JP3164697U - Teaching material for learning solid figures - Google Patents

Abstract

Provided is a teaching material with a high learning effect that allows a regular polyhedron to be easily experienced as a three-dimensional object and can easily grasp the relationship between the three-dimensional object and a plane, vertices, and sides. A teaching material for learning a three-dimensional figure comprising a plurality of regular polygon pieces each having three or more different regular polygons each having the same length of one side on a surface, each regular polygon piece having The connecting projections 2 and / or the connecting openings 3 for detachably connecting the regular polygon pieces to each side are provided, and the connecting projections are located on the sides of the regular polygonal surface portion, from the sides. The connecting opening includes an opening located on the side of the regular polygonal surface portion, and an opening protection portion that surrounds the periphery of the opening and protrudes from the side. The square pieces are connected by fitting the connecting protrusion and the connecting opening so as to be detachable from each other, and a solid figure model belonging to the regular polyhedron and the regular polyhedron group can be made. [Selection] Figure 1

Description

  The present invention relates to a teaching material for learning three-dimensional figures, and more particularly to a three-dimensional model teaching material for understanding mathematical relations and properties of a regular polyhedron through an experience of actually assembling a regular polyhedron.

  Conventionally, in elementary school and junior high school education courses, learning of various solid figures such as rectangular parallelepipeds, cubes and other polyhedrons, cylinders, cones and the like is required. Among these three-dimensional figure learning, especially for regular polyhedrons, not only mathematical aspects, but also crystal models and nuclear models in the scientific field, so the importance of spatial understanding of solids has increased. It is also featured in textbooks and secondary / high school entrance examination issues.

However, in general textbooks, etc., represent three-dimensional solid figures by replacing them with two-dimensional plane figures such as sketches and development drawings, so students can grasp the three-dimensional spatially, and understand mathematical relationships and It was not easy to improve the ability to understand the nature intuitively.
As a teaching material corresponding to such a request, a lattice-shaped polyhedral puzzle is known (Patent Document 1). However, this puzzle is a polyhedron made by combining connecting rods with the same flexible length, which is enough to understand and feel the combination of regular polyhedron surfaces and the angles formed by each surface. There wasn't.

Japanese Examined Patent Publication No. 54-8142

  The purpose of the present invention is to take into consideration the problems of conventional teaching materials in learning three-dimensional figures, and to make it possible to easily experience a regular polyhedron as a three-dimensional object and to easily grasp the relationship between a three-dimensional object, a plane, vertices, and edges. The purpose is to provide highly effective teaching materials.

In order to achieve the above object, the solid figure learning material of the present invention is a three-dimensional figure learning comprising a plurality of regular polygon pieces each having three or more different regular polygons each having the same side length. Each of the regular polygon pieces has a connection protrusion and / or a connection opening for detachably connecting the regular polygon pieces to each side. It is located on the side of the polygonal surface part and has a shape protruding from the side, and the connection opening surrounds the opening located on the side of the regular polygonal surface part and the periphery of the opening and protrudes from the side A plurality of regular polygonal pieces, which are connected by detachably fitting the connecting protrusion and the connecting opening, to form a three-dimensional figure model belonging to the regular polyhedron and the regular polyhedron group. It is something that can be done.
Further, the teaching material for learning solid figures of the present invention is a regular polygon piece having a regular polygon piece having a regular triangular face part, a regular polygon piece having a square face part, and a regular polygon having a regular pentagonal face part. It is desirable to consist of pieces.
Furthermore, the teaching material for learning three-dimensional figures of the present invention is such that the regular polygon piece has one of the connection protrusion and the connection opening on the side of the surface portion of the regular polygon, and the surface portion having the same shape. The polygonal piece is preferably composed of two types of regular polygonal pieces having different numbers of connecting protrusions and connecting openings or attachment positions.
Furthermore, the teaching material for learning a three-dimensional figure of the present invention is such that the regular polygon piece has both the connecting protrusion and the connecting opening on the side of the surface portion of the regular polygon, and has the same shape surface portion. In the square piece, it is preferable that the square piece is composed of one type of regular polygon piece having the same number of connecting protrusions and connecting openings and the mounting position.

According to the teaching material for learning a solid figure of the present invention, a regular polyhedron model can be easily assembled by a student without creating a troublesome development drawing by using a small number of regular polygonal pieces having simple connecting portions. And since the assembled regular polyhedron model maintains a strong shape in spite of simple connection parts, the regular polyhedron model is viewed from various angles, and the number of sides touching at each apex angle of the regular polyhedron is calculated. Students learn the spatial and mathematical understanding of the regular polyhedron simultaneously by counting, grasping the shape of the cross-section, etc. by seeing, touching, and experiencing the sides, faces, and vertices of the regular polyhedron. It is suitable for.
Furthermore, the teaching material for learning three-dimensional figures of the present invention is composed of regular polygonal pieces having simple connection parts, and can easily disassemble the assembled regular polyhedron model. By extending the connection to the plane while leaving a part of the connection, various variations of the development of the regular polyhedron can be easily formed, and the student's understanding of the solid figure can be further deepened.

It is an example of the regular polygon piece of the teaching material for solid figure learning which concerns on one Embodiment of this invention. It is an example of the regular polyhedron assembled with the teaching material for solid figure learning which concerns on one Embodiment of this invention. It is the example which developed the regular polyhedron assembled with the teaching material for solid figure learning concerning one embodiment of the present invention on the plane. It is an example of the regular polygon piece of the teaching material for solid figure learning which concerns on other embodiment of this invention.

The teaching material for 3D figure learning of the present invention allows students to easily assemble a regular polyhedron model without creating a troublesome development in 3D figure learning, and not only can touch and experience the edges and vertices of the regular polyhedron. The assembled model can be easily disassembled, and the development diagram can be learned in the process of disassembly.
In addition, the teaching material for learning solid figures of the present invention is not limited to regular polyhedron models, but can also assemble solid figure models belonging to the group of regular polyhedrons called advanced star-shaped regular polyhedrons, quasi-regular polyhedrons, and Zargara polyhedrons. It is a thing.

There are various types of solid figures called regular polyhedron groups, but regular polyhedrons are also called Plato solids, which are convex polyhedrons in which all faces are composed of the same regular polygon and the number of faces that touch at all vertices is equal. is there. Currently, there are five types of regular polygons: regular tetrahedron, regular hexahedron, regular octahedron, regular dodecahedron, and regular icosahedron.
The regular tetrahedron, regular octahedron, and regular icosahedron are configured by equilateral triangles, the regular hexahedron is configured by squares, and the regular dodecahedron is configured by regular pentagons.
In addition to the regular polyhedron, the solid figure called the regular polyhedron group is a convex polyhedron that can be created by combining several regular polygons with the same length of one side, convex shape such as quasi-regular polyhedron, zargara polyhedron Polyhedra are known.
Further, the regular polyhedron group includes four types of star-shaped regular polyhedrons called Kepler-Poisson solids if the vertex may be concave.

The teaching material for learning a solid figure of the present invention comprises a plurality of regular polygonal pieces having a connecting projection and a connecting opening, and having a regular polygonal surface, and the connecting protrusion and the connecting opening are fitted to each other. Thus, a three-dimensional model of a regular polyhedron group is completed.
The regular polygon piece of the teaching material for learning three-dimensional figures according to the present invention includes a regular polygonal surface portion, and a connecting projection and a connecting opening protruding from the side of the regular polygonal surface portion.
A regular polygon piece forms a polyhedral surface when creating a three-dimensional model of a regular polyhedron group, and has a regular triangular surface portion for creating a regular tetrahedron, a regular octahedron, and a regular icosahedron. At least three kinds of regular polygons: a polygonal piece, a regular polygonal piece having a square face part for creating a regular hexahedron, and a regular polygonal piece having a regular pentagonal face part for creating a regular dodecahedron Basically it consists of pieces.
Of course, regular hexagonal, regular octagonal, and regular decagonal pieces can be added to the above three types to make it possible to create various quasi-regular polyhedral and zarugala polyhedra.

  The regular polygon piece has a connection projection and / or a connection opening for removably connecting the regular polygon pieces to each side. The connection protrusion and the connection opening are formed so as to protrude from the side of the regular polygon surface portion of the regular polygon piece.

The connecting projections of the regular polygon pieces are fitted into connecting openings of other regular polygon pieces for connecting the pieces, and have a shape protruding from the sides of the regular polygon pieces.
As long as the shape of the connecting projection is a shape that can be inserted into and removed from the connecting opening, it may be a quadrangle or a semicircular shape, but it can be inserted into the connecting opening in accordance with repeated creation and disassembly of a regular polyhedron model. Therefore, a tongue-like shape with a rounded tip is preferable. In addition, in order to stabilize the shape when the regular polyhedron model is assembled, the tip of the connection protrusion may be wider than the base part, and in particular, the attachment and detachment from the connection opening is easy and the regular polyhedron model. As a shape that is not easily detached when assembling, a mushroom shape having a rounded tip portion or a head shape of a round countersunk screw is preferable.

The connection opening of the regular polygonal piece includes an opening for inserting the connection protrusion and an opening protection part projecting around the opening to protect the opening.
The shape of the opening of the connection opening is an elongated rectangle into which the protrusion can be inserted, and the length of the short side only needs to be longer than the thickness of the regular polygon piece, and the length of the long side is the length of the connection protrusion. When the tip of the connecting projection is longer than the width of the base portion, the length is preferably shorter than the longest width and can be inserted by slanting the connecting projection.
In addition, an opening protection part that protrudes around the opening is provided around the opening of the connection opening to protect the opening. The opening protection portion may have a so-called “margin” shape that protrudes over the entire side of the regular polygon, and may protrude only around the opening.

In addition, a bending groove is provided along the side at the boundary between the connecting projection and the connecting opening and the side of the regular polygonal surface portion so that the connecting projection and the connecting opening can be easily bent. It is preferable that
The groove for folding may be provided only on one side, but it is more preferable that it is provided on both the front and back sides. Easy to understand.
The shape of the groove for bending and the formation method are arbitrary, but in general, the groove is 0.5 to 1 mm wide by compression or the like, and when a thick material is used as the material of the regular polygon piece, a wedge-shaped groove is used. A groove having a shape may be used.

The material of the regular polygon piece is not particularly limited, but it can be manufactured from cardboard, a plastic sheet or the like from the viewpoint of practicality such as ease of assembly and finish after assembly.
In addition, it is desirable that the 3D figure learning material of the present invention is created by each student and each person can experience the 3D figure model. Therefore, the 3D figure learning material of the present invention is as inexpensive as possible. It is desirable that the regular polygonal piece be made of an inexpensive cardboard material.

The thickness of the regular polygonal piece is not particularly limited, but is strong enough not to leave a crease fixed when the connecting protrusion is fitted into the connecting opening, and easily deformed when the regular polyhedron is assembled. It is sufficient that the thickness has a hardness that does not occur, and is usually 0.2 to 3 mm.
The size of the regular polygon piece is preferably such that the student can assemble on the desk, disassemble the assembled regular polyhedron and spread it on the desk as a development view, and one side of the regular polygon is about 4 cm to 10 cm. It is desirable to be.

  The color of the regular polygon piece of the teaching material for solid figure learning of the present invention is arbitrary, but it is desirable to be transparent in order to understand the mutual relationship of the sides constituting the polyhedron when the polyhedron is assembled. Furthermore, it is more preferable to color each side of a regular polygon piece made of a transparent sheet into an opaque line. In addition, when learning the relationship between the polyhedron and the development, it is preferable to color the regular polygon piece in various colors so that the positional relationship between the contacting surfaces can be understood.

From the viewpoint of ease of assembly and cost, the regular polygon piece of the teaching material for three-dimensional figure learning of the present invention is of a combination type of the connecting position of the connecting projection and the connecting opening of the regular polygon piece of the same regular polygon. It is desirable to have as little as possible.
In the case of single-sided use with coloring on one side and the regular polygon piece with the front and back sides, for a regular polygon with an even number of sides, the number of connecting projections and connecting openings in one polygon piece Since the same number can be used, one type of piece is sufficient, but in a regular polygon having an odd number of sides, the number of connecting projections and connecting openings in one polygon piece cannot be the same. Therefore, at least two kinds of pieces are required.
Further, when the regular polygon piece can be used on both sides, by arranging one connection projection and one connection opening on one side of the regular polygon, one type of the polygon can be used regardless of whether the number of sides is odd or even. A regular polyhedron can be assembled with regular polygonal pieces.

  The teaching material for learning 3D graphics according to the present invention can be used in the classroom, but the teaching material for learning 3D graphics created by the inventor creates a 3D model of a regular polyhedron with each student's own hands. It is preferable to learn mathematical relations and properties in a specific experience.

In FIG. 1, the example of the regular polygon piece of the teaching material for solid figure learning which concerns on one Embodiment of this invention is shown.
The teaching material for solid figure learning shown in FIG. 1 is composed of 50 regular polygonal pieces, and the shape of the surface part is two pieces of regular triangle pieces (A1) and (A2), 16 pieces each, a total of 32 pieces. There are 2 square pieces (B1) and (B2), 3 each, 6 pieces in total, and regular pentagonal pieces are 2 types (C1) and (C2), 6 pieces each, 12 pieces in total. With the 50 regular polygon pieces, all of the 5 types of regular polyhedrons can be assembled.

The size of each regular polygon piece is the same for all sides, is 6 cm, and is formed of cardboard with a thickness of 0.5 mm. The thick paper of 0.5 mm thickness, which is the material of the regular polygon piece, has flexibility and strength that can withstand deformation during assembly.
The surface part of the regular polygon piece is colored, and the shape of the surface part is blue for a regular triangle piece, white for a square piece, and yellow for a regular pentagonal piece.

Each of the six types of polygonal pieces (A1) to (C2) shown in FIG. 1 has a regular polygonal surface portion 1, a connecting protrusion 2 protruding from the side of the surface portion 1, and a connecting opening 3. ing. The shape of the connection protrusion 2 is a protrusion with a sharp tip provided at the center of the side, and the connection opening 3 is an opening protection portion having a marginal shape with the opening 3a provided at the center of the formed side. It consists of 3b.
Further, the connecting protrusion 2 and the opening protection part 3b are provided with a groove 4 for folding on both the front and back surfaces.

(A1) and (A2) in FIG. 1 are regular polygonal pieces having a regular triangular surface portion 1A. The regular polygon piece of (A1) has two connection projections 2 and one connection opening 3. The regular polygon piece of (A2) has one connection projection 2 and two connection projections 2. It has a connecting opening 3.
(B1) and (B2) of FIG. 1 are regular polygonal pieces having a square surface portion 1B. Both (B1) and (B2) have two connection protrusions 2 and two connection openings 3, but the attachment positions of the connection protrusions 2 and the connection openings 3 are different.
The regular polygonal piece having the square surface portion 1B is one kind of regular polygonal piece having two connection projections 2 and two connection openings 3, and a regular hexahedron can be assembled. When assembling a quasi-regular polyhedron such as a 62-hedron using a large number of learning materials for 1-dimensional figure learning, if there are two types of regular polygon pieces with different positions of the connecting projection 2 and the connecting opening 3, Becomes easier.

  (C1) and (C2) in FIG. 1 are regular polygonal pieces having a regular pentagonal surface portion 1C. The regular polygon piece of (C1) has three connection projections 2 and two connection openings 3, and the regular polygon piece of (C2) has two connection projections 2 and three It has a connecting opening 3.

FIG. 2 shows five types of regular polyhedrons assembled using the regular polygonal pieces shown in FIG. In FIG. 2, (A) is a regular tetrahedron, (B) is a regular hexahedron, (C) is a regular octahedron, (D) is a regular dodecahedron, and (E) is a regular icosahedron.
The teaching material for learning three-dimensional figures according to the present invention can assemble regular polyhedrons easily for elementary school children by connecting necessary regular polygon pieces one by one.

FIG. 3 shows a state in which the assembled regular icosahedron is disassembled and expanded in a developed view. The wavy line in the figure shows the connecting projection and the connecting opening on the back side of the regular polygon piece.
The teaching material for 3D figure learning according to the present invention is a connecting method that is easy to attach and detach, so the assembled polyhedron can be easily disassembled into a flat state, and students can understand the relationship between the 3D figure and the development view. Useful for.

FIG. 4 shows a regular polygon piece used in Example 2 of the teaching material for solid figure learning according to the present invention.
The types of regular polygonal pieces shown in FIG. 4 are (A) equilateral triangle pieces, (B) square pieces, and (C) regular pentagonal pieces, each of which is a total of three kinds.
The number of regular polygonal pieces is 50 in total: 32 regular triangle pieces, 6 square pieces, and 12 regular pentagonal pieces.

The size of each regular polygon piece is equal to 6 cm in length on both sides,
It is made of a lightly colored transparent plastic sheet. The plastic sheet, which is a material of the regular polygonal piece, is semi-rigid and has flexibility and strength that can withstand bending and twisting during assembly.
In addition, the regular polygon piece has a lightly colored transparent surface portion, and an opaque black line is drawn on both sides of the regular polygon surface portion along the side.

Each side of the surface portion 1 of each regular polygon piece has one connecting projection 2 and one connecting opening 3. The shape of the connecting protrusion 2 is a tongue-like protrusion having a rounded tip, and the connecting opening 3 is composed of an opening protecting part 3b having a marginal shape. The connecting projections 2 and the openings 3a are formed at positions where they fit into the openings 3a and the connecting projections 2 of the other regular polygon pieces, respectively, and are alternately arranged on each side of the polygonal surface portion. Yes.
Further, the connecting protrusion 2 and the opening protection part 3b are provided with a groove 4 for folding on both sides, and can be used without distinction between the front and back sides.

  The teaching material for solid figure learning of the present invention allows students to easily assemble regular polyhedron models with their own hands by combining a few types of regular polygon pieces, and by experiencing the regular polyhedrons, regular polyhedrons You can deepen your spatial and mathematical understanding.

DESCRIPTION OF SYMBOLS 1 surface part 1A equilateral triangle surface part 1B square surface part 1C regular pentagonal surface part 2 connection protrusion part 3 connection opening part 3a opening part 3b opening protection part 4 groove | channel for bending

Claims (7)

A teaching material for learning a solid figure composed of a plurality of regular polygon pieces each having three or more different regular polygons each having the same length of one side on the surface,
The regular polygonal piece has a regular polygonal shape surface portion, and a connecting projection and / or a connecting opening for detachably connecting the regular polygonal pieces,
The connecting protrusion is located on the side of the regular polygonal surface, and has a shape protruding from the side.
The connection opening includes an opening located on a side of the regular polygonal surface portion, and an opening protection portion that surrounds the periphery of the opening and protrudes from the side.
The plurality of regular polygonal pieces can be connected by detachably fitting the connection protrusion and the connection opening to each other to form a three-dimensional figure model belonging to a regular polyhedron and a regular polyhedron group. Teaching materials for learning 3D figures.   The regular polygon piece comprises a regular polygon piece having a regular triangular surface portion, a regular polygon piece having a square surface portion, and a regular polygon piece having a regular pentagonal surface portion. Item 3. A teaching material for learning solid figures according to Item 1. The regular polygon piece has one of the connection protrusion and the connection opening on the side of the surface portion of the regular polygon;
The three-dimensional figure according to claim 1, wherein the regular polygonal piece having the same shape surface portion is composed of two types of regular polygonal pieces having different numbers or attachment positions of the connecting protrusions and the connecting openings. Learning material.   The teaching material for learning solid figures according to claim 3, wherein the material of the regular polygon piece is a paper material. The regular polygon piece has both the connection protrusion and the connection opening on the side of the surface portion of the regular polygon.
2. The three-dimensional object according to claim 1, wherein the regular polygon piece having the same shape surface portion is formed of one type of regular polygon piece having the same number and the attachment position of the connection protrusion and the connection opening. Teaching material for figure learning.   2. The three-dimensional figure learning material according to claim 1, wherein the material of the regular polygon piece is a transparent plastic sheet.   7. The teaching material for learning solid figures according to claim 6, wherein an opaque line is drawn along a side of the regular polygon of the transparent regular polygon piece.

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