CN220459905U - Complete square formula deduces building blocks - Google Patents
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- CN220459905U CN220459905U CN202321756044.8U CN202321756044U CN220459905U CN 220459905 U CN220459905 U CN 220459905U CN 202321756044 U CN202321756044 U CN 202321756044U CN 220459905 U CN220459905 U CN 220459905U
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- 238000003475 lamination Methods 0.000 claims description 14
- 239000002023 wood Substances 0.000 claims description 14
- 238000000034 method Methods 0.000 abstract description 11
- 239000003086 colorant Substances 0.000 abstract description 6
- 238000004519 manufacturing process Methods 0.000 abstract description 4
- 239000011449 brick Substances 0.000 description 13
- 238000009795 derivation Methods 0.000 description 10
- 238000010586 diagram Methods 0.000 description 6
- 230000009286 beneficial effect Effects 0.000 description 3
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Abstract
The utility model discloses a complete square formula deducing building block, and relates to the technical field of square formulas. The utility model comprises four layers of 10 building blocks: first layer (base layer): a building block, a square (1) with a side length of a; second layer (auxiliary layer): four building blocks, one square (2) with side length b (b < a), one square (3) with side length (a-b), two rectangles (4) and (5) with length and width b (a-b) respectively, wherein the colors of the building blocks (2), (3), (4) and (5) are the same, but different from those of the building blocks of the first layer (base layer) and the third layer (deduction layer); third layer: the pushing layer, four building blocks, a square (6) with side length of b. The utility model reflects the mathematical principle through the combination of the figures, has simple and clear operation, clear deduction process, low manufacturing cost and easy popularization.
Description
Technical Field
The utility model belongs to the field of square formulas, and particularly relates to a complete square formula deducing building block.
Background
The complete square formula contains two formulas, namely: (1) square of sum of two numbers: (a+b) 2=a2+2ab+b2, (2) square of two number differences: (a-b) 2=a2-2ab+b2, wherein the related complete square formula in teaching is mainly deduced through algebraic operation, a few teachers carry out graphic deduction on the complete square formula (square of sum of two numbers), the complete square formula (square of difference of two numbers) is obtained through algebraic operation by changing operation symbols, and the deduction process of the obtained formula deviates from the mathematical number-shape combination principle, lacks support of perceptual activity and is unfavorable for students to deeply understand the mathematical operation principle.
For this purpose, a complete square formula deriving building block is proposed to solve the above drawbacks.
Disclosure of Invention
The utility model aims to overcome the defects of the prior art, reflects the mathematical principle through digital combination, has simple and clear operation, clear derivation process and low manufacturing cost, is easy to popularize and solve the problems that the digital combination principle deviating from mathematics lacks support for inductive activity and is unfavorable for students to understand the mathematical operation principle deeply, and provides the complete square formula derivation building block.
In order to solve the technical problems, the utility model adopts the basic conception of the technical scheme that:
the utility model provides a complete square formula derives building blocks, includes by four layers totally 10 building blocks constitute:
first layer (base layer): a building block, a square (1) with a side length of a;
second layer (auxiliary layer): four building blocks, one square (2) with side length b (b < a), one square (3) with side length (a-b), two rectangles (4) and (5) with length and width b (a-b) respectively, wherein the colors of the building blocks (2), (3), (4) and (5) are the same, but different from those of the building blocks of the first layer (base layer) and the third layer (deduction layer);
third layer: the laminated wood comprises a pushing layer, four blocks, a square (6) with a side length of b, a square (7) with a side length of (a-b), two rectangles (8) and (9) with a length and a width of b and (a-b), wherein the laminated wood (6), (7), (8) and (9) have the same color and the same size as the auxiliary laminated wood, but have different colors.
Fourth layer: the control layer is a building block, the length and width of the building block are respectively rectangular with a and b, the building blocks (6) and (8) in the pushing layer can be spliced into a building block, the building blocks (6) and (9) can be spliced into a building block, the building blocks (2) and (4) in the auxiliary layer can be spliced into a building block, the building blocks (2) and (5) can be spliced into a building block, the area of the building block is equal to the sum of the square with the side length b and the area of the rectangular with the length and width b and the area of the rectangular with the side length b and the length and width b.
The principle used is as follows:
1. according to the scheme schematic diagram of the patent, 10 building blocks are respectively spliced in a first layer, a second layer, a third layer and a fourth layer, and four building blocks are stacked together to form a square with a side length of a in a top view;
2. covering the bricks (6, 8) of the third layer with the bricks (6, 8) of the fourth layer, proving that the sum of the areas of the bricks (6, 8) is equal to ab, and covering the bricks (6, 9) of the third layer with the bricks (6, 9), proving that the sum of the areas of the bricks (6, 9) is equal to ab;
3. removing the fourth lamination plate;
4. deducing on the third layer of the pushing layer, and removing the building blocks (6) and (8) which are equivalent to subtracting one ab on the building block (1);
5. continuing to deduce on the third pushing layer and the second auxiliary layer, and taking down the building blocks (9) and (2) which are equivalent to subtracting one ab from the building block (1);
6. in the derivation of the third layer (derivation layer), the building blocks (2) of the second layer (auxiliary layer) are removed, and the building blocks (2) need to be replaced on the auxiliary layer, so b2 should be added;
7. only the building blocks (7) are left on the pushing layer, and the area of the building blocks is (a-b) 2;
8. the following is derived: (a-b) 2=a2-2ab+b2.
The complete square formula contains two formulas, namely: (1) square of sum of two numbers: (a+b) 2=a2+2ab+b2, (2) square of two number differences: (a-b) 2=a2-2ab+b2, the related complete square formula in teaching is mainly obtained through algebraic deduction, a few teachers carry out graphic deduction on the squares of the sum of two numbers, the squares of the difference of the two numbers are obtained through algebraic operation by changing operation symbols, and the deduction process of the obtained formula is deviated from the mathematical digital combination principle, lacks support of inductive activity, and is not beneficial to students to deeply understand the mathematical operation principle.
This patent is dedicated to the derivation of the full squaring formula (square of the difference of two numbers).
This patent comprises 10 blocks, arranges the blocks respectively at four layers when deriving:
a first layer: the base layer is formed by splicing a square with a side length of a;
a second layer: the auxiliary layer (the color of the laminated wood is different from that of the first basic layer and the third basic layer) does not participate in the final deduction of the formula, but only plays an auxiliary role in the deduction process, and the auxiliary role is similar to an auxiliary line in mathematical evidence, and the original appearance is restored after deduction is finished.
The auxiliary layer is formed by splicing four building blocks, one side is a square with the length of b (b < a), one side is a square with the length of (a-b), and two lengths and widths are respectively a rectangle with the length of b (a-b);
third layer: the pushing layer is formed by splicing four building blocks, one side of the pushing layer is square with the length of b, the other side of the pushing layer is square with the length of (a-b), and the two lengths and the widths of the pushing layer are respectively rectangle with the length of b and the width of (a-b);
the deducing lamination is used for the deduction of the complete square formula (square of two differences). The deduced lamination blocks are identical to the auxiliary lamination blocks in size, and are distinguished in color for the purpose of clear deducing process.
Fourth layer: a contrast layer, a building block, the length and the width of which are respectively a and b rectangles; the control layer has only one building block, the area of which is equal to the sum of the areas of two patterns of square with side length b and rectangle with length and width b and (a-b) in the pushing layer, and the function of the control layer is used for describing that the sum of the square with side length b and rectangle with length and width b and (a-b) in the pushing layer is ab.
The derivation of the full square formula (square of the difference between two numbers) was performed using building blocks.
A first layer: base layer: a square building block, wherein the side length of the square building block is square (1), the side length of the square building block is a, and the area of the square building block is a2, as shown in the figure 1 of the specification;
a second layer: auxiliary layer: the building block comprises four building blocks, wherein one side of the building block is square (2) with the length of b (b < a), one side of the building block is square (3) with the length of (a-b), two long and wide rectangles (4) and (5) with the length of b and the width of (a-b) are respectively, and the color of the building block is different from that of the first layer of foundation layer and the third layer of deduction building block;
square (2), side length is b, area is b2;
square (3), side length is (a-b), area is (a-b) 2;
a rectangle (4) with length and width of b, (a-b) and area of b (a-b);
rectangle (5), length and width are b, (a-b) and area is b (a-b), as shown in figure 2 of the specification;
third layer: a pushing layer: the building block consists of four building blocks, wherein one side of the building block is square (6) with the length of b, one side of the building block is square (7) with the length of (a-b), and two long and wide building blocks are rectangles (8) and (9) with the length of b and the width of (a-b) respectively;
square (6), side length is b, area is b2;
square (7), side length is (a-b), area is (a-b) 2;
a rectangle (8) with length and width of b, (a-b) and area of b (a-b);
rectangle (9) has length and width of b, (a-b) and area of b (a-b), as shown in figure 3 of the specification.
And a fourth layer, a contrast layer, a rectangle with length and width a and b respectively and area ab, as shown in figure 4 of the specification.
After the technical scheme is adopted, compared with the prior art, the utility model has the following beneficial effects, and of course, any product for implementing the utility model does not necessarily need to achieve all the following advantages at the same time:
the combination of the figures reflects the mathematical principle, the operation is simple and clear, the deducing process is clear, the manufacturing cost is low, and the popularization is easy.
The following describes the embodiments of the present utility model in further detail with reference to the accompanying drawings.
Drawings
The drawings in the following description are only examples of embodiments from which other drawings may be derived by those skilled in the art without the exercise of inventive faculty. Attached at
In the figure:
FIG. 1 is a schematic diagram of a first embodiment of the present utility model;
FIG. 2 is a schematic diagram of a second embodiment of the present utility model;
FIG. 3 is a third schematic diagram of an embodiment of the present utility model;
fig. 4 is a schematic diagram of a fourth embodiment of the present utility model.
It should be noted that these drawings and the written description are not intended to limit the scope of the inventive concept in any way, but to illustrate the inventive concept to those skilled in the art by referring to the specific embodiments.
Detailed Description
The following description of the embodiments of the present utility model will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present utility model, but not all embodiments. The following description of at least one exemplary embodiment is merely exemplary in nature and is in no way intended to limit the utility model, its application, or uses.
In order to keep the following description of the embodiments of the present utility model clear and concise, the detailed description of known functions and known components thereof have been omitted.
Referring to fig. 1-4, in this embodiment, a complete square formula deriving building block is provided, which comprises four layers of 10 building blocks:
first layer (base layer): a building block, a square (1) with a side length of a;
second layer (auxiliary layer): four building blocks, one square (2) with side length b (b < a), one square (3) with side length (a-b), two rectangles (4) and (5) with length and width b (a-b) respectively, wherein the colors of the building blocks (2), (3), (4) and (5) are the same, but different from those of the building blocks of the first layer (base layer) and the third layer (deduction layer);
third layer: the laminated wood comprises a pushing layer, four blocks, a square (6) with a side length of b, a square (7) with a side length of (a-b), two rectangles (8) and (9) with a length and a width of b and (a-b), wherein the laminated wood (6), (7), (8) and (9) have the same color and the same size as the auxiliary laminated wood, but have different colors.
Fourth layer: the control layer is a building block, the length and width of the building block are respectively rectangular with a and b, the building blocks (6) and (8) in the pushing layer can be spliced into a building block, the building blocks (6) and (9) can be spliced into a building block, the building blocks (2) and (4) in the auxiliary layer can be spliced into a building block, the building blocks (2) and (5) can be spliced into a building block, the area of the building block is equal to the sum of the square with the side length b and the area of the rectangular with the length and width b and the area of the rectangular with the side length b and the length and width b.
The principle used is as follows:
according to the scheme schematic diagram of the patent, 10 building blocks are respectively spliced in a first layer, a second layer, a third layer and a fourth layer, and four building blocks are stacked together to form a square with a side length of a in a top view;
covering the bricks (6, 8) of the third layer with the bricks (6, 8) of the fourth layer, proving that the sum of the areas of the bricks (6, 8) is equal to ab, and covering the bricks (6, 9) of the third layer with the bricks (6, 9), proving that the sum of the areas of the bricks (6, 9) is equal to ab;
removing the fourth lamination plate;
deducing on the third layer of the pushing layer, and removing the building blocks (6) and (8) which are equivalent to subtracting one ab on the building block (1);
continuing to deduce on the third pushing layer and the second auxiliary layer, and taking down the building blocks (9) and (2) which are equivalent to subtracting one ab from the building block (1);
in the derivation of the third layer (derivation layer), the building blocks (2) of the second layer (auxiliary layer) are removed, and the building blocks (2) need to be replaced on the auxiliary layer, so b2 should be added;
only the building blocks (7) are left on the pushing layer, and the area of the building blocks is (a-b) 2;
the following is derived: (a-b) 2=a2-2ab+b2.
The complete square formula contains two formulas, namely: (1) square of sum of two numbers: (a+b) 2=a2+2ab+b2, (2) square of two number differences: (a-b) 2=a2-2ab+b2, the related complete square formula in teaching is mainly obtained through algebraic deduction, a few teachers carry out graphic deduction on the squares of the sum of two numbers, the squares of the difference of the two numbers are obtained through algebraic operation by changing operation symbols, and the deduction process of the obtained formula is deviated from the mathematical digital combination principle, lacks support of inductive activity, and is not beneficial to students to deeply understand the mathematical operation principle.
This patent is dedicated to the derivation of the full squaring formula (square of the difference of two numbers).
This patent comprises 10 blocks, arranges the blocks respectively at four layers when deriving:
a first layer: the base layer is formed by splicing a square with a side length of a;
a second layer: the auxiliary layer (the color of the laminated wood is different from that of the first basic layer and the third basic layer) does not participate in the final deduction of the formula, but only plays an auxiliary role in the deduction process, and the auxiliary role is similar to an auxiliary line in mathematical evidence, and the original appearance is restored after deduction is finished.
The auxiliary layer is formed by splicing four building blocks, one side is a square with the length of b (b < a), one side is a square with the length of (a-b), and two lengths and widths are respectively a rectangle with the length of b (a-b);
third layer: the pushing layer is formed by splicing four building blocks, one side of the pushing layer is square with the length of b, the other side of the pushing layer is square with the length of (a-b), and the two lengths and the widths of the pushing layer are respectively rectangle with the length of b and the width of (a-b);
the deducing lamination is used for the deduction of the complete square formula (square of two differences). The deduced lamination blocks are identical to the auxiliary lamination blocks in size, and are distinguished in color for the purpose of clear deducing process.
Fourth layer: a contrast layer, a building block, the length and the width of which are respectively a and b rectangles; the control layer has only one building block, the area of which is equal to the sum of the areas of two patterns of square with side length b and rectangle with length and width b and (a-b) in the pushing layer, and the function of the control layer is used for describing that the sum of the square with side length b and rectangle with length and width b and (a-b) in the pushing layer is ab.
The derivation of the full square formula (square of the difference between two numbers) was performed using building blocks.
A first layer: base layer: a square building block, wherein the side length of the square building block is square (1), the side length of the square building block is a, and the area of the square building block is a2, as shown in the figure 1 of the specification;
a second layer: auxiliary layer: the building block comprises four building blocks, wherein one side of the building block is square (2) with the length of b (b < a), one side of the building block is square (3) with the length of (a-b), two long and wide rectangles (4) and (5) with the length of b and the width of (a-b) are respectively, and the color of the building block is different from that of the first layer of foundation layer and the third layer of deduction building block;
square (2), side length is b, area is b2;
square (3), side length is (a-b), area is (a-b) 2;
a rectangle (4) with length and width of b, (a-b) and area of b (a-b);
rectangle (5), length and width are b, (a-b) and area is b (a-b), as shown in figure 2 of the specification;
third layer: a pushing layer: the building block consists of four building blocks, wherein one side of the building block is square (6) with the length of b, one side of the building block is square (7) with the length of (a-b), and two long and wide building blocks are rectangles (8) and (9) with the length of b and the width of (a-b) respectively;
square (6), side length is b, area is b2;
square (7), side length is (a-b), area is (a-b) 2;
a rectangle (8) with length and width of b, (a-b) and area of b (a-b);
rectangle (9) has length and width of b, (a-b) and area of b (a-b), as shown in figure 3 of the specification.
And a fourth layer, a contrast layer, a rectangle with length and width a and b respectively and area ab, as shown in figure 4 of the specification.
The combination of the figures reflects the mathematical principle, the operation is simple and clear, the deducing process is clear, the manufacturing cost is low, and the popularization is easy.
The two lengths and the widths are respectively b, (a-b) rectangle (4) and rectangle (5), and the colors of the second lamination block (2), the building block (3), the building block (4) and the building block (5) are the same;
the second lamination wood is different from the first layer of basic lamination wood in color.
The second laminated wood is different from the third layer of the deduced laminated wood in color, and the bricks (6) and (8) in the pushing layer can be spliced into a building block unit
The above embodiments may be combined with each other.
It should be noted that the terms "first," "second," and the like in the description and claims of the present application and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that embodiments of the present application described herein may be implemented in sequences other than those illustrated or described herein.
In the description of the present utility model, it should be understood that the azimuth or positional relationships indicated by the azimuth terms such as "front, rear, upper, lower, left, right", "lateral, vertical, horizontal", and "top, bottom", etc., are generally based on the azimuth or positional relationships shown in the drawings, merely to facilitate description of the present utility model and simplify the description, and these azimuth terms do not indicate and imply that the apparatus or elements referred to must have a specific azimuth or be constructed and operated in a specific azimuth, and thus should not be construed as limiting the scope of protection of the present utility model; the orientation word "inner and outer" refers to inner and outer relative to the contour of the respective component itself.
Claims (7)
1. A complete square formula deriving building block comprising: consists of 10 building blocks in four layers:
first layer (base layer): a building block, a square (1) with a side length of a;
second layer (auxiliary layer): four building blocks, one square (2) with side length b and one square (3) with side length b;
the building blocks comprise a third layer (deriving layer), four building blocks, a square (6) with a side length of b and a square (7) with a side length of a-b;
a fourth layer (contrast layer) of building blocks, a rectangle with length and width of a and b respectively, the area of the building blocks being equal to the sum of the square with side length b and the area of two patterns with length and width of b and a-b respectively.
2. A complete square formula derived building block according to claim 1, characterized in that the two rectangles (4), rectangle (5) of length and width b, a-b respectively, the second lamination (2), building block (3), building block (4), building block (5) are of the same colour.
3. A complete square formula derived building block according to claim 1, characterized in that the two rectangles (8), blocks (9) of length and width b, a-b respectively, the third layer derived lamination (6), blocks (7), blocks (8), blocks (9) are of the same colour, of the same size as the auxiliary lamination, but of different colour.
4. A complete square formula derived block according to claim 1, wherein the second layer of laminated wood is of a different colour than the first layer of base laminated wood.
5. A complete square formula development toy building block according to claim 1, characterized in that the second layer of development toy building blocks is of a different colour than the third layer of development toy building blocks, the toy building blocks (6), (8) in the push-off layer being able to spell into one toy building block component.
6. A complete square formula derived building block according to claim 1, characterized in that the building blocks (6), (9) can be spliced into one building block system.
7. The deriving block according to claim 1, wherein the blocks (2) and (4) in the auxiliary layer can be spliced into a block, and the blocks (2) and (5) can be spliced into a block.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202321756044.8U CN220459905U (en) | 2023-07-06 | 2023-07-06 | Complete square formula deduces building blocks |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202321756044.8U CN220459905U (en) | 2023-07-06 | 2023-07-06 | Complete square formula deduces building blocks |
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| CN220459905U true CN220459905U (en) | 2024-02-09 |
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| CN202321756044.8U Active CN220459905U (en) | 2023-07-06 | 2023-07-06 | Complete square formula deduces building blocks |
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2023
- 2023-07-06 CN CN202321756044.8U patent/CN220459905U/en active Active
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