GB2258335A

GB2258335A - Apparatus for use in the study of mathematics.

Info

Publication number: GB2258335A
Application number: GB9116254A
Authority: GB
Inventors: Robert J Fisk-Moore
Original assignee: FISK MOORE ROBERT J
Current assignee: FISK MOORE ROBERT J
Priority date: 1991-07-27
Filing date: 1991-07-27
Publication date: 1993-02-03
Anticipated expiration: 2011-07-27
Also published as: GB9116254D0; GB2258335B

Abstract

Apparatus for use in the study of mathematics includes a base 10 having a row of spigots 14, 15 on which stacks of pieces 11, 12, 13 can be fitted. A plate 22 behind the stacks represents a maximum content of a stack. Mathematical symbols 18, 19 can also be fitted onto the base. The base is made up of a number of bodies 25, 26 which can be separated from each other and can be joined end-to-end to form a base of any required length. <IMAGE>

Description

Title: Apparatus for use in the study of mathematics Description of Invention According to the present invention, there is provided a set of apparatus for use in the study of mathematics and comprising a base and a plurality of pieces which are stackable on the base, wherein the base has a row of receiving formations for receiving respective stacks of the pieces.

The pieces preferably have respective interfitting formations for releasably holding the pieces together in a stack.

The pieces can be used to represent quantities. Each piece may represent a single unit or a larger quantity. In a case where the pieces have respective interfitting formations for releasably holding the pieces together in a stack, a stack representing a quantity greater than the quantity represented by an individual piece can be manipulated as a single entity, can be separated into smaller stacks and can be increased by one or more pieces.

The preferred set further comprises a background member releasably connected with the base and extending upwards from the base to form a background, against which the stacks on the base can be viewed. The background member is useful to represent a limit on the magnitude of a stack on the base.

For example, if a decimal system is being used, the height of the background member may correspond to the height of a stack consisting of nine pieces.

Alternatively, the height of the background member may correspond to the height of a stack of ten pieces and have a mark at the height of a stack of nine pieces.

If a different limit is required to be represented, the background member can be removed from the base and replaced with a different member having a different height.

It will be understood that, although the set of apparatus is conveniently used with each stack extending upwards from the base, the apparatus could alternatively be used in a different orientation. For example, each stack could extend horizontally from the base. References herein to stacks, to height and to directions are not intended to limit the scope of the present invention to use of the apparatus in any particular orientation.

The base preferably comprises a row of members which can be separated from each other and the base preferably includes retaining formations for releasably retaining the base members assembled together in a row. With this arrangement, the length of the row may be varied.

The set of apparatus preferably further comprises indicators for attachment to said pieces and/or to the base. The indicators may bear indicia representing mathematical operations or values. The indicators are preferably an interference fit with the pieces and also with the base.

Examples of sets of apparatus embodying the present invention will now be described, with reference to the accompanying drawing, wherein: FIGURE 1 shows a perspective view of-certain components of a set, assembled together, FIGURE 2 shows the underside of a base member of the set and FIGURE 3 shows a cross section through certain components represented in Figure 1 and FIGURE 4 illustrates a part of a modified base which may be substituted for the base of the set shown in Figure 1.

The apparatus illustrated in Figures 1, 2 and 3 of the accompanying drawing comprises a base 10 and a number of pieces which are stackable on the base. Three only of these pieces are represented in Figure 1 and are identified by the reference numerals 11, 12 and 13. The base 10 has a row of receiving formations for receiving respective stacks of the pieces. Two representative formations of the base are identified by the reference numerals 14 and 15. In the example illustrated, the base is elongated and the receiving formations of the base are arranged in a rectilinear row extending along the base. The receiving formations are at a uniform pitch along the row.

The pieces 11, 12 and 13 have respective interfitting formations for releasably holding the pieces together in a stack. The particular pieces illustrated in the accompanying drawing each has the form of a cube with a spigot 16 protruding at one face of the cube. An opposite face of the cube has an aperture in which the spigot 16 of a further piece can be received with an interference fit.

The spigot and the portion of the piece defining the aperture constitute the interfitting formations. It will be understood that alternative formations and alternative numbers of formations may be provided on each piece for releasably holding the pieces together in a stack. It will also be understood that pieces having a shape other than that of a cube may be stacked on the base.

Each of the receiving formations 14 and 15 has the form of a spigot and has a shape and dimensions equal to those of the spigot 16. Accordingly, any one of the pieces 11, 12 and 13 can be received on the spigot 14 with an interference fit and with the spigot 16 of the piece remote from the base 10. A single piece or a stack of pieces can be mounted on any one of the row of receiving formations on the base in this way.

The base 10 could be modified by substituting for the spigots 14 and 15 sockets suitable for receiving the spigot 16 with an interference fit. This arrangement also would facilitate releasably mounting a single piece or a stack of pieces on the base at any receiving formation of the base.

The apparatus further comprises a number of indicators. Three representative indicators are shown in Figure 1 and are identified by the reference numerals 17, 18 and 19. One or more selected indicators can be applied to any one of the pieces 11, 12 and 13 to identify that piece. In Figure 1, indicator 17 is shown on piece 11. Provision is made for the indicators to be releasably attached to the pieces. In the example illustrated, each indicator has a spigot (not shown) which can be received with an interference fit in an opening 20 in a face of any one of the pieces 11, 12 and 13, other than the faces at which the spigot 16 and corresponding opening are provided. In the example illustrated, the opening 20 is hexagonal and the spigots on the indicators may have the same shape or a shape which can be inscribed in the hexagonal opening.However the opening 20 could be of another shape with the spigots on the indicators being of corresponding, or at least interfitting, configuration. Openings identical with the opening 20 may be provided at four faces of each piece.

The base 10 is adapted to receive one or more selected ones of the indicators, for example the indicators 18 and 19. For this purpose, there are formed in the base openings, one of which is identified by the reference numeral 21. The opening 21 may be identical with the opening 20 in size and shape, in which case each indicator can be applied either to one of the pieces 11, 12 and 13 or to the base. All of the indicators may have spigots of the same size and shape to fit in the opening 21. Alternatively, indicators could be specific either to the base or to the pieces and the size and/or shape of the openings in the base and in the pieces could differ, the spigots on the indicators differing in a corresponding manner.

The indicators bear information which is presented visually. For example, an indicator may bear a symbol representing a mathematical operation.

Other indicators may bear symbols representing quantities or other values.

The apparatus further comprises a background member 22 which is releasably connected with the base 10 and extends upwardly from one margin of the base. In the example illustrated, the member 22 has the form of a substantially flat, rectangular plate and has a rectilinear edge which is remote from the base 10 and is parallel to the length of the base. The member 22 is connected with the base by means of spigots on the member 22, one of which is indicated by the reference numeral 23, and which project into sockets formed in the base. The base may have a number of sockets greater than the number of spigots on the member 22. There may be provided a number of background members which differ in size, both in length and in height, and any selected one of which can be attached to the base to form a background, against which stacks of the pieces on the base can be viewed. Each background member has a height such that, when attached to the base, its edge remote from the base is at the level of the top of one element of a stack of pieces on the base. The background member therefore represents a limiting value of the number of pieces which can be included in a stack on the base, without exceeding the height of the background member.

Preferably, there is on the background member 22 a mark or a visible boundary which is spaced down from the edge remote from the base 10 by a predetermined distance, for example, the height of the piece 11.

It will be appreciated that the background member may have alternative forms. For example, there may be provided an angular background member having a foot which extends under the base 10 and an upright portion corresponding to the member 22. Generally, the length of the background member will be substantially equal to the length of the base although the background member may be longer than or shorter than the base.

The base 10 has receiving formations additional to the spigots of the row 14, 15. The additional receiving formations illustrated in the accompanying drawing are constituted by a number of rectilinear bars, one of which is indicated at 24. The base 10 is formed with a number of sockets or holes for receiving end portions of respective bars. As shown in the drawing, each of these holes may lie within one of the receiving formations 14, 15. The height of the bars is large, relative to the height of the spigots 14 and 15. A number of bars of different lengths may be included in the set. The bar 24 can be removed from the base and replaced by a further bar. Bars may be placed at selected positions along the base, in some only of the spigots of the base.

When a stack of pieces is to be placed on the base 10, a bar corresponding to the bar 24 is preferably inserted into the spigot of the base in which the stack is to be placed. The bar will then stabilise the stack of pieces.

Even if the pieces are not properly fitted together, the bar will retain them in substantially the required positional relation with one another. It will be understood that, in a case where the bar 24 is used, the spigot may be omitted from the base. The bar will receive and locate the stack of pieces. Furthermore, in a case where the bar is provided, it is not essential for the pieces to have interfitting formations which hold the pieces together in the stack. The pieces would be held in the stack by gravity and by the bar 24, provided that the height of the stack does not substantially exceed the height of the bar, in order to receive a spigot.

It will be noted that the pieces are not captive on the bar 24. Whilst an end portion of the bar remains in the base 10, pieces can be placed over and removed from an upper end portion of the bar. In a case where the pieces have respective interfitting formations which hold the pieces in a stack, the height of the stack can exceed the height of the bar by a substantial amount, for example an amount corresponding to the height of a stack of several pieces.

The pieces 11, 12 and 13 are hollow and have in the spigot 16 and in an opposite face apertures through which the bar can extend. The bar is a sufficiently close fit in the aperture in the spigot 16 to provide the required degree of stability to a stack. It will be understood that the opening in the opposite face of each piece is considerably larger than the transverse cross section of the bar, in order to receive a spigot.

The base 10 illustrated in the accompanying drawing comprises a row of members, two of which are identified by the reference numerals 25 and 26.

The base members have retaining formations for releasably retaining the base members assembled together in a row. In the example illustrated, each base member has a projection 27 of dovetail shape and a complimentary recess 28 at its opposite side. Each base member can be placed over the projection of an adjacent base member to connect the base members together. The base members can be separated from each other by raising each base member, in turn, from the projection of an adjacent base member.

The base member 25 has the receiving formation 14 and a hole to accept one bar corresponding to the bar 24. This base member also has the opening 21, this opening being spaced from the formation 14 in one direction, and there may be a further opening, identical with the opening 21, spaced in the opposite direction from the formation 14. As shown in the drawing, the base member 25 may have a top face which bears the formation 14 and which is substantially horizontal, in typical use of the base, a front face which is inclined downwardly from the top face at an angle within the range 25 to 65" and a corresponding inclined rear face. The opening 21 is formed in the inclined front face and a corresponding opening is provided in the inclined rear face.

Each of the other base members may be identical with the base member 25. Alternatively, the base members may differ in respect of colour or some other visual characteristic. Furthermore, the set may include base members which are longer than the base member 25. For example, a longer base member may have two or more spigots for receiving respective stacks of pieces. It will be noted that the base can be extended or shortened to any required length by the addition or removal of base members. Conveniently, each base member has sockets into which the spigot 23 could be inserted.

The background member 22 may be adapted to hold the base members together in a row. For example, the background member may have a spigot 23 for each base member. In this case, the retaining formations 27 and 28 may be omitted from the base members. A background member which has a foot, as herein before mentioned, is particularly suitable for releasably retaining the base members assembled together in a row.

The apparatus illustrated in the accompanying drawing may be modified by substitution, for the bar 24, of alternative stabilising means for a stack of pieces. One alternative stabilising means comprises a group of four bars which collectively surround a stack. A further alternative is a pair of L-shaped columns which embrace corner portions of a stack. The stabilising means preferably has a height corresponding to the height of a stack of at least two pieces.

The pieces 11, 12 and 13 are hollow, open-sided frames. Each frame defines a 2cm cube. The indicator 17 overlaps with and partly covers the frame.

The indicator preferably has a diameter of 2cm. Cubes of other sizes may be used. The pieces illustrated in the accompanying drawing may be modified by alteration of the shape of the spigots 16. For example, these spigots and the spigots 14 and 15 may be square in shape, the openings in the pieces which receive these spigots also being square. The opening 20 and other openings for receiving the indicators also may be square and may be of the same size as the spigot 16, so that a spigot on one piece would fit into any one of five openings in an adjacent piece. In a case where suitable stabilising means is provided on the base, the spigots 16 may be omitted from the pieces. In this case, apertures of the same size may be formed in all six faces of each cube. Connectors, each having a pair of spigots corresponding to the spigot 16, may be provided for joining pieces together in a stack.

The opening 21 and the opening 20 may have the same size and shape, which may be any one of a variety of polygons with straight or curved sides or an oval or other curved shape. The spigot 16 and the corresponding opening may have the same size and shape as the openings 20 and 21. The base 10 may be adapted to receive one or more indicators on the top of the base. For example, in place of the spigots 14 and 15 on the base, there may be provided recesses of a size and shape suitable for receiving the spigot 16 of the element 11 and the indicators may have respective spigots identical with the spigot 16, the opening 21 having the same size and shape as the recesses at the top of the base. In a case where an indicator can be fitted on the top of the base in this way, each of the openings 21 may be omitted from the base.

If desired, instead of the opening 21 being provided on an inclined side faces of each of the base members 25, 26, openings may be provided on a vertical face V, which would need to be deeper than indicated in the drawings, or openings like opening 21 may be provided both on an inclined side faces and on a vertical face V of the base members 21, each to receive a desired indicator means like indicator means 18 or 19 for examples.

The apparatus illustrated in Figures 1, 2 and 3 of the accompanying drawings may be further modified by substituting for the background member 22 an alternative background member which represents a limiting value of the number of pieces which can be included in the stack on the base. The bar 24 and each of the other stabilising means herein before described constitutes such an alternative background member. If a stack of pieces is placed over the bar 24, the limiting value of the stack will be represented by the top of the bar and the pieces of the stack can readily be viewed against the background of the bar. The background member 22 has the advantage of establishing the same limiting value for all of the stacks on the base.

The apparatus illustrated in Figure 1 may be modified by substitution for the base 10 shown in Figure 1 of the base 110 shown in Figure 4. Certain features of the base 110 correspond to those herein before described with reference to the apparatus of Figure 1 and such corresponding features are identified in Figure 4 by like reference numerals with the prefix 1. The preceding description is deemed to apply to these features, except for the differences hereinafter mentioned.

The base of Figure 4 has a depth greater than that of the base 10 shown in Figure 1. The upright faces at the front and rear of the base have a correspondingly greater height and are of sufficient size to accommodate formations, which may be identical with the opening 21, for receiving indicators identical with the indicators which can be fitted to the base 10. Although a hexagonal recess 130 has been shown in the front face of the base member 125, by way of example, it will be understood that formations having different shapes, as herein before mentioned, may be provided for receiving the indicators. By way of example, an indicator 131 is shown mounted on the front face of the base member 126. Of course, if only a single indicator is required to be fitted to each base member, then the formation 121 may be omitted from the base member 125.

To use the apparatus of Figure 1 for addition in a number system with a base having the value 10, there is fitted to the base of the apparatus a background member having a height corresponding to that of a stack of ten pieces. On the background member there is a mark at the height of a stack of nine pieces. A number of pieces representing the first quantity to be added is formed into a stack and placed on the base member 25. The mathematical symbol for addition is placed in the opening of the base member 26 corresponding to the opening 21. A stack of pieces which represents the second quantity to be added is placed on the next adjacent base member. An indicator bearing an equals sign is placed on the next adjacent base member and the user places on a further base member a stack of pieces containing the sum of the number of pieces in the first two stacks.These pieces can then be counted.

If desired, an indicator bearing a numerical value or a symbolic representation of the number of pieces in a stack, may be placed in the opening of the base member on which the pieces of the stack are formed.

The apparatus presents the complete mathematical computation in a static manner. If the height of one of the stacks exceeds the height of the mark on the background member, this indicates that the maximum permitted value of pieces in a stack has been exceeded. This encourages the user to remove ten pieces from the stack and to represent these ten pieces by a single piece in an adjacent stack. The apparatus can be used in a similar manner to represent subtraction. Indeed, the stacks represent the corresponding subtraction computation without the stacks being moved. The difference between the last and middle stacks can be observed and compared with the first stack.

The apparatus can also be used to represent multiplication and division. Again, since all elements of the computation are represented in a static manner by the apparatus, the same arrangement of stacks represents both a multiplication and a division. The user is assisted to develop the concept of reversing multiplication to carry out division and vice versa. It will be noted that there is no positive limit to the number of pieces in a stack. Comparison with the background member indicates that the permitted number in a stack has been exceeded and the user then faces the problem of eliminating this excess. This assists with the development of the concept of place value.

The features disclosed in the foregoing description, or the following claims, or the accompanying drawings, expressed in their specific forms or in terms of a means for performing the disclosed function, or a method or process for attaining the disclosed result, as appropriate may, separately or in any combination of such features, be utilised for realising the invention in diverse forms thereof.

Claims

1. A set of apparatus for use in the study of mathematics and comprising a base and a plurality of pieces which are stackable on the base, wherein the base has a row of receiving formations for receiving respective stacks of the pieces.

2. A set according to Claim 1 wherein said pieces have respective interfitting formations for releasably holding the pieces together in a stack.

3. A set according to Claim 1 or Claim 2 further comprising a background member releasably connected with the base and extending upwards from the base to form a background, against which the stacks on the base can be viewed.

4. A set according to any preceding claim wherein the base comprises a row of members which can be separated from each other.

5. A set according to Claim 4 wherein the base includes retaining formations for releasably retaining the base members assembled together in a row.

6. A set according to Claim 4 or Claim 5 wherein the base members are of the same size and shape.

7. A set according to Claim 5 wherein substantially identical retaining formations are provided on each of said base members.

8. A set according to any one of Claims 4 to 7 wherein each base member has a receiving formation for receiving a stack of pieces.

9. A set according to any one of Claims 4 to 7 wherein each base member has a single receiving formation for receiving a stack of pieces.

10. A set according to any preceding claim wherein the receiving formations of the base include formations which interfit with respective ones of said formations of the pieces and are thereby adapted to hold a stack of said pieces releasably in a predetermined position on the base.

11. A set according to any preceding claim wherein said pieces are of substantially the same size and shape.

12. A set according to any one of Claims 1 to 10 wherein each of said pieces has formations identical with those of the other pieces and capable of interfitting with formations of the other pieces.

13. A set according to any preceding claim wherein the pieces are hollow and wherein the receiving formations of the base include bars having respective dimensions such that each bar can be received in a stack of said pieces.

14. A set according to Claim 13 wherein each bar has a free end and joins the base at its opposite end.

15. A set according to any one of Claims 1 to 12 wherein the receiving formations of the base include elongated stabilising means for stabilising a stack of said pieces on the base and wherein the stabilising means has a height corresponding to the height of a stack of at least three of said pieces.

16. A set according to Claim 15 wherein the stabilising means has a free end remote from the base and pieces engaged with the stabilising means can be moved along the stabilising means and past its free end to be disengaged from the stabilising means.

17. A set according to any preceding claim further comprising indicators for attachment to said pieces.

18. A set according to Claim 17 wherein the indicators interfit mechanically with said pieces.

19. A set according to Claim 17 wherein the indicators are an interference fit with said pieces.

20. A set according to any preceding claim wherein each said piece is an open-sided frame.

21. A set according to any preceding claim further comprising indicators for attachment to the base.

22. A set according to Claim 21 wherein the base has a plurality of mounting formations, each adapted to receive one of said indicators.

23. A set according to Claim 22 wherein the mounting formations of the base have dimensions substantially the same as corresponding dimensions of said pieces and wherein said indicators fit both said pieces and said mounting formations of the base.

24. A set of apparatus substantially as herein described with reference to the accompanying drawing.

25. Any novel feature or novel combination of features disclosed herein or in the accompanying drawing.