Multifunctional geometry teaching demonstrator

Abstract

A multifunctional geometry teaching demonstrator comprises a main body frame, an upper supporting plate, a lower supporting plate, a switch pulling plate, a leakage pipe and a demonstration supporting box which are made of organic glass are arranged on the upper face and the lower face of the main body frame respectively, and small steel balls and horizontal supporting legs of the demonstration supporting box are movably arranged in the demonstration supporting box. Small steel balls in the upper supporting plate demonstration supporting box can fall into the lower supporting plate demonstration supporting box. The demonstration supporting box is divided into teaching demonstration suites of a circle area calculation formula and a cylinder, cone and sphere volume calculation formula, and the teaching demonstration suites can be replaced according to needs of teaching demonstration. The teaching aid is simple in structure, is a teaching aid as well as a learning aid, is visual in demonstration effect from intuition to abstraction and from old knowledge to new knowledge, and guides students to summarize and conclude circle area, cylinder volume, cone volume and sphere volume calculation formulas on the basis of demonstration and practical operation of teachers and students. The teaching aid accords with the cognitive law, improves the teaching efficiency, and is multifunctional, innovative and creative.

Description

Technical Field

[0001] The utility model relates to the field of general teaching aids, in particular to a multifunctional geometry teaching demonstrator. Background Art

[0002] Various versions of textbooks in my country all arrange the calculation of the area of ​​a circle in the fourth and fifth grades of primary school. It is very difficult for primary school students to learn to enclose a circle with curves for the first time, and the calculation of the area of ​​a circle is a difficult and key point in primary school teaching.

[0003] The "volume calculation of cylinders, cones and spheres" throughout primary, middle and high school is even more difficult. In addition to being confused by the school's ranking, teachers have no choice but to use the "one piece of chalk, one blackboard, one textbook, one mouth" teaching mode, forcing students to memorize calculation formulas and complete teaching tasks by force, entering a vicious circle of high scores and low abilities. It seriously neglects to let students personally participate in the process of nurturing and producing the calculation formulas of pi, circle area, cylinder volume, cone volume and sphere volume; it seriously violates the cognitive law of "to know the reason, you must know the reason".

[0004] How to solve this teaching difficulty that has long plagued teachers, students and teaching and research workers has become a major issue. Utility Model Content

[0005] The purpose of this utility model is to overcome the shortcomings of the existing technology and provide a reasonable design, simple structure, easy operation, which is both a teaching aid and a learning aid. From intuitive to abstract, from old knowledge to new knowledge, students can personally participate in the gestation and production process of the calculation formulas of pi, circle area, cylinder volume, cone volume and sphere volume; on the basis of the demonstration and practice of teachers and students, guide students to summarize the calculation formulas of circle area, cylinder volume, cone volume and sphere volume. It optimizes the students' learning process and improves the teaching efficiency of teachers. It is a multifunctional geometry teaching demonstration teaching aid and learning aid that conforms to the students' cognitive laws.

[0006] The device comprises a main frame, which is a rectangular parallelepiped frame; an upper support plate and a lower support plate made of organic glass are respectively arranged on the upper and lower surfaces of the main frame, thereby achieving the effect of facilitating observation and replacement of the kit.

[0007] Demonstration boxes made of plexiglass are correspondingly arranged on the upper and lower pallets. The demonstration boxes correspond to one group up and down, and three groups are arranged at intervals. A middle leakage hole is arranged in the middle position of the bottom surface of the upper pallet demonstration box, and the bottom surface of the upper pallet demonstration box is a micro-slope surface slightly inclined toward the middle leakage hole. Upper pallet leakage holes are arranged on the upper pallet corresponding to the leakage holes on the bottom surface of the upper pallet demonstration box.

[0008] A small steel ball is movably arranged in the upper support plate demonstration support box.

[0009] The lower surface of the upper pallet is provided with a pallet slot, a pull-out pallet is movably provided in the pallet slot, the upper surface of the pull-out pallet is fitted with the lower surface of the upper pallet, and a pull-out pallet leak hole is provided at a position corresponding to the upper pallet leak hole, so as to form a pull-out switch pull plate. The effect achieved by this is that by pulling the pull-out pallet, the upper pallet leak hole is made to correspond to the pull-out pallet leak hole, so that the small steel ball in the upper pallet demonstration tray box can be dropped into the lower pallet demonstration tray box.

[0010] Furthermore, downwardly extending leakage pipes are respectively arranged at the outlets of the leakage holes of the pull-out tray, and the outlets at the ends of the leakage pipes are slightly higher than the horizontal plane of the upper opening of the demonstration tray box of the lower tray, so as to prevent the small steel balls from splashing when they fall into the demonstration tray box of the lower tray.

[0011] The top surface of the lower support plate demonstration support box is open, and its setting position corresponds one-to-one with the upper support plate demonstration support box.

[0012] Furthermore, the upper pallet demonstration tray and the lower pallet demonstration tray are two sets, which are divided into a teaching demonstration kit for the circle area calculation formula and a teaching demonstration kit for the cylinder, cone, and sphere volume calculation formula, which are movably placed on the upper pallet and the lower pallet respectively and replaced according to the needs of the teaching demonstration.

[0013] The depth of the demonstration trays of the teaching demonstration kit for calculating the circle area formula is consistent and slightly larger than the diameter of the small steel balls, so as to ensure that the small steel balls in the demonstration trays can only be laid out in one layer on the bottom of the box. The upper tray demonstration tray is a rectangular tray, and the lower tray demonstration tray is a circular tray. The internal widths of the three rectangular trays are respectively equal to the internal radius lengths of the corresponding circular tray bottom surfaces, and the internal lengths of the three rectangular trays are respectively equal to half of the internal circumferences of the corresponding circular trays.

[0014] The upper support plate demonstration tray of the teaching demonstration kit for the volume calculation formula of the cylinder, cone and sphere is composed of three rectangular trays with equal length, width and height. The lower support plate demonstration trays are respectively a cylindrical tray, a conical tray and a hemispherical tray, and horizontal support legs are respectively provided under the conical tray and the hemispherical tray. The inner length and width of the bottom surface of the rectangular tray are equal to the inner radius of the maximum circular cross-section of the cylindrical tray, the conical tray and the hemispherical tray, as well as the inner height of the cylindrical tray, the conical tray and the hemispherical tray. The inner height of the rectangular tray is equal to half of the inner circumference of the maximum circular cross-section of the cylindrical tray, the conical tray and the hemispherical tray.

[0015] The bottom of the lower support plate demonstration tray of the teaching demonstration kit for calculating the circle area formula is provided with horizontal supporting legs so that its upper horizontal plane is consistent with the upper horizontal plane of the lower support plate demonstration tray of the teaching demonstration kit for calculating the volume formula of the cylinder, cone and sphere.

[0016] The beneficial effects of the utility model are: the utility model has a simple structure, a low cost, and an intuitive demonstration effect, and can be used for the derivation teaching demonstration of the circle area calculation formula, and can also be used for the derivation teaching demonstration of the cylinder, cone, and sphere volume calculation formula.

[0017] During the students' hands-on practice, they can personally experience the conception and generation of calculation formulas for the area of ​​a circle, the volume of a cylinder, a cone and a sphere; following the cognitive law of "if you want to know something, you must know why it is so" can improve students' learning enthusiasm, learning efficiency and academic performance.

[0018] It is a multifunctional teaching and learning tool that can string together, link together, and weave together knowledge related to the three stages of primary, middle, and high school. What's more amazing is that it can allow primary school students around ten years old to easily understand and master the calculation formulas for the area of ​​a circle, the volume of a cylinder, and the volume of a cone. It even includes the calculation formula for the volume of a sphere in high school, which is enough to reflect the unique innovation and creativity of this demonstrator. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a structural schematic diagram of a multifunctional geometry demonstration teaching aid embodiment 1 of the utility model;

[0020] Figure 2 It is a structural schematic diagram of a second embodiment of a multifunctional geometry demonstration teaching aid described in the utility model;

[0021] 1-Pull-out tray 2-Main frame 3-Upper tray demonstration tray 4-Lower tray demonstration tray 5-Leakage pipe 6-Horizontal support leg

[0022] The realization of the purpose, functional features and advantages of the utility model will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0023] Please refer to the attached Figure 1 , Attachment Figure 2 The following is described in conjunction with the embodiments:

[0024] A multifunctional geometric demonstration teaching aid, comprising a main frame 2, wherein the main frame 2 is a rectangular parallelepiped frame; an upper support plate and a lower support plate made of organic glass are respectively arranged on the upper and lower surfaces of the main frame 2, thereby achieving the effect of facilitating observation and replacement of the kit;

[0025] Demonstration trays made of plexiglass are correspondingly arranged on the upper and lower trays. The demonstration trays correspond to one group up and down, and three groups are arranged at intervals. A middle leakage hole is arranged in the middle position of the bottom surface of the upper tray demonstration tray 3, and the bottom surface of the upper tray demonstration tray 3 is a micro-slope surface slightly inclined toward the middle leakage hole. Upper tray leakage holes are arranged on the upper tray corresponding to the leakage holes on the bottom surface of the upper tray demonstration tray 3.

[0026] A small steel ball is movably arranged in the upper support plate demonstration support box 3.

[0027] The lower surface of the upper pallet is provided with a pallet slot, and a pull-out pallet 1 is movably provided in the pallet slot. The upper surface of the pull-out pallet 1 is fitted with the lower surface of the upper pallet, and a pull-out pallet leak hole is provided at a position corresponding to the upper pallet leak hole to form a pull-out switch pull plate. The effect achieved by this is that by pulling the pull-out pallet 1, the upper pallet leak hole is made to correspond to the switch pull plate leak hole, and the small steel ball in the upper pallet demonstration tray box 3 can be realized to fall into the lower pallet demonstration tray box 4.

[0028] Furthermore, downwardly extending leakage pipes 5 are respectively arranged at the outlets of the leakage holes of the pull-out support plate, and the outlets at the ends of the leakage pipes 5 are slightly higher than the upper horizontal plane of the lower support plate demonstration support box 4 to prevent the small steel balls from splashing when they fall into the lower support plate demonstration support box 4.

[0029] The top surface of the lower support plate demonstration tray box 4 is open, and its setting position corresponds to the upper support plate demonstration tray box 3 one by one.

[0030] Furthermore, the upper pallet demonstration tray 3 and the lower pallet demonstration tray 4 are two sets, which are divided into a teaching demonstration kit for circle area calculation and a teaching demonstration kit for cylinder, cone and sphere volume calculation formulas, which are movably placed on the upper pallet and the lower pallet respectively and replaced according to the needs of teaching demonstration.

[0031] The depth of the demonstration tray of the teaching demonstration kit of the circle area calculation formula is equal and slightly larger than the diameter of the small steel balls, so as to ensure that the small steel balls in the demonstration tray can only be laid out in one layer on the bottom of the box. The upper tray demonstration tray 3 is a rectangular tray, and the lower tray demonstration tray 4 is a circular tray. The internal widths of the three rectangular trays are respectively equal to the internal radius lengths of the corresponding circular tray bottom surfaces, and the internal lengths of the three rectangular trays are respectively equal to half of the internal circumferences of the corresponding circular trays.

[0032] The upper support plate demonstration support box 3 of the teaching demonstration kit for the volume calculation formula of the cylinder, cone and sphere is threeThe lower support plate demonstration support boxes 4 are cylindrical support boxes, conical support boxes and hemispherical support boxes respectively. The length and width of the bottom surface of the rectangular support box are equal to the inner radius of the largest circular cross section of the cylindrical support box, conical support box and hemispherical support box, as well as the inner height of the cylindrical support box, conical support box and hemispherical support box. The height of the rectangular support box is equal to half of the inner circumference of the largest circular cross section of the cylindrical support box, conical support box and hemispherical support box.

[0033] The bottom of the lower support plate demonstration tray 4 of the teaching demonstration kit for calculating the circle area formula is provided with horizontal support legs 6, so that the upper horizontal plane of the lower support plate demonstration tray 4 of the teaching demonstration kit for calculating the volume formula of the cylinder, cone, and sphere is consistent with the upper horizontal plane of the lower support plate demonstration tray 4. The cone tray and the hemispherical tray are also provided with horizontal support legs 6 to ensure their uprightness.

[0034] Example 1: Teaching demonstration and derivation of the formula for calculating the area of ​​a circle;

[0035] The rectangular tray and the circular tray are both shallow trays with a depth of 0.5 cm. The ends of the three drain pipes 5 are 1 cm away from the upper horizontal plane of the cylinder, cone and hemisphere;

[0036] There are three rectangular trays, whose internal widths from left to right are 2 cm, 3 cm, and 4 cm, and whose internal lengths are 6.28 cm, 9.42 cm, and 12.56 cm, respectively; and the internal radii of the circular trays from left to right are 2 cm, 3 cm, and 4 cm, respectively;

[0037] Specific implementation steps:

[0038] Step 1: Have students pour steel balls with a diameter of 0.4 cm into three rectangular trays, filling them up and placing only one layer.

[0039] Step 2: Have students use their existing knowledge to list the formulas for the areas of three rectangles filled with a layer of steel balls:

[0040] S 长左 =2×6.28; S 长中 =3×9.42; S 长右 =4×12.56.

[0041] Step 3: Have students pull the switch plate by hand, and let the steel balls in the three rectangular trays leak through three leaking tubes into the three corresponding circular trays below. Let students see with their own eyes: the steel balls just fill up the circular trays, that is, they are flat on the bottom of the circular trays;

[0042] Step 4: Have students say: The areas of the three rectangles above are equal to the areas of the three circles below, and write three equations:

[0043] S 长左 =S 圆左 ; S 长中 =S 圆中 ; S 长右 =S 圆 right;

[0044] Step 5: Have students calculate the inner circumferences of the three circular trays:

[0045] C 圆左 =2×πr=2×3.14×2=12.56

[0046] C 圆中 =2×πr=2×3.14×3=18.84

[0047] C 圆右 =2×πr=2×3.14×4=25.12

[0048] Step 6:

[0049] ——Teacher’s guidance prompt: The length of the rectangle is 6.28, which is exactly ½ of the circumference of the circle 12.56, that is, ½×2πr;

[0050] Have students write out the equation:

[0051] S 长左 =S 圆左 =2×6.28=2×½×12.56

[0052] = r × ½ circumference of a circle

[0053] =r×½×2πr

[0054] =rπr

[0055] =πr²

[0056] ——Teacher’s guidance prompt: The length of the rectangle is 9.42, which is exactly ½ of the circumference of the circle 18.84, that is, ½×2πr;

[0057] S 长中 =S 圆中 =3×9.42=3×½×18.84

[0058] = r × ½ circumference of a circle

[0059] =r×½×2πr

[0060] =rπr

[0061] =πr²

[0062] ——Teacher’s guidance prompt: The length of the rectangle, 12.56, is exactly ½ of the circumference of the circle, 25.12, that is, ½×2πr;

[0063] S 长右 =S 圆右 =4×12.56=4×½×25.12

[0064] = r × ½ circumference of a circle

[0065] =r×½×2πr

[0066] =rπr

[0067] =πr²

[0068] Step 7: Teachers and students jointly summarize the formula for the area of ​​a circle: S=πr²

[0069] With this kind of teaching, primary school students can not only understand the formula for calculating the area of ​​a circle thoroughly, remember it firmly, and use it flexibly. If students can memorize the "values ​​of 1π - 10π", they can calculate the area of ​​a circle mentally, which will improve their calculation speed and accuracy, thereby achieving outstanding results that exceed the requirements of the "Primary School Curriculum Outline".

[0070] Example 2: Teaching demonstration and derivation of volume calculation formulas for cylinders, cones, and spheres

[0071] The upper support plate demonstration tray 3 is a rectangular tray, and three rectangular trays are provided;

[0072] The lower support plate demonstration tray 4 is provided with three corresponding ones, namely a cylindrical tray, a conical tray and a hemispherical tray; the ends of the three leakage pipes 5 are 1 cm away from the upper horizontal plane of the cylindrical cone and the hemispherical;

[0073] The length and width of the bottom surface of the rectangular support box, the inner radius of the largest circular cross section of the cylindrical support box, the conical support box and the hemispherical support box, and the inner height of the cylindrical support box, the conical support box and the hemispherical support box are all 5 cm. The inner height of the rectangular support box is 15.7 cm, which is equal to half of the inner circumference of the largest circular cross section of the cylindrical support box, the conical support box and the hemispherical support box, that is: ½×2πr.

[0074] The conical support box and the rectangular support box on the upper part of the hemispherical tray are also provided with marking lines divided into three equal parts.

[0075] Specific implementation steps:

[0076] The teacher should make preparations in advance to replace the three rectangular, cylinder, cone and hemisphere demonstration trays of the demonstrator.

[0077] Step 1: Have students pour the steel balls into three rectangular trays according to the trisection lines of the rectangular trays. Fill the left one fully, the middle one ⅓ full, and the right one 2 / 3 full.

[0078] Step 2: Have students use their existing knowledge to list the volume formulas of the steel balls in the three rectangular boxes:

[0079] V 长左 =15.7×5×5;

[0080] V 长中 =⅓×15.7×5×5;

[0081] V 长右 =2 / 3×15.7×5×5;

[0082] Step 3: Have students pull the switch plate to drain the steel balls in the three rectangular boxes through three leaking pipes 5 into the three corresponding cylindrical, cone and hemispherical boxes with a radius of 5 cm and a height of 5 cm. Let students see with their own eyes that the steel balls in the three rectangular boxes just fill up the cylindrical, cone and hemispherical boxes respectively;

[0083] Step 4: Have students say: The volumes of the entire cuboid on the left, ⅓ of the cuboid in the middle, and 2 / 3 of the cuboid on the right are equal to the volumes of the cylinder, cone, and hemisphere below, respectively, and write three equations:

[0084] V 长左 =V 柱 ; V 长中 =V 锥 ; V 长右 =V 半球 ;

[0085] Step 5: Have students calculate the inner circumference of the largest circular section of the cylinder, cone, and hemispherical support box by hand:

[0086] C 柱 =C 锥 =C 球 =2×πr=2×3.14×5=31.4

[0087] Step 6: The teacher provides further guidance and prompts:

[0088] ——The height of the cuboid, 15.7, is exactly ½ of the inner circumference of the largest circular cross-section of the cylinder, cone, and hemisphere, 31.4, that is, ½×2πr; let the students write the following formula by hand:

[0089] V 长左 =V 柱 =15.7×5×5=½×31.4×r×h

[0090] = ½ × circumference of the base × r × h

[0091] =½×2πr×r×h

[0092] =πr²h

[0093] =sh

[0094] V 长中 =V 锥 =⅓×15.7×5×5=½×31.4×r×h

[0095] =⅓×½×circumference of the base circle×r×h

[0096] =⅓×½×2πr×r×h

[0097] =⅓×πr²h

[0098] =⅓×sh

[0099] V 长右 =V 半球 =2 / 3×15.7×5×5=2 / 3×½×31.4×r×h

[0100] =2 / 3×½×circumference of base circle×r×h

[0101] =2 / 3×½×2πr×r×h

[0102] =2 / 3×πr²h

[0103] =2 / 3×πr³

[0104] V 球 =V 半球 ×2

[0105] =2 / 3×πr³×2

[0106] =4 / 3×πr³

[0107] Step 7: Teachers and students jointly summarize:

[0108] V 柱 =πr²h=sh

[0109] V 锥 =⅓×πr²h=⅓×sh

[0110] V 球 =4 / 3×πr³

[0111] If teachers take advantage of the situation, they can complete the derivation and teaching of the high school level formula for calculating the volume of a sphere in the primary school stage, and achieve extraordinary results that exceed the requirements of the "Primary School Mathematics Teaching Outline"; allowing primary school students to get ahead and win at the starting line.

[0112] The above shows and describes the basic principle, main features and advantages of the utility model. For those skilled in the art, it is obvious that the utility model is not limited to the details of the above exemplary embodiments, and can be implemented in other specific forms without departing from the spirit or basic features of the utility model. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the utility model is limited by the attached claims rather than the above description, and it is intended to include all changes within the meaning and scope of the equivalent elements of the claims. Any figure mark in the claims should not be regarded as limiting the claims.

[0113] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A multifunctional geometry teaching demonstrator, comprising a main frame, wherein the main frame is a rectangular parallelepiped frame, characterized in that: An upper support plate and a lower support plate made of organic glass are respectively arranged on the upper and lower surfaces of the main frame, and demonstration boxes made of organic glass are correspondingly arranged on the upper and lower support plates, and the demonstration boxes correspond to one group up and down, and three groups are arranged at intervals, and a middle leakage hole is arranged in the middle position of the bottom surface of the upper support plate demonstration support box, and the bottom surface of the upper support plate demonstration support box is a micro-slope surface slightly inclined toward the middle leakage hole, and an upper support plate leakage hole is arranged on the upper support plate corresponding to the leakage hole on the bottom surface of the upper support plate demonstration support box; A small steel ball is movably arranged in the upper support plate demonstration support box; The lower surface of the upper support plate is provided with a support plate slot, a pull-out support plate is movably provided in the support plate slot, the upper surface of the pull-out support plate is in contact with the lower surface of the upper support plate, and a pull-out support plate leakage hole is provided at a position corresponding to the upper support plate leakage hole, so as to form a pull-out switch pull plate; The top surface of the lower support plate demonstration support box is open, and its setting position corresponds one-to-one with the upper support plate demonstration support box.

2. A multifunctional geometry teaching demonstrator according to claim 1, characterized in that: Leakage pipes extending downward are respectively arranged at the outlets of the leakage holes of the pull-out support plate, and the outlets at the ends of the leakage pipes are slightly higher than the upper horizontal plane of the demonstration box of the lower support plate, so as to prevent the small steel balls from splashing when they fall into the demonstration box of the lower support plate.

3. A multifunctional geometry teaching demonstrator according to claim 1, characterized in that: The upper pallet demonstration tray and the lower pallet demonstration tray are two sets, which are divided into a teaching demonstration kit for the circle area calculation formula and a teaching demonstration kit for the cylinder, cone and sphere volume calculation formula. They are movably placed on the upper pallet and the lower pallet respectively and can be replaced according to the needs of the teaching demonstration.

4. A multifunctional geometry teaching demonstrator according to claim 3, characterized in that: The depth of the demonstration tray of the teaching demonstration kit of the circle area calculation formula is consistent and slightly larger than the diameter of the small steel balls to ensure that the small steel balls in the demonstration tray can only be laid out in one layer on the bottom of the box; the upper tray demonstration tray is a rectangular tray, and the lower tray demonstration tray is a circular tray. The internal widths of the three rectangular trays are respectively equal to the internal radius lengths of the three corresponding circular tray bottom surfaces, and the internal lengths of the three rectangular trays are respectively equal to half of the internal circumferences of the three corresponding circular trays.

5. A multifunctional geometry teaching demonstrator according to claim 4, characterized in that: The bottom of the lower support plate demonstration support box of the teaching demonstration kit for the circle area calculation formula is provided with horizontal supporting legs.

6. A multifunctional geometry teaching demonstrator according to claim 3, characterized in that: The upper pallet demonstration boxes of the teaching demonstration kit for the volume calculation formulas of the cylinder, cone and sphere are three rectangular boxes with equal length, width and height; the lower pallet demonstration boxes are respectively a cylindrical box, a conical box and a hemispherical box, and the internal length and width of the bottom surface of the rectangular box are equal to the internal radius of the maximum circular cross-section of the cylindrical box, the conical box and the hemispherical box, as well as the internal height of the cylindrical box, the conical box and the hemispherical box; the internal height of the rectangular box is equal to half of the internal circumference of the maximum circular cross-section of the cylindrical box, the conical box and the hemispherical box.

7. A multifunctional geometry teaching demonstrator according to claim 6, characterized in that: Horizontal supporting legs are respectively arranged under the conical supporting box and the hemispherical supporting box.

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