JPS59229590A - Graphic panel combination teaching aid - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

[Detailed Description of the Invention] The present invention is intended to be useful for learning arithmetic and arts and crafts.
It is about the seven graphic boards and how to use them.

The figure board consists of a total of 4 fan-shaped boards: 1 semicircle (1), 1 quadrant (2), and 2 octants (3), and a circle (4) board that can be made from 4 fan shapes. A right-angled isosceles triangle whose base is the radius of (
5) Right angled isosceles small triangle formed by connecting 2 plates and 4 plates (6) and 2 plates (6) with the same radius as the sides that sandwich the right angle. (7)・Square (
8)・One plate of each parallelogram (9), two small trapezoid αO plates made by connecting one small and medium triangle (5 and 6) with the sides, and one plate of the same medium thick triangle (6 and 7). ) It consists of 1 kana and 2 dog trapezoid α℃ plates connected by the sides, making a total of 17 pieces.

By combining 13 shapes (5 to 11) other than sectors, you can simultaneously create triangles and squares, which are the basics of geometric shapes.
, (14 and 15), and (16 and 17) can be made in three ways.

All are right-angled isosceles small triangles (5), which are the smallest units of area.
This is an effective configuration for learning 2 fractions. In addition, the above 13 plate pieces can be combined into one to form various polygons, that is, convex polygons, including the rectangle of figure (G), 14 types of squares in 4 types, 6 types of pentagons in 4 types, and 13 types of 3 types. A total of 37 shapes: a hexagon, one heptagon, and three squares.
An infinite number of concave rectangular shapes can be created, from quadrangles to 45 pentagons. Heart shapes (19, 20), spade shapes (2L 22), etc. can also be made using metal plates or parts of them, including fan-shaped plates.

All of these board pieces (1 to 3, 5 to 11) may be made of thick cardboard, plastic board, wood, or thin boards.

We will discuss an example in which a graphic board is used for learning the four arithmetic operations.

The sum, for example 1+2, indicates that the area of the trapezoid O, which is created by combining a figure (5) plate with an area of 10 and a figure (6) plate with an area of 2, is 3. If this is done in between the usual learning of the sum of numbers and the expression of the sum of abstract numbers in the formula 1+2=3, it will be possible to fill the gap in the transition.
Helpful for better understanding.

The difference, for example 5-2, means the trapezoid remaining after removing the triangular (6) board from the pentagonal (to) board of the combination of the drawing boards (5 and 8) with areas 1 and 4, and is the figure (1).

The same goes for sums and differences of fractions.

The product, for example the fraction 2x8, is a square (for negative.

The area 2 of the triangle (6) which is bluer than the upper or lower half triangle which is 1 of the whole is - of the area 32 of the whole square.
Therefore, we can learn that the formula 2'4""1'6 holds true.

The quotient, for example, ÷ ゛, is a square 05 with an area of 32)
, we can operationally find out how many triangles (6) with an area of 2, which is the responsibility of the whole, are included in the triangle with an area of 16 in the upper or lower half, which is the wife of the whole. Since there are 4, 1÷1 1 ×8
Learn the establishment of =:4.

821 The same applies to products and quotients of integers.

Regarding the properties of figures, almost all polygons handled in arithmetic learning are included in the figure (5 to 11) board or can be constructed from them, so the shape and size of the two figures, symmetry, congruence, etc. Manipulative learning about similarities, etc. can be performed. Also, regarding enlarging/reducing two figures, for example, a triangle has an area of 1 (figure 5), 2 (figure 6), and 4 (
In addition to figure 7), area 8 (figure 12), 9.16.1
8. Since the right isosceles triangles of 32 (figure 16) and 36 (which can be easily made from figure 13) can be constructed, 5
You can learn through operations that when you double, triple, or quadruple the length of a side, the area is multiplied by 4, 9, or 16. You can also learn about quadrilaterals, pentagons, and hexagons in a similar way.

Due to its structure, the present invention not only has the effect of effectively carrying out arithmetic learning that cannot be carried out with conventional figure combination toys, but also has the effect of being able to effectively carry out arithmetic learning that cannot be carried out with conventional figure combination toys. You can make shadow puppets of things. In addition to being able to perform all the conventional tangrams, lucky puzzles, and heart puzzles, it can also add new spade puzzles, providing a wide range of uses for 2nd art learning, and has the effect of helping to develop 2nd figure composition ability and aesthetic sense. I have it.

[Brief explanation of drawings]

The drawings show one embodiment of the present invention, in which Fig. 1 is a plan view of 17 plate pieces, Fig. 2 is a side view of Fig. 1, and Fig. 3 is a circle and a right isosceles triangle made up of these plate pieces. Figure 4 is a plan view of one rectangle made up of 13 plate pieces excluding the fan-shaped plate, and Figure 5 is a plan view of two heart-shaped pieces made up of some of the 17 plate pieces. Figure 6 is a plan view of a spade carving machine made up of some and all 17 board pieces, Figure 7 is a plan view showing dashi 3j and subtraction using board pieces, and Figure 8 is a plan view of a spade carving machine made of all 17 board pieces. It is a shadow puppet made of puzzles. 1- Half disk 2- Quarter disk 3- Quarter disk 4- Structured disk 5- Small triangular plate 6- Medium bead square plate 7- Large king square plate 8-
Square plate 9- Parallelogram plate 10- Small trapezoidal plate 11---
Dog trapezoidal plate 12, 14.16 ---- structured triangular plate 13, 1
5.17--Constructed square plates 18--11 configured rectangular plates 19, 20--1 configured notebook-shaped plates 21, 22-1-1 configured spade-shaped plates phantom-configuration Pentagonal plate patent applicant Shigehiro Kobayashi Procedural amendment (method) September 74, 1982. Indication of the case 1982 Patent Application No. 91919 2
Name of the invention Graphic board combination teaching tool 3 Relationship between the person making the amendment and the case Special W "Applicant address 1655-4 Tsuruichi-cho, Takamatsu-shi, Kagawa Prefecture, date of amendment order (1 August 30, 1980, 5, subject of amendment) Specification 6, Contents of the amendment Copywriting of the specification (no change to the content) Procedural amendment (voluntary) July 7, 1980 Manabu Shiga, Commissioner of the Patent Office 1 Indication of the case Patent Application No. 091919 of 1988 III Ban (Mi1h Sayogu)
Let's try +152 Title of the invention Graphic board combination teaching tool and its usage 3 Relationship with the case of the person making the amendment Patent applicant postal code 761 (Telephone number 0878-33-16
70) 4 Number of inventions increased by the amendment 06 Contents of the amendment (a) ``Drawing board combination teaching tool j'' is amended to read ``r drawing board combination teaching tool and its usage j.'' (b) (c) As shown in the attached sheet. Contents of the amendment Description 16 Name of the invention Graphic board combination teaching tool and its use 2, Claims (1) Disc into four fan-shaped boards: semicircle, quarter circle, octant circle, and octant circle The divided one, two small right-angled isosceles triangles whose bases are the radius of the circle, four right-angled isosceles medium triangles whose sides sandwich the right angle, and the two medium sphere triangles above with the top sides. One each of right-angled isosceles large triangles, squares, and parallelograms formed by connecting them, two small trapezoids formed by connecting one of the small and medium triangles with supporting sides, and one each of the medium and large triangles. A total of 17 graphic board combinations with two large trapezoids connected by side edges (2) Combine all or part of the 17 graphic boards of Saturn without overlapping them on a plane or doubly by overlapping them. , to create figures by arranging them, and in arithmetic, ′ and `` are set.
17. 17. Methods and 2. Kyouhobutsu to cultivate compositional ability and aesthetic sense in drawings 3. Detailed explanation of the invention The present invention is designed to improve the ability to compose figures in arithmetic learning, especially the integrated learning of quantities and shapes, and 9. This book contains 17 graphic boards intended to help develop aesthetic sense and how to use them. The figure board is made of a total of 4 fan-shaped boards, including the semicircle (1st eye, 1 quadrant (2), and 2 octants (3)) in Figure 1, and 4 fan-shaped boards. Two plates of right-angled isosceles small triangles (5) whose bases are the radius of circle (4) in Figure 3, and four plates of right-angled isosceles small triangles (6) whose sides have the same radius as the right angle. A right angled isosceles Great triangle (7), a square (8), a parallelogram (9) made by connecting two medium triangle (6) plates side by side.
), two small trapezoidal (10) plates made by connecting one small and medium triangle (5 and 6) kana side by side, and one small and medium triangle (6 and 7) kana. A large trapezoid (1
1) Consists of 2 plates, totaling 17 pieces. The surface area of each plate is 1 if the area of the small triangular (5) plate, which is the smallest plate piece, is 1, and the surface area of the medium triangular (6) plate is 2. The small trapezoid (lO) plate is 3 degrees, and the large triangle (7), square (8), and parallelogram (9) plates are all 4 degrees. The large trapezoid (11) plate is 6, the sector plate has a pi of 2277, and the small is 11/7. Inside is 22/7. Large is 44/7. By combining 13 shapes (5 to 11) other than sectors, we can simultaneously create triangles and squares, which are the basics of geometric shapes, as shown in Figure 3 (1).
2 and 13), (14 and 15), (16 and 17)
It can be made in three ways, all of which include a right-angled isosceles small triangle (5), which is the smallest unit of area, and convex polygons made by combining parts of the above 13 shape plates range from triangles to octagons. Approximately 600 shapes 1 area 2 to 39 (minimum triangle area 1
) The convex polygon with an area of 40 formed by combining 13 one-figure boards, which can be made into any integer up to
A total of 38 shapes, including 6 types of pentagons in 4 types, 14 types of hexagons in 3 types, 1 heptagon, and 3 types of octagons.
An infinite number of concave rectangular shapes can be created, from quadrangles to 45 pentagons. Furthermore, 17 shapes (1 to 3,
5-11) When some or all of the plates are combined, the heart shape (19, 20) shown in Figure 5 or the spade shape (21, 22) shown in Figure 6 can be created.
) can also be created. For these graphic (1-3, 5-11) boards, thick cardboard, plastic temporary, wood, or base board-like materials may be used as desired. We will explain how to use the graphic board to learn the four arithmetic operations. Sum of integers 1 For example, 1+2 is the sum of the numbers such that 1 and 2 of any figure boards add up to 3, and a figure with 1 area of 1 (5)
If you combine the board and the figure (6) board with an area of 2, you will get a small trapezoid (10) board with an area of 3 as shown in Figure 7. In other words, it contains the sum of quantities. By the way, a figure with an area of 2 can be a figure with an area of 1 (5), and depending on how the two plates are combined, it can be a square or a parallelogram, as well as a square or a parallelogram (6), and furthermore, a figure with an area of l ( 5) If you add more plates and combine them, it can become an isosceles trapezoid (23) of size 3. In this way, I+2=3 is a very abstract mathematical formula that holds true for numbers and quantities regardless of the difference in form. However, usually
In arithmetic, school children are forced to make a huge leap forward by immediately moving from learning the sum of numbers to learning formulas for the sum of abstract numbers. We need to fill this leap gap and deepen our understanding. To do this, use this graphic board combination teaching tool to help students learn the sum of quantities graphically. By doing so, we can make mathematics more tangible for schoolchildren. In this way, the present invention enables integrated learning of quantities and shapes. As with the case of sums, fused learning of quantities and shapes is possible for integer differences 1, for example, 5-2. The explanation as a difference in numbers will be omitted, or as a difference in ■, for example, the area 1
A triangle (6) with an area of 2 from the pentagon (24) or trapezoid (25) in Figure 7, which is a combination of the figure boards 4 and 2 and 3.
The figure 00) means the remaining trapezoid after removing the square, parallelogram, and parallelogram. Before we talk about the sum and difference of fractions, we will explain how to make fractions.9For example, for the fraction 1/2, place a small triangular (5) plate and a medium spherical square (6) plate above and below the fraction bar on a plane instead of numbers. It can be obtained by placing it on top or by stacking it on top and bottom. Similarly, the half fraction 1/3 can be made using a small triangular (5) plate and a small trapezoid (10) plate. These are irreducible fractions, but in the form of irreducible fractions, i.e. 2/4°3/6.4/8 and 2/6
, 3/9, etc. Children can easily learn how to create fractions graphically through their daily life experience of dividing sweets and fruits into two or three equal parts. In addition, if you use a diagram board to reaffirm the known facts that can be considered wisdom in daily life, such as adding two halves, or 1/2, or adding 1/3 and 273, you will be able to compare the size of fractions and add and subtract. In the case of fractions with the same denominator, you can directly compare the two numerators or add or subtract them; in the case of fractions with different denominators, first change the denominators of both fractions to the same one, and then use 9, for example, 1/2.
The system of converting 173 to 376 and 2/6 before performing the calculation can be graphically understood, and there is no chance of making mistakes in the mathematical operations of addition and subtraction. Multiplication of integers is an expedient method for repeated addition, so the explanation will be omitted. Regarding division of integers, if the number is divisible by 2, the answer is the number of times the number can be subtracted repeatedly, and if the number is not divisible by 1, the answer is not a decimal but a 5-fraction. This is included in the next explanation of multiplying and dividing fractions. Multiplying and dividing fractions 1 For example, ■215 x 3 or ■215÷3
Alternatively, you can have students understand the calculation mechanism by having them perform ■215 X 3/4 and ■215 ÷ 3/4 while manipulating the diagram board by hand. ■215 X'3 does not add three fractions with the same denominator. Therefore, it is better to create a fraction by multiplying the two numerators by three, while keeping the denominator as is. ■For 215÷3, multiplying the fraction of the answer by 3 gives 275, or 6/15, so 1 fraction is 275.
Multiply both the denominator and numerator by 3 to create a fraction with a numerator divisible by 3 (2 is multiplied by the numerator, but multiplication is the inverse operation of arithmetic, so division can also be done by just dividing the numerator by 3 with the denominator unchanged.) In other words, 2/(5X3) −
Multiply 2/15 and the denominator by 3 to get the answer. ■For 215 x 3/4, the 2 fraction 374 is 3÷4
Therefore, 215 X (3÷4)=215X3÷4=
I ended up using the diagram board to confirm that 615÷4 = G/20 = 3710. To multiply fractions, multiply the denominator by the denominator, and the numerator by the numerator by the numerator, i.e. 215x3/4=(2x3)/(5
Help students understand that X 4) = 6/20 = 3/10. ■215÷374 is the same as before, 215÷(3÷4)=21
5÷3×4−2/i5 X 4 = 8/15 is confirmed manually on the graphic board.In the end, when dividing a fraction, multiply the reciprocal of the fraction of the divisor by the fraction of the dividend. That is 21
5÷374-215x4/3=(2x4)/(5x3)
= 8/15. Next, a method for operationally learning shapes in arithmetic will be explained. Create a circle and investigate its properties. By combining some or all of the 13 shape boards excluding the fan board, you can make over 600 shapes ranging from triangles to quadrilaterals, so use these polygons to learn about the properties of polygons, sides and diagonals when learning shapes in math. You can learn the length, angle, and area of , and the congruence, expansion, and contraction of two shapes.For example, a triangle has areas 1 (shape 5), 2 (shape 6), and 4 (shape 7). ), area 8 (figure 12), 9.16, 18, 2
It is possible to construct a right-angled isosceles triangle of 5.32 (Figure 16)', 36 (which can be easily made from Figure 13), so multiplying the lengths of the two sides by 2.3, 4, and 5.6 yields an area of 4.
, 9.16, 25.36 times, etc. Similarly, you can learn how to enlarge and reduce rectangles, pentagons, and hexagons. Due to its structure, the present invention not only enables manipulative arithmetic learning that was not possible with conventional figure combination toys, but also allows for the creation of shadow puppets of concrete objects such as people, animals, plants, and utensils in the same way as conventional figure combination toys. can also be done. In addition to being able to create a variety of shapes made from the traditional Kungram, Lucky Puzzle, and Heart Puzzle, you can also add new additions to the Spade Puzzle. Figure 8 shows some examples of shadow puppets that can be made with spade puzzles. Being able to make many shadow puppets provides a wide range of ways to use RLI in learning 5 arts and crafts, and also has the effect of helping to develop 1 figure composition ability and aesthetic sense. For the purpose of simplifying the explanation, we will give an example of how to use it to develop figure composition ability and aesthetic sense.
6 and 10) Describe a crow made using a total of 8 boards0
Make the neck and body, which will become the mother body of the bird, using six pieces, excluding one each for areas l and 2, as shown in Figure 9 (a). (2) (E) There are 4 ways to attach one head, so it is 12 fiu, and if you move the small triangle on the neck and use the two small triangles for the legs, you can get long legs (g).
It can be made with short legs (chi), and 12 states can be created with variations of nine heads and a tail. By changing the moving figure board to another board, it is possible to make about 508 birds from the mother body in (a). In addition, birds born from different mothers, such as (su), can be easily changed into more than 500 forms by moving a part of them to an appropriate position.
There are many other types of birds that can be made, so even with just 8 graphic boards, thousands of birds can be created.9 Many different types of birds can be created, so try to combine the graphic boards to create as beautiful a bird as possible. In the process, children can develop their ability to compose figures and develop their aesthetic sense, and sparrows can also be used in education to enhance concrete creativity. 4. Brief description of the drawings The drawings show an embodiment of the present invention. Fig. 1 is a plan view of 17 graphic boards, Fig. 2 is a side view of Fig. 1, and Fig. 3 is a diagram of these graphic boards. The constructed circle, right-angled isosceles triangle, and square, the fourth
The figure shows a rectangle made up of 13 Japanese cedar boards, excluding the fan-shaped boards.
Figure 5 shows two heart shapes made up of parts of 17 figure boards C, Figure 6 shows a spade carving made up of some and all of 17 figure boards, and Figure 7 shows an example of addition and subtraction using figure boards. Figure, 8th
The figure shows an example of the configuration of a shadow puzzle made of a spade puzzle using all the 17 and 17 figure boards, and Figure 9 shows a crow made of 8 figure boards with an area of 1.2.3. ■-Semicircle plate 2-Quadrant disk 3--Large disk 4-Constructed circle 5-Small triangular plate 6--Medium triangular plate 7-Large triangular plate 8-Square plate 9-Parallelogram plate 1 〇-Small trapezoidal plate 11--Large trapezoidal plate 12, 14.16--Constructed triangle 13, 15.1
7-Constructed square I8-Constructed rectangle 19, 20--Constructed heart-shape 21, 22--Constructed spade-shape 23--Isosceles trapezoid 24-Constructed triangle 25--Constructed Trapezoid applicant Shigehiro Kobayashi

Claims (2)

[Claims] (1) A disk divided into four fan-shaped plates: a semicircle, a quarter circle, an octant, and an octant, and two small right-angled isosceles triangles whose bases are the radius of the circle, Four isosceles right-angled medium polygons whose sides are right angles, one each of isosceles right-angled large triangles, squares, and parallelograms formed by connecting the two medium polygons with their sides, and the small Small trapezoid 2 made by connecting two triangles with sides
A total of 17 graphic board combinations, including two large trapezoids made by connecting one each of the medium and large triangles with their sides. (2) A method for learning about the four arithmetic operations, properties of shapes, congruence and similarity, enlargement and reduction, by combining all or part of the 17 figure boards and arranging them on a plane without overlapping them to create figures. A drawing board combination teaching tool that can provide a means for cultivating the composition ability and aesthetic sense of two-dimensional artists.