Title of Invention

DEVICE TO AID LEARNING OF FRACTIONS AND MATHEMATICAL OPERATIONS

Abstract

The present invention is directed ot creating an educational and entertainm,enmt device and in particular to learn concept of fracion and its addition, subtraction and equvalence to children through game and play. This is an interactive game and hepls in internalizaion of idea shile playing game. It allows felxible approcah to understand complete concept of fracion. Various rounds of game can be started differently including randomized moves for starting the game hence process of learning the fracions is varied thereby reinforcing hte concepts with various rounds of the game. The device comprises of starter means, playing means, shaped fracional provisions corresponding to the shapes determined by playing means and francional area with centrally disposed selectively shaped area with extending arm/s.

Full Text

THE PATENT ACT, 1970 (39 OF 1970) SPECIFICATION (See Section 10) TITLE OF INVENTION Vevice to Aid Learning of Fractions and Mathematical Operations " (a) INDIAN INSTITUTE OF TECHNOLOGY Bombay (b) having administrative office at Powai, Mumbai 400076, State of Maharashtra, India and (c) an autonomous educational Institute, and established in fndia under the Institute of Technology Act 1961. The following specification particularly describes the nature of the invention and the manner in which it is to be preformed. Field of invention The present invention is directed to creating an educational and entertainment device and in particular to learn concept of fraction and its addition, subtraction and equivalence to children through game and play. Background of invention It is common to teach mathematical operations and principles by representing concepts graphically. Typically fractions are taught by starting with a circle or pie which has been divided or cut into an equal number of pieces or slices, each piece or slice representing a section or fraction of the total circle or pie. These essentially non-interactive devices are usually demonstrative in nature and are unable adequately and consistently hold a learner"s attention for long time. Description of prior art US Patent 6,293,800 describes an educational and entertainment device includes n layers stackable in a predetermined order one on top of the other to define a tower having n layers. The xth layer, where x varies between 1 and n, is divided into x sections, at least one of the x sections of the xth layer having a passage segment formed there through such that with the n layers stacked one on top of the other in the predetermined order, the passage segments of the n layers are in communication with each other to define a passage which extends through the tower. The device also includes art indicator element passable through the passage to confirm that the n layers have been assembled in the predetermined order. The game is complex to play and involves too many intricate steps does not help children in their formative stages with easy learning of fractions and their operations. US Patent 6,308,955 discloses a mathematical board game for 2 to 8 players, invented primarily for beginners and individuals struggling with the four basic formats of mathematics. The banker is allocated by use of a spinner, players then determine who moves first, by use of this spinner, and in which of the four formats they will play, these are: Subtraction, Multiplication, Addition and Division. Players then move by taking four steps. (1) Taking a question card out of the appropriate question bag; (2) Working out the relevant sum; (3) Looking up the answer on the correlating Answer Value Chart, which converts the answer of the mathematical sum to a given value, which is a number; (4) Moving that number of spaces on the board and receiving that amount of money from the bank. The board"s defined numbered travel path is from 1 to 144 spaces. Some spaces are marked with various symbols, which require various actions that affect the players. Players move their playing piece horizontally from left to right, right to left, to a Finish Award they have nominated, which conveniently gives players the choice of a quick, medium or lengthy game. The Answer Value Charts enables the three sections; Sub-Junior, Junior and Senior-players of varying ages and abilities, to play together, with an equal chance of achieving equal values. The winner is the player with the most money on completion, thereby winning by chance not academically. Other known facts incorporated, enable every player to attain the correct answers, while facilitating their personal learning styles. This game too though interactive does not help the children to learn fractions and their operations with ease and fun. US Patent 6,447,300 describes an educational game 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, As is evident from this game, one is unable to comprehend fractions and their operations and hence does not teach how to design a game for learning of fractions. There are several other games described in the prior art and a brief review of those is presented below. Pizza Party (Source- www.adhd.com/educ/ mathfun2.htm) This set of 12 realistic 12-inch pizzas is the "main course" upon which eight different fraction games are based. Includes 12 cardboard pizzas cut into halves, thirds, fourths, sixths, eighths, ninths, twelfths, and sixteenths, plus two spinners and an activity sheet. Comes in a sturdy pizza parlor box! For 2-6 players Grades 1-6. The game pizza party has 12 different bases as pizza to teach fractions and random values to pick pieces come from spinners. It has activity sheets to work on. It does not include the exchange and interaction of pieces amongst players. Not many shapes can be combined to make different shapes- hence the flexibility to perceive fraction through varied combination of shapes is missing. It uses different bases to explain different values of fraction. The mathematical operations are based only on the values in spinner. Basic Fraction Circles (Source- www.adhd.com/educ/ mathfun2.htm) Deluxe Sets include nine circles or squares divided into halves, thirds, fourths, fifths, sixths, eighths, tenths, twelfths and 1 whole with storage box/ work tray. Basic Sets include six complete shapes representing halves, thirds, fourths, sixths, eighths and 1 whole. Teaching Notes included. Grade Level: 1-6 Basic Fraction Squares (Source- www.adhd.com/educ/ mathfun2.htm) Deluxe Sets include nine circles or squares divided into halves, thirds, fourths, fifths, sixths, eighths, tenths, twelfths and 1 whole with storage box/ work tray. 3 Basic Sets include six complete shapes representing halves, thirds, fourths, sixths, eighths and 1 whole. Teaching Notes included. Grade Level: 1-6 Basic fraction circles and basic fraction squares are educational devices that merely display fractions in particular geometric shape. There is no game strategy or players involved in it. It does not incorporate action to show mathematical operations on fractions. Available games focus more on demonstartion of the concept of fraction somewhat directly and in limited ways. These are not relevant to current invention, which allows flexible approach to understand complete concept of fraction to emerge through internalisation of idea while playing a game. Summary of the invention The main object of the invention is to provide an educational device that makes learning about fractions an interactive fun with multiple levels of challenge. An object of the present invention was to provide new mathematical board game to help children who struggle with understanding of fraction. Another object of the invention is to provide a process for the self-motivational learning of fractions and their mathematical operations. It is yet another object of the invention to provide a process for the learning of fractions and their mathematical operations with strategic options thereby enhancing the creativity of the learner. It is yet another object of the invention to provide a game for the learning of fractions involving plurality of players. Another object of the invention is to provide a self-packaged game so designed as to self contain and carry the various playing components of the learning device. Thus in accordance with this invention, it provides an educational game for 2 to 4 players designed to teach children concept of fraction coupled with mathematical principles like addition and subtraction. The game comprises a checkered board with areas demarcated for placing playing tile pieces of various shapes as required by the process of the game to combine fractional shapes to complete a shape the game being started and progressed by the throwing of designed dices that indicate the tile fractional shaped pieces to be used by the player for placing on the checkered board to complete a shape, the winner being the one who completes the final shape with the minimum use of the fractional pieces and the minimum number of throws of the dices. With the throw of a dice, the player picks up a tile piece and places it on a specific area of the checkered board. With every subsequent throws, the player picks up the other shaped pieces from the pack to complete the final shape. The sequences of operations of the learning process can be varied, with varying startup piece, use of the number of dices etc giving diverse options to the players interactive fun with multiple levels of challenge, 4 creativity, self-motivational learning of fractions and their mathematical operations. The game also provides a platform for team learning. Detailed description of the invention Description of the drawings Figurel. The Board Figure 2. Start Tiles Figure 3. Tiles Figure 4. Starter dice Figure 5. Playing dice Figure 6. When to get bonus points Figure 7. Avoid such blank spaces Figure 8. Small tiles replace the big ones Figure 9. Contributing tiles to common area irrespective of shapes Figure 10, Change in the shape of pieces Figure 11. Change in the basic grid Figure 12. Change in the basic shape to be filled in Figure 13. Bonus points in variation Figure 14. Exchange/contribution of tiles Figure 15. Exchange/contribution of tiles Figures16-24. Illustrating rules of the game-Rule book front and back The game comprises of a playing Board (refer figure 1) with common areas 11 to keep the tile pieces 16 (Shop), with individual areas to fill in 14 (Room) and to keep the pieces that the player cannot use 15 (Roof), start pieces 21, 22, or 23 to start, the fractional pieces of varied shapes 31, 32, 33 or 34.Startup dice. (figure 4), Playing dice (figure 5) and process rules (figure 16 to figure 24). A preferred construction of the educational device is shown in figure 4, with the device having a central square area 11 with four square arms radiating 12 from each of the four sides of the central square, giving a cross shaped structure, the central square sectioned into area blocks of squares and polygons for placement of the playing pieces 16, the radiating squares further sectioned into squares to arrange the playing pieces of each player in an array 15,14. With the throwing of the dice (figures 4&5), which has 6 faces with six distinct shapes marked on them, the player picks up the shaped piece 21, 22, or 23 for figure 4 and 31, 32, 33 or 34 for fig5 that is determined by the upper face of the dice appearing after the throw. The player then places this shaped piece to combine with the shaped piece places earlier on the square of the checkered board 14. This operation is repeated by the player at each turn and thus finally combines the playing pieces to form mathematical operations to complete a predetermined shape. In a variant of the design of the board figure 1, the central area marked 11 for storing the common fractional pieces optionally indicating location and number of pieces to be played The four houses 12 attached to the central area are divided into territories four players based on proximity. Each house had two areas. 5 1. Rectangular area 15 (adjacent to the common central area) with grid (2X4) eight divisions to keep extra pieces 2. Outward to the above-mentioned rectangular area a square area 14 with grid (4X4) sixteen divisions is provided for each player. This is to be covered with the pieces acquired by throwing a dice. The 16 divisions base 14 offers options to the player to design his/her strategy for playing the game to ensure early completion and wining higher points. The corners 13 between the two adjacent houses are optionally creased to fold the wings to make a 3 dimensional self-packaging construction to store various components of the game. Description of Pieces Refer figures 2 & 3 There are two kinds of pieces 1. Start pieces 21,22,23 can be picked by throwing the startup dice figure 4. It explores strategies to fill area for an individual in that particular game. 2. Fill pieces 31,32,33,34 can be picked by players to fill the given area while playing the game. Description of dice Refer figures 4 & 5 There are two dice 1. Startup dice figure 4 - It has pictures of the start fractional pieces that each player picks when the game starts. It explores strategies to fill area for an individual in that particular game. 2. Playing dice figure 5- It has pictures of the fractional pieces and its value that each player picks while playing the game. It gives element of luck to fill area with fractional pieces for an individual in that particular game. General process of fraction learning using the device. The process of learning uses the board with the two kinds of dices figures 4&5 and two kinds of tile pieces figures 2&3. The goal is to cover area given to each player 14 as fast as possible by leaving minimum number of unulitised pieces. The number of players decides how many pieces to play with (to create situations where players run short of certain pieces - strategy). The startup dice figure 4 is thrown by each player to pick a start pieces 21,22 or 23s allows a player to plan a different strategy each time. The play dice figure 5 is thrown to pick the fill pieces 31,32,33 or 34 - an element of luck, while filling the area assigned to each player. The goal of completely/ partially covering the area 14 is based partly on luck and partly on player"s strategy to ensure early completion. 6 Once the area is filled, the players calculate their scores by seeing how fast they filled and how less pieces they left unutilised. Following the rules, the concepts and mathematical operations can be learnt, while playing the game. Modification of the process rules changes the mathematical concepts that can be learnt through this game. Winning not only depends on faster completion but leaving behind minimum unutilized pieces. The game is designed in a manner to enable the player has an opportunity to start the game differently. Player"s actions partially depend on chance, avail rewards when they fulfill the objectives. Examples. Example 1 The object of the game To fill in the 14 "room" as fast as possible with minimum wastage of tiles How to play the game Refer figures 16 to 24. Each player throws the startup dice figure 4 and places the start tiles 21,22or 23 in their rooms 14. Once placed, a tile cannot be moved. Then each player throws the playing dice figure 5 and places the tiles in their room 14. Once placed, a tile cannot be moved. Each player tries complete 1/4, 1/2 or 3/4 of the room to get the rewards as follows Ref. figure 6. When 1/4 complete -1 extra chance to throw dice. When 1/2 complete - 2 extra chances to throw dice. When 3/4 complete - pick one piece of your choice. Tiles that a player is unable to use are kept in their roofs 15 that are given for this purpose. How to finish the game Players completely fill their rooms 14. Arranges the spare pieces in the grid of the roof 15. Winner calculates the score as follows: = 16 - number of small squares filled in the roof 15. = 15 - number of small squares filled in the roof 15. = 14 - number of small squares filled in the roof 15. = 13 - number of small squares filled in the roof 15. Each player First Second Third Fourth 7 Information on components The dice have the image and the fractional notation of the fractional tiles. The board has number of tiles to be used during the game. Information on marked spaces Each individual square 14(room) has divisions that are specifically highlighted to reinforce certain fractions 14&15. The common area (shop) 11 has notations that can be universally understood without any language barrier 16. Miscellaneous rules and information Tiles that a player is unable to use are to be kept in the roof 15. Player has to avoid leaving certain kinds of empty spaces while filling in the square. Ref. figure 7 If larger pieces get finished in the common area - pick 2 small pieces of the same shape instead. Ref. figure 8 If the tiles in the shop finish, the players are supposed to contribute same value of pieces back. The shapes of the tiles can vary but if the players put these tiles on the grid, they should cover same number of smaller squares in the grid. Ref. figure 9 Example 2 In another version of the game, the name of spaces and objects such as tiles , shop, room and roof is changed so as to call them as bank, bank, house, garden etc. The shape of pieces are changed keeping the same grid for the square. Ref figure 10. The grid is changed and hence changing the value of fractional pieces. Ref figure 11 The basic shape is changed which needs to be filled and hence changing the shape of fractional pieces too. Ref figure 12. The process rules are changed a) The number of pieces to play with can be varied and hence changing the character of the game. b) With the presence or absence of start pieces or with the change in their shapes the game can be varied, figure 10 8 c) The value of fraction can be taken as with lowest terms of with a different value. For example: 2/16 can be written as 1/8. d) The bonus points such as When 1/4 of room is filled -1 extra chance to throw dice. When 1/2 of room is filled - 2 extra chances to throw dice. When 3/4 of room is filled - pick one piece of your choice. The way to complete 1/4, 1/2 or 3/4 0f the square can also be varied, figure 13 The reward can be of a different kind or the reward can be for a different goal all together. Here, the rewards can vary like- number of chances, choice/ exchange of pieces, keeping unused pieces back, passing on the pieces, etc. The goals can be different - like instead of making 1/4 make fraction of a targeted value given by other player, etc. e) Once a player completes1/2 1/2 or 3/4 of the square, a bonus piece, which is equivalent to 1/4 or 2, or 3 such pieces or pieces that are equal to1/4, 1/2, or 3/4 can be picked and placed and the fractional pieces can be kept back in the shop 11. This way one avoids the situation where certain tiles are "out of stock" and also reinforcing the concept of 1/4, 1/2 and 3/4. Ref. figure 13. Or If larger pieces get over, smaller pieces of same shape and equivalent value can be taken. Ref. figure 14. Or/ and If certain pieces finish in 11, players can contribute the same value of pieces back to 11. However, the shapes may vary. This way players learn comparison, equivalence, addition and subtraction of fractions. Ref. figure 15. f) The scoring is done such that a player wastes least amount of pieces else the points are deducted, figures 23& fig 24 The impact of the clause is that a player has to plan and place the pieces strategically; else he loses the first place even if he fills 11 first. The removal of modification of this clause would change the whole aspect of strategy and planning in the game. The role played by the players is of significance. The number of players could vary from 2 to even more than 10 players. The game could have individual trays instead of board, which could be filled in by the fractional pieces. Teaming up of players can lead to joint effort to fill the shape. Hence borrowing, sharing, exchanging of pieces can take place. Even a carrying over points to next game can be done at higher levels. To increase interaction and change the strategy, players of opposite ends can be partners. 9 The idea of getting random value of fraction is not merely applicable to a 6 faced dice but it could be a dice more faces. Or It could be a set of dice that gives values of numerator and denominator. Or It could be a pack of cards with varied values of fractions/ values of numerator and denominator that can be randomly picked by the players. The basic principle of the game would remain the same but the values and the complexity can vary according to the levels. There can be a computer game made with this invention. The board material can change to plastic sheet, metal sheet or wood too. It is a group learning device that is self-motivating, and enables the players to "learn" concept of fraction, mathematics of fraction and mathematical operation with fraction, while playing the game. Repeated playing will consolidate the learning process. This game also teaches them addition, subtraction and equivalence of fractions to certain extent. Also a child learns about the varied shapes. Certain amount of strategy and management is also involved which a child becomes more proficient in when the game is played. It incorporates an emphasis on fun (as the child has to plan his moves) while fraction is being learnt and revised. The game is useful as an interactive tool, encouraging social skills in players, such as turn taking. Through novel and exciting ways it uses many different yet positive avenues to keep the player entertained. For example, Awards (bonus points or extra moves) can be achieved, by filling the desired fractions. Chance also plays a large part in the game due to act of throwing of dice and picking pieces accordingly. So it makes the game unpredictable to certain extent. The score is to be calculated in such a way that even if a player has filled in the square first, is unlikely to win if the pieces that the player gets are not used properly. Parents or grown up will appreciate the aspect of being able to choose the length of time they wish to spend playing with their child/children. The structural components of the game may be provided of conventional materials for board games, using conventional manufacturing processes that are not to limit it only to this media. Moreover, the features, advantages and method of play described above, are believed to be set forth in sufficient detail, as to enable those skilled in the art, to practice the invention. Still further, various substitutions and modifications may be made, without departing from the scope and spirit of the invention. This process of learning using the device of this invention provides several advantages over many known methods using other devices. Some of them are listed below: ■ Various rounds of the game can be started differently including randomized moves for starting the game and hence the processing of 10 learning the fractions can be varied thereby reinforcing the concepts with various rounds of the game. ■ The various ways in which the tile shapes can be fitted gives a clear concept of combining fractions to give the whole. This process also easily conveys relationship between various fractions and their operations. This is reinforced while filling the spaces on the board with the diversely shaped pieces and also relating the pieces to be picked by players with throwing of the dice. ■ Scoring pattern ensures that a player intelligently uses pieces rather than wasting them. ■ Folding of board provides a self-packaged game so designed as to self contain and carry the various playing components of the learning device 11 We claim 1 A device/kit for learning fractions comprising: a multiarmed layout, plurality of shaped operating pieces, atleast two cubes of which one is a start cube and the other an operating cube, wherein, the multiarmed layout has a central zone/area with radiating out arms as play zones/areas; wherein the central zone/area has storage space for stacking operating pieces; wherein the radiating arms making the operating zones/area, comprise of alteast two matrices containing quadrants of which atleast a first matrix is located adjacent to the central zone and the other matrix adjacent to the first matrix and away from the central zone; wherein the said operating pieces are of two types namely "start pieces" and "fill pieces", wherein the start pieces are of diverse geometric shapes constructed from squares and triangles, and the "fill pieces" are of diverse geometrical shapes constructed from triangles and squares wherein the geometrical shapes represent specific fractions; wherein the start and operating cubes have six faces, wherein the start cube has faces representing shapes of the "start pieces" and the operating cube having faces representing the shapes of the "fill pieces"; the multiarmed layout optionally having edges along which folds may be made to result in a boxlike structure. 2. A device/kit for learning of fractions as claimed in claim 1, wherein the central zone/area is a matrix optionally defining the number of pieces needed to operate with a set number of operators and also to stack operating pieces. 3. A device/kit for learning fractions as claimed in claim 1, wherein the first matrix is located adjacent to the central zone in the play zone comprise rectangular area with grid (2X4) eight divisions to keep extra pieces. 4. A device/kit for learning fractions as claimed in claim 1, wherein the other matrix adjacent to the first matrix and away from the central zone comprise a 4x4 grid of sixteen divisions to be covered with the pieces selected based on the resulting top face after the operating cube dice is operated. 12 5. A device/kit for learning fractions as claimed in claim 1 wherein the start operating pieces are polygons of varying areas constructed from basic shapes such as triangles, squares, rectangles, and combinations thereof 6. A device/kit for learning fractions as claimed in claim 1 wherein the "fill pieces" are polygons of various areas constructed from basic shapes such as triangles, squares, rectangles, and combinations thereof. 7. A device/kit for learning fractions as claimed in claim 1 wherein the triangles constructing the start operating pieces and the "fill pieces" as claimed in claims 1, 5-6, are right-angled triangles. 8. A device/kit for learning fractions wherein the start cube as claimed in claim 1 has each face illustrating a polygon constructed from right angled triangles wherein the polygons are of three types and of equal areas, each occurring in two opposite faces. 9. A device/kit for learning fractions wherein the operating cube as claimed in claim 1 has each face illustrating shapes constructed from a combination of triangles resulting in triangles, rectangles and squares representing specific fractions. 10.A device/kit for learning fractions as claimed in claims 1-9, wherein the multiarmed layout is constructed using any suitable material that is preferably selected from board, plastic sheet, metal sheets, wood or adapted to operate in an electronic media. . A device / kit-forlearning fractions as claimed in claims 1-10 wherein the operators use the components to learn fractions as described herein. Dated: October 8 2004 Agent on behalf of Applicant 13

Documents:

1167-mum-2003 abstract.pdf

1167-mum-2003 claim.pdf

1167-mum-2003 correspondence(ipo).pdf

1167-mum-2003 correspondence.pdf

1167-mum-2003 description(granted).pdf

1167-mum-2003 drawing.pdf

1167-mum-2003 form 1.pdf

1167-mum-2003 form 13.pdf

1167-mum-2003 form 2(granted).pdf

1167-mum-2003 form 2(title page).pdf

1167-mum-2003 form 26.pdf

1167-mum-2003 form 5.pdf

1167-mum-2003 pct-isa-220.pdf

1167-mum-2003 power of attorney.pdf

1167-mum-2003-abstract-(08-10-2004).pdf

1167-mum-2003-abstract.doc

1167-mum-2003-cancelled pages-(08-10-2004).pdf

1167-mum-2003-claims(granted)-(08-10-2004).doc

1167-mum-2003-claims(granted)-(08-10-2004).pdf

1167-mum-2003-claims.doc

1167-mum-2003-correspondence(ipo)-(07-09-2006).pdf

1167-mum-2003-correspondence-(19-06-2006).pdf

1167-mum-2003-discription(granted).doc

1167-mum-2003-drawing-(08-10-2004).pdf

1167-mum-2003-form 1-(07-11-2003).pdf

1167-mum-2003-form 13-(07-09-2007).pdf

1167-mum-2003-form 19-(08-0910-2004).pdf

1167-mum-2003-form 2(granted)-(08-10-2004).doc

1167-mum-2003-form 2(granted)-(08-10-2004).pdf

1167-mum-2003-form 2(granted)..doc

1167-mum-2003-form 3-(07-11-2003).pdf

1167-mum-2003-form 5-(08-10-2004).pdf

1167-mum-2003-power of attorney-(07-11-200-3).pdf

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