Abstract: Apparatus and methods based on applied cognitive science, where children play the lead role in storylines staged upon a rule-enforcing apparatus and by so doing, become self-enlightened about denumerability, rank-wise denumerability, addition, subtraction, multiplication, division, and other change-of-state processes encountered in mathematics and the quantifiable sciences.

Abstract: A learning tool for identifying and memorizing fractional indicia on measuring devices including tape measures, rulers, other lined media, and the like, including incorporated into a fun to play game that emphasizes the above skills development while additionally utilizing and improving tactile feel, dexterity, eye-hand coordination and speed to accomplish work tasks by requiring picking up and properly manipulating small objects analogous to handling and placement of nails for hammering and screws for inserting them into specified holes. The tool can additionally incorporate measureable metrics for determining progress and identifying areas requiring additional practice.

Abstract: Disclosure for representing one or more numbers as a geometric counting mechanism that comprises an arrangement of geometric shapes and decoding the geometric counting mechanism into the represented number or numbers is provided. Decoding a geometric counting mechanism includes at least identifying a container geometry, determining a primary multiplier, a secondary multiplier, and an additive component value based on the geometric shapes identified in the geometric counting mechanism and their locations in the arrangement. The geometric counting mechanism can be decoded in a clockwise and/or counterclockwise manner, therefore one geometric counting mechanism can represent more than one number.

Abstract: The invention is embodied in the form of a flight simulator in the conditions of vortex danger and in conditions when a pilot is informed about the possibility to penetrate into said dangerous area of vortex sheddings produced by a vortex generator.

Abstract: A visual mathematical learning aid of numbers and their increasing values as they increase from left to right and from bottom to upward direction through the use of a container with lid for vertically maintaining a plurality of calibrated rods representing the units 1-10 in ascending order from right to left.

Abstract: A mathematical manipulative comprising a board with at least one row of numbers having one or more first cooperating answer elements associated with the row of numbers and one or more answer markers having a second cooperating answer element for removable engagement and/or connection with at least one of the one or more first cooperating answer elements.

Abstract: A math game and method includes a game board having a plurality of elongated slots therein. Each of the slots defines a row arranged in a plurality of columns. The columns each have a number of rows therein equal to a number of columns provided. A plurality of different multiplier indicia is positioned on the game board and positioned adjacent to one of the columns. A plurality of multiplicand indicia is positioned on the game board and positioned adjacent to one of the left ends of the rows. The columns each include multiplicand indicia beginning with a numeral 1 and progressing by one for each subsequent row. Each of a plurality of game pieces is mounted in one of the slots and is selectively positioned along a length thereof. A random number indicator indicates a number between 1 and a number equal to the number of the columns.

Abstract: A new mathematical graph board for teaching linear equations and linear inequalities. The inventive device includes a board having an outer peripheral edge. The board includes a pair of peg boards secured within the outer peripheral edge. The pair of peg boards have a plurality of apertures therethrough. One of the peg boards has a four quadrant system disposed thereon. A plurality of graphing lines couple with the peg boards of the board. Each of the graphing lines is defined by a pair of pegs dimensioned for being received within the apertures of the peg boards. The pair of pegs have an elastic band extending therebetween. The elastic band varies a length of the graphing lines.

Abstract: A arithmetic teaching device for teaching a child mathematics. The arithmetic teaching device includes a housing that has a bottom and a peripheral sidewall upwardly extending from the bottom. A counting box has an open upper face and a plurality of compartments therein. The counting box is removably disposed in the housing. A plurality of counting objects are disposed in the housing. The counting objects are positionable in the compartments of the counting box.

Abstract: A mathematical game is comprised of a game board with holes arranged in a regular array and playing pieces bearing integer numbers. Players compete to combine the playing pieces and mathematical operations to form a mathematical expression which equals a given answer. Playing pieces used in these mathematical expressions are placed on the game board on the holes. After all holes are filled with playing pieces, playing pieces are stacked on top of the previous layer of pieces by putting the playing pieces into gaps created by the playing pieces of the lower level. More levels of playing pieces are assembled as the game progresses, creating a three-dimensional pyramid shape.

Abstract: The present invention is a method and an apparatus to teach students the relation of numbers and identical items to mathematics by having the students visually and manually associating numbers with items and the adding and subtracting of these items. The apparatus hardware and the teaching method are designed to be depicted on a computer monitor screen with visual and manual manipulations of items on the hardware or on the screen to teach and relate skills to students by permitting use in either or both media.

Abstract: The present invention is directed to an apparatus and method for teaching addition and subtraction. The apparatus includes a game board, a plurality of movable dowels having predetermined lengths with spaced apart indicia marked thereon, and a number generator such as a pair of dice. The game board has a pair of spaced apart dowel receiving rows corresponding to "in play" and "out of play" positions. The rows may also include a plurality of pegs for supporting the dowels in a vertical position. In addition, optional segmented slots enable the player to lay the dowels vertically end to end on the game board without having them roll off of the board if the game is played on a surface which is not level. The separation distance between adjacent slot segments slots and the indicia associated with the dowels assist the player with the addition and subtraction computations. The game board also includes a plurality of dice receiving spaces and aligned with the slot segments.

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: The present invention provides an educational apparatus for creating both mental and physical tasks. The apparatus includes a peg board, manipulative members sized to cooperatively engage the peg board and a template for locating specific indicia with respect to the pegs on the peg board. Corresponding indicia are disposed on the manipulative members such that a preferred association exists between a given manipulative member and a given peg. The user initially performs the mental task of forming the preferred association, and subsequently performs the physical task of cooperatively engaging the manipulative member upon the corresponding peg.

Abstract: An educational aid and educational method for teaching pattern recognition and numerical skills to young children. The aid includes plural groups of game pieces each incorporating a different number of game pieces, the game pieces in different groups bearing different indicia such as different colors. The child matches the game pieces to matching target areas in a series of matching operations requiring progressively higher levels of abstract reasoning, ranging from simple color matching to matching the number of pieces to a numeral. The matching target areas may be defined on a substrate and on a series of auxiliary matching targets, each associated with one group of game pieces. The game pieces may be attached to the auxiliary matching targets and the resulting assemblies may then be matched to matching target areas on the substrate.

Abstract: An educational puzzle including a board having a plurality of identical openings extending therethrough and each receiving an identically shaped removable board piece. Each board piece, on the front side thereof, is provided with indicium such as alpha or numeric indicium so that the respective piece is correctly positionable in only one or a selected number of openings according to the overall purpose of the puzzle. The back side of the board and board pieces define one or more lines or patterns which are visible only from the back side. When all of the board pieces are properly inserted into the respective openings, then continuous lines are formed on the back side of the board to provide a visual determination that the puzzle has been solved correctly.

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 multi-use number board including a board having a series of substantially square raised surfaces or lands arranged in rows and columns on the top surface of the board and separated by an array of substantially perpendicular channels, and including holes at the intersections of the channels; the pegs having two ends, both of which may be inserted into the holes, one end being easily removable, the other end forming a friction fit so the peg extends fixedly from the surface of the board.

Abstract: A game for children and adults alike providing a cheerful and entertaining atmosphere. The game includes a plurality of peg boards with associated pegs for scoring by a plurality of players of the resulting number obtained by rolling a single die. The peg boards contain a total of 21 peg receptacles segregated to resemble the numbers one through six with the matching numbers on the die.

Abstract: A toy adapted to instruct young children by association. The toy teaches proper numeric, alphabetic, or color sequences and the standard left to right reading convention, by utilizing blocks that are inserted into shafts in a stand. Blocks inserted out of proper sequence will fall through the stand but passage of blocks inserted in the proper sequence will be obstructed and those blocks will not fall through but will remain supported within the stand.

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: A combination system such as may, for example, be embodied in a matching game or instructional device or in a set of locks and keys consists of a number of receivers and an associated number of plugs with both the receivers and the plugs having cooperable coding features coded according to unique rules, derivable from N-dimensional geometry, assuring a desired form of cooperation between a plug inserted in a receiver only when the code of such plug matches the code of the receiver.