Abstract: An electronic toy appliance designed to stimulate the development of a child's mind using audio feedback, the toy comprising an object having a plurality of substantially planar sides adapted for manipulation by a child on a substantially flat surface so that a child may select different sides of the object to face upwardly. The appliance prompts the child with more difficult prompts depending on the child having provided correct previous responses.

Abstract: A visual method of teaching arithmetic, in which graphical representations of familiar objects are used instead of numbers, is particularly well suited for children who are visually oriented and have difficulty with numbers. The shapes of the objects resemble the numerals zero through nine. The objects may appear in any visual medium. Students are first shown examples of multiplication, division, addition, and subtraction, in which objects replace numbers. Each object is then shown by itself. The numeral that corresponds to the number value of each object is then overlaid on top of each object. Students are also shown groups of colored dots or balls, in which the colors of the dots match the colors of the objects and the number of dots corresponds to the numerical value represented by its corresponding object.

Abstract: A covered money holding tray with a series of toy money holding compartments and a cavity for receiving a book such that when the cover is closed with the book in place, the compartments are closed off, preventing the contents of the open compartments from spilling out should the tray be moved about, with the cover in a preferred embodiment being clear or translucent so that the cover or back of the book can be read when the cover is closed.

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 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: An educational game for teaching mathematics has a game board with a continuous play path along its edge. Spaces are labeled with a mathematical category and a monetary amount. Each mathematical category has its own deck of cards with questions, answers and explanations. At least one of the spaces of the game board is labeled with the help category. When a player lands on this space they receive a help card, which permits that player to ask another player for help in solving a question. The game is played by moving a marker along the play path. If the marker stops on a space that has a mathematical category the player selects corresponding card. If the player's solution to the question and answer on the card match the player collects play money in the amount printed on the space. If not, play proceeds to the next player and the first player continues to work on the question, giving that player the ability to self-correct.

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 basic mathematics teaching and learning aid comprises of nine arrays of square spaces placed with powers of 10 from 10−4 to 106, numbers formed by repeated addition of some of those powers of ten, and other numbers. Dot and dash are in some of square spaces. Numbers, sign, arrows, mathematical symbols, percentages, equations and condition are in open spaces among the arrays. Formation, presentation and relations among these numbers, dots, dashes, sign, arrows, mathematical symbols, percentages, equations and condition are primarily used as an aid in teaching and learning fundamental areas of basic mathematics which mainly includes numbers in base-ten number system, addition, subtraction, multiplication, division, relations of a number of n with zero (number 0) in mathematical operations, whole numbers, fractions, and percentage.

Abstract: Two to four players can play. Players will use sign tiles (16), sign roller (1), solution boards (4), racks (4), achievement medals (5) and number tiles (100) for level I and (120) for level II. Sign tile has two different math symbols on the face of the tile and either one can be used in the equation. The player who will play first will roll the sign roller and the sign on top will be the math sign to be used. The players will form the math equations on their solution boards using their number tiles and sign tiles identical to the math sign on top of the sign roller. Players need to replace the pieces of number tiles they used in every play. The players to form four correct math equations on the solution board will earn the 1st achievement medal. The player who earns two medals wins.

Abstract: A mathematical instructional aid device for teaching fractions or multiplication, in one embodiment, consists of a circularly shaped base having 12 sections. Each section represents a number from 1 to 12. Each section has within it a number of steps with all the steps of the 12 sections converging to a top most plane. Within each section, each step is spaced from an adjacent step by a number representing a multiple of the base value in the base of each section. Values in steps of different sections are co-planar to assist in understanding the concept of multiplication and fractions.

Abstract: A system for teaching basic arithmetic facts to students and for measuring their progress and rating their knowledge using a computer program that provides repetitive practice and immediate positive reinforcement is provided. The system features structured practice using problem sets of progressing levels of difficulty with problems selected randomly from each set. Progress made by individual students is tracked by generating a proficiency rating that reflects the arithmetic function tested, the level of difficulty of the problems presented, and the percentage of correct answers provided within a preset time period. Summary reports are generated and displayed at the end of each session as are the proficiency ratings.

Abstract: A mathematical game of amusement including a game board having generally planar upper and lower surfaces. The game board has a square center aperture therethrough. The upper surface of the game board is divided into a series of spaces. Each of the spaces has a predetermined point value associated therewith. A selected number of the spaces are designated as bonus spaces. A launching mechanism is positionable within the square center aperture of the game board. A plurality of disc-shaped game pieces are dimensioned for being positioned atop the launching mechanism. The game pieces are divided into at least two sets of game pieces distinguishable from one another by color. The game pieces are launchable by the launching mechanism onto the series of spaces of the game board to achieve a score.

Abstract: A system where a child or other individual arranges one or more computer-recognizable characters on a working platform to spell words or provide a mathematical result in response to computer generated questions or prompts, the system then indicating whether the words or mathematical result is correct.

Abstract: An interesting educational game is provided which is fun, appealing, and effective to readily teach children arithmetic. The child-friendly educational game can include a set of playing cards. Each card can have a different graphical representation of one or more Arabic numerals corresponding to a number and can also have a word corresponding to another number. In order to further teach children words associated with numbers, each card has a graphical representation of a hand with pointed fingers, such that the number of pointed fingers corresponds to the numerical value of the word appearing on the playing card.

Abstract: The device consists of arms which revolve on a handle. It can be manipulated in a number of ways and adapts both to play and to serious educational purpose. In broad educational mode the device is an exploration tool and toy where children can develop skills and play invented games or invent their own. In its main educational use, the device is a mathematics exploration tool and toy; is of a construction which makes it compatible with the decimal system of number among others; and in particular provides a visual-kinaesthetic method for the teaching/learning/understanding/exploration of mathematics.

Abstract: A numerical problem solving game including a set of questions and a scrambled letter puzzle grid. Each of the questions calls for a numerical answer. The puzzle grids comprise a plurality of letters which spell out verbal representations of the numerical answers. Each of the jumbled letter grids corresponds directly with the single set of numerical questions whereby numerical answers for the single set of mathematical questions can be found in verbal form within the single jumbled letter grid.

Abstract: A numerical problem solving game including a set of questions and a scrambled letter puzzle grid. Each of the questions calls for a numerical answer. The puzzle grids comprise a plurality of letters which spell out verbal representations of the numerical answers. Each of the jumbled letter grids corresponds directly with the single set of numerical questions whereby numerical answers for the single set of mathematical questions can be found in verbal form within the single jumbled letter grid.

Abstract: A mathematical card and dice game comprising a deck of cards, a set of three dice, and a timing device, the deck of cards divided into four suits of fifteen cards each, ten of which are numbered one through ten, the remaining five non-numeric cards having letters which can take on any value as defined by the players prior to the game. A predetermined number of cards are dealt to players who use the values of the three dice rolled, common mathematical operations such as addition, subtraction, multiplication, and division, and their knowledge of math to make mathematical relationships that equate to the value of cards in their hands within a predetermined amount of time as tracked by a timing device. A successful match occurs when the card value equals the numeric result of a mathematical operation involving all three dice.

Abstract: A basic mathematics teaching and learning aid comprises of nine arrays of square spaces placed with powers of 10 from 10−4 to 106, numbers formed by repeated addition of some of those powers of ten, and other numbers. Dot and dash are in some of square spaces. Numbers, sign, arrows, mathematical symbols, percentages, equations and condition are in open spaces among the arrays. Formation, presentation and relations among these numbers, dots, dashes, sign, arrows, mathematical symbols, percentages, equations and condition are primarily used as an aid in teaching and learning fundamental areas of basic mathematics which mainly includes numbers in base-ten number system, addition, subtraction, multiplication, division, relations of a number of n with zero (number 0) in mathematical operations, whole numbers, fractions, and percentage.

Abstract: A lampholder for use with cold cathode lamps intended to be wired in a parallel configuration includes an insulating bulb-end receptacle mounted in a conductor housing. The receptacle is divided into a pair of individual bulb-end receiving portions, each of which is provided with a conductive clip which establishes electrical contact with an inserted bulb. At least one of the clips is in two sections which are configured as switch contacts in series with the mains side of a ballast for the lamps. Insertion of a lamp into the clip closes the switch contacts, establishing the mains circuit and allowing high-voltage to be generated and applied to the lamps. The lampholder insures that high-voltage is not produced unless a lamp is in place.

Abstract: A process is provided for teaching students multiple curriculum subjects through the use of a theatrical production. A play is first selected which has been created for student performance and adapted to the grade level of the students participating. Student lesson plans are provided, including worksheets in multiple curriculum subjects. These subjects include at least two of the following: language arts, math, science, health, and history. The students are assigned speaking or non-speaking roles in the play. Sound recordings are provided which pertain to the play. These sound recordings can include a soundtrack of the script of the play serving as an aid in teaching the students the roles of the play as well as sound effects and audio bites for use during the performance of the play. Templates are provided for creating backdrops and props for the play. A portable stage is erected within a classroom environment and used in performing the play.

Abstract: A method and apparatus for selecting a category from a plurality of categories, where each category comprises a number of elements, and corresponds to a category performance determinant that represents a measurement associated with a given category, and where a category performance determinant biases the selection of a given category.

Abstract: An educational device comprising a holder or axle (2) for a plurality of side by side revolvable arms (3) or counters whereby in use the arms revolve by twirling the holder or by manipulating arms so that when placed on a support surface some arms lie on the left hand side of the holder while the remaining arms lie on the right hand side of the holder. The device consists of arms which revolve on a handle (1). It can be manipulated in a number of ways and adapts both to play and to serious educational purpose. In broad educational mode the device is an exploration tool and toy where children can develop skills and play invented games or invent their own. In its main educational use, the device is a mathematics exploration tool and toy; is of a construction which makes it compatible with the decimal system of number among others; and in particular provides a visual-kinaesthetic method for the teaching/learning/understanding/exploration of mathematics.

Abstract: An educational and recreational apparatus and method having a background grid defining a matrix having a plurality of individual cells, and a plurality of elements each having a first surface, with indicia disposed thereon, said elements being removably disposable on said grid. Each arrangement of said elements disposed on said grid define a magic square, so that each row, column, or diagonal of the magic square is characterized by a defined relationship in accordance with the indicia. A method of manipulating said elements, said method having at least one computer, display device, calculation means, input device and data storage device. The method including displaying a grid defining a matrix on said display device, arranging said elements on said grid using said input device for selecting and inserting said elements therein, manipulating said elements on said grid using said input device and forming a magic square on said matrix by arranging said elements.

Abstract: The teaching aid apparatus provides two balance beams (27, 28), one above the other, on a support post (23). Weight-attachment stations (36) are provided on the left and right arms of both beams, and the stations are marked on the beams with numerals indicative of distance of the station from the beam fulcrum. The beams are connected by means of pinions (32, 34), which constrain the beams to tip in unison in response to unbalance of one beam. The apparatus aids the demonstration of negative concepts to young children.

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: An educational apparatus used for the teaching of mathematical operations that use fractions. A triangular shaped ruler prism has three different side surfaces that are joined together at three common edges with four different numerical value measuring fractional scales on each side surface and a whole unit scale of which all other scales are a fractional part thereof. All scales have the same length as the whole unit scale. Preferably on each prism side there are two different fractional measuring scales adjacent and aligned with each other in a straight line at one of the common joined prism edges. Fractional scale measuring units that have been used include; the whole unit, half units, thirds, fourths, fifths, sixths, sevenths, eights, ninths, tenths, elevenths and twelfths units. By stated procedures employing marking on a writing surface, fractions may be represented by lengths and added or subtracted from each other as well as mixed numbers with fractions.

Abstract: A method of incorporating small graphs on to pages of text or calculations by using small adhesive-backed appliques or labels which have been pre-printed with a graphical coordinate grid. These appliques eliminate the necessity of a separate piece of graph paper or the tedium of drawing or gluing a coordinate grid directly on the report or calculation page.

Abstract: A system for teaching mathematics to beginning students includes a series of gloves and/or finger puppets, with the digits representing non-sequential number series (e.g., two, four, six, etc.). Students are taught to count various non-sequential number series using visual and tactile senses by using the gloves and/or finger puppets and associated hand patterns, with further audible reinforcement being provided by stories corresponding to each of the non-sequential series. Various caricatures corresponding to the plots of the stories may be used as further mnemonic aids for students in remembering the procedures and operations taught, with additional caricatures being provided for two and three place (i.e., tens and hundreds) digits for removable installation on the glove or finger puppet digits. Once the non-sequential series are learned, students are taught to multiply, divide, solve fraction problems, and factor numbers using the corresponding factor (e.g., two, for the two, four, six, etc. sequence).

Abstract: The present invention comprises an electronic learning game that provides a plurality of pedagogical and instructional modalities which combine strong kinesthetic, auditory, and visual stimulation to assist a child to learn basic arithmetical concepts. The inventive game utilizes a combination of voice statements, rhythmic music, a visual display, and manual inputs from number dials and a response switch to achieve multi-modal learning or arithmetic concepts. The ergonometric size and structure of the present invention promotes a strong kinesthetic learning modality.

Abstract: An educational device and method is provided. Comprising a first glove having a first set of digits for receiving the fingers and thumb of one hand and a second glove having a second set of digits for receiving the fingers and thumb of the other hand. A first set of indicia is provided. Located on each digit is an indicia. The indicia located on each digit on the first glove represent a first set of indicia. This first glove further includes a second set and a third set of indicia. The indicia located on each digit of the second glove represent a fourth set of indicia. This second glove includes a fifth and sixth set of indicia. The first set of indicia and the fourth set of indicia are used to learn to count while the second indicia and the fifth indicia are used to learn right from left. The fifth indicia and the sixth indicia are used to learn geometry.

Abstract: The invention provides a child's counting or activity book having successive leaves formed with ascending numbers of sockets for mounting corresponding numbers of individual button-like, counters of a set. Each counter is anchored to a spine region by a ribbon permitting movement of the counter between any sockets. The counters are selected by the child according to instructions provided on a facing page by words, arabic numbers and illustrations of the corresponding counters. All counters of the set are initially mounted in through-sockets in the cover for storage and display.

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: The invention provides one or more question cards and one or more answer cards, where each answer card corresponds to one or more question cards, and whereby a student is can associate each question card with an answer card, and learn by confirming the matching of pattern s located on each card to determine if a correct answer has been chosen. The question card may display an illustration sketch or diagram, or express a statement, an incomplete statement, a question or a mathematical expression, or any of these images separately or in combination. The answer card may express the truth or falsehood of a statement of a corresponding question card, a word or sentence fragment which can be used in combination with an incomplete statement of a corresponding question card to complete a statement, a statement that comprises a correct answer to a question of a corresponding question card and/or a mathematical expression or value that comprises a correct answer to a mathematical expression of a question card.

Abstract: A lampholder for use with cold cathode lamps intended to be wired in a parallel configuration includes an insulating bulb-end receptacle mounted in a conductor housing. The receptacle is divided into a pair of individual bulb-end receiving portions, each of which is provided with a conductive clip which establishes electrical contact with an inserted bulb. At least one of the clips is in two sections which are configured as switch contacts in series with the mains side of a ballast for the lamps. Insertion of a lamp into the clip closes the switch contacts, establishing the mains circuit and allowing high-voltage to be generated and applied to the lamps. The lampholder insures that high-voltage is not produced unless a lamp is in place.

Abstract: A value bingo-type game is provided including a plurality of player boards each having a matrix of squares situated thereon. The matrix has a plurality of columns each with a unique color and a plurality of squares each with a number within a predetermined range. Next provided is a plurality of tokens. A set of caller cards is included each indicative of one of the numbers of the boards, wherein each of the caller cards has one of the colors printed thereon.

Abstract: An educational instrument for numbers for providing students with an educational tool that would be fun and challenging. The educational instrument for numbers includes a base member having a top side, a recessed portion in the top side, a first longitudinal slot, a second longitudinal slot, a first longitudinal groove extending from the recessed portion and terminating near a first end of the base member, a second longitudinal groove extending from the recessed portion and terminating near a second end of the base member, a matrix of numbers disposed in the recessed portion, a first cover means slidably disposed in the first longitudinal slot and movable over the recessed portion, and a second cover means slidably disposed in the second longitudinal slot and movable over the recessed portion and over the first cover member.

Abstract: An educational board game which is used with a conventional deck of playing cards. The game includes a board which has a matrix of spaces in vertical and horizontal rows. Some of the rows are guide rows containing suit and numerical value indicia relating to the playing cards. The remaining spaces contain numerical values having a mathematical relationship to corresponding spaces in the guide rows. Each of the remaining spaces is covered by a removable tile that bears the numerical value of the space and one of the suits of the playing cards.

Abstract: A method of playing a game which includes (i) a game board which is divided into a plurality of sections such that each of the sections defines a playing location, (ii) a number disposed on each of the playing locations, (iii) a plurality of cards, and (iv) a number disposed on each of the cards is disclosed. The game includes the steps of (a) providing a game player with a multiplicity of the cards, (b) the game player determining if the number indicated on any one of the cards is a first mathematical multiple of the number indicated on any one of the playing locations, (d) removing from the multiplicity of the cards a first card that has the number indicated thereon which is the first mathematical multiple of the number indicated on one of the playing locations, and (e) positioning the first card on one of the playing locations such that the number indicated on the first card is the first mathematical multiple of the number indicated on the playing location on which the first card is positioned.

Abstract: A finger ring counting device enables persons to accurately count prayers while saying the Rosary. The counting device is embodied in a ring structure which can be inconspicuously worn on the hand, and on which there are a number of beads which are manually movable around the circumference of the ring for counting. The device includes a finger ring having a continuous outwardly facing surface and a continuous circumferential channel formed in the outwardly facing surface. Eleven spherical beads are slidably captured within the channel where they are slidably movable around the outside of the ring. The counting device further includes a gate structure including a body portion having a bottom wall which straddles the channel and a top wall constructed and arranged for receiving an ornamental element thereon. The bottom wall cooperates with the aid channel to form a passage through which the beads slidably pass.

Abstract: The present invention is a mathematical skills game that uses a self-correcting method to enable self-learning of basic math skills. A board or other medium includes several card receiving members for receiving a card therein. A mathematical expression or a number is printed on a plurality of cards. Likewise a number or mathematical expression is associated with each card receiving member. The user determines which card matches the mathematical expression or number associated with the card receiving member. A pattern may be printed on both the medium and cards so that when the card is placed in the proper recessed area, the pattern on the card is in alignment with the pattern on the medium. If the pattern on the card does not align with the pattern on the medium, the user is then able to determine that the card has not been placed in the proper recessed area and may take the steps necessary to correct the error. An alternative embodiment includes card receiving pockets.

Abstract: A math playing and training system is disclosed. The system comprises two sets of playing pieces, each having a pair of numbers on both sides. The first set has ten pairs of numbers with each pair having a number on the back one number less than that on the front. Besides one pair of symbols of "+" and "-", the second set has 9 pairs of numbers with each having two numbers equal to a sum of 10. For these 9 pairs of tiles there is a symbol of "-" on the front and "+" on the back. A turnover of two tiles at the same time gives players a direct result for addition or subtraction, and a better understanding of regrouping and pair concepts. The system employs the playing pieces and the pair concepts for playing and training in a vertical math operations specially in the fields of addition and subtraction. The system helps math beginners to master basic concepts of addition and subtraction and to reach the stage of mental arithmetic through entertaining playing and systematic training.

Abstract: This invention relates to children's banks. A product which provides storage for money within the home, primarily for children, but can be used by all. The ATM bank is composed of a hard plastic shell frame for the bank portion and holder for the LED viewer, printer and calculator. The calculator component is a standard function calculator that includes deposit, withdrawal, and balance keys. A manual savings register is also an intricate component part of the invention as a learning tool. It also has a variable power supply 110V or battery.

Abstract: A flexible planar apparatus fabricated from polyvinylchloride has a matrix of foldable lines defining a plurality of quadrilateral tiles. Said tiles are configured to convey information, such as a multiplication table using numerals or Braille characters. The foldable lines allow a first fold of the apparatus to be manually effected followed by a second substantially orthogonal fold of said apparatus, thereby uniquely identifying one of the tiles, which may represent the product of multiplicands in a times table.

Abstract: The present invention is directed to an instructional method based on the concept that as a student learns to perform a mental task consisting of a set of elements or steps, whether conceptual or concrete, the student develops a distinct mental connection or path for every element related to the primary mental task being learned. For example, as a student learns to type a particular key on a keyboard, (the primary mental task), the student develops a distinct mental impression for every typing key logically associated with the first key. In other words, a distinct connection or path is defined as a link between two or more elements, one key being a primary element, the other being a related key connected to the primary key by a logical mental step. The present method is also useful for learning a musical instrument, a foreign language, mathematics, test taking skills, and the like logical though processes.

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: The invention herein relates to a kind of teaching tool that allows children at play to perform simple addition, subtraction, multiplication and division arithmetical operations, learning decimal concepts and practices through experience and, furthermore, learn about year, month, day and day of the week as well as the hour, minute and second clock positions, which enables the invention herein to be an multi-functional teaching tool that combines fun with learning and the promotion of intellectual development.

Abstract: An educational device having a base page, which may be transparent and multiple intervening transparent pages and a structure to hold the multiple intervening transparent layers in registration in which the base layer has a set of problems which are modified by each succeeding overlying layer and in which the numbers are formed by using seven segment blocks similar to those used by light emitting diodes or liquid crystal displays for forming and modifying the numbers and the indication of the operation to be performed if formed by using one to four segment blocks.

Abstract: The present invention involves the use of numerical digits with markers and attribute tags as a means to represent quantities, facilitate mathematical manipulation, and solve problems. The given number of markers on each digit corresponds to the value of the digit. For example, the digit three is enhanced with three markers. The attribute tags are also provided with a given number of markers, for example, ten, for math problems in base ten. The digits and the attribute tags are then used to represent and solve math problems including, but not limited to, learning ones, tens, hundreds, thousands columns, addition, multiplication, subtraction, and division, of whole numbers, of fractions, of negative whole numbers and of negative fractions, as well as decimals and exponents. The problems are quantitatively viewed, manipulated, and solved directly on the numerical digits incorporating the markers and attribute tags.

Abstract: A three-dimensional instructional model used to exhibit and represent specific point groups used in the application of group theory to symmetry operations and molecular structure. A pair of blocks, each have a pair of spaced faces with peripheral side surfaces extending between the faces, the number of side surfaces being equal to the principal rotational axis order of the point group to be represented. The blocks are connectable to one another with a face of each of the blocks opposing. The connection between the blocks can be made using a circular shaft inserted through openings in the blocks, by pins inserted in holes in abutting opposing faces of the blocks, or by adhering the face of one block directly to the face of the other to hold them rigidly in engagement with each other. The interconnection can also be made using a rotational locking mechanism allowing the blocks to rotate with respect to one another.