JPH0719761U - 3D learning materials - Google Patents

Abstract

(57) [Abstract] [Purpose] To improve the learning effect on solid figures by making it easier to understand the relationship between solid figures and plane figures such as developed views. [Structure] A cubic block is cut along at least one plane and is configured so that it can be separated or joined at its cut surface, and is substantially transparent in the shape of an expanded view in which the six sides of this cubic block are expanded into a plane. Different expansion sheets are combined, and the expansion sheet is folded into a cube so as to wrap the cube block, or it is expanded into a development view. As the expansion sheet, a line corresponding to the cut edge of the cube block may be drawn in advance, or the line may be written or erased afterward according to the cut edge of the cube block.

Description

[Detailed description of the device]

[0001]

[Industrial applications]

 The present invention relates to a teaching material for three-dimensional figure learning, and is particularly used for learning the shape of a cut edge when a cube is cut in a plane.

[0002]

[Prior art]

 Conventionally, in the curriculum of elementary schools and junior high schools, learning of various solid figures such as rectangular parallelepipeds, cubes and other polyhedrons, cylinders and cones is required. In learning solid figures, one of the most important tasks is to accurately understand the shape of the cut surface, that is, the shape of the cut surface that is formed when a solid is cut along a plane. It is taken up in the problems of entrance examinations.

However, in textbooks and the like, in general, three-dimensional solid figures are expressed by replacing them with two-dimensional plane figures, for example, sketches, so that the students cannot see the three-dimensional figures, especially from the outside. It is not easy to grasp the surface shape spatially. For this reason, in educational settings, for example, a cube was formed from clay and cut at various positions to show the cut surface to students. Moreover, in order to better understand solids and in calculating their surface area and volume, it is necessary to consider solids in relation to their sketches, developments, projections, and the like.

[0004]

[Problems to be solved by the device]

 However, the above-mentioned auxiliary method is very inconvenient for each student to learn solid figures. Moreover, since it is only possible to think of a solid as a lump, it is necessary to understand the relationship between the three-dimensional solid and the two-dimensional development view, the projected view, and the relationship between each face of the solid. There was a problem that it was difficult.

Therefore, the teaching material for three-dimensional figure learning according to claim 1 has been made in view of the problems of the above-described conventional techniques, and its purpose is to develop a three-dimensional solid and a two-dimensional developed view. , A material with a high learning effect that allows you to easily understand solid figures through the relationship with the projection drawing and the relationship between each surface of the solid, and the relationship between the solid and the plane. Is to provide.

In addition to the above, the teaching material for three-dimensional figure learning according to claim 2 intends to provide a teaching material that is easier to handle and further enhances the learning effect.

[0007]

[Means for Solving the Problems]

 The present invention is intended to achieve the above object, and the contents thereof will be described below with reference to the embodiments shown in the drawings.

The teaching material for three-dimensional figure learning according to claim 1 is a cube block that is cut along at least one plane and can be separated or combined with each other at the cut surface, and six sides of this cube block are formed into a plane. It is characterized in that it is composed of a substantially transparent expansion sheet having an expanded shape, and the expansion sheet is bendable so as to form a cube that closely encloses the cube block.

The teaching material for three-dimensional figure learning according to a second aspect further comprises, in addition to the characteristic points according to the above-mentioned first aspect, a transparent case capable of accommodating a cubic block and a development sheet folded so as to wrap the cubic block. It is characterized by

[0010]

[Action]

 Therefore, according to the teaching material for three-dimensional figure learning according to claim 1, the cube blocks are divided or rejoined, and the substantially transparent expansion sheet is bent to cover the cube blocks or spread them on a flat surface, thereby Can be used in combination. With this, not only can the shape of the cut surface of the cube be grasped, but if a development sheet with a cutting line drawn in advance is used, the development sheet is placed on the cube block and the cutting line conforms to the cutting line of the cube block. As you can see, you can see through and cover them, and you can confirm their correspondence. When using a development sheet that does not have cutting lines drawn, the cutting line can be copied and written on the surface of the development sheet with the development sheet covered with the cube block, and the cube can be expanded by spreading it. You can see how the cutting line in the figure appears in the development view. That is, it is possible to easily understand the relationship between the cube which is three-dimensional and the development drawing which is two-dimensional.

According to the teaching material for three-dimensional figure learning according to the second aspect, the cubic block can be held in a stable state in a transparent case by covering it with the cubic block or the expansion sheet folded into the cubic block. By accommodating only one of the separated parts or the expansion sheet folded into a cube in a transparent case, the relationship between the entire cube and the cut part, and the expansion drawing when assembled into a cube The state of the cutting line can be seen through the wall of the transparent case to the back side.

[0012]

【Example】

 FIG. 1 schematically shows a preferred embodiment of the teaching material for three-dimensional figure learning according to the present invention. The teaching material 1 is basically composed of a cubic block 2 and a substantially transparent expansion sheet 3 in which six surfaces of the cube are expanded in a plane.

The cube block 2 is made of a synthetic rubber material, and is cut by a plane including a vertex A, a midpoint I of a side BF, a vertex G, and a midpoint J of a side DH, as shown in FIG. It is composed of two upper and lower sub-blocks 4, 5. In each of the sub-blocks, diamond-shaped cut surfaces 6 and 7 connecting the points A, I, G and J are formed. Disc-shaped permanent magnets 8 and 9 are embedded in the respective cut sections 6 and 7 at corresponding positions near the center thereof. It is convenient to orient the magnetic poles of these magnets 8 and 9 so that they are always cubic when both sub-blocks 4 and 5 are attracted to each other and coupled. Therefore, the sub-blocks 4 and 5 are normally connected to each other integrally by the attraction force of the magnets 8 and 9 to form a cube, but they can be divided or re-connected to the original cube if necessary. With this configuration, according to the present invention, it is possible to easily understand the cut edge when the cube is cut along the plane.

At this time, if the cut surfaces 6 and 7 are colored in the same color or different colors using an appropriate color, it is convenient because the shape of the cut surfaces can be grasped more clearly. Further, the entire peripheral edge of each of the cut surfaces 6 and 7 is edged with a thin line having the same color as that of the cut surface. These edging lines 10 and 11 are convenient because the cutting line of the cubic block 2 can be clearly seen as shown in FIG. 1 even when both sub-blocks are connected. Further, the type, shape, size, number, arrangement and the like of the permanent magnets 8 and 9 can be appropriately selected according to the conditions such as the size and shape of the cut surface and the material of the cubic block. For example, a thin sheet or plate made of magnetic rubber may be attached to the cut surface. In another embodiment, the magnets may be provided on only one of the cut surfaces 6 and 7, and a thin metal plate such as an iron plate may be attached to the other surface for adsorption.

The expansion sheet 3 is a transparent thin sheet material in which six squares of approximately the same size corresponding to the six sides of the cubic block 2 are continuous in the shape of the expansion diagram, and for example, polyethylene or poly A flexible plastic material such as vinyl acetate is formed so as to be repeatedly bendable at the adjacent boundary lines 12 of the respective square shapes. In the shape of such an expanded view, there are a total of 11 different expanded patterns as shown in FIG. 3, including the cross shape of the pattern (I) illustrated in FIG.

When the unfolding sheet 3 is bent at a right angle at each of the boundary lines to form a box shape, a cube having substantially the same size as the cube block 2 is formed. Therefore, when the cube block 2 is placed on one of the squares of the expansion sheet 3 and the expansion sheet is bent in accordance with each surface of the expansion sheet 3, the cube block 2 can be tightly wrapped therein. On the unfolding sheet 3, a line 13 corresponding to the cutting line when the cube block 2 is covered in this way is drawn. The line 13 is preferably colored in the same color as the cut surface corresponding to the cubic block 2. Since the unfolding sheet 3 is formed of the transparent material as described above, the cutting line of the cube block 2 can be confirmed and the line 13 can be fitted and covered. Therefore, according to the present invention, as shown in FIG. 4A, by covering the cubic block 2 that can be separated and joined at the cut surface with the expansion sheet 3 or by spreading the covered expansion sheet 3 in a plane. , It is easy to understand how the cutting line of the cube appears in the development view. Further, the relationship between the cube and the projected view, the relationship between each projected surface and the projected surface, etc. can be learned from the individual squares of the developed sheet 3 and the portions of the lines 13 that appear therein.

Furthermore, by covering a cubic block with a development sheet having another different pattern and copying the cutting line on the surface of the development sheet with a pencil or a pen, the same cutting line changes depending on the pattern of the development view. You can learn what to do. For example, in the pattern (I) of FIG. 3, the same cutting line that appears as shown in FIG. 4 (A), but in the spread sheet 14 of the pattern (IX) of FIG. 3 the line 15 as shown in FIG. 4 (B). You can see that it is expressed by. This makes it possible to grasp the differences in the patterns of the developed views and the mutual positional relationship of the faces of the cube at a higher level. As well understood from the above description, the material of the expansion sheet 3 is substantially transparent so that the cutting line can be sufficiently recognized from the outside when the expansion sheet 3 is covered with the cubic block. It doesn't matter if it is good or semi-transparent.

According to the present invention, the three-dimensional figure learning material 1 further includes a cubic transparent case 16 for accommodating the cubic block 2 covered with the expansion sheet 3, as shown in FIG. The case 16 is made of a relatively hard transparent plastic material such as acrylic resin so that its inner dimension is substantially equal to that of the cubic block 2. In this embodiment, as shown in FIG. 6, two transparent U-shaped members 17 and 18 in which three transparent square thin plates are connected at right angles to each other are provided, and the tapered peripheral portions 19 and 20 are connected to each other. A commercially available acrylic resin case is used which is assembled so that the squares on the left and right sides of the U-shape are engaged and fitted inside. The transparent case 16 allows the expansion sheet 3 to be held in a state of being covered with the cube block 2, whereby the relationship between the cut surface or the cut line of the cube and the development view can be clearly confirmed.

The transparent case 16 can be used as shown in FIGS. 7 and 8 as well as accommodating the cubic block 2 covered with the expansion sheet 3 in a stable state as shown in FIG. In the embodiment of FIG. 7, only the lower sub-block 5 is housed in the case 16. As a result, the relationship between the entire cube and the cutting plane 7 and the cutting line 12 can be easily grasped visually from various angles. In the embodiment shown in FIG. 8, only the expansion sheet 3 folded into a cube is accommodated in the case 16. As a result, the development sheet 3 is held in the shape of a cube, and the state of the cutting line when the development view is assembled into the cube can be seen through the line 13 to the back side of the cube. The relationship with the figure becomes easier to understand.

Although the expansion sheet 3 made of soft plastic and the case 16 made of a relatively hard material are separately provided in the above embodiment, they can be integrally formed in another embodiment. For example, the entire expansion sheet is made of a thin acrylic plate, and the borders of adjacent squares are made thin so that they can be folded, or a flexible synthetic resin film is attached to a square acrylic thin plate to connect them, and Can be In this case, it is more convenient to provide, for example, concavo-convex portions that engage with each other on each side of the squares that are joined to each other when they are combined in a box shape, and to snap them together. Such a case / deployable sheet can be assembled into a cube using various other engaging means.

FIG. 9 shows another embodiment of the teaching material according to the present invention in which a cubic block is cut along a cutting surface different from that in FIG. In this embodiment, the cubic block 21 is divided into two sub-blocks cut along a plane including the midpoints K, I, L, M, J and N of the sides AB, BF, FG, GH, HD and DA. 22 and 23, and hexagonal cutting planes 24 and 25 are formed by the respective midpoints. Similar to the embodiment of FIG. 1, a permanent magnet (not shown) is embedded in each of the cut surfaces and can be integrally connected or separated by its attractive force. The cut surfaces 24 and 25 are colored in a different color from that of the embodiment of FIG. 1, and the entire peripheral edges thereof are bordered by thin lines 26 and 27 of the same color, respectively. The teaching material of this embodiment has a transparent or translucent development sheet 28 made of a soft plastic sheet material having the same pattern as that of the embodiment shown in FIG. On the spreading sheet 28, a line 29 corresponding to the cutting line of the cube block 21 is drawn in the same color as the cutting faces 24 and 25.

Further, according to the present invention, the cubic block is cut along various planes so that cutting surfaces of various shapes such as triangle, quadrangle, pentagon, etc. other than the above-mentioned rhombus, hexagon and the like can be obtained. It is easy to understand that the learning effect of solid figures can be enhanced by combining development sheets with corresponding cutting lines. Furthermore, a set of teaching materials is constructed by combining a large number of cubic blocks thus cut on different planes and a large number of expansion sheets with pre-drawn cutting lines corresponding to the respective blocks. be able to. In addition to the above-mentioned development sheet, this teaching material can be combined with 11 auxiliary development sheets which are made up of 11 different patterns shown in FIG. In this way, the student can cover the cubical block with the appropriately selected auxiliary deployment sheet and freely copy or erase the cutting line with a pencil, water-based pen, etc., which promotes students' motivation for learning. The learning effect is further enhanced. Further, for example, it is possible to use the pattern (I) of the expansion sheet 3 of FIG. 1 as a basic pattern to correspond to each cube block, and to configure the auxiliary expansion sheet with 10 types of patterns other than that.

In the embodiments of FIGS. 1 and 9 described above, the cubic blocks 2 and 21 are each cut in one plane, but in another embodiment, the cubic block can be cut in a plurality of planes. As a result, one cubic block can obtain a plurality of cut surfaces having different shapes. Each cut surface can be easily identified by coloring it with a different color. In this case, a plurality of cutting lines may be drawn on one unfolding sheet in different colors corresponding to each other, or a plurality of unfolding sheets corresponding to the number of cutting planes may be prepared and different cutting lines may be drawn. Moreover, these cut surfaces may intersect with each other.

In a further embodiment of the present invention, one cubic block is cut along a plurality of planes, but the sub-blocks are not completely separated and can be bent at one side of the cut surface. It is connected to the. As shown in FIG. 10, the cube block 30 is cut into two sub-blocks 33 and 34 on the trapezoidal cut surfaces 31 and 32, but the cube block 30 is folded by leaving the lower side 35 of the trapezoid thin. It is bendably connected and its shape can be confirmed by opening the cut surface. In another embodiment, both subblocks 33 and 34 can be foldably connected by using a flexible synthetic resin film or an adhesive tape. Further, the cubic block 30 is cut along each of the planes indicated by the cutting lines 36 to 38, and is similarly connected to one side of each cut surface. It is convenient to color each of the cut surfaces with a different color and to trim the perimeter with the same color. Although not shown in the drawing, a line corresponding to each cutting line of the block is drawn in the same color on the expansion sheet used for such a cubic block. The teaching material consisting of one cubic block and one unfolding sheet cut along a large number of planes as described above does not require many cubic blocks and unfolding sheets as in the above-described embodiment, and thus is convenient to carry. Yes, there is an advantage that students can study at any time and place they like.

Although the present invention has been described in detail above with reference to its preferred embodiments, the present invention can be implemented by making various modifications and changes to the above embodiments within the technical scope thereof. You can For example, the cubic block can be formed of various materials such as synthetic resin, natural rubber, wood, paper, etc., in addition to the above-mentioned synthetic rubber. In addition to the magnets, the sub-blocks can be separated and re-bonded to each other by various means such as fasteners such as so-called Velcro (trademark) and adhesives that can be repeatedly bonded. Furthermore, the teaching material of the present invention can be similarly applied to rectangular parallelepipeds other than cubes.

[0026]

[Effect of device]

 Since the present invention is configured as described above, it has the following effects.

According to the teaching material for three-dimensional figure learning according to claim 1, a cubic block that can be divided / joined at a cut surface is used in combination with a foldable substantially transparent expansion sheet, so that a simple cube is obtained. Not only the shape of the cut surface of the cube, but also the relationship between the cutting line appearing in the cube and the cutting line drawn in the development view, the relationship between the three-dimensional cube and the development view expressing it in two dimensions is very high. Since it becomes easier to understand, the learning effect of solid figures can be enhanced.

In addition to the above, according to the teaching material for three-dimensional figure learning of claim 2, the cubic block covered with the expansion sheet that is integrally connected or folded is held in a transparent case in a stable state. In addition, if only one part of the separated cube block or the expansion sheet folded into a cube is accommodated in the transparent case, the cube wall can be seen through and the cut surface inside the cube and the cut line on the back side can be cut off. Since the figure can be visually grasped as it is in 3D, the relationship between the cube and the cutting plane, the relationship between the cutting line and the development view, etc. can be visually clarified, making the handling easier and The learning effect can be further enhanced.

[Brief description of drawings]

FIG. 1 is a perspective view schematically showing an embodiment of a three-dimensional learning material according to the present invention.

2 is an exploded perspective view showing the cube block of FIG. 1. FIG.

FIG. 3 is a plan view showing a set of 11 expansion sheets used in the present invention.

4 is composed of FIGS. A and B, and FIG. 4A is a plan view showing a cutting line in the expansion sheet of FIG. 1, and FIG. 4B is a cutting when another expansion sheet is used for the cubic block of FIG. It is a top view which shows a line.

5 is a schematic perspective view showing a state where the cube block and the expansion sheet of FIG. 1 are housed in a transparent case.

FIG. 6 is an exploded perspective view showing an embodiment of a transparent case.

FIG. 7 is a perspective view showing a state where a lower block forming the cube block of FIG. 1 is housed in a transparent case.

FIG. 8 is a perspective view showing a state where the development sheet of FIG. 1 is housed in a transparent case.

FIG. 9 is an exploded perspective view showing another embodiment of the present invention when the cubic block is cut in a plane different from that in FIG.

FIG. 10 is a perspective view showing a cube block according to still another embodiment of the present invention.

[Explanation of symbols]

 1 Teaching material 2 Cubic block 3 Expansion sheet 4, 5 Sub-block 6, 7 Cutting surface 8, 9 Permanent magnet 10, 11 Edge line 12 Boundary line 13 Line 14 Development sheet 15 Line 16 Transparent case 17, 18 U-shaped member 19, 20 Side part 21 Cubic block 22, 23 Sub-block 24, 25 Cutting surface 26, 27 Edging 28 Development sheet 29 Line 30 Cubic block 31, 32 Cutting surface 33, 34 Sub block 35 Lower side part 36-38 Cutting line

Claims (2)

[Scope of utility model registration request] 1. A cubic block that is cut along at least one plane and is separable and connectable with each other at its cut surface, and has a shape in which six sides of the cubic block are expanded into a plane, and closely encloses the cubic block. A three-dimensional figure learning material comprising a substantially transparent expansion sheet that can be folded to form a cube. 2. A transparent case capable of accommodating the cubic block and the expansion sheet bent so as to wrap the cubic block is further provided.
The three-dimensional figure learning material described.