Title:

Kind
Code:

A1

Abstract:

The devices for teaching elementary fractional concepts each include a board having a raised periphery and central depression representing unity. Each embodiment includes a series of fractional pieces of different sizes for removable installation therein, with the number of pieces of each size having a total span equal to the span of the central depression. Thus, each piece represents the denominator of a fractional portion of the central recess. The pieces may be stacked in several layers, thus demonstrating the equivalency of different sizes of fractional pieces subtending the same area of the recess. The devices may be formed in rectangular or circular configurations, and may represent the basic abstract concept of fractions, monetary values in different systems, time and divisions thereof, etc. Separate boards may be provided for each embodiment, or inserts may be provided for placement within recesses of correspondingly configured boards.

Inventors:

Garmirian, Barbara E. (Reading, PA, US)

Application Number:

11/898511

Publication Date:

03/13/2008

Filing Date:

09/12/2007

Export Citation:

Primary Class:

International Classes:

View Patent Images:

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Primary Examiner:

BALDORI, JOSEPH B

Attorney, Agent or Firm:

Richard C. Litman (Alexandria, VA, US)

Claims:

I claim:

1. A device for teaching elementary fractional concepts, comprising: a board having a raised periphery defining a central recess therein, the recess subtending a span; a plurality of numerical designators disposed upon the raised periphery; and a first group and a second group of fractional pieces selectively and removably installed within the central recess of the board and forming a first stratum and a second stratum of fractional pieces when placed within the recess of the board, the fractional pieces within each of the groups being a plurality of pieces equal in size to one another, each of the groups having pieces distinctive in size and number, each of the pieces representing a denominator of a fraction, the pieces within each of the groups having a total span equal to the span of the central recess of the board.

2. The device for teaching elementary fractional concepts according to claim 1, wherein: the central recess of the board has a rectangular configuration, the span of the central recess being equal to the length of the central recess; and each of the fractional pieces has a rectangular shape having a width corresponding to a fraction of the span of the central recess.

3. The device for teaching elementary fractional concepts according to claim 1, wherein: the central recess of the board has a circular configuration, the span of the central recess subtending the circumference of the central recess; and each of the fractional pieces comprises a circular sector subtending an arc corresponding to a fraction of the span of the central recess.

4. The device for teaching elementary fractional concepts according to claim 3, further including: at least an hour hand and a minute hand pivotally secured concentrically within the central recess; and a time quantity representation disposed upon each of the fractional pieces, the amount of each time quantity representation corresponding to the size of the fractional piece upon which the time quantity representation is disposed.

5. The device for teaching elementary fractional concepts according to claim 1, further including: an insert removably installed within the central recess of the board, the insert having a raised periphery defining a central recess therein; and a plurality of numerical designators disposed upon the raised periphery of the insert.

6. The device for teaching elementary fractional concepts according to claim 1, wherein: the plurality of numerical designators of the raised periphery comprise monetary divisions; a monetary coin representation is disposed upon each of the fractional pieces; and each coin representation has a value corresponding to the size of the fractional piece upon which the coin representation is disposed.

7. The device for teaching elementary fractional concepts according to claim 6, wherein at least some of the fractional pieces further include representations of a plurality of smallest denomination coins disposed thereon, corresponding to the fractional value represented by the size of the fractional piece upon which the smallest denomination coin representations are disposed.

8. The device for teaching elementary fractional concepts according to claim 1, wherein each of the fractional pieces has a first side having a first color disposed thereon, and a second side opposite the first side having a second color disposed thereon.

9. A device for teaching elementary fractional concepts, comprising: a board having a raised periphery defining a rectangular central recess therein, the recess having a length defining the span of the rectangular recess, the raised periphery having a plurality of fractional numerical designators thereon; a first group and a second group of fractional pieces selectively and removably installed within the central recess of the board and forming a first stratum and a second stratum of fractional pieces, each of the fractional pieces having a rectangular shape and a width corresponding to a fraction of the span of the central recess, the fractional pieces within each of the groups being a plurality of pieces equal in size to one another, each of the groups having pieces distinctive in size and number, each of the pieces representing a denominator of a fraction, the pieces within each of the groups having a total span equal to the span of the central recess of the board.

10. The device for teaching elementary fractional concepts according to claim 9, further including: an insert removably installed within the central recess of the board, the insert having a raised periphery defining a central recess therein; and a plurality of numerical designators disposed upon the raised periphery of the insert.

11. The device for teaching elementary fractional concepts according to claim 9, wherein: the plurality of numerical designators of the raised periphery comprise monetary divisions; a monetary coin representation is disposed upon each of the fractional pieces; and the value of each coin representation corresponds to the size of the fractional piece upon which the coin representation is disposed.

12. The device for teaching elementary fractional concepts according to claim 11, wherein at least some of the fractional pieces further include representations of a plurality of smallest denomination coins disposed thereon, corresponding to the fractional value represented by the size of the fractional piece upon which the smallest denomination coin representations are disposed.

13. The device for teaching elementary fractional concepts according to claim 9, wherein each of the fractional pieces has a first side having a first color disposed thereon, and a second side opposite the first side having a second color disposed thereon.

14. A device for teaching elementary fractional concepts, comprising: a board having a raised periphery defining a central recess therein, the recess having a circular configuration defining a span subtending the circumference of the central recess, the raised periphery having a plurality of numerical designators thereon; a first group and a second group of fractional pieces selectively and removably installed within the central recess of the board and forming a first stratum and a second stratum of fractional pieces, each of the fractional pieces being a circular sector subtending an arc corresponding to a fraction of the span of the central recess, the fractional pieces within each of the groups being a plurality of pieces equal in size to one another, each of the groups having pieces distinctive in size and number, each of the pieces representing a denominator of a fraction, the pieces within each of the groups having a total span equal to the span of the central recess of the board.

15. The device for teaching elementary fractional concepts according to claim 14, further including: at least an hour hand and a minute hand pivotally secured concentrically within the central recess; a time quantity representation disposed upon each of the fractional pieces, the amount of each time quantity representation corresponding to the size of the fractional piece upon which the time quantity representation is disposed.

16. The device for teaching elementary fractional concepts according to claim 14, further including: an insert removably installed within the central recess of the board, the insert having a raised periphery defining a central recess therein; and a plurality of numerical designators disposed upon the raised periphery of the insert.

17. The device for teaching elementary fractional concepts according to claim 14, wherein: the plurality of numerical designators of the raised periphery comprise monetary divisions; a monetary coin representation is disposed upon each of the fractional pieces; and the value of each coin representation corresponds to the size of the fractional piece upon which the coin representation is disposed.

18. The device for teaching elementary fractional concepts according to claim 17, wherein at least some of the fractional pieces further include representations of a plurality of smallest denomination coins disposed thereon, corresponding to the fractional value represented by the size of the fractional piece upon which the smallest denomination coin representations are disposed.

19. The device for teaching elementary fractional concepts according to claim 14, wherein each of the fractional pieces has a first side having a first color disposed thereon, and a second side opposite the first side having a second color disposed thereon.

1. A device for teaching elementary fractional concepts, comprising: a board having a raised periphery defining a central recess therein, the recess subtending a span; a plurality of numerical designators disposed upon the raised periphery; and a first group and a second group of fractional pieces selectively and removably installed within the central recess of the board and forming a first stratum and a second stratum of fractional pieces when placed within the recess of the board, the fractional pieces within each of the groups being a plurality of pieces equal in size to one another, each of the groups having pieces distinctive in size and number, each of the pieces representing a denominator of a fraction, the pieces within each of the groups having a total span equal to the span of the central recess of the board.

2. The device for teaching elementary fractional concepts according to claim 1, wherein: the central recess of the board has a rectangular configuration, the span of the central recess being equal to the length of the central recess; and each of the fractional pieces has a rectangular shape having a width corresponding to a fraction of the span of the central recess.

3. The device for teaching elementary fractional concepts according to claim 1, wherein: the central recess of the board has a circular configuration, the span of the central recess subtending the circumference of the central recess; and each of the fractional pieces comprises a circular sector subtending an arc corresponding to a fraction of the span of the central recess.

4. The device for teaching elementary fractional concepts according to claim 3, further including: at least an hour hand and a minute hand pivotally secured concentrically within the central recess; and a time quantity representation disposed upon each of the fractional pieces, the amount of each time quantity representation corresponding to the size of the fractional piece upon which the time quantity representation is disposed.

5. The device for teaching elementary fractional concepts according to claim 1, further including: an insert removably installed within the central recess of the board, the insert having a raised periphery defining a central recess therein; and a plurality of numerical designators disposed upon the raised periphery of the insert.

6. The device for teaching elementary fractional concepts according to claim 1, wherein: the plurality of numerical designators of the raised periphery comprise monetary divisions; a monetary coin representation is disposed upon each of the fractional pieces; and each coin representation has a value corresponding to the size of the fractional piece upon which the coin representation is disposed.

7. The device for teaching elementary fractional concepts according to claim 6, wherein at least some of the fractional pieces further include representations of a plurality of smallest denomination coins disposed thereon, corresponding to the fractional value represented by the size of the fractional piece upon which the smallest denomination coin representations are disposed.

8. The device for teaching elementary fractional concepts according to claim 1, wherein each of the fractional pieces has a first side having a first color disposed thereon, and a second side opposite the first side having a second color disposed thereon.

9. A device for teaching elementary fractional concepts, comprising: a board having a raised periphery defining a rectangular central recess therein, the recess having a length defining the span of the rectangular recess, the raised periphery having a plurality of fractional numerical designators thereon; a first group and a second group of fractional pieces selectively and removably installed within the central recess of the board and forming a first stratum and a second stratum of fractional pieces, each of the fractional pieces having a rectangular shape and a width corresponding to a fraction of the span of the central recess, the fractional pieces within each of the groups being a plurality of pieces equal in size to one another, each of the groups having pieces distinctive in size and number, each of the pieces representing a denominator of a fraction, the pieces within each of the groups having a total span equal to the span of the central recess of the board.

10. The device for teaching elementary fractional concepts according to claim 9, further including: an insert removably installed within the central recess of the board, the insert having a raised periphery defining a central recess therein; and a plurality of numerical designators disposed upon the raised periphery of the insert.

11. The device for teaching elementary fractional concepts according to claim 9, wherein: the plurality of numerical designators of the raised periphery comprise monetary divisions; a monetary coin representation is disposed upon each of the fractional pieces; and the value of each coin representation corresponds to the size of the fractional piece upon which the coin representation is disposed.

12. The device for teaching elementary fractional concepts according to claim 11, wherein at least some of the fractional pieces further include representations of a plurality of smallest denomination coins disposed thereon, corresponding to the fractional value represented by the size of the fractional piece upon which the smallest denomination coin representations are disposed.

13. The device for teaching elementary fractional concepts according to claim 9, wherein each of the fractional pieces has a first side having a first color disposed thereon, and a second side opposite the first side having a second color disposed thereon.

14. A device for teaching elementary fractional concepts, comprising: a board having a raised periphery defining a central recess therein, the recess having a circular configuration defining a span subtending the circumference of the central recess, the raised periphery having a plurality of numerical designators thereon; a first group and a second group of fractional pieces selectively and removably installed within the central recess of the board and forming a first stratum and a second stratum of fractional pieces, each of the fractional pieces being a circular sector subtending an arc corresponding to a fraction of the span of the central recess, the fractional pieces within each of the groups being a plurality of pieces equal in size to one another, each of the groups having pieces distinctive in size and number, each of the pieces representing a denominator of a fraction, the pieces within each of the groups having a total span equal to the span of the central recess of the board.

15. The device for teaching elementary fractional concepts according to claim 14, further including: at least an hour hand and a minute hand pivotally secured concentrically within the central recess; a time quantity representation disposed upon each of the fractional pieces, the amount of each time quantity representation corresponding to the size of the fractional piece upon which the time quantity representation is disposed.

16. The device for teaching elementary fractional concepts according to claim 14, further including: an insert removably installed within the central recess of the board, the insert having a raised periphery defining a central recess therein; and a plurality of numerical designators disposed upon the raised periphery of the insert.

17. The device for teaching elementary fractional concepts according to claim 14, wherein: the plurality of numerical designators of the raised periphery comprise monetary divisions; a monetary coin representation is disposed upon each of the fractional pieces; and the value of each coin representation corresponds to the size of the fractional piece upon which the coin representation is disposed.

18. The device for teaching elementary fractional concepts according to claim 17, wherein at least some of the fractional pieces further include representations of a plurality of smallest denomination coins disposed thereon, corresponding to the fractional value represented by the size of the fractional piece upon which the smallest denomination coin representations are disposed.

19. The device for teaching elementary fractional concepts according to claim 14, wherein each of the fractional pieces has a first side having a first color disposed thereon, and a second side opposite the first side having a second color disposed thereon.

Description:

This application claims the benefit of U.S. Provisional Patent Application Ser. No. 60/844,091, filed Sep. 13, 2006.

1. Field of the Invention

The present invention relates generally to educational tools and devices used for teaching various concepts and skills. More specifically, the present invention relates to devices for teaching elementary fractional concepts encompassing boards or trays, each board or tray having a central recess therein. A series of fractional pieces having sizes proportional to the fractional values represented may be installed in and removed from the central recess, and different sizes of pieces representing different fractional denominators may be placed in a series of layers within the recess.

2. Description of the Related Art

The teaching of most mathematical concepts, including the concept of fractions, is traditionally accomplished by means of blackboard and chalk, pencil and paper, and/or textbooks and workbooks. None of these means provide a solid, three-dimensional, hands-on experience for the student. The result is that many, if not most, students have at least some degree of difficulty in grasping the subject, particularly younger children first learning about fractions. Somewhat the same points apply to teaching younger children about basic money and coin values, in that the basic unit of currency is subdivided into smaller units (e.g., dollars and cents) for just about every currency in the world. At least when learning about the monetary system, the student may actually handle the units (coins, etc.) while gaining some familiarity with their relative values. However, most monetary systems use coins that are often not proportional in size and weight to the values represented. This results in further difficulties for the student learning about basic monetary values, whether in one's native currency or when learning about a foreign currency for a trip abroad.

As a result, a few devices and systems for teaching fractions and monetary values have been developed in the past. Simulated currency (“play money”) has often been used in the past for teaching the value of currency and more particularly paper or folding money, with some development of simulated coins being done in the past as well. A major problem with simulated coins is that they represent the actual sizes of the coins represented, rather than providing any components having proportional sizes to the values of the coins represented. This can make it difficult for the student to grasp the relative values of the coins represented. Others have developed boards with various removable overlays representing different monetary or fractional values. The plethora of such devices attests to the continuing need for tools for teaching fractional concepts.

Thus, devices for teaching elementary fractional concepts solving the aforementioned problems are desired.

The devices for teaching elementary fractional concepts comprise a series of embodiments, each embodiment including a board having a relatively large central recess defined by a raised periphery. The central recess represents unity, or a value of one unit. Each embodiment further includes a series of fractional pieces of different sizes proportional to their fractional values and representing the denominator of a fraction. For example, each piece of a series of four fractional pieces subtends one fourth of the area of the central recess, with each of a series of ten pieces subtending one tenth of the area, etc. Multiple layers of the fractional pieces may be installed atop one another in order to clearly show the equivalent values of different fractions, e.g., five 1/10 pieces may be placed atop two ¼ pieces, subtending exactly the same half board area for both and clearly showing their equivalence. Thus, the student can readily see the sizes of the pieces relative to one another and to the size of the central recess of the board to grasp the concept of the fractional quantity represented.

The devices for teaching elementary fractional concepts may be applied to abstract fractional numerical values, and may also be applied to a special case for teaching basic monetary values as well. In the case of the monetary teaching device, the central depression may include a representation of a basic unit of currency, e.g., one dollar, with fractional pieces representing various coin values and subtending areas of the central depression proportional to their values. The same principle may be applied to various currencies of different nations as well. The currency teaching device may be constructed as a stand-alone device, or may be formed as an insert for removable installation within the central depression of the basic fractional teaching device.

The devices may be formed in rectangular configurations with the fractional pieces extending from one edge to the other and having a lateral span or width proportional to their fractional values, or may be formed in circular configurations with each of the fractional pieces subtending a circular sector. In the case of the circular configurations, one embodiment may include a set of selectively positionable clock hands, with the periphery of the board marked in hours and minutes. The fractional pieces may be marked to represent the minutes corresponding to the fractional value of the piece, e.g., a piece covering ⅙ of the circular area could be marked to indicate ten minutes, etc. In any event, all embodiments utilize the common theme of the central depression and multiple values of fractional pieces removably installable therein in multiple layers to show the equivalence of various fractional values.

These and other features of the present invention will become readily apparent upon further review of the following specification and drawings.

FIG. 1 is an exploded perspective view of a first embodiment comprising a rectangular board and fractional pieces for teaching fractions according to the present invention.

FIG. 2 is an exploded perspective view of a removably installable insert for the board of FIG. 1 and fractional pieces for use therewith, with the insert and pieces representing various U.S. monetary values.

FIG. 3 is a perspective view of a group of fractional pieces representing different values of smaller denomination coins for use with the monetary teaching insert of FIG. 2.

FIG. 4 is an exploded perspective view of a removably installable insert for the board of FIG. 1, with the insert and fractional pieces representing various Euro coin monetary values.

FIG. 5 is an exploded perspective view of another alternative embodiment, comprising a circular board and recess with fractional pieces in the form of arcuate circular segments.

FIG. 6 is an exploded perspective view of a removably installable insert for the board of FIG. 5 and fractional pieces for use with the insert, with the insert and fractional pieces representing various U.S. coin values.

FIG. 7 is an exploded perspective view of another alternative embodiment, comprising a circular board and recess with selectively positionable clock hands therein and a series of fractional pieces representing periods of time.

Similar reference characters denote corresponding features consistently throughout the attached drawings.

The present invention comprises a series of embodiments of a device for teaching elementary fractional concepts, e.g., abstract arithmetical fractions, money and small change, time and fractions of an hour, etc. Each of the embodiments includes a board, or insert for a basic board, and a series of groups of fractional pieces, with each group having pieces of like size representing fractional pieces having the same denominator. The various pieces of each group are used to form various strata within the central recess of the board, with the student readily able to see the correspondence in value between different pieces when so overlaid within the board recess.

FIG. 1 provides an exploded perspective view of a first embodiment **100**, comprising a rectangular board **102** having raised opposite first and second or major peripheral edges **1** **04** and **106**, and raised opposite third and fourth, minor or end peripheral edges **108** and **110**. The raised peripheral edge components **104** through **110** form a continuous periphery defining a central recess **112** therein, with the recess **112** subtending a lateral span or major width **114** representing unity and extending between the inner edges of the two end peripheral edges **108** and **110**. The first and second major peripheral edges **104** and **106** preferably include a series of numerical designators **116** thereon, representing arithmetical, monetary, or other values or quantities, as desired.

In the example of FIG. 1, the numerical designators **116** comprise a series of evenly spaced numbers representing fractional divisions of the major width or span **114** of the central recess **112**, with other numbers indicating the factors of non-prime numbers as applicable, e.g., the fractional division **12** has its factors 2, 3, 4, and 6 in adjacent brackets. The numbers along the first or upper periphery **104** are used to represent the numerator of any fractional quantity being represented, and the numbers along the second or lower periphery **106** are used to represent the denominator. While a total of twenty divisions are shown along each of the peripheries **104** and **106**, with each division being equal to 1/20 of the total span **114** of the central recess **112**, it will be understood that any practicable number of divisions may be provided as desired.

A series of relatively thin, flat, planar fractional pieces is provided for removable placement within the central recess **112** of the board **102**. Each series comprises a group of identically sized pieces each having a width less than the span **114** of the board recess **112**, with all of the pieces in any one group having a total width equal to the board recess span **114**.

In the example of FIG. 1, three different series of fractional pieces are shown. The first set or group comprising the largest pieces, e.g., pieces **118***a, ***118***b, *and **118***c, *comprises a total of four pieces (three of which are shown at least partially in FIG. 1), with each piece having a width **120** subtending one quarter of the span **114** of the central recess **112**. The next group or set of pieces comprises a series of ten intermediate pieces, e.g., **122***a, ***122***b, ***122***c, *etc., each having a width **124** subtending one tenth of the central recess span **114**. A third set of pieces comprises a series of twenty smaller pieces of which five are shown in FIG. 1, i.e., **126***a *through **126***e. *Each of these smaller pieces has a width **128** subtending one twentieth of the span **114** of the central recess **112**.

Thus, each piece represents the denominator of a fraction, with the denominator being equal to the number of pieces within each group or set. One or more of the smaller pieces **126***a, *etc. could be subdivided to form even smaller pieces, if so desired, but this may not be practicable. Alternatively, one or more of the smaller fractional pieces **126***a, *etc. could be marked with lines indicating the division of the pieces into still smaller components, while still maintaining a practicable size for handling the pieces. It will be seen that the groups of pieces representing quarter, tenth, and twentieth fractions of the unit represented by the length of the board recess **112** may be adjusted as desired, with the number of pieces and corresponding fractional denominator for each group or set being any practicable integer as desired.

A single group of identical fractional pieces may be used to form a single complete stratum or layer of pieces within the central recess **112**, completely filling the central recess, if so desired, with other groups of identical pieces being placed thereon to form multiple layers or strata of fractional pieces. Alternatively, fractional pieces of different groups may be placed within the same stratum to indicate the equivalency or relative value of a series of smaller pieces compared to a single one or smaller number of larger pieces. In the example of FIG. 1, it will be seen that the width **120** of a single larger fractional piece **118***c *subtends ¼, or 25%, of the total span **114** of the board recess **112**, thus requiring a series of four such pieces to fill the recess **112** completely. In turn, two intermediate width pieces **122***e *and **122***f *are shown disposed above the larger fractional piece **118***c. *As each of the pieces **122***e *and **122***f *has a width **124** equal to one tenth of the total span **114** of the board recess **112**, two such pieces **122***e *and **122***f *subtend only ⅘ of the width **120** of the larger ¼ piece **118***c. *The series of five 1/20 width pieces **126***a *through **126***e *will be seen to have a total width equal to 5/20, or ¼, of the total span **114** of the board recess, or in other words equal to the span or width **120** of a single ¼ piece. The various fractional pieces may be mixed and matched in various layers or strata to show the equivalencies of various fractions, generally as described above.

It will be noted that the various fractional pieces **118***a *through **126***e, *etc., are provided in two different colors or shades. For example, a first surface **130** of each of the pieces could be shaded in red, with the opposite second surface **132** colored black. The use of red and black are particularly suitable for embodiments of the present invention representing monetary fractions, i.e., subtraction and addition of monetary values or profit and loss. However, other colors may be used as desired.

FIG. 2 of the drawings illustrates a second embodiment **200** of the present fractional teaching devices, comprising an insert **202** which may be used with the board **102** of FIG. 1 and a series of fractional pieces for teaching monetary values. The insert **202** essentially serves the same function as the board **102**, i.e., the insert includes a pair of raised, opposed major peripheral edges **204** and **206** that define a central recess **212** therebetween. The recess **212** has a major width or span **214** equal to the width or span **114** of the board **102**, with the recess **212** of the insert **202** fitting into the recess **112** of the board **102** and the two opposed major peripheries **204** and **206** being positioned over the respective peripheries **104**, **106** of the board **102** when the insert **202** is placed thereover.

The purpose of the insert **202** is to provide different numerical designators along the two upper edges or peripheries **204**, **206** of the device, which may be used to indicate different fractions or functions for the use of the device. In the example of the insert **202** of FIG. 2, the numerical designators **216***a *and **216***b *are graduated in hundredths, to represent percentile values or increments. This permits the insert **202** to be used for the teaching of relative monetary values found in coin or other divisions of a basic monetary unit, e.g., nickels, dimes, quarters, etc., with a dollar being the basic monetary unit. Accordingly, the recess **212** of the insert **202** may include a representation **213** of the basic monetary unit, e.g., a dollar bill, thereon. Two different numerical designators **116***a *and **116***b *are shown in FIG. 2, with their values increasing in opposite directions. This facilitates the concept of making change, i.e., subtracting the remainder of the change from a dollar from the amount due in a transaction. The inventive concept of FIG. 2 may be expanded to cover other than U.S. monetary systems as well, as exemplified in FIG. 4 and discussed further below. It will also be noted that the information provided on the insert **202** could be applied to a board similar to the board **102** of FIGS. 1 and 2, if so desired.

A series of relatively thin, flat, planar fractional monetary pieces is provided for removable placement within the central recess **212** of the insert **202**. These monetary pieces are quite similar to the pieces **118***a *through **126***e *shown in FIG. 1 of the drawings and discussed further above, differing only in that each of the fractional monetary pieces of FIG. 2 includes a representation of a coin thereon corresponding to the fractional value of the piece. In the example of FIG. 2, three different series of fractional pieces are shown. The first set or group comprising the largest pieces, e.g., pieces **218***a *through **218***d, *comprises a total of four pieces, with each piece having a width **220** subtending one quarter of the span **214** of the central recess **212** of the insert **202** and representing the value of a quarter coin, or 25 cents. A 25-cent coin symbol or representation **221** may be provided upon each of the ¼ width monetary fractional pieces.

The next group or set of pieces comprises a series of ten intermediate pieces, e.g., **222***a, ***222***b, ***222***c, *etc., each having a width **224** subtending one tenth of the central recess span **214** of the insert **202**. As there are ten such pieces, a dime representation **225** or coin having a value of one tenth of the monetary unit represented by the span **214** of the insert **202** may be provided on each piece. A third set of pieces comprises a series of twenty smaller pieces of which five are shown in FIG. 2, i.e., **226***a *through **226***e. *Each of these smaller pieces has a width **228** subtending one twentieth of the span **214** of the central recess **212** of the insert **202**. A nickel representation **229**, or other coin having a value of one twentieth of the base currency represented, may be provided on the surface of each of the smaller monetary fractional pieces **226***a, *etc.

One or more of the smaller pieces **226***a, *etc. could be subdivided to form even smaller penny or one cent pieces, if so desired, but this may not be practicable. Alternatively, one or more of the smaller fractional pieces could be marked with a plurality of smaller coins having a total value equivalent to that represented by the width of the fractional monetary piece.

An example of the above is illustrated in FIG. 3 of the drawings, with a series of three fractional monetary pieces **326***a, ***326***b, *and **326***c *being shown. Each of the pieces **326***a *through **326***c *has a width **328** equal to the widths **228** of the pieces **226***a *through **226***e *of FIG. 2, i.e., 1/20, or 5/100, of the total span or width **214** of the insert recess **212**. However, rather than displaying a single coin thereon, the pieces **326***a *through **326***c *of FIG. 3 have representations of a series of smaller coins having a total value equal to that of one of the equivalent pieces **226** of FIG. 2. The coin representations **329** on the pieces **326***a *through **326***c *are grouped to indicate different values and remainders, with the first piece **326***a *having all five of the one-cent coin representations **329** grouped together.

The next piece **326***b *shows only four such coins grouped together, with the fifth coin separated. This piece **326***b *also has one fifth of its width shown in a different color, e.g., black, to indicate the relative lessening of value of the piece. Finally, the piece **326***c *has two coins grouped separated, with a black pattern subtending two fifths of its surface. In this manner, the values of the smallest coins may be represented, without the need to subdivide the 1/20 width pieces into narrower pieces that are impracticable to handle. The relative percentages of the areas covered by each color, and the groupings of coins, may be reversed on the opposite sides of the pieces **326***a, ***326***b, *etc., in order to obviate need for a duplicate set of such multiple coin fractional monetary pieces.

FIG. 4 of the drawings illustrates an alternative insert and fractional piece configuration **400** for teaching the relative coin values of a monetary system other than the U.S. monetary system. The Euro monetary system is shown in the example of FIG. 4, but it should be noted that the monetary teaching embodiments of the present invention may be applied to virtually any monetary system using a base unit of currency that is divided into smaller fractional units. The insert **402** of FIG. 4 is quite similar to the insert **202** of FIG. 2, having opposite first and second major peripheries **404** and **406**, each of which is marked with appropriate fractional divisions **416***a *and **416***b *for the monetary units used. The span or major width **414** of the insert recess **412** is essentially equal to the major span or width of the underlying board **102** into which the insert **402** is placed for use. However, rather than placing a representation of a U.S. monetary unit on the recess **412**, a representation **413** of a one euro coin is shown.

Accordingly, the various monetary fractional pieces provided with the insert **402** are sized and marked to correspond with various euro coins that are fractions of the basic euro denomination, which is the one-euro coin. In this example, five larger fractional monetary pieces **418***a *through **418***e *are shown, with each having a width **420** subtending ⅕ of the span or width **414** of the insert **402**. The pieces **418***a *through **418***e *are each marked with a twenty-cent euro coin representation **421**, with each such coin having a value of ⅕ of the one-euro coin shown in the representation **413** in the insert recess **412**. A series of ten intermediate size fractional monetary pieces is also provided, with three such pieces **422***a *through **422***c *being shown in FIG. 4. Each intermediate piece has a width or span **424** equal to one half of the width **420** of one of the larger ⅕ euro pieces **418***a *through **418***e, *with two such intermediate pieces, e.g., pieces **422***b *and **422***c, *subtending a total width equal to that of one of the larger ⅕ euro pieces. Accordingly, each of the 1/10 pieces is marked with a ten-cent euro representation **425**.

In addition to the above pieces, a series of twenty smaller pieces is provided, with each of the smaller pieces representing 1/20 of a euro. Four such pieces **426***a *through **426***d *are illustrated in FIG. 4, with each having a width or span **428** equal to one fourth of the width or span **420** of one of the larger pieces **218***a *through **218***e. *Accordingly, each of the smaller pieces, e.g., pieces **426***a *through **426***d, *is marked with a five-cent euro representation **429**. It will be seen that other groups of pieces having sizes corresponding to other euro coin denominations may be provided as desired. Smallest denominations may be represented in the manner shown for the pieces **326***a *through **326***c *of FIG. 3. Also, while color is not indicated for the euro fractional monetary embodiment **400** illustrated in FIG. 4, it will be recognized that opposite surfaces of the various fractional pieces may be colored, shaded, marked, or designated differently from one another if so desired, similarly to the manner shown in FIGS. 1 and 2 and discussed further above.

FIG. 5 illustrates a fourth embodiment **500** of the present device for teaching fractional mathematical concepts, wherein the board **502** has a circular configuration and the fractional pieces are each in the form of a circular sector subtending an arc equal to a fraction of the circumferential span of the circular board. The board **502** has much the same structure as the board **102** of FIGS. 1, **3**, and **4**, in that the board **502** includes a raised peripheral edge **504** forming a continuous periphery defining a central recess **512** therein. The recess **512** subtends a circumferential span **514** representing unity, and extends around the central recess **512** and concentric to the circumferential periphery **504**. The circumferential peripheral edge **504** may include a series of numerical designators thereon representing arithmetical, monetary, or other values or quantities as desired, generally as shown on the opposed peripheral edges **104** and **106** of FIG. 1. Examples of such are illustrated in the embodiments of FIGS. 6 and 7, and discussed further below.

A series of relatively thin, flat, planar fractional pieces is provided for removable placement within the central recess **512** of the board **502**, with each of the pieces being in the form of a circular sector. Each series of pieces comprises a group of identically sized pieces each having an arcuate width or span less than the circumferential span **514** of the board recess **512**, with all of the pieces in any one group having a total width equal to the board recess span **514**.

In the example of FIG. 5, three different series of fractional pieces are shown. The first set or group comprising the largest pieces, e.g., pieces **518***a *and **518***b, *comprises two pieces, with each piece having an arcuate span or width **520** subtending one half of the circumferential span **514** of the central recess **512**. The next group or set of pieces comprises a series of four intermediate pieces, with two such pieces **522***a *and **522***b *shown in FIG. 5. Each of the intermediate pieces has a width **524** subtending one quarter of the central recess span **514**.

A third set of pieces comprises a series of eight smaller pieces of which four are shown in FIG. 5, i.e., **526***a *through **526***d. *Each of these smaller pieces has a width **528** subtending one eighth of the span **514** of the central recess **512**. Thus, each piece represents the denominator of a fraction, with the denominator being equal to the number of pieces within each group or set. One or more of the smaller pieces **526***a, *etc. could be subdivided to form even smaller pieces, if so desired, but this may not be practicable.

Alternatively, one or more of the smaller fractional pieces **526***a, *etc. could be marked with radial lines indicating the division of the pieces into still smaller components, while still maintaining a practicable size for handling the pieces. It will be seen that the groups of pieces representing half, quarter, and eighth fractions of the unit represented by the circumferential span **514** of the board recess **512** may be adjusted as desired, with the number of pieces and corresponding fractional denominator for each group or set being any practicable integer as desired.

A single group of identical fractional pieces may be used to form a single complete stratum or layer of pieces within the central recess **512**, completely filling the central recess, if so desired, with other groups of identical pieces being placed thereon to form multiple layers or strata of fractional pieces. Alternatively, fractional pieces of different groups may be placed within the same stratum to indicate the equivalency or relative value of a series of smaller pieces compared to a single one or smaller number of larger pieces. In the example of FIG. 5, it will be seen that the width **520** of a single larger fractional piece **518***a *subtends ½, or 50%, of the total circumferential span **514** of the board recess **512**, thus requiring two such pieces to fill the recess **512** completely. In turn, two intermediate width pieces **522***a *and **522***b *are shown disposed above the larger fractional piece **518***a. *As each of the pieces **522***a *and **522***b *has an arcuate width **524** equal to one fourth of the total arcuate span **514** of the circular board recess **512**, two such pieces **522***a *and **522***b *are equal in arcuate width to one of the larger ½ pieces **518***a. *The series of four ⅛ width pieces **526***a *through **526***d *will be seen to have a total width equal to 4/8, or ½, of the arcuate span **520** of one of the half width pieces **518***a *or **518***b, *with eight such ⅛ pieces being used to cover the entire area of the circular recess **512** of the board **502**. The various fractional pieces may be mixed and matched in various layers or strata to show the equivalencies of various fractions, generally as described above.

It will be noted that the various fractional pieces **518***a *through **526***d, *etc., are provided in two different colors or shades. For example, a first surface **530** of each of the pieces could be shaded in red, with the opposite second surface **532** colored black. The use of red and black are particularly suitable for embodiments of the present invention representing monetary fractions, i.e., subtraction and addition of monetary values or profit and loss. However, other colors may be used as desired.

FIG. 6 of the drawings illustrates a fifth embodiment **600** of the present fractional teaching devices, comprising a circular insert **602** which may be used with the circular board **502** of FIG. 5 and a series of fractional pieces for teaching monetary values. The insert **602** essentially serves the same function as the circular board **502**, i.e., the insert includes a raised peripheral edge **604** forming a continuous periphery defining a central recess **612** therein. The recess **612** subtends a circumferential span **614** representing unity, and extends around the central recess **612** and concentric to the circumferential periphery **604**. The circumferential peripheral edge **604** may include a series of numerical designators **616** thereon representing arithmetical, monetary, or other values or quantities as desired, generally as shown on the opposed peripheral edges **104** and **106** of FIG. 1.

The purpose of the insert **602** is to provide different numerical designators along the circumferential upper edge or periphery **604** of the device, which may be used to indicate different fractions or functions for the use of the device. In the example of the insert **602** of FIG. 6, the numerical designators **616** are graduated in tenths. This permits the insert **602** to be used for the teaching of relative monetary values found in coin or other divisions of a basic monetary unit, e.g., nickels, pennies, etc., with a dime being the basic monetary unit. Accordingly, the recess **612** of the insert **602** may include a representation **613** of the basic monetary unit thereon. The inventive concept of FIG. 6 may be expanded to cover other coins or other than U.S. monetary systems as well, as exemplified in FIG. 4 and discussed further above. It will also be noted that the information provided on the insert **602** could be applied to a board similar to the board **502** of FIG. 5, if so desired.

A series of relatively thin, flat, planar fractional monetary pieces is provided for removable placement within the central recess **612** of the insert **602**, with each of the pieces being in the form of a circular sector. These monetary pieces are quite similar to the pieces **518***a *through **526***d *shown in FIG. 5 of the drawings and discussed further above, differing only in that each of the fractional monetary pieces of FIG. 6 includes a representation of a coin thereon corresponding to the fractional value of the piece. In the example of FIG. 6, two different series of fractional pieces are shown. The first set or group comprising the largest pieces, e.g., pieces **618***a *and **618***b, *comprises two pieces, with each piece having a width **620** subtending one half of the circumferential span **614** of the central recess **612** of the insert **602** and representing the value of a nickel, or 5 cents. A 5-cent coin symbol or representation **621** may be provided upon each of the ½ width monetary fractional pieces.

The next group or set of pieces comprises a series of ten intermediate pieces **622***a *through **622***j, *each having an arcuate width **624** subtending one tenth of the central recess circumferential span **614** of the insert **602**. As there are ten such pieces, a penny representation **625** or coin having a value of one tenth of the monetary unit represented by the circumferential span **614** of the circular insert **602** may be provided on each piece. It will be seen that if a larger value coin is represented in the recess **612** of the insert **602**, then more groups of fractional monetary pieces having different arcuate widths or spans and corresponding values from one another may be provided.

FIG. 7 of the drawings illustrates a sixth embodiment **700** of the present invention, in which a circular board **702** (or alternatively, insert for a circular board) is used to teach time increments. The circular board **702** has a general configuration much like the circular board **502** of FIG. 5, i.e., having a continuous circular raised periphery **704** defining a circular central recess **712** therein, with the central recess subtending a circumferential span **714**. However, the board **702** of FIG. 7 further includes an hour hand **706** and minute hand **708**, extending from a central pivot point **710** and independently positionable thereon. A conventional clock motor drive (not shown) could be used to drive the two hands **706** and **708**, if so desired, but the intent of the time teaching embodiment **700** of FIG. 7 is to allow the user or teacher to position the two hands as desired, to demonstrate various time increments and their indication by means of the hands. The raised circumferential periphery **704** preferably includes a series of numerical designators **716** in accordance with conventional clock or timepiece markings. Alternatively, a circular insert similar to the insert **602** of FIG. 6 (but including clearance for the clock hands **706** and **708**) could be provided with some alternative numerical designators, e.g., twenty-four hour clock markings, etc.

A series of relatively thin, flat, planar fractional pieces is provided for removable placement within the central recess **712** of the board **702**, with each of the pieces being in the form of a circular sector. Each series of pieces comprises a group of identically sized pieces each having an arcuate width or span less than the circumferential span **714** of the board recess **712**, with all of the pieces in any one group having a total width equal to the board recess span **714**. Each piece further includes a truncated relief at the apex thereof, for clearance for the central clock hand pivot **710**.

In the example of FIG. 7, three different series of fractional pieces are shown. The first set or group comprising the largest pieces, i.e., pieces **718***a *through **718***d, *comprises four pieces, with each piece having an arcuate span or width **720** subtending one quarter of the circumferential span **714** of the central recess **712**. The four quarter-hour pieces **718***a *through **718***d *may be marked with appropriate indicators **721** to indicate their value or represented time span, e.g., 15, to indicate the 15-minute time increment represented by each quarter hour piece. The next group or set of pieces comprises a series of five intermediate pieces **722***a *through **722***e. *Each of the intermediate pieces has an arcuate width or span **724** subtending one tenth of the central recess span **714**, or a time span of one tenth of an hour or six minutes.

Accordingly, each of these pieces **722***a *through **722***e *may be marked to show the time increment **725** represented, i.e., six minutes. It will be seen that a total of ten such pieces may be provided to cover the entire central recess **712** of the clock board **702**, if so desired. A third set of pieces comprises a series of six smaller pieces **726***a *through **726***f. *Each of these smaller pieces has a width **728** subtending one sixth of the span **714** of the central recess **712**. Thus, each piece represents a time span of five minutes, with six such pieces equaling thirty minutes or half an hour, and twelve such pieces (if provided) equaling one hour and completely covering the clock board recess **712** when placed thereon. The corresponding time period may be indicated by an appropriate numerical designator **729** placed upon each of the pieces **726***a *through **726***f. *

As in the other embodiments of the present invention discussed further above, the various fractional time pieces could be further subdivided into smaller increments, or alternatively marked with one or more radial lines to indicate smaller time increments. Other fractional time increments may be provided as desired, e.g., one third hour pieces representing twenty minutes, one twentieth hour pieces representing three minutes each, etc. as desired. As in the case of the other embodiments of the present invention, a single group of identical fractional pieces may be used to form a single complete stratum or layer of pieces within the central recess **712**, completely filling the central recess, if so desired, with other groups of identical pieces being placed thereon to form multiple layers or strata of fractional pieces. Alternatively, fractional pieces of different groups may be placed within the same stratum to indicate the equivalency or relative value of a series of smaller pieces compared to a single one or smaller number of larger pieces.

It will be noted that the various fractional pieces **718***a *through **726***f *are provided in two different colors or shades. For example, a first surface **730** of each of the pieces could be shaded in red, with the opposite second surface **732** colored black. Other colors may be used as desired. The provision of different colors on opposite surfaces of the various fractional time pieces serves to facilitate an understanding of such concepts as “half past the hour,” “quarter to the hour,” etc.

In conclusion, the devices for teaching elementary fractional concepts provide a series of tools that greatly facilitate the ability of the student to visualize the concepts being taught. The various embodiments include devices for teaching abstract fractional concepts, as well as monetary and time concepts. Some concepts, e.g., the basic abstract fractional concept, are adapted for a linear, rectangular presentation, others, e.g., the teaching of time using a conventional clock configuration, are better suited to a circular presentation or configuration. However, it will be seen that either configuration as disclosed herein may be adapted to the teaching of virtually any fractional concepts. Accordingly, the devices for teaching elementary fractional concepts will prove to be most useful in the classroom and as educational toys for teaching such concepts.

It is to be understood that the present invention is not limited to the embodiments described above, but encompasses any and all embodiments within the scope of the following claims.