Probability model demonstration teaching aid

Abstract

The utility model provides a probability model demonstration teaching aid, which relates to the technical field of math teaching aids, and comprises a body, corners and an inner circle, a square inner cavity is arranged in the body, the inner circle is marked in the inner cavity, the diameter of the inner circle is equal to the side length of the square at the bottom surface of the inner cavity, and the corner is arranged at the bottom surface of the inner cavity. The inner circle divides the corners at the four corners of the bottom face of the inner cavity, the four edges of the bottom face of the inner cavity are all tangent to the inner circle, the center of the bottom face of the inner cavity coincides with the center of the inner circle, and a plurality of small balls are further included. According to the utility model, the design is concise and visual, students can randomly throw the small balls into the inner cavity through actual operation and directly observe and record experiment results, and through the interaction mode, the students can more visually understand probability distribution and statistical laws, and the learning interest and the understanding effect are enhanced.

Description

Technical Field

[0001] The utility model relates to the technical field of mathematical teaching aids, in particular to a probability model demonstration teaching aid. Background Art

[0002] Probability model demonstration teaching aids are an important auxiliary tool in the teaching process, especially in the teaching of probability theory and statistics. Through intuitive demonstration, students can more easily understand and master abstract mathematical concepts. In the current educational environment, many probability model demonstrations rely on computer simulations, but this may not be conducive to students' intuitive understanding of the practical application of probability in some cases. Compared with electronic devices, physical teaching aids can better provide interactivity and intuitive feelings, enabling students to deepen their understanding of concepts such as probability distribution, statistical laws, and the law of large numbers through hands-on operations.

[0003] In the probability model, there is a statistical simulation method that estimates mathematical expectations and other quantities through a large number of random sampling. In this method, estimating pi is a demonstration example, which estimates the value of pi by randomly scattering points in a unit square and calculating the proportion of points that fall within the unit circle. However, there is currently a lack of physical teaching aids designed specifically for this purpose on the market, and teachers often need to design them themselves or use existing, incompletely suitable tools for demonstration. This not only increases the complexity of teaching preparation, but may also affect the demonstration effect.

[0004] In order to solve the above problems, the utility model provides a specially designed probability model demonstration teaching aid, which can simplify teaching preparation, improve teaching effect, and enhance students' understanding of probability concept through practical operation. The teaching aid is reasonably designed and easy to use, and can effectively demonstrate the principle and process of estimating pi by Monte Carlo method. Utility Model Content

[0005] In order to solve the technical problems in the prior art, the utility model provides a probability model demonstration teaching aid.

[0006] The technical solution provided by the embodiment of the utility model is as follows:

[0007] The utility model provides a probability model demonstration teaching aid, comprising:

[0008] A body, corners and an inner circle, wherein a square inner cavity is opened in the body, the inner circle is marked in the inner cavity, the diameter of the inner circle is equal to the side length of the square of the inner cavity bottom surface, the inner circle divides the corners at the four corners of the inner cavity bottom surface, the four sides of the inner cavity bottom surface are tangent to the inner circle, the center of the inner cavity bottom surface coincides with the center of the inner circle, and also includes a plurality of small balls.

[0009] Preferably, the side length of the bottom surface of the inner cavity is at least greater than or equal to the sum of the diameters of 10 small balls. If the number of small balls that the inner cavity can accommodate is too small, it will affect the subsequent estimation accuracy.

[0010] Preferably, two mutually perpendicular sides of the upper end surface of the main body are provided with mutually perpendicular levels for keeping the teaching aids level when setting the teaching aids.

[0011] Preferably, a base is provided on the bottom surface of the main body for supporting the main body and making it more convenient to take.

[0012] Preferably, the base is circular, so that it is more stable when setting up the teaching aid.

[0013] The beneficial effects brought by the technical solution provided by the embodiment of the utility model include at least:

[0014] (1) In the present invention, the probability model demonstration teaching aid is concise and intuitive. Students can throw the ball randomly into the inner cavity through actual operation, directly observe and record the experimental results. Through this interactive method, students can more intuitively understand the probability distribution and statistical laws, and enhance their learning interest and understanding effect;

[0015] (2) In the present invention, the design of the teaching aid takes the estimation accuracy into consideration. The side length of the bottom surface of the inner cavity is at least greater than or equal to the sum of the diameters of 10 small balls, ensuring that a sufficient number of small balls can be accommodated, thereby increasing the sample size of the experimental data. After the sample size increases, according to the law of large numbers, the estimated value of pi will be closer to the true value, thereby improving the accuracy and reliability of the experiment;

[0016] (3) In the utility model, the spirit level arranged on the upper end surface of the main body ensures that the teaching aid is placed horizontally during use, avoiding the influence of tilt on the experimental results. In addition, the base is designed to be circular, which makes the teaching aid more stable when placed, increasing the repeatability and accuracy of the experiment. At the same time, the base design makes the teaching aid easy to take, carry and use, thereby improving the practicality and portability of the teaching aid and making it suitable for use in various teaching environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0018] Figure 1 A schematic diagram of the structure of a probability model demonstration teaching aid provided by an embodiment of the utility model;

[0019] Figure 2 An enlarged view of point A in the structural schematic diagram of a probability model demonstration teaching aid provided by an embodiment of the utility model;

[0020] Figure 3 A structural top view of a probability model demonstration teaching aid provided by an embodiment of the utility model when in use;

[0021] Figure 4 A structural cross-sectional view at point BB of a probability model demonstration teaching aid provided by an embodiment of the utility model;

[0022] Figure 5 A structural bottom view of a probability model demonstration teaching aid provided by an embodiment of the utility model.

[0023] In the figure: 11, main body; 12, base; 13, level; 14, inner cavity; 21, corners; 22, inner circle. DETAILED DESCRIPTION

[0024] The technical solution of the present utility model is described below in conjunction with the accompanying drawings.

[0025] In the embodiments of the present invention, words such as "exemplarily" and "for example" are used to indicate examples, illustrations or explanations. Any embodiment or design described as "example" in the present invention should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of the word "example" is intended to present the concept in a specific way. In addition, in the embodiments of the present invention, the meaning expressed by "and / or" can be both, or it can be either of the two.

[0026] In order to make the technical problems to be solved, technical solutions and advantages of the present invention more clear, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0027] Reference Manual Attached Figure 1-5 The present utility model embodiment provides a probability model demonstration teaching aid, including:

[0028] like Figure 1 As shown, a main body 11, corners 21 and an inner circle 22 are provided in the main body 11. A square inner cavity 14 is provided in the inner cavity 14. An inner circle 22 is marked in the inner cavity 14. The diameter of the inner circle 22 is equal to the side length of the square of the bottom surface of the inner cavity 14. The inner circle 22 divides the corners 21 at the four corners of the bottom surface of the inner cavity 14. The four sides of the bottom surface of the inner cavity 14 are tangent to the inner circle 22. The center of the bottom surface of the inner cavity 14 coincides with the center of the inner circle 22. A plurality of small balls are also included.

[0029] The side length of the bottom surface of the inner cavity 14 is at least greater than or equal to the sum of the diameters of 10 small balls. If the number of small balls that the inner cavity 14 can accommodate is too small, the subsequent estimation accuracy will be affected.

[0030] like Figure 2 As shown, two mutually perpendicular sides of the upper end surface of the body 11 are provided with mutually perpendicular levels 13 for keeping the teaching aids level when setting the teaching aids.

[0031] A base 12 is provided on the bottom surface of the body 11 for supporting the body 11 and making it more convenient to take.

[0032] The base 12 is circular, so that the teaching aids can be more stable when being set.

[0033] The method of using the utility model to estimate pi is as follows: after the body 11 is placed horizontally according to the level 13, the student or teacher throws a number of small balls into the inner cavity 14 in sequence or together, so that the small balls randomly fall at different positions in the inner cavity 14;

[0034] like Figure 3 As shown, the utility model embodiment is Figure 3 Take the case as an example to illustrate that 30 small balls are thrown into the inner cavity 14 , 6 small balls fall into the corners 21 , and 24 small balls fall into the inner circle 22 .

[0035] Because the side length of the bottom of the inner cavity 14 is equal to the diameter of the inner circle 22, and the ratio of the number of balls falling in the inner circle 22 to the total number of balls should be infinitely equal to the ratio of the area of ​​the inner circle 22 to the area of ​​the bottom of the inner cavity 14, so

[0036]

[0037] In the above formula, πr 2 represents the area of ​​the inner circle 22, 4r 2 represents the bottom area of ​​the inner cavity 14, π represents the estimated pi, B c represents the number of balls falling into the inner circle 22, and B represents the number of balls thrown into the inner cavity 14. After a simple calculation, the following formula is obtained:

[0038]

[0039] According to the above formula, the value of pi can be estimated. Figure 3 Ball data inside: B c =24, B=30, we can get

[0040]

[0041] After multiple experiments, finding the average of the estimated pi or increasing the number of balls can increase the accuracy of the estimate, making the estimated pi closer to the true value of pi.

[0042] The beneficial effects brought by the technical solution provided by the embodiment of the utility model include at least:

[0043] (1) In the present invention, the probability model demonstration teaching aid is concise and intuitive. Students can throw the ball randomly into the inner cavity through actual operation, directly observe and record the experimental results. Through this interactive method, students can more intuitively understand the probability distribution and statistical laws, and enhance their learning interest and understanding effect;

[0044] (2) In the present invention, the design of the teaching aid takes the estimation accuracy into consideration. The side length of the bottom surface of the inner cavity is at least greater than or equal to the sum of the diameters of 10 small balls, ensuring that a sufficient number of small balls can be accommodated, thereby increasing the sample size of the experimental data. After the sample size increases, according to the law of large numbers, the estimated value of pi will be closer to the true value, thereby improving the accuracy and reliability of the experiment;

[0045] (3) In the utility model, the spirit level arranged on the upper end surface of the main body ensures that the teaching aid is placed horizontally during use, avoiding the influence of tilt on the experimental results. In addition, the base is designed to be circular, which makes the teaching aid more stable when placed, increasing the repeatability and accuracy of the experiment. At the same time, the base design makes the teaching aid easy to take, carry and use, thereby improving the practicality and portability of the teaching aid and making it suitable for use in various teaching environments.

[0046] The above is only a specific implementation of the utility model, but the protection scope of the utility model is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the utility model, which should be included in the protection scope of the utility model. Therefore, the protection scope of the utility model should be based on the protection scope of the claims.

[0047] There are a few points to note:

[0048] (1) The drawings of the embodiments of the present utility model only relate to the structures related to the embodiments of the present utility model, and other structures may refer to the conventional designs.

[0049] (2) For the sake of clarity, in the drawings used to describe the embodiments of the present invention, the thickness of the layers or regions is enlarged or reduced, that is, these drawings are not drawn according to the actual scale. It is understood that when an element such as a layer, film, region or substrate is referred to as being "on" or "under" another element, the element may be "directly" "on" or "under" the other element or there may be an intermediate element.

[0050] (3) In the absence of conflict, the embodiments of the present invention and the features therein may be combined with each other to obtain new embodiments.

[0051] The above are only specific implementation methods of the present utility model, but the protection scope of the present utility model is not limited thereto. The protection scope of the present utility model shall be based on the protection scope of the claims.

Claims

1. A probability model demonstration teaching aid, characterized in that: include: The invention relates to a body (11), corners (21) and an inner circle (22), wherein a square inner cavity (14) is provided in the body (11), the inner cavity (14) is marked with the inner circle (22), the diameter of the inner circle (22) is equal to the side length of the square of the bottom surface of the inner cavity (14), the inner circle (22) divides the corners (21) at the four corners of the bottom surface of the inner cavity (14), the four sides of the bottom surface of the inner cavity (14) are tangent to the inner circle (22), the center of the bottom surface of the inner cavity (14) coincides with the center of the inner circle (22), and a plurality of small balls are also included.

2. A probability model demonstration teaching aid according to claim 1, characterized in that: The side length of the bottom surface of the inner cavity (14) is at least greater than or equal to the sum of the diameters of the 10 small balls.

3. A probability model demonstration teaching aid according to claim 1, characterized in that: Two mutually perpendicular sides of the upper end surface of the main body (11) are provided with mutually perpendicular spirit levels (13).

4. A probability model demonstration teaching aid according to claim 1, characterized in that: The bottom surface of the body (11) is provided with a base (12).

5. A probability model demonstration teaching aid according to claim 4, characterized in that: The base (12) is circular.

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