referring now to fig1 , there is disclosed mathematical matrix ( 1 ) presenting a single integrated apparatus depicting conceptual relationships between numbers 0 to 100 which allows children to count each of the numbers individually and to count to 100 by 1 &# 39 ; s , 2 &# 39 ; s , 5 &# 39 ; s or 10 &# 39 ; s as well as to count by odd or even numbers . the mathematical matrix ( 1 ) is organized about a vertical y - axis and a horizontal x - axis with stations ( 103 ). a pair of top terminal stations having the numbers 50 and 50 and a pair of bottom terminal stations having the numbers 0 and 100 . a balanced display of numbers from 0 to 100 is presented in fig1 . in some embodiments the 50 and 50 pair and the 0 and 100 pair may be on the left and right of the x - axis . considering the structure of the matrix more specifically , ascending numbers from 0 to 50 are arranged in a first string a on the left side of the y - axis and descending numbers from 100 to 50 are arranged in a second string , b on the right side of the y - axis . numbers which are on lines parallel to the x - axis always sum to the number 100 ( 105 ), for example 47 and 53 ; 21 and 79 , and 9 and 91 . thus , the matrix provides an apparatus to teach addition and subtraction . in order to make numbers countable by 10 &# 39 ; s more readily distinguishable , these numbers occur in straight lines parallel to the y - axis with numbers other than 50 , 50 and 0 , 100 being offset substantially from the y - axis . each of the 10 &# 39 ; s numbers occurs at an apex with portions strings approaching the 10 &# 39 ; s number converging . each number ending in 5 , so as to be wholly divisible by 5 is located at an apex in - board of the numbers evenly divisible by 10 . consequently , the matrix allows a student to readily count by 10 &# 39 ; s and by 5 &# 39 ; s while clearly showing that the 5 &# 39 ; s occur evenly between the 10 &# 39 ; s , and upon counting are always separated by 10 digits . referring now to fig2 , there is shown a puzzle arrangement wherein the numbers at stations ( 203 ) in the strings a and b are not present . students are then presented with the task of entering the numbers which are provided on chips ( 201 ) in a separate pile . the chips ( 201 ) may be in a container which can be shaken . the chips ( 201 ) may pour out on a table or desk surface next to the matrix . the student &# 39 ; s task is to properly place the chips in the matrix while initially viewing a complete or partially complete matrix displayed to the class . in order to distinguish even numbers from odd numbers , all even numbers occur at stations ( 203 ) represented by circles and all odd numbers occur at stations ( 203 ) represented by triangles . in some embodiments all the stations ( 203 ) are the same shape and in some embodiments the shape of the station ( 203 ) is determined by the number in the digit ( n ) or ( m ) in that the station ( 203 ) has the same number of sides as the number in the digit ( n ) or ( m ) for example see fig5 . optionally , the matrix may further distinguish even and odd numbers by color , for example , the even number stations ( 203 ) may be red , and the odd number stations ( 203 ) may be blue . in order to make it easier to count by 10 &# 39 ; s , the stations ( 203 ) with numbers 0 , 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 , and 100 may optionally be the same color . also , the stations ( 203 ) with numbers counting by 5 , but not ending in 0 , may be a particular color . in lieu of having a mechanical arrangement a computerized version of the game is shown in fig3 in which an electronic image ( 200 ) of the matrix of fig1 is displayed with numbers up to ( 100 ). another image ( 300 ) of the matrix is provided with empty or partially empty stations . a separate image ( 400 ) with a bank of numbers from 0 to 100 is also provided for filling in empty stations the image ( 300 ). there are options for placing numbers from the numbers bank ( 400 ) in stations on the matrix ( 300 ) which can be done either with the image ( 200 ) present at another location or located on separate sheets at the location of each computer terminal . children may be instructed to place all of the 10 numbers on the board and then perhaps all of the 5 numbers on the board . finally , students can be requested to place all the numbers between the 10 &# 39 ; s and 5 &# 39 ; s on the board . various exercises can be performed using the image of the matrix ( 300 ) with empty or partially empty stations so that the students may work with the numbers and learn what the matrix has to teach them about the relationship between the various numbers between 0 and 100 . in other embodiments other ranges may be substituted for 0 - 100 for example 100 - 1000 . if necessary , an element of competition may be introduced into the instruction by timing how long it takes each student or group of students to insert a random distribution of numbers in the matrix . when a student correctly places the numbers , an audible or non - audible finish signal is provided so that those who complete the task by a selected time are rewarded . this game has many options for encouraging kids to learn about the numbers 0 to 100 . while the matrix and associated learning activities are the primary use of the matrix , other uses of the matrix have been conceived , such as but not limited to , table gaming wherein wagerers place bets on numbers they select and are rewarded according to formulas derived from the relationship of selected numbers to complements thereof which equal 100 . fig4 is an illustrative example of the game in hypothetical play . the stations ( 403 ) are shown alternating between circles and triangles where circles correspond to even numbers and triangles correspond to odd numbers . special movement spaces and examples of their effects ( 405 , 407 , 409 , 411 , and 413 ) are used by a user / player ( 419 ) when they perform an action that grants them access to the spaces for example landing on the space , answering a question , or drawing a card . when landing on a space granting downward diagonal movement a slide ( 405 ) may be used to transfer the user ( 419 ). when landing on a space granting movement directly across to the other string a car on a road ( 409 ) may be used to transfer the user ( 419 ). when landing on a space granting upward diagonal movement an airplane ( 413 ) may be used to transfer the user ( 419 ). when landing on a space granting upward movement a latter ( 411 ) may be used to transfer the user ( 419 ). when landing on a space granting downward movement an elevator ( 407 ) may be used to transfer the user ( 419 ). the special movement spaces and examples of their effects ( 405 , 407 , 409 , 411 , and 413 ) are illustrative examples and are not meant to be limiting for example an escalator could be used to show upward or downward diagonal movement . math problem bubbles ( 415 ) may optionally be displayed in the computerized embodiments when user lands on a space or before a user may move from a space . the math problem bubbles ( 415 ) may be any type of math questions for example a word problem , identifying the next number in a sequence , an algebra problem , a calculus problem , naming a geometric shape , or a geometry problem . in some embodiments math problems are written on cards ( 417 ). the cards ( 417 ) may be real or displayed on a computer . fig5 shows a series of ten stations where each station is a represented by a geometric shape with the number of sides of the shape corresponding to the ones digit of the number associated with it . numbers ending in 0 are represented by a circle ( 501 ). numbers ending in 1 are represented by a horizontal line segment ( 503 ). numbers ending in 2 are represented by an absolute value sign ( 505 ). numbers ending in 3 are represented by a triangle ( 507 ). numbers ending in 4 are represented by a square ( 509 ). numbers ending in 5 are represented by a pentagon ( 511 ). numbers ending in 6 are represented by a hexagon ( 513 ). numbers ending in 7 are represented by a heptagon ( 515 ). numbers ending in 8 are represented by an octagon ( 517 ). numbers ending in 9 are represented by a nonagon ( 519 ). fig5 is an illustrative example using regular polygons . some embodiments may use irregular polygons or have their sides correspond to numbers other than those in the ones digit position . without further elaboration , it is believed that one skilled in the art can , using the preceding description , utilize the present invention to its fullest extent . the preceding preferred specific embodiments are , therefore , to be construed as merely illustrative , and not limitative of the remainder of the disclosure in any way whatsoever . the entire disclosures of all applications , patents and publications , cited herein and of corresponding u . s . provisional application ser . no . 61 / 318 , 514 , filed mar . 29 , 2010 , are incorporated by reference herein . from the foregoing description , one skilled in the art can easily ascertain the essential characteristics of this invention and , without departing from the spirit and scope thereof , can make various changes and modifications of the invention to adapt it to various usages and conditions .
teaching aid math games utilizing a mathematical matrix organized about x and y axises where the game is played by correctly associating numbers with their corresponding stations . the matrix comprises a first string of stations and a second string of stations where the first and second strings have the same number of stations . each station is associated with a numerical value , and each station on the first string is parallel to a corresponding station on the second string where each corresponding station pair add up to the same numerical value . the display of the matrix provides visual associations for mathematical relationships .