GB2357174A

GB2357174A - Teaching apparatus for arithmetic

Info

Publication number: GB2357174A
Application number: GB0024820A
Authority: GB
Inventors: Michael Jerrold Oppenheim
Original assignee: Individual
Current assignee: Individual
Priority date: 2000-10-11
Filing date: 2000-10-11
Publication date: 2001-06-13
Also published as: GB0024820D0

Abstract

Apparatus for teaching arithmetic comprises at least one base or track member 1 carrying markings comprising a sequence of numbers and/or symbols, one or more counting modules (9, fig 2a) selected from a plurality of fixed length counting elements, and a releasable zero stop 10 for use in positioning at least one counting element. Also disclosed is apparatus for teaching subtraction which includes a blocking element (20, fig 4b) which may have a T-shaped cross-section and which obscures at least some of the numbers and/or symbols on the base or track member.

Description

2357174 Title: Teachinq Aid for Arithmetic

DESCRIPTION

The present invention relates to apparatus for use in teaching arithmetical processes including at least one of addition, subtraction, multiplication and division and preferably all four, but without limitation to same.

In my co-pending UK Patent Application No. 9714165.9 there is described a teaching aid for arithmetic. The present application describes certain useful improvements to my earlier proposals.

Accordingly one aspect of the present invention provides apparatus comprising at least one elongate base or track member having markings comprising a sequence of numbers and/or symbols which may be representative of said numbers and providing the base or track with a plurality of divisions of equal unit length; and one or more counting modules for use in association with the base or track member, the counting module being selected from a plurality of counting elements of fixed length whose length is a multiple of said unit lengths, and further comprising a releasable zero stop for use in positioning at least one counting element.

The zero stop serves as a positioning element for the fixed length counting elements when counting from zero. The base or track member conveniently incorporates a longitudinal groove which is dimensioned to receive slidably -therein at least part of said counting element. Alternatively said counting element may be 2 grooved to receive and slide on an elongate track member. Conveniently mutually complementary projection and recess means may be provided on the base and/or the counting elements to aid longitudinal positioning relative to the unit length divisions. A particularly convenient arrangement is provided by a spring loaded ball element and a co-operating recess. Conveniently a series of recesses are provided at intervals spaced along the length of the base or track member - said spacings corresponding to said unit lengths - and each counting element may be provided with one spring loaded ball element.

A plurality of the aforementioned fixed length counting elements are provided. There will be different lengths of fixed length counting elements and it is preferred to have a plurality of each length. The width of the fixed length element is dimensioned to be complementary to the width of the recess in the base member so as to be slidable therealong. In one embodiment the cross- section of each fixed length element corresponds to the cross-section of the recess in the base member. Alternatively it can be advantageous if the depth of the fixed length counting element is greater than the depth of the groove in order to aid gripping and movement of the element in use.

The fixed length counting elements conveniently have division markings corresponding to said unit lengths and optionally carry a marking indicative of the unit length of the counting element.

The apparatus preferably further comprises a blocking element which has a part dimensioned to be cooperable slidably with the base or track member and an offset part which blocks off numbers on the base or track member. The 3 blocking element is used in conjunction with a fixed length counting element and serves as a positioning element for same. Thus it determines the longitudinal position of a fixed length counting element with respect to the base or track member. Optionally there may be a blocking element specifically for addition although one blocking element could serve all purposes.

Means may be provided for securing two or more track members together in end to end relation.

Another aspect of the present invention proves a method of teaching subtraction utilising apparatus comprising at least one elongate base or track member having markings comprising a sequence of numbers andlor symbols which may be representative of said numbers and providing the base or track with a plurality of divisions of equal unit length; and one or more counting modules for use in association with the base or track member, the counting module being selected from a plurality of counting elements of fixed length whose length is a multiple of said unit lengths and a blocker element. adapted for co- operating engagement with the base, in which method the blocking element is positioned to the right of the number andlor symbol from which a fixed number is to be subtracted, and a fixed length counting module of the appropriate length is placed up to the blocker element in a position to obscure the unit length numbers andlor symbols so that the answer to the calculation is the next number visible to the left thereof.

The above-described apparatus and the method of use will now be described further hereinafter by way of example only, with reference to the 4 accompanying drawings in which: - Figure 1 is a perspective view of a base or track member according to one embodiment, Figures 2a and 2b are perspective views of two alternative fixed length counting elements, Figure 3 is a perspective view of one embodiment of blocking element, Figure 4a is a perspective view of an alternative blocking element, Figure 4b is a perspective view of the underside of the blocking element figure 4a Figure 5a is a plan view illustrating the use of fixed length counting elements with a zero stop for addition, Figure 5b is a plan view illustrating use of a fixed length counting element with a blocking member, for subtraction, and Figure 6 is a plan view illustrating part of two base elements aligned prior to interconnection for handling negative numbers.

Figure 1 illustrates a base or track member 1 having a longitudinal groove 3 formed in an upper side thereof. A wing 5 to one side of the groove carries markings, conveniently lines 7, creating a number of equal length divisions. The divisions are numbered and in the illustrated embodiment are numbered 1 through to 13. In the illustrated embodiment the left-hand end is un- nunibered and corresponds in length to the unit division. It equates to the zero position. The groove in the zero position has a bore 8 to receive releasably a zero stop 10. The zero stop may be any convenient shape to facilitate insertion and removal. The zero stop has a cross-section such that when inserted it provides an abutment surface which aligns with the zero-one boundary. It may be dimensioned to project above the top of the base. In practice the base will be longer than that illustrated, perhaps having twenty equal length divisions. Means is provided to connect two or more bases together in end to end relation. One possible connection system is illustrated and comprises two spaced bores 4 in ends which are to be adjacent. The bores receive two removable pegs or dowels 6 whereby two adjacent bases can be interconnected. Figure 6 shows the adjacent ends of two bases aligned for interconnection.

Figures 2a and 2b illustrate fixed length counting elements, each comprising a rectangular section elongate member. Figure 2a is three units long and Figure 2b is four units long. The width corresponds substantially with the cross section of the groove 3, but has a greater depth in order to better facilitate handling. Preferably means is provided for identifying even and odd unit length counting elements. Counting elements which have odd unit lengths preferably have their centre unit in a different colour to the other units.

Reference is now made to Figure 5a which illustrates the left hand end of a base or track member 1 and (in dotted outline) two fixed length counting elements 9. The left hand counting element 9 has its left most division aligned with the unit division numbered 1 of the base and as it is three units long occupies three unit divisions of the base. For ease of alignment, the zero stop 10 is installed and the counting element pushed up to the zero stop. The right hand fixed length counting member 9 is placed up to the end of the left hand counting element and 6 as in this illustration it has a unit length of 3 it occupies a further three unit divisions of the base member. This serves to illustrate that 3 plus 3 equals 6 i.e.

the number on the rightward most division of those divisions occupied by the two counting elements. On the other hand the same counters can be used to demonstrate multiplication i.e. 2 x 3 = 6. Counting elements of the same length have to be used for multiplication whereas for addition different lengths of counting elements can be employed. This identical set-up also demonstrates division. In this case 6 - 3 is illustrated. The number of equal length elements which fill the space constitutes the result of dividing the initial number (on the base) opposite the right end of the rightmost element base - by the value of each fixed length element. The zero stop is usually used when performing arithmetic on positive numbers. The zero stop may be removed during subtraction, for example, when the subtrahend is greater than the minuend.

Referring now to Figure 3, a blocking element is illustrated which comprises a body portion 28 dimensioned to be received in the groove 3 of the base or track member I and a lateral offset portion 30 which projects to one side of the body 28. One end may be cut away or provided with aperturing 32 c)r may be constructed of transparent material 33 say over unit length A compared with an obscure portion B. It may be used for addition with fixed counting elements without using fixed length counting elements from the starting number.

Figures 4a and 4b illustrate a blocking element 20 which maybe used for all the arithmetic operations and comprises a body 28' dimensioned to be received in groove 3 and two offset portions 30', 30" which in this instance extend 7 the full length of the body. Figure 5b illustrates the base of Figure 1 and now it is used with the blocking member shown in 4a and 4b and fixed length counting element of Figure 2a for the purpose of subtraction. In the example, 3 is to be subtracted from 6 and accordingly the blocking element is positioned in the groove 3 so that the left hand end of the offset portion 30' is immediately to the right of the number 6. Thereafter in this instance the fixed length counting element is positioned over the unit markings rather than in the groove. The fixed length counting element is moved up to the blocking element. The fixed length element obscures numbers on the track member. The number visible to the left of the fixed length counting element is the result of subtracting 3 from 6 i. e. 3.

For ease of positioning of the blocking elements it is preferred to provide a projection and recess means which in the illustrated embodiment comprises a spring ball 40 mounted to the underside of the body 28,28' of the blocking elements and complementary recesses 42 are disposed in the base of the groove 3. Such projection means may be provided on the fixed length counting elements if felt desirable.

The apparatus may be used to teach basic understanding of negative numbers by extending in the negative direction. Thus as illustrated in Figure 6 a negative number base 1' is positioned to align with the zero end of the base 1.

The bases 1 and 1' are pushed together for use. The base 1' has a groove 3' and side wings 5' with one of the wings carrying unit markings commencing with -1 and incrementing by one unit. The negative base may be 20 units long. There may be multiple negative bases of longer or shorter unit length. The zero stop 8 may be removed where the calculation involves moving from negative to positive numbers or vice versa.

Conveniently the elements used are accommodated in a purpose made box. It is preferred to have the following number of fixed length counting elements: - Unit Lenqth No of elements 1 20 2 10 3 7 4 5 4 6 4 7 3 8 3 9 3 2 Conveniently the box accommodates at least one base element and preferably two (one for + ve numbers and one for -ve numbers). The elements of each unit length are conveniently contained within separate areas of the box dimensioned to accept all the elements of that unit length. The separate areas are formed as 9 depressions, conveniently cut into the surface of the box where formed of wood, but may be moulded when materials for the box such as plastics so dictate. The preferred material is wood. The depressions are preferably shallower than the depth of the counting elements to facilitate easier removal. The depressions are rectangular. The counting elements having the same unit lengths are disposed side by side to form a rectangular depression. The counting elements of unit length 1 are conveniently disposed in a 4 x 5 matrix array. Other configurations are possible.

Claims

Apparatus comprising at least one elongate base of track member having markings comprising a sequence of numbers and/or symbols which may be representative of said numbers and providing the base or track with a plurality of divisions of equal unit length; and one or more counting modules for use in association with the base or track member, the counting module being selected from a plurality of counting elements of fixed length whose length is a multiple of said unit lengths, and further comprising a releasable zero stop for use in positioning at least one counting element.
2. Apparatus as claimed in claim 1 in which the zero stop serves as a positioning element for the fixed length counting elements when counting from zero.
3. Apparatus for teaching subtraction, the apparatus comprising at least one elongate base or track member having markings comprising a sequence of numbers and/or symbols which may be representative of said numbers and providing the base or track with a plurality of divisions of equal unit length; and one or more counting modules for use in association vvith the base or track member, the counting module being selected from a plurality of counting elements of fixed length whose length is a multiple of said unit lengths, and a blocking element adapted for co-op-erating engagement with the base, in which the blocking element is positic)ned to the right of the number and/or symbol from which a fixed number is to be subtracted, and a fixed length counting module of the appropriate length is placed up to the blocker element in a position to obscure the unit length numbers and/or symbols so that the answer to the calculation is the next number visible to the left thereof.
4. Apparatus as claimed in claim 1, 2 or 3 in which the base or track member incorporates a longitudinal groove and in which the divisions of unit length extend along one side of the groove.
5. Apparatus as claimed in claim 3 or 4 when appendant to claim 3 in which the blocking element has a cross-section which is T-shaped and in which the offset part is formed by one limb of the T-shaped head.
6. Apparatus as claimed in anyone of the preceding claims in which means is provided for securing two or more track members together in end to end relation.
7. Apparatus as claimed in claim 6 in which said means comprises two spaced bores and two complimentary projecting elements.
8. Apparatus constructed and arranged substantially and hereinbefore described with reference to and as illustrated in the accompanying drawings.
9. Apparatus for teaching subtraction constructed and arranged substantially as hereinbefore described with reference to and as illustrated in the accompanying drawings.