Abstract: The present invention relates to a method of extracting regularity for an arbitrary number sequence and a device using the same, and especially provides a method and a device for finding regularity for an arbitrary number sequence using objects and computing the number that appears after a certain amount of time or times.

Abstract: Methods and apparatuses for displaying information relating to a roulette game. A roulette game display comprises at least one of a hot bet field, a number frequency field, and an even-money bet road chart. The hot bet field displays a message including information relating to a highest ranking event stored in an event history. The number frequency field includes an arrangement of indicator spaces configured for marking to show recent results of a plurality of roulette wheel spins. The even-money bet road chart includes a grid for displaying a plurality of recently winning even-money bets.

Abstract: A manipulative for modeling quantitative concepts, said manipulative comprising a flat, marking surface, said marking surface having a linear track with a defined start and end point representing a quantity to be measured therebetween, and a plurality of loose articles which can be placed upon the track representing segments of said quantity to be measured.

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: A hand held device (10) for measuring automatically the Hormonal Quotient and correlated hormonal status of an individual, providing a measure of index finger for ring finger. The device (10) includes a base (30) upon which a concentrically arranged disc (40) is rotatable mounted by a central fastener (11). The base (30) carries a ruler face (32), a first finger-length logarithm scale (36), a Hormonal Quotient logarithm scale (38) and an arrow indicator of the gonadal hormone exposure index (39). The disc (40) carries a second finger-length logarithm scale (42) and the Hormonal Quotient arrow (44). When scales (42) and (36) are properly aligned the Hormonal Quotient arrow (44) inserts automatically into the resulting Hormonal Quotient in the Hormonal Quotient scale (38) and the correlated gonadal hormone exposure (39).

Abstract: A method and device for teaching mathematics comprises a plurality of elongated members used to teach mathematics concepts. Each of the plurality of elongated members represent an associated numerical value. At least some of the plurality of elongated members are of different lengths, wherein the length of each of the plurality of elongated members is proportional to the numerical value represented by the elongated member. A plurality of retention members configured to receive the elongated members. Each of the plurality of retention members is configured to receive at least two of the plurality of elongated members. The device also comprises a numberline associated with the plurality of retention members. When the elongated members are placed on the retention member, various mathematical concepts may be shown.

Abstract: A device and method for teaching, solving, and/or illustrating mathematical principles and equations is disclosed. The device comprises a set of increasing numerical values arrayed on a spectrum, each numerical value represented by a length, each length comprising a visual marker representative of the numerical value; wherein the visual marker is repeatedly displayed on the spectrum in a pattern corresponding to or at intervals in accordance with the visual marker's numerical value. Alternatively, the device may comprise a set of increasing numerical values on a spectrum, each numerical value represented by a length, each length comprising distinct visual markers representative of mathematical factors of the numerical value.

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: A method and device for teaching mathematics comprises a plurality of elongated members used to teach mathematics concepts. Each of the plurality of elongated members represent an associated numerical value. At least some of the plurality of elongated members are of different lengths, wherein the length of each of the plurality of elongated members is proportional to the numerical value represented by the elongated member. A plurality of retention members configured to receive the elongated members. Each of the plurality of retention members is configured to receive at least two of the plurality of elongated members. The device also comprises a numberline associated with the plurality of retention members. When the elongated members are placed on the retention member, various mathematical concepts may be shown.

Abstract: The present invention generally relates to a set of blocks and casings that have various features which provide multi-sensory (e.g., visual, auditory, kinesthetic and tactile) input to the user so as to aid the user in learning mathematics, reading, phonetics, matching and other basic skills. Each block includes a number projections on a first face which are equal in number to recesses on second face. The number of recesses or projections on a particular face block signifies to the user a digit corresponding to that block. Additionally, each block is assigned a color which phonetically cues the user to the number corresponding to the block. Similarly, a casing corresponding in size, shape and color is provided for each block. The casings serve similar functions as the blocks. Preferably, both the casings and the blocks have a textured surface to provide tactile input to the user, thereby encouraging the user to use the blocks and take advantage of its multi-sensory features.

Abstract: A mathematics education apparatus comprises a base array. The base array includes a plurality of rows, with each row having ten receiving positions. The mathematics education device further comprises a plurality of number pieces that each correspond to a number, including at least one number piece corresponding to numbers one through ten. Each number piece has a linear length that is proportional to the number corresponding to that number piece. Additionally, each number piece is configured to cover a quantity of receiving positions on the base array equal to the number corresponding to that number piece.

Abstract: The present invention relates to a math manipulative educational learning game in which a plurality of rods are provided for use in various manipulative games designed to teach rudimentary arithmetic skills. In the preferred embodiment, the rods are of various lengths and/or volumes, with the shortest length comprising a unit length, and other rods being formed in integral multiples of the unit length. Various games are disclosed in which a child is encouraged to manipulate the rods in various ways and in order to learn various arithmetic lessons. For example, in one game a Game Master selects any of the rods except the rod having unit length and places it upon a game playing surface. Thereafter, the Partner must select a plurality of rods whose combined lengths equal the length of the rod played by the Game Master. These rods are laid end-to-end along side the rod played by the Game Master in order to demonstrate their length equality.

Abstract: The present invention provides a measuring device for teaching incremental measurements to a user of the measuring device. The measuring device comprises a fastener and a plurality of rulers containing graduated markings and rotatably attached to the fastener. Each ruler is positioned to horizontally align and vertically juxtaposed the graduated markings of consecutive rulers. In a preferred embodiment, the sets of graduated markings vary in numerical increment from other sets of graduated markings. Also each ruler varies in color from the other rulers of the measuring device.

Abstract: A kit containing an Instructor unit sized for presentation to a group and multiple Child training units both set up to allow students to visually model and relate addition, subtraction, multiplication, and division in primary mathematics. The manipulative units include a plurality of colored cubes arranged in slots so that the movement of particular cubes from one side of the slots to the other side represents numbers in a mathematical operation. Tally trays of five slots may be removed from the device and hold up to 10 cubes to demonstrate regrouping operations on a mat.

Abstract: A teach-aiding weight set includes a white, a red, a light green, a purple, a yellow, a green, a black, a brown, a blue, and an orange weight. Each of the weights is provided with spaced shallow grooves to show a plurality of equal sections corresponding to a specific weight thereof. The specific color, weight, and shallow-groove-divided sections of each of the weights help small children to learn primary mathematical concepts, particularly the concept of weight.

Abstract: A teaching aid is disclosed herein that includes at least one gallon model, four quart models, two pint models, and two cup models. The appropriate measurement is attached to each model, thus showing a student how many of each measurement are in each model. A method for teaching students is also disclosed herein, using the teaching aid and the associated models.

Abstract: The present invention relates to a math manipulative educational learning game in which a plurality of rods are provided for use in various manipulative games designed to teach rudimentary arithmetic skills. In the preferred embodiment, the rods are of various lengths and/or volumes, with the shortest length comprising a unit length, and other rods being formed in integral multiples of the unit length. Various games are disclosed in which a child is encouraged to manipulate the rods in various ways and in order to learn various arithmetic lessons. For example, in one game a Game Master selects any of the rods except the rod having unit length and places it upon a game playing surface. Thereafter, the Partner must select a plurality of rods whose combined lengths equal the length of the rod played by the Game Master. These rods are laid end-to-end along side the rod played by the Game Master in order to demonstrate their length equality.

Abstract: A kit containing an Instructor unit sized for presentation to a group and multiple Child training units both set up to allow students to visually model and relate addition, subtraction, multiplication, and division in prinmry mathematics.

Abstract: A concrete manipulative for teaching the properties of odd and even numbers. The manipulative includes an elongated channel having end walls at each end, and a plurality of rods that fit at least partially within the channel. The rods are in two sets of different lengths, with each length being represented by more than one rod. Rods of even length are visually and/or tactilely distinguishable as a set from rods of odd length. The elongated channel displays markings at precise intervals, with the spacing between markings generally being twice the length of the shortest rod. Through a variety of activities involving placement and manipulation of various combinations of the rods within the channel, students are able to identify properties of odd and even numbers.

Abstract: A set of blocks used as an aid for teaching mathematical concepts, in which blocks of different sizes are provided with characteristic dimensions that bear a relationship to preselected numbers in the Fibonacci series. The Fibonacci series is defined as an infinite sequence of numbers starting with 1 that builds by adding the present number to the prior number to form the next number in the series. The first part of the series progresses: 1, 1, 2, 3, 5, 8. 13, 21, 34, 55, . . . , with 0 being understood as the number prior to 1. The series is related to the Golden Ratio of approximately 1:1.618, a ratio found in nature and in certain works of art, by the ratio of adjacent numbers, after thirteen, in the series. The blocks can be used to teach students mathematical concepts such as pattern recognition, the Fibonacci series and related Golden Ratio, and the interrelations between mathematics and other disciplines such as biology, botany, and architecture.

Abstract: A measuring and instructional device containing a base panel having a top surface and perimeter bounded by at least one edge, with the top surface having evenly spaced apart linear rulings perpendicularly disposed to the edge and defining a non-linear standard unit of measure; and a top transparent sheet having a top surface and a perimeter bounded by at least one edge, wherein the top transparent sheet top surface has evenly spaced apart linear rulings perpendicularly disposed to the long edge of the top transparent sheet and defining fractional increments of the non-linear standard unit of measure; wherein the transparent sheet is positionable over the base panel so that the fractional increments of the unit of measure may be aligned with the units of measure to demonstrate the relationship between the unit of measure and the fractional increments thereof.

Abstract: A mathematical teaching apparatus comprising block elements that fit inside a block element container. The block element container will not close until the proper number of block elements are inserted. For teaching counting and addition concepts for a number base, such as base ten, a user will quickly grasp the concepts of grouping an arbitrary number of block elements into units, such as ones, tens and hundreds. A container for holding block element containers is also provided. The block elements and containers have the same shape, and maintain a proportional ratio with each other. All block elements and containers are counted and grouped using counting devices which provide an indication of the number of units of each type present. The counting devices also signal when ten block elements or ten block element containers are inserted, signaling to a user that the block elements or containers should be inserted into a next-larger size container.

Abstract: The present invention is an apparatus and method of educating the fundamentals of numbers and/or mathematics. The apparatus is designed to replicate mathematical problems appearing on books and other media and includes a base having a front surface. This front surface includes a plurality of recesses, oriented in a column fashion. Each column represents the one's, ten's, and hundred's. The recesses receive numerical plates which are sized according to the specific column. An operator recess for receiving an operator plate is also provided to enable mathematical process to be performed by a user.

Abstract: A mathematical teaching apparatus comprising block elements that fit inside a block element container. The block element container will not close until the proper number of block elements are inserted. For teaching counting and addition concepts for a number base, such as base ten, a user will quickly grasp the concepts of grouping an arbitrary number of block elements into units, such as ones, tens and hundreds. A container for holding block element containers is also provided. The block elements and containers have the same shape, and maintain a proportional ratio with each other. All block elements and containers are counted and grouped using a counting devices which provide an indication of the number of units of each type present. The counting devices also signal when ten block elements or ten block element containers are inserted, signaling to a user that the block elements or containers should be inserted into a next-larger size container.

Abstract: A measuring and instructional ruler device is provided for use by children and persons during the instruction of linear measurement, and for use in the measuring and drawing of objects. The device is comprised of a base panel having a top surface having standard units of measure delineated thereon, and at least one transparent sheet having fractional increments of the same standard unit of measure delineated thereon, wherein the transparent sheet is positionable over the base panel so that the delineated fractional increments of the standard unit of measure may be aligned with the delineated standard units of measure to demonstrate the relationship between the unit of measure and the fractional increments thereof.

Abstract: A factor blocks kit having a plurality of cubic, rectangular and triangular prisms and rectangular mats. These prisms have edges (sides) that measure either 1 unit or a 1-digit prime number of units in length. These prisms are scored with unit markings on some of their sides. The bases of the triangular prisms form a 3-4-5 unit right triangle. The kit also includes a number of rectangular mats with sides being a one digit number of units in length. The mats are divided into unit squares. The kit includes teachers guides and student work books in both print and electronic form on the World Wide Web or the Internet.

Abstract: An apparatus and method for teaching mathematical expressions includes a plurality of four-sided members that represent the variables of factors of a mathematical expression. Each four-sided member has a different area representing a different variable in the mathematical expression. The apparatus enables a math student to visualize the rules that apply to mathematical expressions. The four-sided members include a first side having a first color and a second side having a second color, different from the first color, wherein the first side represents a positive number, and the second side represents a negative number. Alternatively, the sign may be distinguished by varying surface roughness of the members. The four-sided members can be used for teaching by illustration simple multiplication and division, multiplication, division and factorization of polynomials, linear equations including inequations and absolute value, and systems of linear equations.

Abstract: A mathematical teaching apparatus comprising block elements having a front and back side, including indentations and protrusions to allow the blocks elements to stack. The block elements are inserted into a block element sleeve, which hold 10 stacked block elements. Block element sleeves are also stacked and inserted into a large sleeve, which holds 10 stacked block element sleeves. Block element sleeves also include indentations and protrusion to allow stacking. All three units are counted by counting devices which provide an indication of the number of units of each type present. The counting devices also signal when 10 block elements or 10 block element sleeves are inserted, signalling to a user that the blocks or sleeves should be inserted into a next-larger size sleeve. The mathematical teaching apparatus allows children to learn the concepts of number magnitude, addition and subtraction, including carrying and borrowing.

Abstract: The present invention relates to a multi-functional game and learning device. More particularly, the present invention relates to a multi-functional game and learning device which can be used as a general wood block stacking toy designed to educate and instill simple arithmetic concepts even as games are being played, as well as to construct various toy figures and building structures. Thus, this multi-functional game learning device is both a toy and a learning tool.

Abstract: An apparatus and a method for playing a math-teaching board game which enables a player student while manipulating game-pieces to gain an understanding of the concept of fractions and arithmetical operations associated therewith. The game is played by 2 to 4 players. The game includes a pyramidical-shaped board having a continuous path of steps, individual game tokens, a die, a plurality of decks of question cards for respective arithmetic operators, fraction boards and a slide box for placement of the fraction boards thereon. In playing the game, the player skillfully moves a selective game token up a number of steps based on the roll of the die. Each step on the board displays an arithmetical operator which determines which deck of question cards is selected. The player uses the fraction boards and the slide board in an attempt to visually determine the answer to a selected question. If the player answers the question correctly, the player remains on the step advanced by the die roll.

Abstract: An apparatus and method for teaching mathematical expressions includes a plurality of four-sided members that represent the variables of factors of a mathematical expression. Each four-sided member has a different area representing a different variable in the mathematical expression. The apparatus enables a math student to visualize the rules that apply to mathematical expressions. The four-sided members include a first side having a first color and a second side having a second color, different from the first color, wherein the first side represents a positive number, and the second side represents a negative number. The four-sided members can be used for teaching by illustration simple multiplication and division, multiplication, division and factorization of polynomials, linear equations including inequations and absolute value, and systems of linear equations.

Abstract: A didactic-educational toy for elementary arithmetic operations includes a plurality of transparent plates. Each of the transparent plates has ten circular orifices. The orifices are distributed symmetrically in two rows. Each row has five of the orifices. Each of the orifices has substantially the same diameter. A plurality of plates each has cylindrical stepped protuberances. Each of the protuberances has a base with a diameter corresponding to a diameter of the orifices of the transparent plates to provide for close-fitting insertion of the base into a corresponding one of the orifices. Each of the protuberances has an upper portion having a diameter smaller than the diameter of its base to facilitate the insertion of the protuberance into a corresponding orifice. The plurality of plates, which have cylindrical stepped protuberances include plates has a different number of protuberances. The surface area of each plate is substantially proportional to the number of protuberances.

Abstract: An assembly for teaching mathematical concepts includes a plurality of interlocking components, each having at least one connecting end so that the components can be combined in any order or length. Each component is assigned a mathematical value according to its length, and this value may be indicated by indicia on its face or by color coding. A base is also provided for retaining the columns of components in vertical formations. Means are provided on the platform of the base for engaging the bottom component in each column.

Abstract: A teaching aid for teaching young children counting in the tens numbering systems, in which four side by side stacks of nine blocks are each slidable on respective rods held in a frame, each of the nine blocks having one face of each block in the stack imprinted in order with a cardinal number, the blocks in the second, third, and fourth stacks also marked respectively with one, two, and three zeros to the left of the cardinal number appearing thereon. Each of the cardinal numbers on the blocks in each stack are in distinct colors, the zeros color matched to the color of the cardinal number of the corresponding place on the adjacent stack. The blocks in each stack are progressively sized wider to the left in proportion to the number of number and zero digits imprinted thereon.

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: A visual teaching aid adapted for the versatile teaching of various mathematical relationships, incremental scales, and other sequential and educational concepts. The teaching aid includes an elongated board, a plurality of elongated insert cards each being interchangeably mountable on the board and having numerical indicia on a face thereof, and at least two pointers that are supported for movement along the board for pointing selected indicia on the insert card and for movement relative to each other. The insert cards are removably mountable on the board without removal and replacement of auxiliary fastening means and can be used in conjunction with relatively small sized base or whole number insert cards to assist in drills of mathematical relationships.

Abstract: A mathematical and spatial toy apparatus is arranged to include a grooved rack board arranged to receive individual block components to teach children the mathematical cumulative effect of such boards to provide rudimentary teaching in mathematical and spatial relationships.

Abstract: Base-ten blocks for teaching arithmetic to children, in which each block (19) has a projecting boss (27) with curved (bowed-out) sides (29) and an aperture (33) with straight sides (35), so that blocks (19) can be securely joined together to form multiples of units. Integrally made rows (37) of ten blocks each have two end bosses (41) for joining to other rows (37) to make flats (47) of one hundred units. Each flat has four bosses (51) for joining to other flats (47) to make a cube of one thousand units. The blocks have one color for units, a different color for rows of tens, a different color for flats of one hundred, and a still different color for cubes of one thousand. The blocks can be used to teach addition, multiplication, subtraction, division, etc., to children.

Abstract: Base-ten blocks for teaching arithmetic to children, in which each block (19) has a projecting boss (27) with curved (bowed-out) sides (29) and an aperture (33) with straight sides (35), so that blocks (19) can be securely joined together to form multiples of units. A row of integral blocks (37) has common wall thicknesses (42) between adjacent blocks equal to twice the thickness of the end wall (45) of the row so that the row can be correctly mated with a row of single blocks or end-to-end rows of shorter blocks. Integral rows (37) of ten blocks each have two end bosses (41) for joining to other rows (37) to make flats (47) of one hundred units. Each flat has four bosses (51) for joining to other flats (47) to make a cube of one thousand units. The blocks have one color for units, a different color for rows of tens, a different color for flats of one hundred, and a still different color for cubes of one thousand. The blocks can be used to teach addition, multiplication, subtraction, division, etc.

Abstract: A toy includes a casing having a number of holes formed in an upper surface. A board which has a number of symbols printed on an upper surface is insertable into the bottom of the casing. A number of blocks, each can be inserted into a hole. An opening is formed in each of the blocks. A tongue is formed on each of the blocks and is engageable within the opening of another block so that the blocks can be assembled together. A numeral is printed on each of the tongues. Children can select and insert a block into a hole which has a numeral identical to that of the block so that the toy can also be used as a teaching aid.

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: A fractal mathematics learning kit includes a plurality of boards each in the shape of an equilateral triangle having defined thereon a pattern of ten smaller equilateral triangles, and a plurality of manipulative elements made of one or more connected equilateral triangles which are attached to the equilateral triangles defined on the boards. A set of tokens thick enough to stand on an edge and comprising combinations of equilateral triangles to represent numbers is also included. Also included in the kit is a mat defining rows and columns of fractal representations of numbers by which various mathematical operations can be understood. A set of nesting pyramids of graduated sizes representing numbers of magnitudes generally corresponding to the sizes is also provided, as are pyramids of different sizes which can be stacked through the use of trays and transparent covers. The kit includes a work book and a user's manual.

Abstract: This invention deals with a multi-purpose learning device for mathematics, language, logic reasoning, and classification of objects.

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: An educational device useful for teaching numbers, addition, subtraction, reading, and logic comprising a flat playing surface having rows of equally dimensioned boxes, ascending numerical indicia associated with the boxes in each horizontal row, blocks of varying dimensions having numbers thereon proportional to their relative horizontal dimensions and being adapted to fit in each row in such a way that the number appearing to the right of the block or block will indicate how may boxes are covered by the block or blocks in that row. In a preferred embodiment there is also provided a set of card containing a numbered card corresponding to each numbered block.

Abstract: A puzzle or game including a set of pieces combinable to form a rectangular array and a retainer for holding said pieces in a tubular or circular form dimensioned in accordance with the Phi factor, (.phi.). The set of pieces is divided into three subsets of different colors to be combined in rows of equal length in which no piece of any given subset abuts any other piece of the same subset end-to-end or side-to-side. The pieces carry indicia also to be combined in the array in distinctive fashion related to .phi..

Abstract: An apparatus for teaching mathematics which applies and puts to work in various ways the modern teaching of mathematics for all levels of elementary education through set theory, comprises a horizontal board divided into eleven zones and having two outwardly-projecting subsidiary boards. In use, objects can be placed in selected zones of the horizontal board to demonstrate mathematical operations, and information relating to the operation is written on appropriate zones of the vertical board and on the subsidiary boards. The horizontal board has a bevelled front edge portion on which further information can be written, and two portions in which objects to be placed in the zones of the horizontal board can be placed beforehand.

Abstract: The instant invention relates to an aid for the carrying out of a didactic game in order that any (n) based number system may be learned.It consists of a series of containers decreasing in size, each containing an (n) number of smaller containers which are equal to each other; the smallest container holds an (n) number of pieces each representing a numerical unit. A desk is provided with colored squares or frames arranged in such a way that the last square (frame) on the right is of the same color as the unit of the first order, the penultimate the same color as the unit of the second order and so on.

Abstract: A manipulative system is disclosed which is adapted to teach basic relationships between coins and bills of different denominations and basic change-making skills to students with limited learning capacity. A board overlayed with the images of one hundred coins of the smallest denomination disposed in a five by twenty array is used in conjunction with first and second series of overlays, each having several subsets. The overlays have various quantities of images of the smallest denomination coin imprinted thereon. Some overlays in a first series have a tab carrying the image of a coin equivalent in value to the summation of the coins of the lowest denomination imprinted on a given overlay. The two overlay series have distinctly different background colors to facilitate an understanding of the changemaking process.

Abstract: A mathematics teaching aid kit comprises a storage box, teachers manual, task cards, and manipulative components used to teach a mathematics program. The manipulative components comprise sets of individual thin rectangular and square plates or stair members of different colors divided into separate squares forming ten distinct shapes ranging from one square to ten composite multiple squares illustrating the numbers one to ten. The reverse side of the stair members is divided identically, but of different color or surface texture. The teaching components comprise square or rectangular tile members, some with positive numbers on one side and negative numbers on the other and others with arithmetic symbols printed on one side, and a pair of thin elongated rectangular members or number line bars, one divided into evenly spaced increments bearing positive numbers, and the other having identical increments and indicating negative numbers.