Abstract: A set of nesting cups includes two or more cups, each cup including a respective rim having a flange, and a respective bowl depending from the rim. The respective bowl of each cup is formed by a curved side wall and one or two straight side walls extending from the respective rim of the cup to a closed bottom of the bowl. The curved side wall of each bowl has an upper edge at the rim of the cup, the upper edge forming a circle segment completed by a perimeter of the flange. The circle segments formed by the upper edges of the curved side walls of the cups define different included angles, and the bowls of the cups are sized to nest.

Abstract: A set of nesting cups includes two or more cups, each cup including a respective rim having a flange, and a respective bowl depending from the rim. The respective bowl of each cup is formed by a curved side wall and one or two straight side walls extending from the respective rim of the cup to a closed bottom of the bowl. The curved side wall of each bowl has an upper edge at the rim of the cup, the upper edge forming a circle segment completed by a perimeter of the flange. The circle segments formed by the upper edges of the curved side walls of the cups define different included angles, and the bowls of the cups are sized to nest.

Abstract: Templates for identifying equivalent fractions in one example comprise a plate defining a plurality of aligned rows, each row having an equal length and representing a respective fraction. Each row defines a number of slots through the plate, positioned to divide a row into equal parts corresponding to the respective fraction. Slots or markers in respective rows corresponding to equivalent fractions are vertically aligned. An elongated slot may be provided on the template or on a separate template to draw a boundary to mark a fraction, identify equivalent fractions and perform mathematical operations. In another example, a first template includes a plurality of aligned rows with marks to indicate fractions and a second, transparent template for placement over the first template. Fractions may be drawn in a Unit box defined on the second template. Methods of using a template, and virtual templates, are also disclosed.

Abstract: The present invention relates to a fractal-based mandala drawing toolset, comprising at least one pair of rulers each having a different cross-sectional width, where each pair of rulers is related by the ratio between their cross-sectional widths, wherein said related pair of rulers and the combination of their widths are utilized for drafting a master grid with a predetermined shape and resolution, which is utilized as the infrastructure for creating a mandala drawing.

Abstract: A method for an inter-disciplinary teaching curriculum to combine the arts with core studies, comprising placing within quadrants of a circle, the circle being defined on a surface of an object, a plurality of circular sector objects of various sizes in relation to the circle, the plurality of circular sector objects having displayed thereon a music note according to the size of the particular circular sector object, performing a rhythm depicted by the music notes displayed on the circular sector objects that were placed into the quadrants of the circle, and analyzing a plurality of information displayed on each one of the plurality of circular sector objects, the plurality of information displayed on each one of the plurality of circular sector objects being associated with the size of the particular circular sector object.

Abstract: In a computer-implemented educational environment, four particular features are provided, which may be used separately or in combination, to drive the instruction of a particular curriculum, e.g. the instruction of fractions. In another implementation, educators and authors may use permutations and combinations of such features to construct in a graphical user interface a progression of interactive elements which help guide a student from visual concepts to procedures, such as equations and formulas. In a particular implementation, by using these features carefully, a curriculum author may design instructional sequences that provide careful, step-by-step sequences that help students progress from understanding the visual concepts, e.g. of fractions, to mastering procedures, e.g. fractions equations.

Abstract: The invention provides a method and apparatus for operations of addition, subtraction, multiplication, and division of fractions, decimals, percents, proportions and equations. It allows the students to find the transparent area models on their sheets with the correct parts shaded, (2) students can count the total number of parts and the total number of shaded parts in each model, (3) the relationship of the shaded parts to the total number in each model can be named, (4) by intersecting the vertical transparent area model for one whole with horizontal transparent area models for one whole to show examples of one whole being renamed several different ways.

Abstract: In an embodiment, an apparatus includes a first perimeter including a facsimile of a clock, a second perimeter including a plurality of fractions, a third perimeter including a plurality of decimal numbers, a fourth perimeter including a plurality of percentages, and a fifth perimeter including a plurality of degree magnitudes. The apparatus is useful in relating one set of information to another set of information.

Abstract: A mathematical teaching aid includes a plurality of sectional pieces representing fractions of a circle. The pieces are preferably colored corresponding to respective fractions, wherein fraction pieces having a prime number denominator are of primary colors, and other section pieces are of secondary colors. The colors are assigned to the pieces such that primary number denominator sectional pieces of primary colors can be overlaid to form a secondary color, with the sectional piece of that secondary color being representative of a common denominator. The sectional pieces can be combined with a base unit and used for teaching multiplication, division, addition and subtraction of fractions.

Abstract: A mathematical teaching aid includes a plurality of sectional pieces representing fractions of a circle. The pieces are preferably colored corresponding to respective fractions, wherein fraction pieces having a prime number denominator are of primary colors, and other section pieces are of secondary colors. The colors are assigned to the pieces such that primary number denominator sectional pieces of primary colors can be overlaid to form a secondary color, with the sectional piece of that secondary color being representative of a common denominator. The sectional pieces can be combined with a base unit and used for teaching multiplication, division, addition and subtraction of fractions.

Abstract: An educational and entertainment device includes n layers stackable in a predetermined order one on top of the other to define a tower having n layers. The xth layer, where x varies between 1 and n, is divided into x sections, at least one of the x sections of the xth layer having a passage segment formed therethrough such that with the n layers stacked one on top of the other in the predetermined order, the passage segments of the n layers are in communication with each other to define a passage which extends through the tower. The device also includes an indicator element passable through the passage to confirm that the n layers have been assembled in the predetermined order.

Abstract: An educational apparatus used for the teaching of mathematical operations that use fractions. A triangular shaped ruler prism has three different side surfaces that are joined together at three common edges with four different numerical value measuring fractional scales on each side surface and a whole unit scale of which all other scales are a fractional part thereof. All scales have the same length as the whole unit scale. Preferably on each prism side there are two different fractional measuring scales adjacent and aligned with each other in a straight line at one of the common joined prism edges. Fractional scale measuring units that have been used include; the whole unit, half units, thirds, fourths, fifths, sixths, sevenths, eights, ninths, tenths, elevenths and twelfths units. By stated procedures employing marking on a writing surface, fractions may be represented by lengths and added or subtracted from each other as well as mixed numbers with fractions.

Abstract: An apparatus and a method for playing a math-teaching board game which enables a player student while manipulating game-pieces to gain an understanding of the concept of fractions and arithmetical operations associated therewith. The game is played by 2 to 4 players. The game includes a pyramidical-shaped board having a continuous path of steps, individual game tokens, a die, a plurality of decks of question cards for respective arithmetic operators, fraction boards and a slide box for placement of the fraction boards thereon. In playing the game, the player skillfully moves a selective game token up a number of steps based on the roll of the die. Each step on the board displays an arithmetical operator which determines which deck of question cards is selected. The player uses the fraction boards and the slide board in an attempt to visually determine the answer to a selected question. If the player answers the question correctly, the player remains on the step advanced by the die roll.

Abstract: An assembly for teaching mathematical concepts includes a plurality of interlocking components, each having at least one connecting end so that the components can be combined in any order or length. Each component is assigned a mathematical value according to its length, and this value may be indicated by indicia on its face or by color coding. A base is also provided for retaining the columns of components in vertical formations. Means are provided on the platform of the base for engaging the bottom component in each column.

Abstract: A design for a circular, piece-matching math educational aid is disclosed. It contains a holding plate and various fraction pieces. The circular holding plate has a clockwise spiral bottom, designed in such a way that a sloped cliff is formed at the joint of the starting and ending point. The edge of the cliff is lined up with a guiding mark "0" on a fraction scale marked on an elevated wall on the outer circumference of the holding plate. The fraction pieces contain numerous pie-shaped segments. Any of the segments can precisely depict a fraction, based on the ratio of its center angle to the circle, 360 degrees. The pieces can be made with any center angles, such as 5, 7.5, 10, 30, 45, 60, 90, 180 degrees, etc.

Abstract: A polyhedron with indicia carrying sections, for example a cube. The polyhedron is comprised of a first plurality of first larger sections, e.g. two halves of the cube, and the two larger sections are hinged together along neighboring edges. Their abutting, opposed surfaces, are hidden from view. When the larger sections are opened apart, this exposes indicia, e.g. a fraction, indicative of the portion of the whole polyhedron which each fractional larger sections comprises. Each of the larger sections of the polyhedron, e.g. a cube, are in turn openable apart around hinges to define smaller sections of the larger section. Surfaces of the hinged together smaller sections, which are hidden from view when the smaller sections are assembled, are exposed to view when the smaller sections are opened apart to define still smaller sections. Those indicia are related to the size of the smaller sections and, e.g., recite the fraction of the whole polyhedron which those smaller sections comprise.

Abstract: A fractal mathematics learning kit includes a plurality of boards each in the shape of an equilateral triangle having defined thereon a pattern of ten smaller equilateral triangles, and a plurality of manipulative elements made of one or more connected equilateral triangles which are attached to the equilateral triangles defined on the boards. A set of tokens thick enough to stand on an edge and comprising combinations of equilateral triangles to represent numbers is also included. Also included in the kit is a mat defining rows and columns of fractal representations of numbers by which various mathematical operations can be understood. A set of nesting pyramids of graduated sizes representing numbers of magnitudes generally corresponding to the sizes is also provided, as are pyramids of different sizes which can be stacked through the use of trays and transparent covers. The kit includes a work book and a user's manual.

Abstract: This invention deals with a multi-purpose learning device for mathematics, language, logic reasoning, and classification of objects.

Abstract: The present invention is directed to a method and apparatus for teaching fractions to school age children. The invention provides an instrument having a base with at least two aligned scales of corresponding numerical indicia subdivided into different fractional units, as for example halves, thirds, quarters, sixths, and eighths. The base defines a space or gap between the different fractional scales so that a writing media, such as a piece of paper, may be inserted between the scales and moved either horizontally or vertically relative to one or more of the scales. The instrument provides an easy manner for a student to compare fractional units of the same integer and also to add and subtract both fractions and mixed numbers. In the preferred embodiment of the invention, the base of the instrument may be transparent so that all fractional scales are visible to the student simultaneously.

Abstract: A playing board with paths thereon, each made up of a series of squares. Playing pieces are moved along the paths, and at certain locations are instructions for picking up award pieces, which are items making up a sandwich, including bread, ham and cheese, The award pieces are in whole slices, half slices, and quarter slices, for teaching a child. Educational clues are used for beginning the game, including mathematics clues, puzzle indicators, and general information answer indicators.

Abstract: A measuring and instructional ruler device is provided for use by children and persons having learning impediments or physical handicaps. The device is comprised of a base panel having one inch subdivisions delineated by both visual indicia and tactile features, and a top panel adapted to slide upon the base panel and having a series of tabs whose widths sequentially increase in fractions of an inch. The device is used by aligning the first or zero subdivision with a first of two points between which the distance is to be measured, determining the appropriate subdivision closest to the second point, and adding to such closest subdivision the fractional value of the tab that fills the space between the end of the closest subdivision and the second point of the distance being measured.