Education and demonstration – Mathematics – Arithmetic
Reexamination Certificate
2000-12-18
2003-06-10
Banks, Derris H. (Department: 3712)
Education and demonstration
Mathematics
Arithmetic
C434S207000, C434S208000
Reexamination Certificate
active
06575755
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to a teaching apparatus and method and, more particularly, to a teaching apparatus and method using colored sections of a circle to facilitate teaching of mathematical principles with respect to fractions.
A current trend in teaching mathematics is the physical representation of rules and concepts so that students can visualize how the math works without difficult memorization and application of the concept rules. One currently available fraction learning aid is composed of a flat-bottom plate and a single piece pie-shaped guiding segment. The user has to move the guiding piece and manually mark on the fraction scale for each fraction to be worked on. Another device is disclosed in U.S. Pat. No. 5,470,234, wherein a circular holding plate is marked in {fraction (1/24)}
ths
about its periphery, and a number of fraction pieces containing numerous pie-shaped segments are used to depict fractions based on various center angles.
SUMMARY OF THE INVENTION
An important part of teaching fractions is the ability to determine a common denominator, for instance, with respect to addition and subtraction of fractions. Additionally, a student's understanding can be facilitated with the use of colored segments or sections that represent various fractions. To assist in the teaching and understanding of mathematical principles associated with fractions, the sections are placed side-by-side to provide a visual illustration for the student. For example, for addition, two or more of the segments can be placed side-by-side in a base unit holding the segments, illustrating the sum of the fractions represented by the segments, respectively.
According to the present invention, the colored pieces are preferably translucent such that color combinations can be achieved by overlaying one plastic section with another plastic section. Fractions having a denominator that is a prime number are formed of primary colors, and fractions having denominators that are not prime numbers are formed of secondary colors that correspond to the combination of primary colors to thereby illustrate the color of a common denominator. The overlaid colors can also be used to demonstrate fraction multiplication and division.
In accordance with an exemplary embodiment of the invention, a teaching apparatus includes a plurality of colored fraction pieces shaped in varying fractional arc segments of a circle. Colored fraction pieces of fractions having a prime number denominator are formed of primary colors and other colored fraction pieces are formed of secondary colors. The respective primary and secondary colors are assigned to particular fraction pieces such that a denominator of a secondary color fraction piece is a common denominator of primary color fraction pieces where the secondary color of the secondary color fraction piece is a combination of the primary colors of the primary color fraction pieces. The fraction pieces of a prime number denominator to an n
th
power are preferably formed of the same color to an n
th
intensity. The colored pieces may be formed of translucent plastic.
In accordance with another exemplary embodiment of the invention, a teaching apparatus includes a plurality of sectional pieces representing fractions of a circle. The sectional pieces are colored such that a sectional piece of a secondary color that results from a color combination of overlaid primary color fractions represents a relationship of the overlaid fractions. The relationship is preferably a common denominator. The teaching apparatus may further include a base unit with a circular opening that is shaped to receive one or more of the colored fraction pieces in a side-by-side relation. The base unit has markings about a periphery of the circular opening corresponding to respective portions of the circular opening circumference. Markings may be spaced in ⅛
th
intervals or {fraction (1/12)}
th
intervals.
In accordance with another exemplary embodiment of the invention, a method of teaching fractions using a plurality of sectional pieces representing fractions of a circle includes the steps of providing the sectional pieces in varying colors respectively corresponding to particular fractions, and overlaying sectional pieces of primary colors such that the resulting secondary color represents a relationship of the fractions represented by the overlaid pieces.
REFERENCES:
patent: 342651 (1886-05-01), Southworth
patent: 841158 (1907-01-01), Koops et al.
patent: 2946135 (1960-07-01), Eickmeyer et al.
patent: 3204344 (1965-09-01), McMeen
patent: 4096644 (1978-06-01), Nesher et al.
patent: 5470234 (1995-11-01), Sher
patent: 15073 (1909-03-01), None
Banks Derris H.
Fernstrom Kurt
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