GB2403932A

GB2403932A - Mathematical aid for drawing a Galosian grid

Info

Publication number: GB2403932A
Application number: GB0316479A
Authority: GB
Inventors: Paul Richards
Original assignee: Individual
Current assignee: Individual
Priority date: 2003-07-15
Filing date: 2003-07-15
Publication date: 2005-01-19
Anticipated expiration: 2023-07-15
Also published as: GB2403932B; GB0316479D0

Abstract

A mathematical aid comprising a template 200 for drawing a Galosian grid (100, Fig.1). A Galosian grid comprises a scheme for setting up a multiplication problem. The template 200 may comprise a plate with slots 202 provided therein.

Description

À . , 2403932

MATHEMATICAL AID

This invention concerns a mathematical aid primarily used to assist in the solution of multiplication problems.

It will be appreciated that there are various ways to solve a multiplication problem - for example using a calculator, mental arithmetic or as a long multiplication where products are summed. A further example is provided by 'Galosian', 'Italian' or 'Arab' multiplication (the same method is known by all three terms), which provides a geometrical picture as an aid. Herein, for reasons of consistency, the term Galosian Multiplication is used. An example of a problem set out in a 'Galosian grid' is shown in Figure 1.

It will be appreciated that many people find multiplication challenging.

In particular, this applies to school children and people with learning difficulties such as dyslexia. It can be that different methods appeal to different people, and while a Galosian grid may be favoured by some people, it is time consuming to draw and has a complex form.

According to a first aspect of the present invention, there is provided a mathematical aid comprising a template for drawing a Galosian grid.

This is advantageous as the form of the Galosian grid need not be recalled by the user. Further, the drawing process can be made easier and quicker by use of a template. Further still, the result will be neat and regular, ensuring that there is space to carry out the multiplication process using the grid without confusion.

Preferably, the template comprises a plate with a plurality of slots provided therein, said slots being arranged in the form of a Galosian grid. l i 2

Such an arrangement is a convenient way of providing a template, which is likely to be more robust than other techniques - such as providing the template from a plurality of wires, etc. Preferably, the template is at least partially transparent. This is advantageous in that it allows the template to be repositioned without obscuring any portion of a pattern drawn therewith. This may be required when multiplying numbers with a greater number of digits than the grid formed by the slots of the template can accommodate.

Preferably, the template comprises a plastics material. This is advantageous in that plastic is a durable material which can easily be formed or punched into the desired shape.

Conveniently, the template is arranged to be suitable to multiplying two two digit numbers. As such, the template may provide a first and second input box, each input box comprising two spaces. Further, in a template providing a grid allowing two two digit numbers to be multiplied, there may be provided a first, second, third and fourth product box. This is advantageous as this may be a standard application of the template.

Indeed, the number of product boxes may comprise the product of the number of digits of the numbers that can be multiplied together. In one embodiment the template allows two digit numbers to be multiplied and there are therefore four product boxes. In another embodiment the aid may allow three digit numbers to be multiplied and there therefore may be nine product boxes.

Each product box may be divided into two portions. !

The template may comprise one or more answer spaces. Preferably, the number of answer spaces on the template equals the total number of digits in the numbers being multiplied together. For example if the template allows two two digit numbers to be multiplied there are preferably four answer spaces.

In some embodiments, the template may further comprise a handle. This is advantageous when a Galosian grid is to be drawn on a vertical or substantially vertical surface, for example a blackboard or a white board.

Preferably, the handle is arranged such that, in use of the template, a user may draw through the slots when holding the template to a writing surface.

According to a second aspect of the present invention there is provided a method of drawing a Galosian grid comprising providing a template according to the first aspect of the invention, a writing surface and a writing implement, the method further comprising marking a grid through the slots in the template on the writing surface using the writing implement.

Generally, the slots are provided by moulding when the template is produced but may be provided by a material removal technique such as cutting.

According to a third aspect of the invention, there is provided a mathematical kit comprising a template according to the first aspect of the invention.

There is now described an embodiment of the present invention, by way of example only and with reference to the accompanying figures of which: Figure 1 shows a multiplication problem set out as a Galosian multiplication problem; Figure 2 shows a template according to a first embodiment of the present invention; and Figure 3 shows a template according to a second embodiment of the present invention.

Figure 1 shows a multiplication problem '42 x 31' set out in a Galosian I grid 100 arranged to find the product of two two digit numbers. The Galosian grid 100 comprises nine vertical lines 102 arranged in three parallel columns 104a, 104b, 104c, each column 104a, 104b, 104c comprising three vertical lines 102 linearly arranged. The Galosian grid 100 further comprises nine horizontal lines 106 arranged in three parallel rows 108a, 108b, 108c, each row 108a, 108b 108c comprising three horizontal lines 106 linearly arranged. The columns 104a, 104b, 104c and the rows 108a, 108b, 108c intersect to define a first llOa, second llOb, third llOc and fourth llOd square product box and a first 112a, second 112b, third 112c and fourth 112d three sided input box. Each product box llOa, llOb, llOc, llOd is defined by two vertical lines 102 and two horizontal lines 106, although it will be appreciated that any of the lines 102, 104 may contribute to more than one product box l lea, l lob, l lOc, l led.

The four product boxes llOa, llOb, llOc, llOd are arranged to form a square where the upper left hand quadrant is provided by the first product box llOa, the upper right hand quadrant is provided by the second product box llOb, the lower left hand quadrant is provided by the third product box llOc and the lower right hand quadrant is provided by the fourth product box llOc.

The four three-sided input boxes 112a, 112b, 112c, 112d are arranged as follows. The first input box 112a is arranged above the first product box llOa and is defined by one horizontal line 106 and two vertical I lines 102. The second input box 112b is arranged above the second product box llOb and is defined by one horizontal line 106 and two vertical lines 102. The third input box 112c is arranged to the right of the second product box llOb and is defined by two horizontal lines 106 and one vertical line 102. The fourth input box 112d is arranged to the I right of the fourth product box llOd and is defined by two horizontal lines 106 and one vertical line 102.

The Galosian grid also comprises nine forward slash lines 114. The forward slash lines 114 are arranged such that each product box llOa, llOb, llOc, llOd is bisected along a diagonal by one forward slash line 114 into an upper and lower portion. The remaining four slash lines 114 define a first answer space 116a, a second answer space 116b, a third answer space 116c and a fourth answer space 116d arranged about the right hand edge and the bottom edge of the square formed by the four product boxes llOa, llOb, llOc, llOd. The first answer space 116a is defined by one forward slash line 114 connected at its tip to the top left corner of the first product box llOa (which, it will be appreciated, is also the bottom left corner of the first input box 112a), the left hand vertical line 102 of the first product box llOa and a second forward slash line 114 1 with its tip towards the bottom left corner of the first product box llOa (which is also the top left hand corner of the third product box llOc).

The second answer space 116b is defined by one forward slash line 114 with its tip towards the bottom left corner of the first product box llOa, the left hand vertical line 102 of the third product box llOc and a second forward slash line 114 with its tip towards the bottom left corner of the third product box llOc. The third answer space 116c is defined by one forward slash line 114 with its tip towards the bottom left corner of the third product box llOc, the bottom horizontal line 106 of the third product box llOc and a second forward slash line 114 with its tip towards the bottom right corner of the third product box 110c. The fourth answer space 116d is defined by one forward slash line 114 with its tip towards the bottom right corner of the third product box llOc, the bottom horizontal line 106 of the fourth product box llOd and a second forward 3 slash line 114 with its tip towards the bottom right corner of the fourth F product box llOd. In this way, the forward slash lines 114 form four diagonals across the Galosian grid 100.

The calculation is then carried out as follows.

The first number is 42. The '4' is written in the first input box 112a and 3 the '2' is written in the second input box 112b. The second number is 31. The '3' is written in the third input box 112c and the '2' is written in the fourth input box 112d. Each digit of the first number is then multiplied with each digit of the second number and the result is recorded in the product box llOa, llOb, llOc, llOd found where the columns and rows that the digits occupy intercept. The products are divided into 'tens' and 'units' e.g. the number 56 comprises five tens and six units. The number of tens is written to the left of the forward slash line 114 in the appropriate product box llOa, llOb, llOc, llOd and the number of units is written to its right.

For example, '4' is in the first input box 112a, '3' is in the third input box so their product is written in the first product box 110a. 4x3 is 12, one ten and two units. '1' is written to the left of the forward slash line 114 in the first product box 110a and '2' is written to its right, and so on.

Now the products in the product boxes llOa, llOb, 110c, llOd should be summed along the diagonals defined by the forward slash lines 114. This is done from the bottom right hand corner of the grid 100, i.e. the result for the fourth answer space 116d is calculated first. In fact, there is no sum here as the diagonal relating to the fourth answer space 116d contains only on digit, '2'. '2' is therefore written in the fourth answer space 116d. To obtain a result for the third answer space 116c, the sum 4+0+6 must be calculated. The result is '10'. The number of units- '0' is written in the third answer space 116c and the number of tens- '1'- is carried to the second answer space.

Continuing in this fashion, the result '1302' is obtained.

A first embodiment of the present invention is shown in Figure 2. A template 200 comprises a sheet of Perspex about 3mm thick. The template 200 has cut therefrom slots 202. The slots are arranged to form the horizontal lines 106, vertical lines 102 and forward slash lines 114 described above to form the Galosian grid 100. In use of the template, a user can draw a grid 100 using a pen, pencil or other writing apparatus and marking a page placed under the template 200 by running the writing apparatus, such as a pen or pencil, through the slots 202.

It will be appreciated that if numbers containing a greater number of digits are used, the template 200 can simply be repositioned on the paper and further lines drawn.

A second embodiment of the present invention is shown in Figure 3. In this embodiment, the multiplication is to be written on a substantially vertical surface, for example a blackboard or whiteboard. In this embodiment, a template 200b additionally comprises a handle 302 arranged such that a user can still draw through the slots. The handle 302 comprises a Perspex skip shaped in an arch. End regions of the strip are connected to the edges of the template and the arch is arranged to allow the handle 302 to project away from the template 200b.

In other embodiments (not illustrated), the handle 302 could comprise a peg or the like.

It will be appreciated that the embodiment of Figure 2 may be suited to drawing the grid on paper on a flat surface. The embodiment of Figure 3 is therefore likely to be larger in size as a grid drawn on a blackboard will usually be viewed from some distance.

Claims

1. A mathematical aid comprising a template for drawing a Galosian grid.

2. A mathematical aid according to claim 1 which comprises a plate with a plurality of slots therein, said slots being arranged in the form of a Galosian grid.

3. A mathematical aid according to claim 2 in which the plate comprises a plastics material.

4. A mathematical aid according to any preceding claim in which the template is at least partially transparent.

5. A mathematical aid according to any preceding claim in which the template is arranged to be suitable to multiplying two two digit numbers.

6. A mathematical aid according to claim 5 which provides a first and second input box, each input box comprising two spaces.

7. A mathematical aid according to claim 5 or claim 6 which provides a first, second, third and fourth product box.

8. A mathematical aid according to any preceding claim in which the template comprises a number of product boxes, the number of product boxes comprising the product of the number of digits of the numbers that can be multiplied together.

9. A mathematical aid according to claim 7 or 8 in which each product box is divided into two portions.

10. A mathematical aid according to any preceding claim in which the template comprises one or more answer spaces.

11. A mathematical aid according to claim 10 in which the number of answer spaces on the template comprises the total number of digits in the numbers being multiplied together.

12. A mathematical aid according to any preceding claim in which the template further comprises a handle.

13. A mathematical aid according to claim 12 in which the handle is arranged such that, in use of the template, a user may draw through the slots when holding the template to a writing surface.

14. A method of drawing a Galosian grid comprising providing a template according to any preceding claim, a writing surface and a writing implement, the method further comprising marking a grid through the slots in the template on the writing surface using the writing implement.

15. A mathematical kit comprising a template according to any of claims 1 to 13.

16. A mathematical aid substantially as described herein and as illustrated in the accompanying Figures 2 and 3.

17. A method of drawing a Galosian grid substantially as described herein and as illustrated in the accompanying Figures.

18. A mathematical kit substantially as described herein and as illustrated in the accompanying Figures 2 and 3.