Triangle congruence condition demonstrator and experiment method thereof

Abstract

The invention relates to the technical field of teaching aids, and provides a triangle congruence condition demonstrator and an experiment method thereof. According to the demonstrator, a circular protractor is fused into equidistant concentric circle spray painting, and is fixed on a substrate together with a nail plate and a graduated scale to be matched with rubber ribs with different colors for use. The experimental method comprises the following steps: firstly grouping and distributing instruments, demonstrating triangles meeting specific congruent conditions (such as SAS) by teachers, autonomously operating and exploring by students, changing conditions (such as ASA, AAS and SSS) by the teachers to enable the students to continue to operate, and then displaying and summarizing by groups. According to the demonstrator, the uniqueness of congruent triangles is utilized, when congruent triangles cannot be judged, different triangles sleeved by different students are different, and when the congruent triangles can be judged, the triangles completely coincide, and conditions are Compared with a traditional drawing method, the demonstrator and the method are more efficient and interesting, can improve the interest of students, enhance the teaching effect, cultivate the abilities of the students, such as practice and logical thinking, can be expanded for exploring the parallel condition of two straight lines, and have higher practical value.

Description

Technical Field

[0001] The present invention relates to the technical field of teaching aids, and in particular to a demonstrator for demonstrating triangle congruence conditions in junior middle school mathematics teaching and an experimental method based on the demonstrator. Background Art

[0002] The conditions for triangle congruence are a crucial topic in junior high school mathematics instruction. Traditional teaching methods rely primarily on diagramming, as found in textbooks. However, these methods have numerous drawbacks. For example, the diagramming process is cumbersome and requires advanced drawing skills; the diagrams are not intuitive enough, making it difficult for students to clearly see how triangles change under different conditions; and the relatively dull teaching process fails to spark student interest, resulting in poor teaching results and difficulty for students to understand and grasp the conditions for triangle congruence.

[0003] Therefore, it is necessary to develop a more efficient, interesting and intuitive teaching aids and experimental methods to improve students' learning effect on the conditions of triangle congruence. Summary of the Invention

[0004] The purpose of the present invention is to provide a triangle congruence condition demonstrator and an experimental method thereof, so as to solve the problems of low efficiency, poor interest and lack of intuitiveness in demonstrating triangle congruence conditions by traditional drawing methods, improve students' understanding and mastery of triangle congruence conditions, and at the same time cultivate students' hands-on operation ability, logical thinking ability and spirit of exploration.

[0005] To achieve the above objectives, the present invention provides the following technical solutions:

[0006] A conditional demonstrator for triangle congruence, comprising a circular protractor component, a concentric circle structure, a nail board module, a scale component, and rubber bands of different colors;

[0007] The circular protractor assembly is provided with a concentric circle structure spray-painted layer with equidistant scales and is fixed on a base plate; the nail board module is fixed on the base plate and has a number of nails evenly distributed thereon for fixing the rubber bars; the scale component is used in conjunction with the circular protractor assembly to measure side lengths and angles; the rubber bars of different colors are used to fit triangles that meet different triangle congruence conditions on the nail board module.

[0008] Furthermore, the radius intervals of the equidistant concentric circles in the concentric circle structure are set according to the ratio of the side lengths of common triangles. During the demonstration, the changes in the side length conditions are intuitively presented through circles of different radii, helping students understand the influence of side length on triangle congruence.

[0009] Furthermore, the rubber bars of different colors correspond to different combinations of triangle congruence conditions, and each color represents a specific relationship between side and angle conditions. The triangle shapes formed by the rubber bars of different colors intuitively display the characteristics of triangles that meet different conditions.

[0010] Furthermore, the base plate is made of environmentally friendly and sturdy wooden material, and the surface is smoothed to prevent students from being scratched during operation; the nails of the nail board module are made of stainless steel, and the nail heads are rounded to ensure safe use.

[0011] Furthermore, the scale accuracy of the circular protractor assembly is 1°, and the scale accuracy of the ruler component is 1 mm, so as to meet the accuracy requirements of junior high school mathematics teaching for triangle side length and angle measurement.

[0012] An experimental method for a conditional demonstrator of triangle congruence comprises the following steps:

[0013] Grouping and preparation: Divide students into several groups according to the number of students. Assign each group a triangle congruence condition demonstrator and give each student a rubber band of a different color.

[0014] Teacher Demonstration: Based on the teaching objectives, the teacher presents a specific triangle congruence condition, such as "side-angle-side," and demonstrates the operation on the demonstrator. Using rubber bands, the teacher forms a triangle that meets this condition on the nail board module. The teacher also explains the operation process in detail to the students, including how to determine angles using the circular protractor component and how to determine side lengths using the concentric circle structure and the scale component.

[0015] Student-led exploration: Students independently manipulate the rubber bands on the demonstrator to create triangles that meet the conditions given by the teacher. During the operation, students are encouraged to communicate and discuss with each other to jointly explore the conditions for triangle congruence. The teacher visits each group, provides timely guidance and assistance, and answers questions encountered by students during the operation.

[0016] Changing conditions to continue exploring: The teacher gradually changes the conditions for triangle congruence, such as giving the conditions of "angle-side-angle," "angle-angle-side," and "side-side-side" in sequence. Ask students to use different colored rubber bands to fit triangles on the nail board module again, observe the changes in the triangles under different conditions, and guide students to think about the impact of different conditions on triangle congruence.

[0017] Presentation and summary: Each group selects a representative to present the triangles obtained by the group and explain the conditions met as well as the findings and experiences during the operation; students from other groups can ask questions and make comments; finally, the teacher guides students to summarize the experimental process, summarize the conditions for the congruence of triangles, and emphasize the role and difference of each condition in determining the congruence of triangles.

[0018] Furthermore, during the experiment, the uniqueness of the existence of congruent triangles was used for verification: when the given conditions could not determine the congruence of the triangles, the triangles produced by different students had different shapes and sizes; when the given conditions could determine the congruence of the triangles, the triangles produced by different students could completely overlap. Through this intuitive comparison, students can deeply understand the conditions for determining the congruence of triangles.

[0019] Furthermore, during the experiment, a classification discussion session was set up to allow students to classify the different triangles that may be formed according to different combinations of given conditions, and analyze whether each type of triangle is congruent, thereby cultivating students' classification ideas and logical thinking abilities.

[0020] Furthermore, after completing the exploration of the conditions for triangle congruence, guide students to use the demonstrator to explore the conditions for two straight lines to be parallel; by changing the position and angle of the rubber band on the nail board module, observe whether the two straight lines formed by the rubber band are parallel when certain conditions are met, and let students summarize the conditions for determining whether two straight lines are parallel to achieve the expansion and application of knowledge.

[0021] The triangle congruence condition demonstrator and experimental method of the present invention have the following beneficial effects:

[0022] Improve teaching effectiveness: This demonstrator and experimental method can show the conditions for triangle congruence in a more concise, intuitive and clear way, making teaching more interesting and making it easier for students to understand and master relevant knowledge. Compared with traditional drawing methods, the teaching effect is significantly improved.

[0023] Cultivate students' abilities: Through students' hands-on operation of the demonstrator, it can promote the development of students' hands-on and thinking abilities, cultivate students' spirit of exploration and logical thinking ability, and help students form their own cognitive system and way of thinking.

[0024] Enhance learning interest: Rubber bands of different colors and interesting experimental operation processes can greatly stimulate students' interest in learning, enable students to learn mathematical knowledge in a relaxed and pleasant atmosphere, and improve their enthusiasm and initiative in learning.

[0025] Multifunctional application: This demonstrator can not only be used to demonstrate the conditions for the congruence of triangles, but can also be improved to demonstrate and explore the conditions for the parallelism of two straight lines. It has high practicality and versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 Schematic diagram of the structure of the condition demonstrator for triangle congruence in the present invention (1);

[0027] Figure 2 Schematic diagram of the structure of the conditional demonstrator of triangle congruence in the present invention (II). DETAILED DESCRIPTION

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0029] In the description of the embodiments of the present invention, "a plurality of" means at least two.

[0030] In the description of the embodiments of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0031] Example:

[0032] This embodiment provides a conditional demonstrator for triangle congruence, comprising a circular protractor assembly 1, a concentric circle structure 2, a nail board module 3, a scale component, and rubber bars 4 of different colors;

[0033] The circular protractor assembly 1 is provided with a spray-painted layer of a concentric circle structure 2 with equidistant scales, and is fixed on a base plate; the nail board module 3 is fixed on the base plate, and has a number of nails evenly distributed thereon for fixing the rubber bars 4; the scale component is used in conjunction with the circular protractor assembly 1 to achieve the measurement of side lengths and angles; the rubber bars 4 of different colors are used to fit triangles that meet different triangle congruence conditions on the nail board module 3.

[0034] Specifically,

[0035] Overall structure: The demonstrator cleverly combines a circular protractor, equidistant concentric circles, a nail board, and a ruler. The circular protractor is spray-painted with concentric circles with equidistant scales, fixed on a wooden board, and a nail board is set on the board, equipped with rubber bands of different colors.

[0036] The circular protractor is used to measure the size of the interior angles of a triangle, helping students to intuitively observe the impact of angle conditions on triangle congruence;

[0037] The design of equidistant concentric circles allows students to intuitively experience the changes in side length conditions through circles of different radii during demonstrations. Circles of different radii correspond to different side lengths. When students use rubber bands to fit a triangle on a nail board, the equidistant concentric circles can clearly demonstrate the relationship between side length and triangle shape.

[0038] The nail board provides a support point for the fixation of rubber bands. Students can put rubber bands of different colors on the nail board to form various triangles. The setting of the nail board allows students to easily adjust the shape and size of the triangle, making it easier to observe the changes in the triangle under different conditions.

[0039] The ruler is used to measure the side length of a triangle. It works in conjunction with equidistant concentric circles to more accurately determine the side length conditions and help students understand the role of side length in determining triangle congruence.

[0040] Rubber bands of different colors are used to intuitively show the shapes of triangles that meet different conditions. Different colors can represent different combinations of conditions. For example, red rubber bands represent one set of side and angle conditions, and blue rubber bands represent another set of side and angle conditions. During the operation, students can more clearly understand the conditions for triangle congruence by observing the triangles formed by rubber bands of different colors.

[0041] Experimental methods

[0042] Experimental teaching objectives

[0043] Through this experimental demonstration, the experimental results are presented in a more concise, intuitive and clear way, which increases the interest of teaching and greatly improves the teaching effect. It allows students to efficiently master the conditions for the congruence of triangles in the process of hands-on and brain-based exploration, and be able to apply them flexibly to improve students' comprehensive abilities.

[0044] Through students' hands-on operations, we promote the development of students' hands-on and thinking abilities. In the process of continuous exploration and summarization, we help students form their own cognitive system and thinking mode, and improve their logical thinking ability.

[0045] Experimental design

[0046] Taking advantage of the uniqueness of congruent triangles, the experimental process is designed to make the demonstration concise, intuitive, clear, and large-scale, which can effectively allow students to independently explore the conditions for the congruence of triangles during group activities.

[0047] Divide students into groups ahead of time, assigning each group a demonstrator and each student a piece of rubber band. The teacher first presents the conditions and demonstrates how to create a triangle that meets the conditions. Then, let students independently demonstrate and present the conditions, verifying the conditions and exploring other possible combinations.

[0048] The demonstrator is safe and reliable, organically integrating a protractor, concentric circles, a nail board and a ruler. It is both safe and environmentally friendly, and is suitable for widespread use in classroom teaching.

[0049] Experimental instrument names and supplies

[0050] Instrument name: Demonstrator for exploring the conditions for triangle congruence

[0051] Instruments and supplies: circular protractor with concentric circles of equal distance scale spray-painted, nails, wooden boards, and rubber bands of different colors.

[0052] Experimental teaching effect

[0053] The demonstration experimental teaching aid is safe and easy to operate, and the demonstration effect is concise, intuitive, clear, and has a large capacity. During the hands-on and brain-based demonstration activities, students can easily explore the conditions for the congruence of triangles, understand the classification ideas, and truly perceive and understand the knowledge.

[0054] Compared with the traditional drawing method, the use of this demonstration teaching aid can significantly enhance students' interest in learning. In the process of independent exploration and summary, students can efficiently complete teaching tasks and improve learning effects.

[0055] Specifically,

[0056] Experimental steps

[0057] Grouping and preparation: Divide students into several groups, assign each group a prepared demonstrator, and give each student a rubber band of a different color;

[0058] Teacher Demonstration: Based on the teaching content, the teacher presents a condition for triangle congruence, such as "two corresponding sides and their included angles are equal." The teacher then demonstrates the operation on a demonstrator, using rubber bands to form a triangle on a nail board that meets this condition. The teacher also explains the operation process and precautions, such as how to use a protractor to determine angles and how to determine side lengths using concentric circles and a ruler.

[0059] Student independent exploration: Students independently manipulate the rubber band on the demonstrator according to the conditions given by the teacher to form a triangle that meets the conditions. During the operation, students can communicate and discuss with each other to jointly explore the conditions for triangle congruence. The teacher will visit each group and provide timely guidance and assistance.

[0060] Changing conditions to continue exploring: The teacher changes the conditions for triangle congruence, such as changing it to "two angles and their included sides are equal", and asks students to use different colored rubber bands to fit triangles on the nail board again, and observe how the triangles change under different conditions;

[0061] Presentation and summary: Each group selects a representative to present the triangles obtained by the group and explain the conditions met. Students from other groups can ask questions and make comments. Finally, the teacher guides students to summarize the experimental process, summarize the conditions for the congruence of triangles, and emphasize the role of each condition in determining the congruence of triangles.

[0062] Discipline Characteristics and Innovation

[0063] This demonstration experiment is simple to make and cleverly integrates multiple teaching tools. During the experiment, students in small groups used different colored rubber bands to construct triangles on a nail board that met the requirements. They then varied the angles and side lengths and had the students repeat the process. Through the process of constructing and demonstrating, students naturally grasped the requirements for triangle congruence. If the given conditions didn't guarantee triangle congruence, the triangles created by different students varied in shape and size. If the given conditions did guarantee triangle congruence, the triangles created by different students would completely overlap, thus verifying the validity of the requirements.

[0064] Using rubber bands of different colors to intuitively show triangular shapes that meet different conditions is simpler, more intuitive, obvious, and more interesting than the drawing method in textbooks, which greatly improves the educational and teaching effects.

[0065] Experimental expansion

[0066] After students have mastered the conditions for triangle congruence, teachers can use the demonstrator to guide them in exploring the conditions for two lines to be parallel. For example, by changing the position and angle of the rubber band on the nail board, they can observe whether the two lines formed by the rubber band are parallel when certain conditions are met, thereby deepening students' understanding of the conditions for two lines to be parallel.

[0067] The present invention and its embodiments are described above. This description is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. In short, if a person skilled in the art is inspired by this and, without departing from the purpose of the present invention, designs structures and embodiments similar to this technical solution without inventiveness, they shall fall within the scope of protection of the present invention.

Claims

1. A conditional demonstrator for triangle congruence, characterized by: Includes circular protractor components, concentric circle structures, nail board modules, scale parts and rubber bands of different colors; The circular protractor assembly is provided with a concentric circle structure spray-painted layer with equidistant scales and is fixed on a base plate; the nail board module is fixed on the base plate and has a number of nails evenly distributed thereon for fixing the rubber bars; the scale component is used in conjunction with the circular protractor assembly to measure side lengths and angles; the rubber bars of different colors are used to fit triangles that meet different triangle congruence conditions on the nail board module.

2. The conditional demonstrator of triangle congruence according to claim 1, characterized in that: The radius intervals of the equidistant concentric circles in the concentric circle structure are set according to the ratio of the side lengths of common triangles. During the demonstration, the changes in the side length conditions are intuitively presented through circles of different radii, helping students understand the influence of side length on triangle congruence.

3. The conditional demonstrator of triangle congruence according to claim 1, characterized in that: The rubber bars of different colors correspond to different combinations of triangle congruence conditions, and each color represents a specific relationship between side and angle conditions. The triangle shapes formed by the rubber bars of different colors intuitively display the characteristics of triangles that meet different conditions.

4. The conditional demonstrator of triangle congruence according to claim 1, characterized in that: The base plate is made of environmentally friendly and sturdy wooden material, and the surface is smoothed to prevent students from being scratched during operation; the nails of the nail board module are made of stainless steel, and the nail heads are rounded to ensure safety in use.

5. The conditional demonstrator of triangle congruence according to claim 1, characterized in that: The scale accuracy of the circular protractor assembly is 1°, and the scale accuracy of the scale component is 1 mm, so as to meet the accuracy requirements of junior high school mathematics teaching for triangle side length and angle measurement.

6. An experimental method based on the conditional demonstrator of triangle congruence according to any one of claims 1 to 5, characterized in that: The following steps are involved: Grouping and preparation: Divide students into several groups according to the number of students. Assign each group a triangle congruence condition demonstrator and give each student a rubber band of a different color. Teacher Demonstration: Based on the teaching objectives, the teacher presents a specific triangle congruence condition, such as "side-angle-side," and demonstrates the operation on the demonstrator. Using adhesive tape, the teacher forms a triangle that meets this condition on the nail board module. The teacher also explains the operation process in detail to the students, including how to determine angles using the circular protractor component and how to determine side lengths using the concentric circle structure and the scale component. Student independent exploration: Students independently operate the rubber band on the demonstrator according to the conditions given by the teacher to form a triangle that meets the conditions; During the operation, students are encouraged to communicate and discuss with each other to jointly explore the conditions for triangle congruence; teachers visit each group, provide timely guidance and help, and answer questions students encounter during the operation; Changing conditions to continue exploring: The teacher gradually changes the conditions for triangle congruence, such as giving the "angle-side-angle," "angle-angle-side," and "side-side-side" conditions in sequence. Have students again use different colored rubber bands to fit triangles onto the nail board module, observing how the triangles change under different conditions. The teacher also guides students to think about the impact of different conditions on triangle congruence. Presentation and summary: Each group selects a representative to present the triangles obtained by the group and explain the conditions met as well as the findings and experiences during the operation; students from other groups can ask questions and make comments; finally, the teacher guides students to summarize the experimental process, summarize the conditions for the congruence of triangles, and emphasize the role and difference of each condition in determining the congruence of triangles.

7. The experimental method according to claim 6, characterized in that: During the experiment, the uniqueness of the existence of congruent triangles was used for verification: when the given conditions could not determine the congruence of the triangles, the triangles produced by different students had different shapes and sizes; when the given conditions could determine the congruence of the triangles, the triangles produced by different students could completely overlap. Through this intuitive comparison, students can deeply understand the conditions for determining the congruence of triangles.

8. The experimental method according to claim 6, characterized in that: During the experiment, a classification discussion session is set up to allow students to classify the different triangles that may be formed according to different combinations of given conditions, and analyze whether each type of triangle is congruent, so as to cultivate students' classification ideas and logical thinking ability.

9. The experimental method according to claim 6, characterized in that: After completing the exploration of the conditions for triangle congruence, guide students to use the demonstrator to explore the conditions for two straight lines to be parallel; by changing the position and angle of the rubber band on the nail board module, observe whether the two straight lines formed by the rubber band are parallel when certain conditions are met, and let students summarize the conditions for determining whether two straight lines are parallel to achieve the expansion and application of knowledge.

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