Abstract: Devices for providing language-like abilities for dogs. Using polygonal layouts, audible, scent, visible and other cues, the devices provide an efficient and novel ability to communicate with dogs in a granular manner. Devices for capturing and releasing scents are provided. Novel button designs and functions are taught with particular suitability for animal training.

Abstract: A method for representing and solving algebraic equations that allows a user to view and solve algebraic equation with a virtual gear system. The virtual gear system includes a virtual primary cog and virtual secondary cogs. The virtual primary cog represents a range of outcomes for the virtual gear system and contains a number of teeth that is quantitatively greater than a numerical constant of the algebraic equation; amongst the teeth is a target tooth that represents the numerical constant. Each virtual secondary cogs represent a term of the algebraic equation and includes a coefficient and a variable. Each of the virtual secondary cogs contains a number of teeth equal to the coefficient. The equation is solved by rotating the virtual secondary cogs until the target tooth is aligned with a fixed pointer where rotation of the virtual secondary cog represents a value input for the variable of a term.

Abstract: A method for representing and solving algebraic equations that allows a user to view and solve algebraic equations through a novel user-interface. The user-interface includes a primary cog and a plurality of secondary cogs as parts of a gear system. The primary cog represents a range of outcomes for the gear system and contains a plurality of teeth that is quantitatively greater than a numerical constant of the algebraic equation; amongst the teeth is a target tooth that represents the numerical constant. Each of the secondary cogs represent a term of the algebraic equation and includes a coefficient and a variable. Each of the secondary cogs contains a number of teeth equal to the coefficient. The equation is solved by rotating the secondary cogs until the target tooth is aligned with a fixed pointer where rotation of the secondary cog represents a value input for the variable of a term.

Abstract: A board game for a plurality of players to learn arithmetic by playing the game with game pieces representative of the players. Each of the players has a first number of tokens, and the game is played on a game board with a dice rollable to advance the game pieces. The board game comprises a vessel for storing a second number of tokens. The game board comprises a plurality of locations extended around a perimeter of the game board. The plurality of locations is delineated for advancement of the game pieces according to a roll of the dice. Each delineated location indicates an arithmetic function operable by each of player based on their corresponding first number of tokens, when the representing game piece arrives on each delineated location.

Abstract: A method of teaching multiplication comprises the steps of providing a pair of multi-digit numbers to be multiplied and diagrammatically arranging the numbers on a work area. The work area includes a Multiplication Zone, an Addition Zone and an Answer Zone. In the Multiplication Zone, the numbers are arranged such that the digits of one number are vertically aligned with the digits of the other number. The Addition Zone has a top row, a bottom row and a plurality of middle rows, with the rows divided into a number of columns. The Answer Zone consists of a row divided into a number of cells. The products of multiplication and cross-multiplication of the aligned digits can be placed in a designated columns and cells in the Addition Zone and Answer Zone such that the sequence of digits in the Answer Zone is the product of the multiplication of the pair of multi-digit numbers.

Abstract: Cardiopulmonary resuscitation (CPR) training manikins and methods of using CPR training manikins are described.

Abstract: Teaching aid math games utilizing a mathematical matrix organized about x and y axises where the game is played by correctly associating numbers with their corresponding stations. The matrix comprises a first string of stations and a second string of stations where the first and second strings have the same number of stations. Each station is associated with a numerical value, and each station on the first string is parallel to a corresponding station on the second string where each corresponding station pair add up to the same numerical value. The display of the matrix provides visual associations for mathematical relationships.

Abstract: In a computer-implemented educational environment, four particular features are provided, which may be used separately or in combination, to drive the instruction of a particular curriculum, e.g. the instruction of fractions. In another implementation, educators and authors may use permutations and combinations of such features to construct in a graphical user interface a progression of interactive elements which help guide a student from visual concepts to procedures, such as equations and formulas. In a particular implementation, by using these features carefully, a curriculum author may design instructional sequences that provide careful, step-by-step sequences that help students progress from understanding the visual concepts, e.g. of fractions, to mastering procedures, e.g. fractions equations.

Abstract: A counting game played by one or more players involving numbers selected from pre-classified categories, suited to be played by players having different levels of mental maturity. A game involves choosing a set of numbers from one or more categories, at random. The object of the game is to generate numbers as high as possible, by using multiple math functions on the randomly generated chosen numbers. A player with the highest generated number wins the game. Apart from providing recreation and entertainment, the game develops math skills and provides mental training exercises, and can therefore be useful as a tool for educational and learning purposes.

Abstract: The present invention includes a phonetic alphabet with clarifiers and modifiers that aid in the teaching of reading skills to individuals with dyslexia, dyscalculia, and other neurological impairments when the present invention letters are connected horizontally in series with clarifiers and modifiers to form a word, a phrase, a sentence, and/or a paragraph. The present invention further includes mathematical symbols for teaching math skills to individuals with dyslexia, dyscalculia, and other neurological impairments when predetermined geometric shapes are arranged to form numbers of a base 10 counting system that are capable for using in additional, subtraction, multiplication, division. The present invention of mathematical symbols includes whole numbers, real numbers, integers, fractions, and decimals. The present invention also includes 2D and 3D tools and methods of using same.

Abstract: An improved method of teaching mathematics which enables students to take an active and enjoyable role in their own learning via an interactive puzzle is disclosed. In the preferred embodiment, each of the ten digits, zero through nine, is “hidden” within one of ten value positions (52). Students must deduce the value of each position by forming sums, differences, products, and/or quotients of the positions. Freedom of selection of positions and operations provides for individualized approaches to puzzle solutions, and the interplay of values and operations promotes number sense. Mathematical reasoning is intrinsic to the puzzle. Programmable settings (72) allow the teacher to modify the puzzle, including substituting more challenging values in place of the digits (98), supplying more complex functions (106) in place of the four elementary arithmetic operations, and adjusting the format of the answers.

Abstract: The present invention relates to a teaching resource for studying mathematics, and more specifically relates to a teaching resource for studying mathematics having the effect of learning by repetition, wherein the teaching resource comprises: a cardinal-number sheet constituted by repeatedly laying out a plurality of unit numbers on a layer of cardboard; and number-display inducing sheets each of which has at least one transparent window and is placed over the cardinal-number sheet so as to induce pre-determined study; being constituted in such a way that a plurality of the unit numbers laid out on the cardinal-number sheet are ex-posed in a limited fashion through the transparent windows of the number-display including sheets, such that children engaged in such study calculate problems by themselves following the basic rules of calculation, and, more particularly, such that said children can continuously and repeatedly study numerical problems of the same type while moving the transparent windows of the numb

Abstract: A learning support device includes a storage unit, first display control unit, detecting unit and second display control unit. The storage unit stores identifying items to identify the type of a word problem which are detectable in the text of the word problem, and stores at least one relation between variables in the identified-type word problem, for each type of the word problem. The first display control unit displays the word problem requiring calculation of an unknown variable from known variables in the text. The detecting unit detects each identifying item in the text of the displayed word problem. The second display control unit reads out a relation about the unknown variable among the relation(s) for the identified-type word problem, and displays the read-out relation as a corresponding relation.

Abstract: A computer-based abacus training system is provided. The system can include a simulated abacus display, means for outputting problems to be solved by a user, means for accepting input from the user, and means for checking the user's solution. Display can be of a simulated abacus, simulated hand movements, or both. Conversion between text-form and abacus-form representations can be included.

Abstract: A manikin for practicing resuscitation, comprising an inflatable body (1). The inflatable body (1) is adapted to absorb compression force exerted during simulated chest compression. Preferably, the manikin also comprises a chest plate (4), the chest plate (4) acting as a pressure distributor on the inflatable body (1). The chest plate (4) being connected to the inflatable body (1) by elastic means (22). The manikin may also comprise a lung part (2), the lung part being connected to a face mask (3). The lung (2) being adapted for inflation through the mouth and/or the nose of the face mask (3). The lung (2) having a chest portion (13) positioned substantially parallel to the chest portion (5) of the inflatable body (1). The face mask (3) being positioned at a head portion (7) of the inflatable body (1).

Abstract: A mathematical teaching aid based on a grid system. There are multiple grid based modules meant to teach math concepts from preK thru college level math. There are modules for teaching how to count, addition, subtraction, multiplication, division, and fraction manipulation (addition, subtraction, multiplication, division, equivalencies and LCD.) The system provides a physical, and visual model of math and lends itself to self-discovery/self-assistance by the student. The system is attractive to the student because coloring by the student is a part of the learning process, so the student is having fun while learning. This system exceeds the criteria for an ideal math model. These criteria are discussed in the definitive article (Murata, Aki (2008) ‘Mathematics Teaching and Learning as a Mediating Process: The Case of Tape Diagrams’, Mathematical Thinking and Learning, 10:4, 374-406.) This system is easy to use, inexpensive, and puts the student on math learning auto-pilot.

Abstract: A mathematics game for playing by a plurality of players using different types of dice, including a first set with predetermined numeric values provided thereon; a second set with “+” or “?” symbols provided thereon (representing positive or negative); and a third set with different mathematical function symbols provided on the respective faces. The game includes a score card provided for each player. The score card includes a region for entering number values corresponding to a throw of the first type of dice; a region for entering “+”/“?” values corresponding to a throw of the second type of dice; a region for entering mathematical functions corresponding to a throw of the third type of dice; a region for entering a mathematical equation based on information in the above regions; and a region for entering a cumulative score of the respective player.

Abstract: A mathematical teaching apparatus includes a base ten platform formed with a planar array of ten receiving elements being substantially equal in size and arranged in a pattern, and ten counting tiles being substantially equal in size and shape. Each of the ten receiving elements is adapted to removably receive one of the ten counting tiles to arrange the ten counting tiles in the pattern of the ten receiving elements, and a base ten cover is adapted to be removably received upon the ten counting tiles received by the respective ten first receiving elements so as to cover the ten counting tiles.

Abstract: An apparatus and method of manipulating numeric panels according to an evaluation of a division operation using a division token is provided. At step (1) of the method, a method participant uses a mathematical operator token to randomly select a mathematical operator from a plurality of mathematical operators one of which being a division operator. At step (2) of the method, upon the selected mathematical operator comprising the division operator, the method participant randomly selects a division operation from a plurality of predefined division operations using a division token and evaluating the selected division operation, the division token comprising a plurality of division indicia each associated with one of the predefined division operations, each of the division operations evaluating solely to an integer quotient. At step (3) of the method, the method participant manipulates a subset of available panels from an array of numeric panels.

Abstract: An activity device including an activity sensor for generating an activity interaction signal responsive to a sustained large-muscle physical activity of a user operating the activity device; a controller, coupled to the activity monitor, generating a virtual environment supporting a virtual user frame-of-reference in the virtual environment, the controller generating a set of virtual education elements in the environment and a goal for the set virtual representation with respect to the virtual education elements wherein the controller is responsive to the activity interaction signal to produce an affected interaction of the virtual representation with the virtual education elements with the controller measuring a conformation of the goal by the affected interaction; and a feedback system, coupled to the controller, for presenting the virtual environment with the frame-of-reference in relation to the virtual education elements for providing the user with feedback.

Abstract: A method of teaching basic arithmetical calculations is embodied in a novelty electronic graphic calculating device having a user interface for displaying method steps. The method involves displaying two or more collections of individual icons associated with two or more operands; selecting an arithmetical operation to be performed on the two or more operands; regrouping the individual icons into a collection of individual icons associated with an answer to the operation on the operands; and, displaying the collection of individual icons associated with the answer in sets having a maximum of ten icons each. The method permits visual regrouping and carry-over for teaching and learning mental computation of the four basic arithmetic skills of addition, subtraction, multiplication and division.

Abstract: A multiplication and division puzzle and method of making thereof include a main table having a plurality of cells in rows and columns, the cells being filled with products and multipliers. A template having a plurality of cells that correspond to the plurality of cells in the main table has selected cells removed to form openings therein to reveal a set of product clues in the main table when the template is superimposed or laid thereon. The product clues include the products in the cells of the main table. The non-selected cells that remain in the template, concealing the multiplier answer and non-selected product answers in the main table. The main table and template are used to form a puzzle blank having a plurality of cells containing the set of product clues and empty cells for the user to fill in missing product answers. The main table contains all of the product and multiplier answers.

Abstract: A method for instructing mathematics includes providing a work surface to a visually impaired student; providing a plurality of movable elements for use in connection with the work surface, each of the movable elements comprising on a front surface thereof at least a portion of a visible mathematical symbol readable via eyesight, each of the movable elements further comprising Braille indicia on the front surface thereof corresponding to the at least a portion of the visible mathematical symbol, each of the moveable elements being movable to any position on the work surface; and having the student arrange a plurality of the moveable element on the work surface to form a standard mathematical expression wherein the mathematical expression comprises multiple lines set forth in a vertical arrangement.

Abstract: A computer-based educational system provides the user or instructor with a suite of graphic editing tools, allowing the design of graphical objects, such as symbols and text that can be displayed to a viewer, such as a student, using a projector or computer terminal. In order to facilitate the educational process, the invention provides the user with robust ability to control parameters of the graphical objects, allowing the user to create simulations or models of subject matter, such as mathematical principles, in order to facilitate the educational process. In the preferred embodiment, the parameters of these graphical objects can actually be defined in terms of variables and specifically functions or expressions including those variables and then the values of the variables controlled in real-time by the user. This ability allows the user to control the execution of the simulations or models, enabling the user or instructor to dovetail the execution of those simulations with the instructional process.

Abstract: An activity device including an activity sensor generating an activity interaction signal responsive to a sustained large-muscle physical activity of a user operating the activity device; a controller, coupled to the activity monitor, generating a virtual environment supporting a virtual user frame-of-reference in the virtual environment, the controller generating a set of virtual education elements in the environment and a goal for the set virtual representation with respect to the virtual education elements wherein the controller is responsive to the activity interaction signal to produce an affected interaction of the virtual representation with the virtual education elements with the controller measuring a conformation of the goal by the affected interaction; and a feedback system, coupled to the controller, presenting the virtual environment with the frame-of-reference in relation to the virtual education elements providing the user with feedback regarding the goal and the conformation of the goal by the

Abstract: A kit for a mathematical equation and concept learning game based upon traditional Bingo. The kit includes a plurality of boards, each with a 5 by 5 matrix of squares filled with equations in each block of the matrix. A row above the matrix of squares includes the letters S, P, I, N and T above each respective column. Further included is a wheel divided into 100 segments, the first twenty segments marked as S1 through S20, the second twenty segments marked as P21 through P40, the third twenty segments marked as I41 through I60, the fourth twenty segments marked as N61 through N80 and finally the fifth twenty segments marked as T81 through T100. A method is provided to play the game by which the wheel is spun and a letter/number combination is called. Players cover squares of their matrix if the number called is an answer to a labeled equation in the called number and column. The first player to fill five squares horizontally, vertically or diagonally calls out “Spin-It” and wins the game.

Abstract: An apparatus includes a plurality of hand manipulative objects including containers with exteriors having substantially identical textures and colors. Each of the hand manipulative objects has a different weight equivalent to an integer multiple of a first weight. Contents of the containers substantially determine the weights. The weights include a consecutive series of weights including increments of one first weight. A user, manipulating the hand manipulative objects, can discern between different hand manipulative objects, thus enabling the user to convert feeling the weights into a representation of numbers and mathematical relationships.

Abstract: A computer-based abacus training system is provided. The system can include a simulated abacus display, means for outputting problems to be solved by a user, means for accepting input from the user, and means for checking the user's solution. Display can be of a simulated abacus, simulated hand movements, or both. Conversion between text-form and abacus-form representations can be included.

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: An educational tool for teaching a user, the tool including at least one first member having a plurality of different visual cues, at least one second member associated with the at least one first member, the at least one second member having a plurality of indicia, each indicia corresponding to at least one visual cue on the at least one first member, wherein indicia of the at least one second member are used in increasing levels of difficulty, to trigger the user to associate and identify indicia on the at least one second member with a corresponding visual cue on the at least one first member.

Abstract: The invention provides a method and apparatus for operations of addition, subtraction, multiplication, and division of fractions, decimals, percents, proportions and equations. It allows the students to find the transparent area models on their sheets with the correct parts shaded, (2) students can count the total number of parts and the total number of shaded parts in each model, (3) the relationship of the shaded parts to the total number in each model can be named, (4) by intersecting the vertical transparent area model for one whole with horizontal transparent area models for one whole to show examples of one whole being renamed several different ways.

Abstract: An educational device is provided which can be used to teach arithmetic. The educational device comprises a track having a scale on an outer surface of said track. The scale is comprised of a plurality of evenly spaced apart unit markings, the markings being spaced apart by a unit length. Blocks are provided which are slidingly received on the track. Each block has a length based on the unit length, and indicium is provided on the each block to identify the length of the block in unit lengths. When a set of blocks is positioned on the track, the end of the last block will line up with a unit marking on the scale representing the overall length of the set of blocks in “units”, and hence showing the sum of the lengths of the set of blocks placed on the track. By adding and removing blocks to the track, addition and subtraction “facts” can be visually taught.

Abstract: Arithmetic Measurement System quantifies arithmetic operations just by measurement and without arithmetic calculation or even counting. Playing cards may be annotated with size-coded marks or card tags to represent face value. For example, a tag representing a face value 5 is half the size of one representing a value 10 using a linear tag scale, or about 7/10th the size using a log10 tag scale. Users align linear tags in a contiguous row to add values or overlap tags to subtract values. Users align logarithmic tags in a row to multiply values or overlap tags to divide values. Integrated and separate measures with corresponding linear or logarithmic tag-scales quantify a total value of aggregate or net tag row size. Product developers may use the Arithmetic Measurement System of tags and measures to provide novel educational math manipulatives and playing card games for players unskilled in arithmetic.

Abstract: An apparatus for educating children includes a first symbol for application to a first article of clothing and a second symbol for application to a second article of clothing. The first article of clothing is worn by a user at a same time as the second article of clothing and the first article of clothing and the second article of clothing are both part of a clothing set. The second symbol is non-identical to the first symbol and the first symbol corresponds to and matches the second symbol based on a relationship of an educational topic.

Abstract: A method of educating includes providing a collectible trading card game with a plurality of trading cards. Each card may contain educational information including a consonant, vowel, number or mathematical operator and the cards are used to form a properly spelled word or to form a mathematically correct equation. In some forms, the method includes providing a game with a playing field and a set of game components with game component types having a predetermined power for affecting play of the game by affecting a power, effect, or value of the game component. The level of skill necessary to play the game may be varied by selectively implementing or disregarding the predetermined power of the game components. An educational game includes first and second game components with different expressions, powers, point values, and identifiers for distinguishing game components and facilitating game play.

Abstract: A method of counting in multiples uses an educational device comprising a base and a set of ten markers positioned on the base spaced apart from one another along a generally annular path. Each marker is associated with a respective one of a range of numbers 0 through 9 in a sequence about the annular path of the device. Elastic bands or some other visually indicating links are used to visually associate the marker having the number 0 associated therewith another one of the markers having the number associated therewith corresponding to the final digit of the next number in the sequence of numbers. Other numbers of the sequence when counting in multiples can similarly be visually indicated with links so that following the links indicates the final digit of each number in the sequence when counting in multiples.

Abstract: An application teaches a student elementary mathematics. A specific embodiment contains 4 modules: 1. Tutorial and Practice; 2. Homework Helper; 3. Test Simulation; 4.Parental Control. Specific embodiments of the 1st and 2nd Modules have a Help feature. The questions in the tutorial and Practice module are automatically and randomly generated by the software without repetition and according to the chapter the student has selected and other parameters (such as might be set by a parent under the Parental Control module). In specific embodiments, the chapters a student may select from include Addition, Subtraction, Multiplication and Division. A score sheet is generated for each session.

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 music and math teaching system teaches fraction computations utilizing musical note names and note values in the form of blocks with varying lengths while simultaneously teaching rhythmic topics of time signatures, beats, and tempo. A rhythm board is used to mount note blocks and beat blocks in the process and a blind is used to block the vision of a student working with the blocks.

Abstract: The systems and methods of the invention are directed to portfolio optimization and related techniques. For example, the invention provides a method for multi-objective portfolio optimization for use in investment decisions based on competing objectives and a plurality of constraints constituting a portfolio problem, the method comprising: generating an initial population of solutions of portfolio allocations; performing a first multi-objective process, based on the initial population and the competing objectives, to generate a first interim efficient frontier; performing a second multi-objective process, based on the initial population and the competing objectives, to generate a second interim efficient frontier; and fusing the first interim efficient frontier with the second interim efficient frontier to create an augmented efficient frontier for use in investment decisioning.

Abstract: A method for teaching mathematics that includes presenting one or more mnemonic tools that are non-arbitrarily associated with a module or “chunk” of information that covers a particular mathematics concept.

Abstract: A device for instructing mathematics includes a work surface and a plurality of movable elements. Each of the movable elements includes, on a front surface thereof, at least a portion of a visible mathematical symbol (including numeric and nonnumeric symbols) thereon readable via eyesight. Each of the movable elements further includes an attachment member on a rearward surface to attach the element to the work surface. The attachment member preferably allows the element to be removed from the work surface and to be slidably positionable to any position on the work surface once attached thereto. The device can further include a frame around the work surface. Preferably, the frame defines a boundary for positioning of the movable elements. In one embodiment, magnetic attraction is used to maintain the attachment member in movable connection with the board.

Abstract: A reversible arithmetic teaching device. In one embodiment, the device comprises a receptacle having on both sides a horizontal row of numbers with a corresponding arithmetic function below which is a window through which a reference number and arithmetically corresponding answers are visible. A slidable card is inserted in the receptacle. The card has on its first side a vertical column of numbers and an array of rows of comprising corresponding numerical answers. One number at a time on each vertical column is displayed through the window. Indicating means permit the indication of a selected arithmetic relationship between any one number in the column of numbers located at one end of the slidable card and any one of the horizontal row of numbers on the receptacle such that, upon applying the arithmetic designation with respect to the two cooperating numbers, a corresponding answer is displayed through the window.

Abstract: The educational math toy includes various embodiments, each having a triangular configuration. The toy is based upon the concept that two numerical factors will always provide a solution when manipulated by a mathematical operation, with the two factors being shown at two corners and the solution being shown at the third corner of the triangle. One series of embodiments includes variations on a mechanical device containing a central idler gear and a series of three outer gears arranged in a triangular array in a housing. The gears, or interchangeable display discs used therewith, rotate in registry, with each displaying one of a series of numbers through corresponding windows in one or both faces of the housing. The monolithic tiles are arranged in the same manner, but display only one fixed set of factors and one solution on each face. Braille may be used in lieu of numbers, if so desired.

Abstract: Hundreds board device comprising a first member having thereon a series of consecutive natural numbers arranged in a ten by ten number array consecutively numbered from one through one hundred; a second member superimposed on the first member and including an array of windows registering with the numbers such that each of the windows has one of the numbers displayed therethrough; a first array of first colored transparent window slider covers horizontally slideably engaged relative to the first and second members for individually opening and closing each of the windows and a second array of second colored transparent window slider covers vertically slideably engaged relative to the first and second members for individually opening and closing each of the windows such that only one of the two colored transparent window slider covers is used at any one time to close any one window for teaching basic mathematical calculations and concepts.

Abstract: An arithmetical manipulative device comprises a plurality of tiles, each tile having an upper surface, a lower surface, a first end and a second end, and a connector member for connecting the first end of one tile to the second end of a neighboring tile. The connector member is configured such that the one tile and the neighboring tile are pivotable relative to each other between a position wherein the upper surface of the one tile lies substantially adjacent the upper surface of the neighboring tile and the lower surface of the one tile lies substantially adjacent the lower surface of the neighboring tile. Further, the connector member is releasably connected to at least the one tile or the neighboring tile to permit a selected number of tiles to be serially assembled with respect to each other. The invention is also for a method for making arithmetical calculations.

Abstract: Methods and systems for providing a solution to a given problem comprising the steps of receiving a request for a solution to a known problem, accessing a first set of data comprising a plurality of template solutions to problems, accessing a second set of data comprising a plurality of problem variable value sets, interfacing the first set of data and the second set of data for generating a solution to the problem, and transmitting the solution over a computer network.

Abstract: A device for instructing mathematics includes a work surface and a plurality of movable elements. Each of the movable elements includes, on a front surface thereof, at least a portion of a visible mathematical symbol (including numeric and nonnumeric symbols) thereon readable via eyesight. Each of the movable elements further includes an attachment member on a rearward surface to attach the element to the work surface. The attachment member preferably allows the element to be removed from the work surface and to be slidably positionable to any position on the work surface once attached thereto. The device can further include a frame around the work surface. Preferably, the frame defines a boundary for positioning of the movable elements. In one embodiment, magnetic attraction is used to maintain the attachment member in movable connection with the board.

Abstract: A system and method for teaching basic mathematical operations and facts; and more particularly it is an apparatus for development of accurate conceptual models for small children in learning certain math facts for the first time. The present invention takes into account that a true conceptual model must consistently and accurately reflect the target system and consider the characteristics of the children learners. In this invention, every digit of any number gets a familiar yet consistent name; that name can be weaved into story and rhyme throughout the learning process in both the math questions and in the math answers. The consistent “name for a digit” advancement over the prior art is better because it creates a conceptual model to which children can indeed relate. Digit consistency throughout the system, series, or television program, helps teachers create relevant meaningful application activities or associative modus operandi.

Abstract: There is shown card game apparatus and method of play for use in educating children in basic mathematical concepts, the apparatus including a six-sided mathematical function indicator, such as a die, used in combination with two sets of cards, the function generator containing notation on a side indicating a different arithmetic operation such as addition, subtraction, multiplication and division, and on a fifth and sixth side game playing instructions. The first set of cards, some dealt to the players, include selected sets of cards each set numbered 1-10. The second set of cards consists of ten cards numbered 1-10 that are stacked to provide unit numbers used in the mathematical process indicated by the function indicator. In playing the game a player determines a problem to be solved by combining a card from the first and second sets and the mathematical function to be utilized, and then uses cards from his hand to demonstrate solution of the problem, the object of the game to rid ones hand of all cards.