Teaching tool for calculation

Abstract

To provide a teaching tool that enables learning of more complex calculations using numerical cubic blocks.SOLUTION: A teaching tool 1 includes a composite cube 2 composed of a×b cubic blocks 20, the composite cube 2 being configured such that boundary surfaces 20X, 20Y, and 20Z between the plurality of cubic blocks 20 form a lattice pattern, and the cubic blocks 20 are arranged on an xy-plane with a blocks aligned in an x-direction and b blocks aligned in a y-direction. The teaching tool 1 further includes rubber bands 3 stretched in parallel with the lattice-shaped boundary surfaces 20X, 20Y, and 20Z of the composite cube 2, the rubber bands 3 dividing the plurality of cubic blocks 20 arranged in the x-direction or the y-direction into a plurality of regions.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a teaching tool for cultivating mathematical thinking ability. [Background technology]

[0002] The Montessori Trinomial Cube is known as one of the teaching tools for cultivating children's mathematical thinking skills. The Trinomial Cube is said to enable children to intuitively learn formulas by touching the 27 cubes, whose longest sides are colored red, blue, and yellow (see, for example, Non-Patent Document 1). Furthermore, puzzles using cubic blocks are known, for example, as described in Patent Documents 1 and 2. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 56-27273 [Patent Document 2] Patent Publication No. 2021-23629 [Non-patent literature]

[0004] [Non-Patent Document 1] “[Montessori Teaching Materials] Introducing how to present the Ternary Cube. Try it at home!”, [online], Dot Peeps Co., Ltd., [Retrieved March 5, 2024], Internet<URL:https: / / montemia.jp / pages / trinomial-cube> Summary of the Invention [Problem to be solved by the invention]

[0005] An object of the present invention is to provide a teaching tool that allows children to learn more complex calculations using a plurality of cubic blocks. [Means for solving the problem]

[0006] The teaching tool of the present invention is a composite cube made up of a number of a × b cubic blocks, which can be arranged on an xy plane with a number of composite cubes arranged in the x direction and b number of composite cubes arranged in the y direction so that the boundary surfaces between the multiple cubic blocks form a lattice pattern, and includes rubber bands that are hung parallel to the lattice-like boundary surfaces of the composite cube and divide the multiple cubic blocks arranged in the x direction or y direction into multiple regions.

[0007] With the teaching aid of the present invention, various calculations can be performed by counting the number of regions of each cubic block divided by rubber bands for multiple cubic blocks arranged diagonally on the xy plane. Furthermore, by using a textbook that explains this calculation method, it is possible to easily learn the calculation method using the teaching aid of the present invention.

[0008] The teaching tool of the present invention can also include a composite cube made up of a number of a × b × c cubic blocks, arranged a number of times in the x direction and b number of times in the y direction on an xy plane so that the boundary surfaces between the multiple cubic blocks form a lattice pattern, and further stacked c times in the z direction, and rubber bands that are hung parallel to the lattice-like boundary surfaces of the composite cube and divide the multiple cubic blocks lined up in the x direction, y direction, or z direction into multiple regions. [Effects of the Invention]

[0009] According to the teaching tool of the present invention, it is possible to learn more complex calculations by counting the number of areas in each cubic block divided by rubber bands. [Brief explanation of the drawings]

[0010] [Figure 1] 1 is a perspective view of a teaching tool according to an embodiment of the present invention. [Figure 2] FIG. 1 is an explanatory diagram showing an example of calculation of two-digit multiplication (12×14). [Figure 3] FIG. 1 is an explanatory diagram showing an example of calculation of two-digit multiplication (22×23). [Figure 4]FIG. 1 is an explanatory diagram showing an example of multiplication of three two-digit numbers (12×12×12). [Figure 5] FIG. 5 is an explanatory diagram showing the teaching tool in FIG. 4 separated in the z direction. DETAILED DESCRIPTION OF THE INVENTION

[0011] Figure 1 is a perspective view of a teaching tool according to an embodiment of the present invention. In Figure 1, the teaching tool 1 according to the embodiment of the present invention is composed of a composite cube 2 made up of a plurality of cubic blocks 20, and a plurality of rubber bands 3 that are hung on the composite cube 2. The rubber bands 3 are stretchable rubber rings.

[0012] The composite cube 2 is made up of a × b × c (a, b, c are positive integers) number of cubic blocks 20. In this embodiment, the composite cube 2 is made up of a plurality of cubic blocks 20 that combine cubes or rectangular parallelepipeds of different sizes so that the boundary surfaces 20X, 20Y, and 20Z between the cubic blocks 20 form a lattice pattern. A number of composite cubes 2 are arranged in the x-direction and b number of composite cubes 2 in the y-direction on the xy plane, and these are further stacked in c layers in the z-direction. Note that, as will be described later, the composite cube 2 may also be made up of a single cube or rectangular parallelepiped.

[0013] The rubber bands 3 are attached parallel to the lattice-like boundary surfaces 20X, 20Y, and 20Z of the composite cube 2. These rubber bands 3 divide the multiple cubic blocks 20 aligned in the x, y, or z direction into multiple regions. In the example shown in FIG. 1 , two rubber bands 3 are attached parallel to the boundary surface 20Y to the multiple cubic blocks 20 aligned in the y and z directions and positioned at the base end in the x direction, thereby dividing the multiple cubic blocks 20 into three regions. Furthermore, one rubber band 3 is attached parallel to the boundary surface 20X to the multiple cubic blocks 20 aligned in the x and z directions and positioned at the base end in the y direction, thereby dividing the multiple cubic blocks 20 into two regions.

[0014] A calculation method using the teaching tool 1 having the above configuration will be explained below using a specific example. Figure 2 is an explanatory diagram showing an example of a calculation of two-digit multiplication (12 x 14). In two-digit multiplication, 2 x 2 (four in total) cubic blocks 21, 22, 23, and 24 are used. When calculating two-digit multiplication (12 x 14), the multiplicand "12" and the multiplier "14" are divided into digits and assigned to cubic blocks 21 to 24 arranged in the x and y directions.

[0015] Specifically, since the units digit of the multiplicand "12" is "2", one rubber band 3 is applied parallel to the boundary surface 20Y to the cubic blocks 22 and 24 that are arranged in the y direction and are located at the tip of the x direction, thereby dividing the cubic blocks 22 and 24 into two regions in the x direction. Since the tens digit is "1", no rubber band 3 is applied and the cubic blocks are left as they are. On the other hand, since the units digit of the multiplier "14" is "4", three rubber bands 3 are applied parallel to the boundary surface 20X to divide the cubic blocks 23 and 24 that are arranged in the x direction and are located at the tip of the y direction into four regions in the y direction. Since the tens digit is "1", no rubber band 3 is applied and the cubic blocks are left as they are.

[0016] As a result, the cubic block 22 is divided into two regions 22A and 22B. The cubic block 23 is divided into four regions 23A, 23B, 23C, and 23D. The cubic block 24 is divided into eight regions 24A, 24B, 24C, 24D, 24E, 24F, 24G, and 24H. The cubic block 21 remains as one region 21A.

[0017] Next, for the multiple cubic blocks 21 to 24 arranged diagonally on the xy plane, the number of regions of each cubic block 21 to 24 divided by the rubber bands 3 is counted. Since there is one cubic block 24 arranged along diagonal line 25A, starting from the lowest digit, the number of regions is "8": regions 24A, 24B, 24C, 24D, 24E, 24F, 24G, and 24H. Since there are two cubic blocks 22 and 23 arranged along diagonal line 25B, the number of regions is "6": regions 22A, 22B, 23A, 23B, 23C, and 23D. Since there is one cubic block 21 arranged along diagonal line 25C, the number of regions is "1." These region numbers represent the numbers of each digit of the multiplication answer, from the lowest digit, as "8," "6," and "1." Therefore, the answer to the multiplication "12 x 14" is "168."

[0018] FIG. 3 is an explanatory diagram showing an example of a two-digit multiplication (22 × 23). As described above, 2 × 2 cubic blocks 21, 22, 23, and 24 are used for two-digit multiplication. In this case, since the units digit of the multiplicand "22" is "2," one rubber band 3 is placed parallel to the boundary surface 20Y on cubic blocks 22 and 24, and since the tens digit is "2," one rubber band 3 is placed parallel to the boundary surface 20Y on cubic blocks 21 and 23. Furthermore, since the units digit of the multiplier "23" is "3," two rubber bands 3 are placed parallel to the boundary surface 20X on cubic blocks 23 and 24, and since the tens digit is "2," one rubber band 3 is placed parallel to the boundary surface 20X on cubic blocks 21 and 22. As a result, the cubic blocks 21 and 22 are each divided into four regions, and the cubic blocks 23 and 24 are each divided into six regions.

[0019] Next, for the multiple cubic blocks 21 to 24 arranged diagonally on the xy plane, the number of regions of each cubic block 21 to 24 divided by the rubber bands 3 is counted. Starting from the lowest digit, there is one cubic block 24 arranged along diagonal line 25A, so the number of regions is "6". Therefore, the first digit of the answer to the multiplication (22 x 23) is "6". Also, there are two cubic blocks 22 and 23 arranged along diagonal line 25B, so the number of regions is "4" + "6", or "10". Therefore, the second digit of the answer to the multiplication is "0", and the "1" is carried over. And there is one cubic block 21 arranged along diagonal line 25C, so the number of regions is "4". Adding the carried over "1" to this, the third digit of the answer to the multiplication is "4" + "1", or "5". Therefore, the answer to the multiplication “22 x 23” is “506”.

[0020] In this way, with the teaching tool 1 of this embodiment, two-digit multiplication can be learned by counting the number of regions of the cubic blocks 20 arranged diagonally on the xy plane, which are divided by the rubber bands 3. Similarly, an increase or decrease in the number of digits of the multiplicand and multiplier can be accommodated by adjusting the numbers (a, b) for arranging the cubic blocks 20 to match the number of digits.

[0021] In this way, with the teaching tool 1 of this embodiment, it is possible to count the number of regions of each cubic block divided by rubber bands for multiple cubic blocks arranged diagonally on the xy plane and perform various calculations. Also, by using a textbook that explains the calculation method as shown in Figures 2 and 3, it is possible to easily learn the calculation method using this teaching tool 1.

[0022] Furthermore, multiplication of three numbers can be learned by stacking them in c layers in the z direction as shown in Figure 1. Figure 4 is an explanatory diagram showing an example of the calculation of multiplication of three two-digit numbers (12 x 12 x 12), and Figure 5 is a diagram in which the teaching aid in Figure 4 has been separated in the z direction for explanatory purposes.

[0023] As shown in Figures 4 and 5, multiplication of three two-digit numbers uses (a=2) x (b=2) x (c=2) (a total of eight) cubic blocks 31 to 38. As mentioned above, the multiplicand "12" and the two multipliers "12" are divided into digits, assigned to the cubic blocks 31 to 38 arranged in the x, y, and z directions, and then wrapped with rubber band 3.

[0024] This rubber band 3 divides the cubic block 31 placed at the base end in the x, y, and z directions into eight regions. In other words, the ones digit of the multiplication answer is "8." Next, the three blocks 32, 33, and 34 that are in contact with this cubic block 31 on their faces are each divided into four regions, totaling 12. In other words, the tens digit of the multiplication answer is "2," with "1" carried over.

[0025] Similarly, the three blocks 35, 36, and 37 that are in contact with these three blocks 32, 33, and 34 on their faces are each divided into two regions, for a total of 6. In other words, the hundreds digit of the multiplication answer is "7," which is "6" plus the carryover "1." Finally, block 38 that is in contact with these three blocks 35, 36, and 37 on its faces is not divided by rubber band 3, so its region number is "1," and the thousands digit of the multiplication answer is also "1." Therefore, the answer to the multiplication "12 x 12 x 12" is "1728." [Industrial Applicability]

[0026] The teaching tool of the present invention is useful as a teaching tool for cultivating mathematical thinking ability. [Explanation of symbols]

[0027] 1 Teaching materials 2 Composite cube 20, 21, 22, 23, 24 cube blocks 3 rubber bands

Claims

1. a composite cube consisting of a number a × b of cubic blocks, which can be arranged on an xy plane with a number a of the composite cubes arranged in the x direction and b number b of the composite cubes arranged in the y direction so that the boundary surfaces between the plurality of cubic blocks form a lattice pattern; a rubber band that is hung parallel to the lattice-like boundary surface of the composite cube, and that divides the plurality of cubic blocks aligned in the x direction or the y direction into a plurality of regions; Teaching aids including.

2. 2. The teaching tool according to claim 1, further comprising a text showing a method for counting and calculating the number of regions of each of the plurality of cubic blocks arranged diagonally on the xy plane, the regions being divided by the rubber bands.

3. A composite cube is made up of a number of a x b x c cubic blocks, and the boundary surfaces between the plurality of cubic blocks are arranged in a grid pattern on an xy plane with a number of cubic blocks arranged in the x direction and b number of cubic blocks arranged in the y direction, and further stacked in c layers in the z direction. a rubber band that is hung parallel to the lattice-like boundary surface of the composite cube, and that divides the plurality of cubic blocks aligned in the x direction, the y direction, or the z direction into a plurality of regions; Teaching aids including.

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