Abstract:
An apparatus and system are disclosed for teaching mathematical concepts and “fact families.” The apparatus comprises an educational toy block configured, in one embodiment, to help young children memorize basic numbers and number facts in an atmosphere focused solely on play. The toy block, in one embodiment, comprises a polygonal-shaped building block having a plurality of faces, wherein a first face features a first mathematical equation and a second face features a second mathematical equation. The toy block may include a display of multiple mathematical equations in order to facilitate teaching children how mathematical operations are related. In a further embodiment, the toy block displays one or more numbers that are numerical elements in a plurality of mathematical equations forming a “fact family.”

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
   This application claims priority to U.S. Provisional Patent Application No. 60/697,794 entitled “Arithmetic Block” and filed on Jul. 8, 2005 for Diane Madeline Bagüés, which is incorporated herein by reference. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   This invention relates to educational toys and more particularly relates to building blocks for teaching mathematical concepts. 
   2. Description of the Related Art 
   More and more is being asked of children academically at an increasingly younger age. Numerous devices of varying complexity are currently available to facilitate teaching basic arithmetic concepts and mathematical facts to young children. Yet ultimately what is required of children is, first, memorization of numbers and mathematical equations, including multiplication tables, and second, a basic recognition of how numbers and mathematical operations are related, including inverse relationships. 
   When teaching inverse operations, such as addition and subtraction and multiplication and division, basic number facts are commonly illustrated using three numbers in a simple equation. Groups of equations using the same three numbers are often referred to as “fact families.” Teaching or illustrating “fact families” helps children recognize the value of a number relative to other numbers. In addition, teaching “fact families” allows children to learn the relationship of mathematical operations, particularly when the sequence of the numbers or the order of the operation is reversed. 
   Devices such as flash cards to practice and test the learning of number facts are well known. Other devices require the child to match numbers and objects or to assemble numbers and arithmetic operands in a correct sequence, such as blocks that each contain a single number or operand from which can be constructed a mathematical equation. Some devices include intricate mechanisms to ensure that the sequence is ordered correctly. Electronic devices and computer programs are also known devices used to teach number facts to children. 
   While the known prior art devices accomplish their goals to varying degrees, all require the child to focus on mastering the given task, which may be appropriate for older or more academically advanced children. None of the devices, however, focuses on providing a child simple familiarity with numbers and equations while engaged in play, in particular while playing with a variation of the traditional alphabet/numbers blocks. 
   From the foregoing discussion, it should be apparent that a need exists for an apparatus and system for an educational toy block that facilitates teaching young children a basic level of familiarity with numbers and mathematical operations. Beneficially, such an apparatus and system would enable the child to comprehend and memorize basic mathematical operations at an accelerated level. In addition, the apparatus and system would provide additional developmentally appropriate learning mechanisms, including a building block for playing. 
   SUMMARY OF THE INVENTION 
   The present invention has been developed in response to the present state of the art, and in particular, in response to the problems and needs in the art that have not yet been fully solved by currently available educational toys and building blocks. Accordingly, the present invention has been developed to provide an apparatus and system for teaching mathematical operations and “fact families” that overcome many or all of the above-discussed shortcomings in the art. 
   The apparatus comprises an educational toy block configured, in one embodiment, to help young children memorize basic numbers and number facts in an atmosphere focused solely on play. The toy block may include a display of multiple mathematical equations in order to facilitate teaching children how mathematical operations are related. In a further embodiment, the toy block displays one or more numbers that are numerical elements in a plurality of mathematical equations forming a “fact family.” 
   The toy block, in one embodiment, comprises a polygonal-shaped building block having a plurality of faces, wherein a first face features a first mathematical equation and a second face features a second mathematical equation. In certain embodiments, the polygonal-shaped building block comprises a cube. In one embodiment, the second mathematical equation comprises the inverse operation of the first mathematical equation. A third face of the building block may feature a third equation wherein the sequence of the numerical elements of the first mathematical equation is reversed. In addition, a fourth face of the building block may feature a fourth equation that comprises the inverse operation of the third equation. A fifth face of the toy block may feature a first number, and a sixth face may feature a second number, wherein the mathematical equations include the featured first and second numbers. 
   The invention may further facilitate tactile learning and visual recognition. In one embodiment, the arithmetic block provides a mathematics learning tool for those who are blind or visually impaired. The numbers and/or elements of the mathematical equations may be raised relative to the surface of the building block in certain embodiments. In a further embodiment, the raised features are distinctively colored. In addition, the toy block may include a Braille transliteration of the featured numbers and/or mathematical equations. Thus, children both with or without disabilities may enjoy and learn mathematical principles from the toy block as well as muscle coordination and tactile sensitivity. 
   A system of the present invention is also presented for familiarizing children with multiple numbers and mathematical operations for “fact families.” The system may be embodied in a set of educational toy blocks. In particular, the system, in one embodiment, includes a plurality of polygonal-shaped building blocks each having a plurality of faces, wherein a first face features a first mathematical equation and a second face features a second mathematical equation. In addition, each building block features a distinct “fact family” illustrated through the operations of the first and second mathematical equations. In certain embodiments, the second mathematical equation comprises the inverse operation of the first mathematical equation. In one embodiment, the set includes ninety-one discrete building blocks each featuring a distinct “fact family” created by a unique pair of numbers from zero to twelve. 
   Reference throughout this specification to features, advantages, or similar language does not imply that all of the features and advantages that may be realized with the present invention should be or are in any single embodiment of the invention. Rather, language referring to the features and advantages is understood to mean that a specific feature, advantage, or characteristic described in connection with an embodiment is included in at least one embodiment of the present invention. Thus, discussion of the features and advantages, and similar language, throughout this specification may, but do not necessarily, refer to the same embodiment. 
   Furthermore, the described features, advantages, and characteristics of the invention may be combined in any suitable manner in one or more embodiments. One skilled in the relevant art will recognize that the invention may be practiced without one or more of the specific features or advantages of a particular embodiment. In other instances, additional features and advantages may be recognized in certain embodiments that may not be present in all embodiments of the invention. 
   The toy block of the present invention enables young children to become familiar with basic numbers and mathematical principles while enjoying the simple nature of the building block. These features and advantages of the present invention will become more fully apparent from the following description and appended claims, or may be learned by the practice of the invention as set forth hereinafter. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In order that the advantages of the invention will be readily understood, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments that are illustrated in the appended drawings. Understanding that these drawings depict only typical embodiments of the invention and are not therefore to be considered to be limiting of its scope, the invention will be described and explained with additional specificity and detail through the use of the accompanying drawings, in which: 
       FIG. 1  is a perspective view illustrating one embodiment of an educational toy block in accordance with the present invention; 
       FIG. 2  is an alternative perspective view illustrating the educational toy block of  FIG. 1 ; 
       FIGS. 3-8  are side views illustrating multiple faces of one embodiment of an educational toy block in accordance with the present invention; 
       FIGS. 9-14  are side views illustrating multiples faces of an alternative embodiment of an educational toy block in accordance with the present invention; 
       FIG. 15  is a perspective view illustrating one embodiment of an educational toy block with a Braille transliteration in accordance with the present invention; 
       FIG. 16  is an alternative perspective view illustrating the educational toy block of  FIG. 15 ; and 
       FIG. 17  is a graph illustrating unique number pairs of a set of educational toy blocks in accordance with the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Reference throughout this specification to “one embodiment,” “an embodiment,” or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases “in one embodiment,” “in an embodiment,” and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment. 
   Furthermore, the described features, structures, or characteristics of the invention may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the invention may be practiced without one or more of the specific details, or with other methods, components, materials, and so forth. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the invention. 
     FIGS. 1-2  depict one embodiment of a toy block  100  in accordance with the present invention. As illustrated, the toy block  100  comprises a cube  102  having six congruent square faces  104   a - f . In an alternative embodiment, the toy block  100  may comprise any polygonal-shaped building block having a plurality of faces  104 . The toy block  100  may be sized, in certain embodiments, to enable small children to handle the block. In particular, the toy block  100  may enable small children to become familiar with mathematical concepts during play. 
   Each face  104  of the toy block  100  may or may not feature distinct mathematical or numerical elements. In certain embodiments, one or more faces  104  may be blank. In one embodiment, mathematical elements are repeated on different faces  104  of the toy block  100 . For example, an octagonal-shaped building block may have two faces  104  that each features a number eight. The additional faces  104  of the block  100  may display mathematical equations or remain blank. Of course, mathematical equations as well as numbers may be repeated on multiple faces  104  of the toy block  100 . 
   In a preferred embodiment, the toy block  100  includes at least a first face  104   a  featuring a first mathematical equation  106  and a second face  104   b  featuring a second mathematical equation  108 . In the depicted embodiment, the cube  102  features a combination of distinct numbers and mathematical equations on each face  104   a - f  of the toy block  100 . The numbers and mathematical equations may illustrate number facts and may demonstrate a “fact family” in certain embodiments. 
   The toy block  100  may be made of a solid material such as wood, plastic, or the like as is known in the art. In a further embodiment, the toy block  100  may be hollow, meshed, or the like, so long as the featured mathematical and numerical elements on the faces  104  are viewable. In one embodiment, one or more faces  104  of the toy block  100  may be removable, interchangeable, rotatable and/or the like in order to add variety to the toy block  100 . In addition, the surface of the toy block  100  may be clear, colored, textured, or the like. In a preferred embodiment, the toy block  100  is structurally designed to enable stacking of multiple toy blocks  100  as is known in the art. 
   The elements featured on the toy block  100  may be raised from the surface of the block  100 , in certain embodiments, to distinguish the featured elements from the background and/or background surface of the toy block  100 . Children may enjoy the tactile experience of feeling the raised elements. A predominantly touch-oriented embodiment with raised Braille numbering is illustrated in greater detail with respect to  FIGS. 15-16 . 
   Alternatively or in addition, the featured elements on the toy block  100  may be colored. In one embodiment, each number is colored differently to help children recognize the individual numbers and unique mathematical operands. In certain embodiments, the featured numbers and mathematical elements are large enough for small children to easily see and feel which may help small children develop muscle coordination, touch sensitivity, and visual recognition. Those of skill in the art will recognize that changes of appearance, composition, and structure of the toy block  100  are within the scope of the invention, and the present invention is not, therefore, limited to the illustrated embodiments. 
     FIGS. 3-8  illustrate in greater detail one embodiment of the faces  104   a - f  of the cube  102  depicted in  FIGS. 1-2 . The first face  104   a  in the depicted embodiment features a first mathematical equation  106  or a simple mathematical fact. The first mathematical equation  106  is a multiplication equation  106  including the numbers three, four, and twelve in the sequence: three multiplied by four equals twelve. The three featured numbers form a “fact family” that is illustrated through the mathematical equations and features on the other faces  104   b - f  of the cube  102 . 
   The second face  104   b  of the illustrated cube  102  displays a second mathematical equation  108 . The second mathematical equation  108 , as depicted, is the inverse operation of the first mathematical equation  106 , or the division equation of twelve divided by four equals three. The division equation  108 , as well as other mathematical equations, may be shown in multiple forms on one or more faces  104  of the toy block  100 . For example, the division equation  108  may be represented in long division form  108   a  and in sentence form  108   b  on a single face  104   b , as depicted. In a further embodiment, the mathematical equations may be represented in Braille. 
   The third face  104   c  of the depicted cube  102  features a third mathematical equation  110  of the “fact family” featuring the same three numbers: four, three, and twelve. The third mathematical equation  110  in the depicted embodiment is an additional multiplication equation  110  or mathematical fact demonstrating the commutative property of multiplication by reversing the sequence of the elements of the first mathematical equation  106 . Thus, the third equation  110 , as depicted, features the sequence: four multiplied by three equals twelve. 
   The fourth face  104   d  of the depicted cube  102  features a fourth mathematical equation  112  illustrating the inverse operation of the third mathematical equation  110 . The fourth mathematical equation  112  is a division equation: twelve divided by three equals four, featured in two forms  112   a ,  112   b . The four equations  106 ,  108 ,  110 ,  112  featured on the four faces  104   a - d  of the cube  102  illustrate a unique numeric relationship for the numbers three, four, and twelve. 
   The fifth face  104   e  of the depicted cube  102  displays a first number  114  of the “fact family,” which is featured in the four equations  106 ,  108 ,  110 ,  112 . Similarly, the sixth face  104   f  of the cube  102  features a second number  116  of the “fact family,” which is also featured in the four equations  106 ,  108 ,  110 ,  112 . The numbers  114 ,  116  and the mathematical equations  106 ,  108 ,  110 ,  112  may be colored distinctly and raised to provide a tactile experience for the user. In addition, the grouping of equations  106 ,  108 ,  110 ,  112  and numbers  114 ,  116  of a “fact family” on a cube  102  may facilitate teaching children the relationship between numbers and mathematical operations in a play environment. 
     FIGS. 9-14  illustrate an alternative embodiment of a toy block  200  in accordance with the present invention. The toy block  200  features a “fact family” illustrated through the operations of addition and subtraction. Similar to the toy block  100 , the toy block  200  comprises a cube  202  with six square faces  204   a - f . In the depicted embodiment, each face  204  features a unique number or mathematical equation. 
   The first face  204   a  of the depicted cube  202  features a first mathematical equation  206 , which is an addition equation: three plus four equals seven. The three numbers in the equation may form a “fact family” featured on the cube  102 . 
   The second face  204   b  of the depicted cube  202  features a second mathematical equation  208  that comprises the inverse operation of the first mathematical equation  206 , or in other words, a subtraction equation. The second mathematical equation  208  illustrates another mathematical fact: seven minus four equals three. 
   The contrast of the first mathematical equation  206  with the second mathematical equations  208  illustrates the value of the numbers featured in the “fact family” relative to each other. Exposing children to similar equations grouped on toy blocks  100 ,  200  may enable children to distinguish the ruling mathematical principles and to recognize mathematical operations at an early age. Alternatively, the toy blocks  100 ,  200  may enable children who are struggling to learn the concepts to review the principles illustrated on the blocks  100 ,  200 . 
   The third face  204   c  of the depicted cube  202  features a third mathematical equation  210 . The third mathematical equation  210  displays the elements of the first mathematical equation  206  in a reversed sequence: four plus three equals seven. The third mathematical equation  210  additionally demonstrates the commutative property of addition. 
   The fourth face  204   d  of the depicted cube  202  illustrates a fourth mathematical equation  212  that illustrates the inverse operation of the third mathematical equation  210 : seven minus three equals four. The four equations  206 , 208 , 210 , 212  together illustrate a distinct numeric relation that exists between the numbers three, four, and seven. 
   The fifth face  204   e  and the sixth face  204   f  of the illustrated cube  202  feature a first number  214  and a second number  216  respectively. The numbers three and four belong to the illustrated “fact family” and are featured in the equations  206 ,  208 ,  210 ,  212 . 
     FIGS. 15-16  illustrate an alternative embodiment of a toy block  300  in accordance with the present invention. The depicted toy block  300  comprises a cube  302  with six congruent square faces  304   a - f . Each face  304   a - f  comprises a distinct number or mathematical equation relative to a “fact family.” 
   The toy block  300 , as illustrated, includes numeric and mathematical elements similar to those featured on the toy block  100  illustrated in  FIGS. 1-8 , including a first mathematical equation  306  and a second mathematical equation  308 . The toy block  300 , however, further comprises a Braille transliteration  310  of the elements featured on the cube  302 . All of the featured numeric and mathematical elements, including the Braille transliterations  310 , may be raised and distinctively colored to provide a tactile experience to the user. Consequently, users may be able to see and feel the contents presented on the toy block  300 . 
   The toy block  300  additionally provides an educational toy designed to facilitate teaching the blind and visually impaired mathematical concepts including, but not limited to, “fact families” and inverse operations. The toy block  300  may facilitate teaching the commutative properties of addition and/or multiplication to young children as well as to older children who struggle with mathematical concepts or have learning disabilities. 
   In certain embodiments, the toy block  300  belongs to a set of toy blocks  300 . In one embodiment, each toy block  300  within a set represents a distinct “fact family.” In an alternative embodiment, each toy block  300  features one or more numbers in multiple equations. The toy blocks  300  may or may not be repeated within a set. 
     FIG. 17  illustrates one embodiment of a set  400  that comprises ninety-one discrete building blocks  100  each featuring a distinct “fact family” created by a unique pair of numbers from zero to twelve. The first number  414  and the second number  416  of the unique pair are illustrated in the individual rows of the depicted columns. 
   In one embodiment, the first number  414  is featured on one of the plurality of faces  104  of the toy block  100 , and a second number  416  is featured on another face  104  of the toy block  100 . The first and second numbers  414 ,  416  are preferably elements of the first mathematical equation  106  and the second mathematical equation  108 , as discussed above. 
   The operations of the first mathematical equation  106  and the second mathematical equation  108  may facilitate illustrating the distinct numeric relationship between the first number  414  and the second number  416  in certain embodiments. In one embodiment, the first mathematical equation  106  is a multiplication equation and the second mathematical equation  108  is a division equation. In an alternative embodiment, the first mathematical equation  106  is an addition equation and the second mathematical equation  108  is a subtraction equation. 
   In addition, the set  400  of building blocks  100  may help children recognize and memorize basic inverse operations and “fact families.” In certain embodiments, the set  400  further encourages children to learn multiplication and division. In an alternative embodiment, the set  400  facilitates learning addition and subtraction. 
   In one embodiment, the set  400  of building blocks  100  comprises a combination of variously-shaped building blocks. For example, the set  400  may include rectangular blocks, cube-shaped blocks, pyramid-shaped blocks, and the like. In addition, the size of the blocks  100  may vary within a set  400 . 
   The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.