Abstract:
A teaching aid for facilitating in the learning and comprehension of multiplication tables is provided. The teaching aid includes a plurality of generally flat tabs including a front surface and a rear surface. At least one of the front surface or the rear surface is capable of having indicia displayed thereon. The tabs include a first end and a second end, the second end including an aperture. A retaining member extends through the aperture of the second end of each of the plurality of tabs for resiliently holding the plurality of tabs together while permitting each of the tabs to rotate with respect to the other. A plurality of indicia are displayed on at least one of the front or rear surface. Wherein, the indicia correspond to a graphical representation of the product of a first number and a second number to be multiplied.

Description:
BACKGROUND 
       [0001]    The present exemplary embodiment relates to the field of teaching aids. It finds particular application in conjunction with methods and systems for teaching students how to multiple basic integers (i.e., whole numbers between zero (0) and ten (10)). However, it is to be appreciated that the present exemplary embodiment is also amenable to other like applications. 
         [0002]    Various types of teachings aids are available for teaching students how to multiply basic integers (e.g., flash cards, multiplication tables, etc.). However, these aids or methods have numerous disadvantages. For example, a basic multiplication table is plain and requires repetitive and mundane memorization of a series of numbers and their respective products. Such a teaching method does not stimulate the learning process and fails to engage or capture a student&#39;s attention for extended periods, thus making the learning process less effective and more time consuming. Moreover, while some students are adept at auditory learning and/or plainly memorizing the associations of various numbers (as in a basic multiplication table), many other students are more adept to learning by fully comprehending the association by some visual, graphical, or tangible representation of the numbers being multiplied. In addition, many teaching aids involve several pieces or cards (e.g., a deck of flash cards), and are not suitable for most teaching environments because pieces of the teaching aid can be easily misplaced, disorganized, or destroyed. 
         [0003]    Accordingly, it is an object of the present invention to develop a new and enhanced multiplication teaching aid which will overcome the foregoing difficulties and others while providing better and more advantageous results. 
       SUMMARY 
       [0004]    According to one aspect of the present invention, a teaching aid for facilitating in the learning and comprehension of multiplication tables is provided. The teaching aid includes a plurality of generally flat tabs including a front surface and a rear surface. At least one of the front surface or the rear surface is capable of having indicia displayed thereon. The tabs include a first end and a second end, the second end including an aperture. A retaining member extends through the aperture of the second end of each of the plurality of tabs for resiliently holding the plurality of tabs together while permitting each of the tabs to rotate with respect to the other. A plurality of indicia are displayed on at least one of the front or rear surface. Wherein, the indicia correspond to a graphical representation of the product of a first number and a second number to be multiplied. 
         [0005]    According to another aspect of the present invention, a method of teaching a student how to multiply using a teaching aid is provided. The method includes providing the teaching aid with a plurality of tabs. The tabs bear indicia that graphically represent the product of a first number to be multiplied by a second number to be multiplied. The first number to be multiplied corresponds to a first set of indicia and the second number to be multiplied corresponds to a second set of indicia. The teaching aid is presented to the student. The association of the product between the first number to be multiplied and the second number to be multiplied and the first set of corresponding indicia and the second set of corresponding indicia, is explained to the student. 
         [0006]    Still other aspects of the invention will become apparent from a reading and understanding of the detailed description of the preferred embodiments hereinbelow. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0007]    The present invention may take physical form in certain parts and arrangements of parts, preferred embodiments of which will be described in detail in this specification and illustrated in the accompanying drawings which form a part of the invention. 
           [0008]      FIG. 1  is a perspective view of a multiplication teaching aid for the 2&#39;s multiplication table depicted in an open or fanned configuration, according to the present invention. 
           [0009]      FIG. 2  is a perspective view the teaching aid of  FIG. 1  in a collapsed or stacked configuration. 
           [0010]      FIG. 3  is an exploded view of a plurality of tabs of the teaching aid of  FIG. 1 , each of the plurality of tabs illustrating a set of numbers to be multiplied, a product of the set of numbers to be multiplied, and a set of indicia corresponding to the product of the set of number to be multiplied. 
           [0011]      FIG. 4  is a front view of the teaching aid of  FIG. 1 . 
           [0012]      FIG. 5  is a front view of another embodiment of a multiplication teaching aid, illustrating the 3&#39;s multiplication table. 
           [0013]      FIG. 6  is a front view of another embodiment of a multiplication teaching aid, in a partially collapsed state, illustrating the 4&#39;s multiplication table. 
           [0014]      FIG. 7  is a front view of another embodiment of a multiplication teaching aid, in a partially collapsed state, illustrating the 5&#39;s multiplication table. 
           [0015]      FIG. 8  is a front view of another embodiment of a multiplication teaching aid, in a partially collapsed state, illustrating the 6&#39;s multiplication table. 
           [0016]      FIG. 9  is a front view of another embodiment of a multiplication teaching aid, in a partially collapsed state, illustrating the 7&#39;s multiplication table. 
           [0017]      FIG. 10  is a front view of another embodiment of a multiplication teaching aid, in a partially collapsed state, illustrating the 8&#39;s multiplication table. 
           [0018]      FIG. 11  is a front view of another embodiment of a multiplication teaching aid, in a partially collapsed state, illustrating the 9&#39;s multiplication table. 
           [0019]      FIG. 12  is a front view of another embodiment of a multiplication teaching aid, similar to that of  FIG. 3 , illustrating raised indicia for a partial series of the 2&#39;s multiplication table. 
           [0020]      FIG. 13  is a side view of the multiplication teaching aid of  FIG. 12  further illustrating the raised indicia. 
       
    
    
     DETAILED DESCRIPTION 
       [0021]    With reference to  FIG. 1 , a first embodiment of a teaching aid  100  is shown. Generally, the teaching aid  100  includes a plurality of tabs  102 . Each of the individual tabs  102   a - 102   i  of the plurality of tabs  102  include a first or forward surface  104  and a second or rear surface  106 . The plurality tabs  102  may be made from any material suitable for carrying or displaying printed and/or embossed images, icons, or other indicia. In addition, the material used for form the tabs  102  can be any sheet material that is generally flat, flexible and resilient (e.g., metal, plastic, vinyl, laminated paper, durable wood, etc.) Furthermore, the material chosen could have a relatively low coefficient of friction and or be coated with a non-stick material, such as PTFE (a/k/a, Teflon®) or any other suitable non-stick and non-toxic material. 
         [0022]    With continued reference to  FIG. 1 , the teaching aid  100  generally illustrates a multiplication series for the number two (2). Specifically, a multiplication series for the number two (2) is illustrated with respect to the range of integer based numbers beginning at one (1) and ending at nine (9). With particular reference to the first tab  102   a  of the plurality of tabs  102  of the teaching aid  100 , a first number  108  is multiplied by a second number  110  to produce a resultant product  112 . Here, the first number is the number one (1) and the second number is the number two (2). Of course, the resultant product  112  is itself, the number two (2). Just below this equation or headline of text (which indicates the numbers to be multiplied), is a graphical representation or icon  114  which corresponds to the resultant product of the first and second numbers  108 ,  110 . By way of example only, the icon or graphical representation illustrated in  FIG. 1  (as well as  FIGS. 2-6 ), involves the use of one side or face of a playing die. Here, the icon  114  used for the plurality of tabs  102 , as illustrated in  FIG. 1 , involves the use of the side of a playing die corresponding to the number two (2). 
         [0023]    Now with reference to the second tab  102   b  of the plurality of tabs  102  in  FIG. 1 , a first number  108   b  to be multiplied is the number two (2) (as opposed to one (1) as illustrated in the first tab  102   a ) and the resultant product  112   b  is four (4). As such, the graphical representation or icons  114   b  illustrate a quantity of icons corresponding to the first number  108   b  and each having or displaying a value corresponding to the second number  110   b . Similarly, the third tab  102   c  of the plurality of tabs  102  includes a quantity of three icons  114   c  which all display the value two (2) of a playing die. In this manner, a student can visually correlate or conceptualize the meaning of a first number being multiplied by a second number and thereby associate those numbers to their resultant product. In the case, for instance, of the third tab  102   c , a student would observe the first number three (3) being multiplied by a second number two (2) resulting in a product of six (6) and would correlate this to three playing dies each having two individual dots therein (which indicates a value of two (2)) and thus be able to comprehend or associate the meaning of such numerical representation. 
         [0024]    Collectively, the tabs  102  can complete a multiplication series for a given number. For example, where the series involves the multiplication of the number two (2), each tab  102   a - 102   i  would successively illustrate the multiplication of 1×2, 2×2, 3×2, 4×2, 5×2, and so forth. Thus, for example, the forth tab  102   d  would illustrate the value of 4×2 and illustrate it having four playing die, each containing two dots so that when the dots are counted, the sum of the dots equals the resultant product captioned on the tab. Similarly, the fifth tab  102   e  graphically illustrates the multiplication of 5×2, the sixth tab  102   f  illustrates the multiplication of 6×2, the seventh tab  102   g  illustrates the multiplication of 7×2, the eighth tab  102   h  illustrates the multiplication of 8×2 and the ninth tab  102   i  illustrates the multiplication of 9×2. 
         [0025]    Now with reference to  FIG. 2 , the plurality of tabs  102  of the teaching aid  100  are illustrated in a closed state, so that the individual tabs are collapsed or are in line with one another, and thus, can be conveniently stored or transported. Furthermore, the collapsible nature of the teaching aid also helps to protect the tabs from damage due to rough handling (i.e., from being ripped or torn). 
         [0026]    Now with reference to  FIG. 3 , the teaching aid  100  is shown in an exploded view such that the plurality of tabs  102  have been disjoined and arranged side-by-side. Each of the tabs  102   a - 102   i  includes a first end  116  and a second end  118 . As illustrated, the first end  116  may include or display the text equivalent of the numbers being multiplied and their resultant product, while the second end  118  may include an aperture  120  for receiving a retaining element or member  122  (as illustrated in  FIGS. 1 and 2 ). In this way, the individual tabs  102   a - 102   i  may be sequentially arranged so that their second ends  118  and their respective apertures  120  are aligned so as to receive the retaining member. The retaining member can be made from any number of materials, including but not limited to wood, steel or plastic. Whatever manner is chosen, the retaining member should be arranged or adjusted so as to permit the individual tabs to rotate about their respective ends. This enables the user or student to fan the tabs in or out so that any or all tabs can be viewed and studied without impairment. By way of example, the teaching aid  100  is shown in a partially fanned out state in  FIG. 4 . In that Figure, nearly all of the individual tabs  102   a - 102   i  can be viewed without impairment. In this manner, as the various tabs are fanned out, the student can see the groupings and progression which will aid in the learning process. 
         [0027]    Now with reference to  FIG. 5 , a second embodiment of a teaching aid  200  is shown resembling in many respects the first embodiment of the teaching aid  100  illustrated in  FIG. 1 . As with the first embodiment, the teaching aid  200  includes a plurality of tabs  202 , each representing a set of first and second numbers to be multiplied. As illustrated here, the multiplication series from 1 through 9 for the number three (3) is shown. Corresponding to the multiplication series of the number 3, is a graphical representation or icon  214  of a surface of a playing die representing the number three (3). Accordingly, for the first tab  202   a , only a single playing die  214   a  is shown since the first number to be multiplied  208   a  is the number one (1). The multiplication series of the second embodiment ends with the multiplication of the first and second numbers 9×3, respectively, as illustrated on the ninth tab  202   i . In particular, the ninth tab  202   i  illustrates nine individual icons  214   i  corresponding to the side of a playing die having the value three (3). Similarly, the remaining tabs  202   b - 202   h  also illustrate a commensurate number of icons corresponding to the respective first number being multiplied. 
         [0028]    With reference to  FIGS. 6-11 , still other embodiments of a multiplication teaching aid  300 ,  400 ,  500 ,  600 ,  700 ,  800  are illustrated depicting, similar to the previously discussed embodiments, the multiplication “tables” or series for the numbers four (4), five (5), six (6), seven (7), eight (8) and nine (9), respectively. While only the ones, fives and nines tabs are visible in  FIGS. 6-11 , it should be understood that the remaining tabs (twos, threes, fours, sizes, sevens, and eights) are also provided for but are hidden from view in these figures. Also, it should be noted that while the teaching aids for the number series between two (2) and six (6) can utilize as one set of indicia the respective side of a playing die, no such playing die face exists for the remaining numbers seven (7), eight (8) and nine (9), as specifically illustrated in  FIGS. 9-11 . As such, the disclosed groupings of the indicia are unique in at least this respect. 
         [0029]    Lastly, with reference to  FIGS. 12 and 13 , yet another embodiment of a multiplication teaching aid  900  illustrates the use of raised or embossed lettering and/or indicia. Similar in nature to the previously discussed embodiments, the teaching aid  900  may include a plurality of tabs  902   a - 902   e , each tab representing a particular number to be multiplied (e.g., two (2) through (5) as illustrated in  FIG. 12 ) for a particular series or multiplication “table” (e.g., the twos (2&#39;s) multiplication tables as illustrated in  FIG. 12 ). However, graphical representations, icons, and/or indicia  914   a - 914   e  of the numbers being multiplied on the respective tab are raised, elevated or otherwise displaced (e.g., forwardly or rearwardly) from the nominal face of the respective tab. This allows the student to “feel” the graphical representation, icon, or indicia of the numbers being multiplied and their resultant product. Such a teaching aid could be particularly suited to students which prefer more tactile learning techniques and/or those that are visually impaired. 
         [0030]    It should be further noted that the plurality of tabs could be made in any general shape having dimensions that are suitable for the needs of a particular teaching environment. However, it has been found that tabs having a length of about 6″, a width of about ¾″ and a thickness of about 1/16″ is suitable in most cases. Moreover, the individual numbers to be multiplied could be made of wood, plastic or metal. Naturally, the tabs and or indicia displayed thereon can be presented in any variety or combination of colors and or the tabs and or teaching aids can be color coded to reflect the multiplication of a particular number series. Furthermore, the teaching aids could be made flat and/or in Braille to assist the visually impaired student. In addition, the individual indicia could be different, rather than being images of the individual surface of a playing die, they could be formed from other indicia that incorporate or can represent numerical values. 
         [0031]    The exemplary embodiments have been described with reference to the preferred embodiments. Obviously, modifications and alterations will occur to others upon reading and understanding the preceding detailed description. It is intended that the exemplary embodiment be construed as including all such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.