IL23970A - Educational aid for the study of mathematics - Google Patents

Description

AN EDUCATIONAL AID FOR THE STUDY OP MATHEMATICS The present invention concerns an educational aid used in the study of mathematics.

An educational aid for the study of mathematics is known. It consists of multiple sets of ten sticks of equal width, each stick being one unit of length longer than the one preceding it. Each size stick has a different color. ¥ith the aid of these sticks a child can be taught addition, subtraction, multiplication, roots, powers and the like.

It is the object of the present invention to provide an educational aid with which the concepts of numbers and mathematical operations can be taught using the concepts of relationships of areas, the ratios of the areas being rational, while the ratios of the bases are either rational or irrational.

The invention consists in an educational aid for the study of mathematics, to teach concepts such as multiplication, square roots, relationships of areas and the like, comprising at least one set of ten patterns, each pattern having the same geometric shape such as square, triangular, hexagonal or the like and each being one unit of area larger than the preceding one, all the sides of each increasing in the same proportion, the unit area being the smallest of the set, each pattern having two surface colors, one on each ¾&®e, whereby each color defines a number, such that the product of the numbers defined by the two colors identifies the area.

The geometric shape of the patterns may be square, triangular, hexagonal,, circular or the like. The ratio ·' ' ' : ■ . :,., :'// ■ . . ■ .. . . .. . ■:: between the9 areas of the patterns in each set is thus a rational oiie, while ihe ratio of their bases, which is the ratio of their sides if the patterns are square, triangular or the like, or the ratio of the r radii or aces, if the patterns are circles or ellipses., for example, is rational or irrational.

The patterns may be made of cardboard, wood, plastics, metal or the like.

In a preferred embodiment of the invention, the educational, aid comprises ten sets of ten patterns, the areas of the patterns within each set being graded b consecutive multiples of the area of the first pattern of the set, the first set starting with a pattern of one standard unit of area, each following set starting with a pattern the area of which is a consecutive multiple of the standard unit.

In a further preferred embodiment of the invention, the patterns are squares, the color scheme for the consecutive multiples of areas being as follower White defines ratio of 1 to the unit.

Pink defines a ratio of 2 times to the unit.

Light blue defines a ratio of 3 times to the unit.

Bed defines a ratio of 4 times to the unit.

Yelloy iLefines a ratio of 5 times to the unit.

Blue defines a ratio of 6 times to the unit.

Grey defines a ratio of ΰ times to the unit.

B r f ne a t o of time o the unit - - The standard unit is preferably 1 square cm.

However, if desired any other standard unit may be chosen.

Instead of the colours defined above, any other color scheme may be used.

In s$ill a further embodiment of the invention, the educational aid comprises a chart in which each set of the ten sets of patterns is printed in horizontal rows according to the color, scheme of the patterns and in progressive order of size, each horizontal and each vertical row starting with a pattern whose area is a consecutive multiple of the standard unit, so arranged that each vertical column contains ai the patterns of the same color.

A few examples of the educational aid according to the invention are given hereinbelow, without, however, limiting the invention, since the possibilities of use are practically without limits. The patterns being used here for illustrative purposes are of square shape using a basic Example 1 Problem! To show that the side of a square is the geometric Example 2 Problemt To show that in a right-angled triangle the square of the hypotenuse is equa to the sum o the squares of tfye two sides (Pythagoras ' theorem) . .

Take the square whose one surface is grey (?) and ' whose other is yellow (5). Area is 35 cm . Put this square at right angles to a square whose one surface is 2 grey (7) and whose other surface is pink (2). Area 14 cm , i.e. the diagonals of both squares lie in a straight line.

Choose a square whose one side completes exactly the triangle formed by the sides of the two other squares.

The square chosen Is grey (7) on both sides, i.e. the 2 one whose area is 49 cm . , ' ' - (b) When a yellow (5) and red (4) square - are 20 cm - is put at right angles to a red (4) and pink (2) square - 2 area 8 cm - the square completing the triangle is red (4) , . ' 2 and grey (7) square - area 28 cm .

Example 3 Problemt To show that the side of a square is the square root of its area.

In this example children will estimate the approximate value of the base by comparing it with a known one and will prove their estimate by measuring the base with a ruler* (a) Taking a square of 30 cm , i.e. one whose colo.rs are blue (6) and yellow (5). Its side will be more than 5 ¾sd==i=e*«=6ita«==6 because the area of the square is larger 2 " . ' .·■ ■ "'·'· ■■".· ■ ' than the one whose area is 25 cm and less than 6 because 2 the: square is smaller than the one whose area is 36 cm . 2 that of the square of 16 cm that to the square 2 of 9 cm . An estimate of 3.8 can be confirmed b measuring. . · ^ Example 4 ·■ < . ■ ' ' . ·. ' Problem: To find a square whose area is half that of another* ■·■:■.¾··. 2 ' Ttcke a square of 30 cm as in example 3, place various squares of unknown area on top of it, so that the corners of the unknown squares meet the 2 ' denter of all four sides of the 30 cm square. 2 Only a square of 15 cm , i.e. one whose colors are yellow (5) and light blue (3) will fit. By measuring the sides of these squares it can be shown that their ratio is accordin to the square roots of these numbers.

While in the present example only squares have been used, similar mathematical operations can be carried out with circles, for example, wherein a comparison of their areas and radii will be made.

The principle underlying the invention can be applied also to solid figures, i.e. cubes* spheres, prisms in sets, wherein each is one unit volume larger than the preceding one and each is defined by three colors which designate numbers whose product indicate the volume;

Claims (2)

1. Ah educational aid for the study, of mathematics, to teach concepts such as multiplication, square roots, relationships of, areas and the like, comprising at least one set of ten patterns, each pattern having the same geometric shape such as square , triangular, hexagonal or the like and each bein one unit of area larger than the preceding one, all the sides of each pattern increasin in the same proportion, the unit area being the smallest of the set, each pattern having two colours, one on each surface, whereby each color defines a number, such that the product of the numbers de ined b the two colours identifies the area.

2. An educational aid for the study of mathematics, as claimed in claim 1 , wherein the patterns are made of cardboard wood, plastics, metal or the like* ø. An educational aid for the study of mathematics, as claimed in any of claims 1 or 2, comprising ten sets of ten patterns, the patterns within each set being graded by consecutive multiples of the first pattern of the set, the first set starting with a pattern of one standard unit of area each following set starting with a pattern the area of which is a consecutive multiple of the standard unit* •v 4» An educational aid as claimed in claim 3, comprising a chart in which each set of the ten sets of patterns is printed in horizontal rows according to the color scheme of the patterns and in progressive order of size, each horizontal and each vertical row starting with a pattern whose area is a consecutive multiple of the standard unit, so arranged that each vertical column contains all the patterns of the s me An educational aid substantially as hereinbe ore Tel-Aviv, 15th day of July, 1965