaced a predetermined distance away from the sidewalls to achieve a desired outflow rate. The different sidewalls can be formed of different shapes as long as each conforms with a formula that yields an integrable function when plugged into the equation for computing the time it takes for the funnel to empty of liquid.

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: A statistical teaching apparatus includes a plurality of parallel circuits selectively coupled to an operational amplifier. Each circuit is adapted to receive a component from a population being statistically evaluated. The circuits include amplifier feedback elements arranged to selectively cause the amplifier to produce an output voltage representing the value of a parameter of any selected component or the average parameter value of any selected group of components so as to permit plotting of actual parameter values of a selected subgroup and measuring the average parameter value of that subgroup.

Abstract: A teaching device, for use in a classroom, comprising a hand-held size calculator adapted to normally include a display for showing the numerical output of the calculator, and adapted to include a face plate having a plurality of keys which are arranged in a particular pattern and which bear indicia indicating the calculator function of the keys. The calculator does include a circuit for producing a signal in response to depression of the face plate keys of the hand-held size calculator. The teaching device further includes an enlarged keyboard including a plurality of enlarged keys arranged in a key pattern simulating the face plate keys of the hand-held size calculator, and indicia on the enlarged keys simulating the indicia on the faceplate keys of the hand-held size calculator. The indicia is readily readable anywhere within the classroom. The keyboard also includes a plurality of switches responsive to depression of the keyboard keys.

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: An educational and recreational mathematical device comprises a ring or set of concentric rings or a band made endless or adapted to have ends thereof fastened to make them endless and a plurality of individual digits imprinted on the band or each ring at regularly spaced intervals. The digits when all read consecutively as a number constitute a quotient obtained by dividing a number constituted of (p-1)/n nines, in which P is a prime number greater than 5 and n is an integer at least 1, by P and adding to the left-hand end of said quotient any number of zeros necessary to increase the number of digits in the quotient to (p-1)/n or a specially chosen multiple of the quotient thus derived, 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 gaming apparatus and method are provided which utilize a number generating device for generating numbers which are statistically predictable in the long run. The device includes a plurality of screening devices arranged in vertically spaced relationship to form n levels and including holes therein through which spherical objects, such as marbles fall, when dropped through the uppermost level. The holes are arranged to provide a Binomial distribution of the objects in receptacles associated with each hole of the n.sup.th level screening device. A number is associated with each receptacle and scoring is based on multiplying the number of objects in a receptacle by the number associated with the receptacle. Spinners determine the number of objects to be played and the target value to be reached during a turn in order to amass a positive score.

Abstract: A device for teaching and refining counting skills includes a multiplicity of standards which are hit in a glissando-like movement by a flexible hand-held blade to produce a series of audible clicks. Indicia are mounted interjacent the standards and the indicia correspond to the number of clicks produced in a series of clicks. The indicia are normally hidden from view and are moved into a viewable position to indicate the correct number of clicks sounded in the series.

Abstract: A method and apparatus for teaching physical principles of fluid flow and .[.the.]. mathematical principles .[.of.]..Iadd., such as .Iaddend.integration.Iadd., .Iaddend.by concrete, measurable examples comprised the use of a plurality of teaching funnels each capable of being supported by a mounting mechanism in a stable position over a receptacle. Each funnel has perimetric sidewalls with interior surfaces that conform to equations that will .Iadd.allow various flow characteristics to be computed, and in preferred embodiments will .Iaddend.provide an integrable function when plugged into the equation for computing the time it takes for the funnel to empty of liquid. The funnels can have a base covering the lower end of the funnel with an outlet orifice formed in the base. The orifice is spaced a predetermined distance away from the sidewalls to achieve a desired outflow rate. The different sidewalls can be formed of different shapes as long as each conforms with a formula that .[.yields an.]. .Iadd.