Rectangle square area and perimeter demonstrator

Abstract

The application relates to a rectangle square area and perimeter demonstrator, and belongs to the technical field of teaching aids and learning aids, which comprises a base plate, a plurality of base columns arranged linearly on one side of the base plate, and a flexible rope capable of forming a closed figure around the base columns. The base plate and the linearly arranged base column structure enable the flexible rope to quickly form rectangle or square closed figures of different sizes around the base columns, which is beneficial to dynamic adjustment of the side length by the user and intuitive display of the linear law that the perimeter changes with the figure size. The implicit corresponding relationship between the base column spacing and the unit length enables students to simultaneously perceive the area calculation logic when measuring the perimeter, thereby optimizing the correlation teaching effect of the perimeter and area formulas.

Description

Technical Field

[0001] This application relates to the field of teaching aids and learning tools, and in particular to a rectangular and square area and perimeter demonstrator. Background Technology

[0002] In elementary school geometry teaching, the concepts of perimeter and area of ​​rectangles and squares are highly abstract, and traditional teaching methods typically rely on blackboard drawings or static illustrations in textbooks for explanation. Teachers need to repeatedly draw shapes of different sizes to demonstrate the changes in formulas. Hand-drawn diagrams are inefficient and it is difficult to ensure accurate proportions. Students are prone to visual fatigue from facing monotonous static illustrations for a long time, and they lack an intuitive understanding of the dynamic relationship between perimeter and area, resulting in a superficial understanding of the formulas. In addition, blackboard drawings cannot simultaneously demonstrate the essential differences between perimeter and area, and students are prone to confusing the concepts. For example, they may mistakenly believe that an increase in perimeter necessarily leads to a corresponding increase in area. The lack of effective physical models to assist in verification further exacerbates the deviation in knowledge comprehension.

[0003] Existing educational tool designs generally suffer from limitations such as single functionality and fragmented operations. For example, measuring perimeter requires using a separate rope to mark the edges of a shape, while area calculation relies on manually counting squares or piecing together standard area blocks. These two tasks cannot be demonstrated simultaneously within the same educational tool, leading to a disconnect between concept teaching and practical application. Furthermore, the fixed dimensions of the educational tools prevent dynamic adjustment of graphic parameters to demonstrate the changing patterns of perimeter and area, thus limiting students' ability to explore the essence of the formulas. Utility Model Content

[0004] To improve the teaching effectiveness of the area and perimeter of rectangles and squares, this application provides a demonstrator for the area and perimeter of rectangles and squares.

[0005] This application provides a rectangular and square area and perimeter demonstrator, which adopts the following technical solution:

[0006] A rectangle and square area and perimeter demonstrator includes:

[0007] substrate;

[0008] Multiple base pillars are linearly arranged on one side of the substrate;

[0009] The flexible rope can wrap around the base column to form a closed shape.

[0010] By adopting the above technical solution, the flexible rope, through the base plate and linearly arranged column structure, can quickly form closed rectangular or square shapes of different sizes around the columns. This allows users to dynamically adjust the side lengths and intuitively demonstrate the linear relationship between the perimeter and the shape's size. The implicit correspondence between unit lengths through the column spacing allows students to simultaneously perceive the logic of area calculation while measuring the perimeter, optimizing the teaching effect of the correlation between perimeter and area formulas. The combination of the flexible rope and the columns simplifies the separation of drawing and measuring tools in traditional teaching, improving the attention span problem for younger students caused by switching between multiple tools. Furthermore, by fixing the standardized parameters of the column spacing, errors in formula derivation caused by proportional deviations in hand-drawn graphics are avoided, strengthening the mapping relationship between abstract formulas and physical models, and improving teaching effectiveness.

[0011] Optionally, the substrate is provided with indicator grid lines, and the base post is located at the intersection of the indicator grid lines.

[0012] By adopting the above technical solution, indicator grid lines are set on the substrate and the base pillars are fixed at the intersection of the grid lines, so that the spacing between the base pillars strictly corresponds to the grid units, which optimizes students' intuitive perception of unit length and area calculation. The visual assistance of the grid lines to the boundary of the shape helps students quickly count the number of small squares corresponding to the indicator grid lines in the area enclosed by the flexible rope, which is conducive to the derivation of the area formula of rectangles and squares and improves the calculation confusion caused by the ambiguity of unit length in traditional teaching aids.

[0013] Optionally, the row spacing and column spacing of adjacent base columns are both 1 cm.

[0014] By adopting the above technical solution, and limiting the row and column spacing of the base columns to 1cm, the side length of the shape formed by the flexible rope directly corresponds to an integer multiple of the unit length, and the area of ​​the small square enclosed by four adjacent base columns is 1cm². 2 This allows students to quickly calculate the perimeter and area of ​​a shape by using the number of base columns; at the same time, the standardized spacing design avoids errors from manual measurement and optimizes the accuracy of formula derivation.

[0015] Optionally, it also includes replaceable graph paper, wherein the substrate is made of transparent or semi-transparent material and has a limiting frame on the side facing away from the base column, and a limiting space for accommodating the replaceable graph paper is formed within the limiting frame, and the grid intersections of the replaceable graph paper correspond to the positions of the base column.

[0016] By adopting the above technical solution, the use of a transparent or semi-transparent substrate and replaceable graph paper allows the pre-drawn graph paper containing the graphic to be demonstrated to be inserted into the limiting frame. Utilizing the strict correspondence between the base column position and the intersection of the grid on the replaceable graph paper, students can directly refer to the base column positioning to perform flexible rope enclosure operations when observing the graphic outline through the substrate. This facilitates the transformation of abstract formula derivation into practical operation training. The constraint design of the limiting frame eliminates the need for repeated grid alignment calibration when replacing the replaceable graph paper, optimizing the efficiency of quickly switching between different preset graphics. Simultaneously, the visualization characteristics of the transparent substrate enhance students' understanding of the correlation between the simultaneous calculation of the perimeter and area of ​​a graphic.

[0017] Optionally, the inner side of the limiting frame is provided with several latches, and a certain gap is left between the latches and the substrate.

[0018] By adopting the above technical solution, during the demonstration, the replaceable graph paper is inserted from the side and laid in the gap. When the substrate is picked up, the latch supports the edge of the graph paper from below through its own structure, preventing it from falling due to gravity. Through the partial contact limiting design of the latch, the replaceable graph paper can be easily and quickly replaced by simply inserting or pulling it out.

[0019] Optionally, multiple elastic coils are also included.

[0020] By adopting the above technical solution, compared with using a flexible rope alone, the addition of an elastic ring can adapt to the fixing needs of quadrilaterals of different sizes by utilizing its elastic deformation characteristics. This allows students to keep the shape stable without continuously holding the end of the rope after enclosing it, which is beneficial for freeing their hands to focus on observing the characteristics of the shape's edges and corners (such as right angles and parallel sides) or performing area calculations, thus optimizing the interactivity and freedom of operation in teaching.

[0021] Optionally, the periphery of the substrate is provided with a smooth structure.

[0022] By adopting the above technical solution, sharp edges or burrs are eliminated, thus optimizing the safety of young students when operating the equipment.

[0023] Optionally, the substrate is provided with a protective frame, which surrounds the outside of the plurality of base pillars, and the height of the protective frame is greater than the height of the base pillars.

[0024] By adopting the above technical solution, a protective frame with a height greater than that of the base column is set around the substrate, so that when the demonstrator is inverted, the end face of the protective frame will first contact the tabletop, avoiding wear or breakage caused by the base column directly bearing pressure; in addition, the design of the protective frame surrounding the base column also prevents the base column from being damaged by impact with hard objects when the teaching aid is accidentally dropped, and can disperse the impact force, improving the durability of the demonstrator.

[0025] In summary, this application includes at least one of the following beneficial technical effects:

[0026] 1. This application utilizes a base plate and a linearly arranged column structure to allow a flexible rope to quickly form closed rectangular or square shapes of different sizes around the columns. This facilitates users in dynamically adjusting the side lengths and visually demonstrates the linear relationship between the perimeter and the shape's size. The implicit unit length correspondence between the column spacing and the perimeter allows students to simultaneously grasp the area calculation logic while measuring the perimeter, optimizing the teaching effect of the correlation between perimeter and area formulas. The combination of the flexible rope and the columns simplifies the separation of drawing and measuring tools in traditional teaching, improving the attention span of younger students due to switching between multiple tools. Furthermore, by fixing the standardized parameters of the column spacing, it avoids formula derivation errors caused by proportional deviations in hand-drawn graphics, strengthening the mapping relationship between abstract formulas and physical models, and improving teaching effectiveness. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the overall structure of a rectangular and square area and perimeter demonstrator according to an embodiment of this application.

[0028] Figure 2 This is a model diagram illustrating the substrate and its integrated components in the embodiments of this application.

[0029] Figure 3 This is a structural schematic diagram illustrating the positional relationship between the base column and the indicator grid line in the embodiments of this application.

[0030] Figure 4 This is a schematic diagram illustrating the structure of the limiting frame and the latch in the embodiments of this application.

[0031] Figure 5 This is a cross-sectional view of the substrate shown in the embodiments of this application.

[0032] Explanation of reference numerals in the attached drawings: 1. Base plate; 11. Indicator grid line; 2. Base post; 3. Flexible rope; 4. Replaceable graph paper; 5. Limiting frame; 51. Limiting space; 52. Tongue; 6. Elastic ring; 7. Protective frame. Detailed Implementation

[0033] The following combination Figures 1-5 This application will be described in further detail below.

[0034] Example:

[0035] This application discloses a demonstrator for the area and perimeter of rectangles and squares. (Refer to...) Figure 2A rectangular and square area and perimeter demonstrator includes a base plate 1, base pillars 2, and a flexible rope 3. Multiple base pillars 2 are linearly arranged on one side of the base plate 1. The flexible rope 3 can wrap around the base pillars 2 to form a closed shape. In this embodiment, the flexible rope 3 is made of natural yarn, such as cotton, wool, or hemp.

[0036] In use, the flexible rope 3, through the linearly arranged base pillars 2 structure, can quickly form closed rectangular or square shapes of different sizes around the base pillars 2. This allows users to dynamically adjust the side lengths and intuitively demonstrate the linear relationship between the perimeter and the shape's size. The implicit correspondence between the unit lengths through the spacing of the base pillars 2 allows students to simultaneously perceive the logic of area calculation while measuring the perimeter, optimizing the teaching effect of the correlation between perimeter and area formulas. The combination of the flexible rope 3 and the base pillars 2 simplifies the separation of drawing and measuring tools in traditional teaching, improving the attention span problem for younger students caused by switching between multiple tools. Furthermore, by fixing the standardized parameters of the base pillar spacing, it avoids formula derivation errors caused by proportional deviations in hand-drawn graphics, strengthening the mapping relationship between abstract formulas and physical models, and improving teaching effectiveness.

[0037] Reference Figure 2 and Figure 3 The base plate 1 has indicator grid lines 11, and the base posts 2 are located at the intersections of the indicator grid lines 11. In this way, the spacing of the base posts 2 strictly corresponds to the grid units, which optimizes students' intuitive perception of unit length and area calculation. The visual assistance of the grid lines to the boundaries of the shape helps students quickly count the number of small squares corresponding to the indicator grid lines 11 within the area enclosed by the flexible rope 3, thereby facilitating the derivation of the area formulas for rectangles and squares and improving the calculation confusion caused by the ambiguity of unit length in traditional teaching aids.

[0038] Furthermore, the row and column spacing of adjacent base pillars 2 is 1cm. By limiting the row and column spacing of base pillars 2 to 1cm, the side length of the shape enclosed by the flexible rope 3 directly corresponds to an integer multiple of the unit length, and the area of ​​the small square enclosed by four adjacent base pillars 2 is 1cm2. This facilitates students in quickly calculating the perimeter and area of ​​the shape based on the number of base pillars 2. At the same time, the standardized spacing design avoids manual measurement errors and optimizes the accuracy of formula derivation.

[0039] Reference Figure 1The demonstrator also includes replaceable graph paper 4. The substrate 1 is made of transparent or semi-transparent material. A limiting frame 5 is integrally formed on the side of the substrate 1 facing away from the base column 2. A limiting space 51 is formed within the limiting frame 5 to accommodate the replaceable graph paper 4. The grid intersections of the replaceable graph paper 4 correspond to the positions of the base column 2. In use, the replaceable graph paper 4, with the pre-drawn graphic to be demonstrated, can be inserted into the limiting frame 5 through the cooperation of the transparent or semi-transparent substrate 1 and the replaceable graph paper 4. Utilizing the strict correspondence between the position of the base column 2 and the grid intersections of the replaceable graph paper 4, students can directly refer to the base column 2 to position and perform the flexible rope 3 enclosure operation when observing the outline of the graphic through the substrate 1. This facilitates the transformation of abstract formula derivation into physical operation training. The constraint design of the limiting frame 5 eliminates the need to repeatedly calibrate the grid alignment when replacing the replaceable graph paper 4, optimizing the efficiency of quickly switching between different preset graphics. At the same time, the visualization characteristics of the transparent substrate 1 enhance students' understanding of the correlation between the simultaneous calculation of the perimeter and area of ​​a graphic.

[0040] Reference Figure 4 and Figure 5 The inner side of the limiting frame 5 is integrally formed with several latches 52, and a certain gap is left between the latches 52 and the substrate 1 to accommodate the replaceable graph paper 4. During the demonstration, the replaceable graph paper 4 is inserted from the side and laid in the gap. When the substrate 1 is lifted, the latches 52 support the edge of the graph paper from below through their own structure, preventing it from falling due to gravity. Through the partial contact limiting design of the latches 52, the replaceable graph paper 4 can be easily and quickly replaced by simply inserting or pulling it out.

[0041] Reference Figure 1 To further improve teaching effectiveness, the demonstrator is also equipped with multiple elastic rings 6. In this embodiment, the elastic rings 6 are rubber bands. Compared to using a flexible rope 3 alone, by adding elastic rings 6, the elastic deformation characteristics can be utilized to adapt to the fixing needs of quadrilaterals of different sizes. This allows students to keep the shape stable without continuously holding the rope end after enclosing it, freeing their hands to focus on observing the characteristics of the shape's edges and corners (such as right angles and parallel sides) or performing area calculations, thus optimizing teaching interactivity and operational freedom.

[0042] Reference Figure 3 and Figure 5 A protective frame 7 is integrally formed on the substrate 1, surrounding the outer side of multiple base pillars 2. The height of the protective frame 7 is greater than the height of the base pillars 2. By setting a protective frame 7 with a height greater than that of the base pillars 2 around the substrate 1, the end face of the protective frame 7 will preferentially contact the table when the demonstrator is inverted, avoiding wear or breakage caused by direct pressure on the base pillars 2. In addition, the design of the protective frame 7 surrounding the base pillars 2 also prevents the base pillars 2 from being damaged by impact with hard objects when the teaching aid is accidentally dropped, and can disperse the impact force, improving the durability of the demonstrator.

[0043] Reference Figure 1 and Figure 2 The periphery of the substrate 1 is set with a smooth structure. In this embodiment, the four corners of the substrate 1 are chamfered to eliminate sharp parts or burrs on the edge of the demonstrator, thereby ensuring the safety of young students when operating it.

[0044] The above are all preferred embodiments of this application, and are not intended to limit the scope of protection of this application. Therefore, all equivalent changes made in accordance with the structure, shape and principle of this application should be covered within the scope of protection of this application.

Claims

1. A device for demonstrating the area and perimeter of rectangles and squares, characterized in that, include: base(1); Multiple base pillars (2) are linearly arranged on one side of the substrate (1); The flexible rope (3) can be wrapped around the base column (2) to form a closed shape.

2. The rectangular and square area and perimeter demonstrator according to claim 1, characterized in that: The substrate (1) is provided with indicator grid lines (11), and the base post (2) is located at the intersection of the indicator grid lines (11).

3. The rectangular and square area and perimeter demonstrator according to claim 1, characterized in that: The row spacing and column spacing of adjacent base columns (2) are both 1cm.

4. The rectangular and square area and perimeter demonstrator according to claim 1, characterized in that: It also includes replaceable grid paper (4), the substrate (1) is made of transparent or semi-transparent material and has a limiting frame (5) on the side facing away from the base column (2), the limiting frame (5) has a limiting space (51) for accommodating the replaceable grid paper (4), and the grid intersection of the replaceable grid paper (4) corresponds to the position of the base column (2).

5. The rectangular and square area and perimeter demonstrator according to claim 4, characterized in that: The inner side of the limiting frame (5) is provided with several latches (52), and there is a certain gap between the latches (52) and the substrate (1).

6. The rectangular and square area and perimeter demonstrator according to claim 1, characterized in that: It also includes multiple elastic coils (6).

7. The rectangular and square area and perimeter demonstrator according to claim 1, characterized in that: The periphery of the substrate (1) is provided with a smooth structure.

8. The rectangular and square area and perimeter demonstrator according to claim 1, characterized in that: The substrate (1) is provided with a protective frame (7), which surrounds the outside of a plurality of base pillars (2), and the height of the protective frame (7) is greater than the height of the base pillars (2).

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