CN112071169A

CN112071169A - Calculus presentation device

Info

Publication number: CN112071169A
Application number: CN202011017225.XA
Authority: CN
Inventors: 张海英
Original assignee: Shandong Vocational College of Industry
Current assignee: Shandong Vocational College of Industry
Priority date: 2020-09-24
Filing date: 2020-09-24
Publication date: 2020-12-11
Anticipated expiration: 2040-09-24
Also published as: CN112071169B

Abstract

The invention relates to a calculus demonstration device, comprising: a support; filling a ball; the upper demonstration component is used for loading the filling balls and is arranged at the upper part of the bracket in a vertically sliding manner; the lower demonstration component is used for loading the filling balls and is arranged at the lower part of the bracket in a vertically sliding manner; the middle demonstration component is used for loading the filling balls and is rotatably arranged in the middle of the bracket; the middle demonstration component comprises: the middle substrate is rotatably connected with the bracket; the limiting columns are arranged at four corners of the middle substrate; the middle transparent plate is arranged at the front end of the middle substrate in a clearance mode, and four corners of the middle transparent plate are sleeved on the limiting columns; the edge strips are arranged on the four sides of the middle substrate in a telescopic mode; the sliding columns are arranged on the middle substrate in a telescopic mode and are uniformly arranged in the area defined by the edge strips; and the spring is sleeved on the limiting column and is positioned between the middle base plate and the middle transparent plate. The method can vividly demonstrate the fixed integral value of the verification function curve.

Description

Calculus presentation device

Technical Field

The invention relates to the technical field of teaching aids, in particular to a calculus demonstration device.

Background

The mathematics teaching contents are difficult to understand and learn by a part of students, and the important reason is the abstraction of mathematics; the mathematical model visualizes and visualizes mathematical knowledge, and not only can play a role in cultivating interest for good students but also students with certain difficulty in learning, so that the students can realize the close relation between mathematics and nature, can realize the application value and the application consciousness of the mathematics, cultivate the creativity and the application capacity of the students, release the students from the problem sea of solving problems in a pure theory, and enable the students to learn lively and lively, so that the mathematics quality education jumps to a new height.

The micro-integration is widely applied in the fields of science, economy and engineering to solve the problems which cannot be effectively solved only by means of algebra. The micro-integration is established on the basis of algebra, trigonometry and analytic geometry.

Where the definite integral is one of the integrals, and is the limit of the integral sum of the function f (x) over the interval [ a, b ]. The constant integral of the function f (x) over the interval [ a, b ] is a numerical value. The fixed integral of the function f (x) over the interval [ a, b ] can also be regarded as the area of the region enclosed by the function curve y ═ f (x), x ═ a, x ═ b, and y ═ 0.

Disclosure of Invention

In order to solve the technical problems in the background art, the invention provides a calculus demonstration device which can vividly and vividly demonstrate a fixed integral value of a verification function curve.

The technical scheme adopted by the invention for solving the technical problems is as follows:

a calculus presentation device comprising:

a support;

filling a ball;

the upper demonstration component is used for loading the filling balls and is arranged at the upper part of the bracket in a vertically sliding manner;

the lower demonstration component is used for loading the filling balls and is arranged at the lower part of the bracket in a vertically sliding manner;

the middle demonstration component is used for loading the filling balls and is rotatably arranged in the middle of the bracket;

the middle demonstration component comprises:

the middle substrate is rotatably connected with the bracket;

the limiting columns are arranged at four corners of the middle substrate;

the gap between the middle transparent plate and the middle base plate is equal to the diameter of the filling ball;

the edge strips are arranged on the four sides of the middle substrate in a telescopic mode;

the sliding columns are arranged on the middle substrate in a telescopic mode and are uniformly arranged in the area defined by the edge strips, and gaps among the sliding columns are smaller than the diameter of the filling balls;

and the spring is sleeved on the limiting column and is positioned between the middle base plate and the middle transparent plate.

Further, the upper presentation component includes:

the upper base plate is arranged on the upper part of the bracket in a vertically sliding manner, and is provided with a groove for accommodating the filling ball;

the upper transparent plate is arranged at the front end of the upper substrate, and the gap between the upper transparent plate and the upper substrate is equal to the diameter of the filling ball;

the flashboard is arranged at the lower end of the upper base plate in a telescopic way;

further, the lower demonstration component comprises:

the lower base plate is arranged at the lower part of the bracket in a vertically sliding manner, and a fixed clamping jaw is arranged on the lower base plate;

the transparent box is detachably connected with the lower substrate.

Furthermore, the upper base plate is provided with a guide strip penetrating through the support, a rotatable positioning rotating shaft is arranged in the guide strip, and two positioning grooves used for being connected with the support in a clamping mode are formed in the positioning rotating shaft.

Furthermore, a first connecting rod and a second connecting rod are sequentially hinged between the bottom of the lower base plate and the bottom of the support, positioning blocks which are magnetically attracted are arranged on the first connecting rod and the second connecting rod, and when the first connecting rod and the second connecting rod rotate to collinear positions, the positioning blocks are attracted.

Furthermore, middle guide wheels are arranged at four corners of the middle substrate, an annular guide groove is formed in the support, and the middle guide wheels are arranged in the guide groove in a rolling mode.

Furthermore, four corners of the upper substrate are provided with upper guide wheels, the support is provided with guide grooves in the vertical direction, and the upper guide wheels are arranged in the guide grooves in a rolling manner.

Furthermore, lower guide wheels are arranged at four corners of the lower base plate, guide grooves in the vertical direction are formed in the support, and the lower guide wheels are arranged in the guide grooves in a rolling mode.

A calculus demonstration method comprises the following steps:

a. a filling ball is placed in the upper demonstration component;

b. a plurality of sliding columns of the middle demonstration component extend out to form a function curve;

c. the middle demonstration component is turned for 180 degrees;

d. filling balls in the upper demonstration assembly enter the middle demonstration assembly until the area enclosed by the function curve formed by the extending sliding columns and the edge strips is filled;

e. the middle demonstration component is turned for 180 degrees;

f. the filler ball in the middle demonstration assembly enters the lower demonstration assembly.

The invention has the beneficial effects that:

(1) the fixed integral value of the verification function curve in a fixed interval range can be demonstrated, and the operation is convenient.

(2) Can be fitted into various function curves through a sliding column with coordinate positioning, and has wider application range.

(3) The fixed integral value of the function curve is represented by the number of the filled balls, so that the ball filling machine is more visual and vivid.

Drawings

The invention is further illustrated with reference to the following figures and examples.

FIG. 1 is a schematic structural view of the present invention;

FIG. 2 is a schematic structural view in another aspect of the present invention;

FIG. 3 is a schematic structural diagram of a middle demonstration assembly of the present invention;

FIG. 4 is a schematic structural diagram of an upper demonstration assembly of the present invention;

FIG. 5 is a schematic structural view of a lower demonstration assembly of the present invention;

FIG. 6 is a partial cross-sectional view of a middle demonstration assembly of the present invention;

fig. 7 is a partial enlarged view at a position a of fig. 2;

fig. 8 is a partial enlarged view at a position B of fig. 2;

fig. 9 is a flow chart of the use of the present invention.

In the figure:

1. the demonstration device comprises an upper demonstration component, a support 2, a middle demonstration component 3, a lower demonstration component 4, a first connecting rod 5, a second connecting rod 6, a positioning block 7, and a filling ball 8

101. An upper base plate, 102 an upper transparent plate, 103 a flashboard, 104 an upper guide wheel, 105 a guide bar, 106 a positioning rotating shaft

301. Middle transparent plate, 302, side bar, 303, sliding column, 304, middle base plate, 305, middle guide wheel, 306, spring, 307, limit column

401. The lower base plate, 402, the transparent box, 403, the fixed clamping jaw, 404, the lower guide wheel.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings.

As shown in fig. 1-2, a calculus presentation device includes: a bracket 2 and an upper demonstration assembly 1, a lower demonstration assembly 4 and a middle demonstration assembly 3 which are arranged on the bracket 2 and used for loading a filling ball 8. Specifically, the upper demonstration assembly 1 is arranged at the upper part of the bracket 2 and can slide up and down along the bracket 2; the lower demonstration component 4 is arranged at the lower part of the bracket 2 and can slide up and down along the bracket 2; the middle demonstration assembly 3 is arranged in the middle of the bracket 2 and can rotate in the vertical direction. And, the horizontal widths of the upper demo assembly 1, the lower demo assembly 4 and the middle demo assembly 3 are equal.

As shown in fig. 3 and 6, the middle demonstration component 3 comprises: the middle base plate 304 is square, the middle guide wheels 305 are arranged at four corners of the middle base plate 304, the middle part of the bracket 2 is provided with an annular guide groove, and the middle guide wheels 305 are arranged in the guide groove in a rolling manner. The spacers 307 are disposed at four corners of the middle substrate 304.

The middle transparent plate 301 is disposed at the front end of the middle substrate 304 with a gap, the middle transparent plate 301 and the middle substrate 304 have the same size, four corners of the middle transparent plate 301 are sleeved on the limiting columns 307, and the gap between the middle transparent plate 301 and the middle substrate 304 is equal to the diameter of the filling balls 8.

The edge strips 302 are telescopically arranged on four sides of the middle base plate 304, when the edge strips 302 extend out, the front end faces of the edge strips can be abutted against the rear end face of the middle transparent plate 301, and when the edge strips 302 are retracted, the front end faces of the edge strips can be flush with the front end face of the middle base plate 304. In order to limit the extension range of the edge strip 302, two ends of the edge strip 302 are also provided with limit bosses. For ease of operation, the back of the edge bar 302 is provided with a handle.

The sliding columns 303 are telescopically arranged on the middle substrate 304, the sliding columns 303 are uniformly arranged in the area defined by the edge strips 302, when the sliding columns 303 extend out, the front end faces of the sliding columns can be abutted against the rear end face of the middle transparent plate 301, and when the sliding columns 303 retract, the front end faces of the sliding columns can be flush with the front end face of the middle substrate 304. In order to limit the telescopic range of the sliding column 303, limiting bosses are further arranged at two ends of the sliding column 303. To prevent the packing balls 8 from slipping between the spools 303, the gap between the spools 303 is smaller than the diameter of the packing balls 8. The middle base plate 304 is plotted with a coordinate system, and each slide column 303 is plotted with its coordinate parameters in the coordinate system.

The spring 306 is sleeved on the position-limiting column 307, and the spring 306 is located between the middle substrate 304 and the middle transparent plate 301. The middle base plate 304 and the middle transparent plate 301 are further provided with grooves for accommodating the compressed springs 306, so that the middle base plate 304 and the middle transparent plate 301 can be tightly attached. Thereby pressing the front end faces of the strake 302 and the slide 303 flush with the front end face of the middle base plate 304.

As shown in fig. 4, the upper demonstration assembly 1 includes: an upper base plate 101, upper guide wheels 104 are installed at four corners of the upper base plate 101, a guide groove in the vertical direction is opened at the upper part of the bracket 2, and the upper guide wheels 104 are arranged in the guide groove in a rolling manner. Moreover, the front end of the upper substrate 101 is provided with a groove for accommodating the filling ball 8; the upper transparent plate 102 is disposed at the front end of the upper substrate 101, and the gap between the upper transparent plate 102 and the upper substrate 101 is equal to the diameter of the filler ball 8. And, the lower extreme of upper base plate 101 is provided with the shutter 103 that can stretch out and draw back, and when shutter 103 withdrawed, the packing ball 8 in the upper demonstration assembly 1 can flow out from the breach that shutter 103 was located. When the shutter 103 is extended, the above-described gap can be closed. For ease of operation, the back of the shutter plate 103 is provided with a handle.

As shown in fig. 5, the lower demonstration component 4 comprises: the lower base plate 401, the four corners of lower base plate 401 have been installed lower guide pulley 404, the guide slot of direction about the lower part of support 2 is seted up, lower guide pulley 404 rolls and sets up in the guide slot. The lower substrate 401 has a fixing jaw 403 for fixing the transparent case 402. The transparent box 402 is open at the upper end and has an inner cavity with a thickness equal to the diameter of the filling ball 8. A coordinate system is drawn on the transparent box 402, and the operator can calculate the amount of the balls 8 filled in the transparent box 402 by multiplying the horizontal and vertical coordinates of the transparent box 402.

As shown in fig. 7, the upper substrate 101 is provided with a guide bar 105 penetrating through the bracket 2, a rotatable positioning rotating shaft 106 is installed in the guide bar 105, two positioning grooves for engaging with the bracket 2 are provided on the positioning rotating shaft 106, and the upper and lower limit positions of the upper substrate 101 on the bracket 2 can be fixed by engaging with the bracket 2 through the positioning grooves at different positions. When the upper base plate 101 is in the upper limit position, it does not affect the rotation of the middle base plate 304; when the upper substrate 101 is in the lower limit position, the lower edge thereof can be attached to the upper edge of the middle substrate 304.

As shown in fig. 8, a first connecting rod 5 and a second connecting rod 6 are sequentially hinged between the bottom of the lower substrate 401 and the bottom of the bracket 2, a positioning block 7 with magnetic attraction is arranged on the first connecting rod 5 and the second connecting rod 6, and when the first connecting rod 5 and the second connecting rod 6 rotate to the collinear position, the positioning block 7 attracts. When lower base plate 401 is in the lower limit position, it does not affect the rotation of middle base plate 304; when lower substrate 401 is in the upper limit position, its upper edge can abut the lower edge of middle substrate 304.

A calculus demonstration method, as shown in fig. 9, comprising the steps of:

a. twist and turn location pivot 106, make its constant head tank and support 2 break away from, will go up demonstration subassembly 1 and push to extreme position, then twist and turn location pivot 106, make its corresponding constant head tank and support 2 block to will go up demonstration subassembly 1 and fix its extreme position.

b. The upper demonstration assembly 1 is placed with the filler ball 8.

c. Pushing out a plurality of sliding columns 303 of the middle demonstration component 3 to form a continuous and fitting function curve; in fig. 9, the function curve formed by the spool 303 is y equal to 0.5 x. And pushes out the edge bars 302 on the left and right sides in this state. The left and right edge strips 302 represent x-0 and x-1, respectively, in the coordinate system of the middle substrate 304.

d. The middle demonstration assembly 3 is turned over 180 deg..

e. Twist and turn location pivot 106, make its constant head tank and support 2 break away from, will go up demonstration subassembly 1 and remove to lower extreme position, then twist and turn location pivot 106, make its corresponding constant head tank and support 2 block to will go up demonstration subassembly 1 and fix at its lower extreme position.

f. The flashboard 103 is pulled open, so that the filling balls 8 in the upper demonstration component 1 enter the middle demonstration component 3 until the function curve formed by the pushed slide columns 303 is filled with the area enclosed by the left side bar 302, the right side bar 302 and the upper side bar 302 in the state; the shutter 103 and the upper edge strip 302 are then pushed out. At this time, the filling ball 8 in the middle demonstration component 3 is sealed and fixed. At this time, the upper side edge bar 302 represents y equal to 0. The filler ball 8 is enclosed in an area surrounded by x ═ 0, x ═ 1, y ═ 0, and y ═ 0.5 x. The area of this region is the constant integral over the interval [0,1] when y is 0.5 x.

g. And d, repeating the step a.

h. And d, repeating the step d.

i. The lower demo assembly 4 is pushed to its upper limit position.

j. The lower side edge bar 302 is pulled open and the fill ball 8 in the middle play set 3 enters the transparent box 402 of the lower play set 4. The area occupied by the filler ball 8 in the transparent box 402 can be calculated by the height of the filler ball 8 in the transparent box 402 and the coordinate system drawn on the transparent box 402. At this time, the area occupied by the filling ball 8 in the transparent case 402 should be 0.25. That is, the constant integral over the interval [0,1] of 0.5x is 0.25.

In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.

Claims

1. A calculus presentation device, comprising:

a support (2);

a filling ball (8);

the upper demonstration component (1) is used for loading the filling balls (8) and is arranged on the upper part of the bracket (2) in a vertically sliding manner;

the lower demonstration component (4) is used for loading the filling balls (8) and is arranged at the lower part of the bracket (2) in a vertically sliding manner;

the middle demonstration component (3) is used for loading the filling balls (8) and is rotatably arranged in the middle of the bracket (2);

the middle demonstration component (3) comprises:

the middle base plate (304) is rotatably connected with the bracket (2);

limiting columns (307) arranged at four corners of the middle substrate (304);

the middle transparent plate (301) is arranged at the front end of the middle substrate (304) in a clearance mode, four corners of the middle transparent plate (301) are sleeved on the limiting columns (307), and the diameter of the clearance between the middle transparent plate (301) and the middle substrate (304) is equal to that of the filling balls (8);

the edge strips (302) are arranged on the four sides of the middle substrate (304) in a telescopic mode;

the sliding columns (303) are arranged on the middle substrate (304) in a telescopic mode, the sliding columns (303) are uniformly arranged in an area defined by the edge strips (302), and gaps among the sliding columns (303) are smaller than the diameter of the filling balls (8);

and the spring (306) is sleeved on the limiting column (307), and the spring (306) is positioned between the middle base plate (304) and the middle transparent plate (301).

2. A calculus presentation device as claimed in claim 1,

the upper demonstration assembly (1) comprises:

the upper base plate (101) is arranged on the upper part of the bracket (2) in a vertically sliding mode, and a groove used for accommodating the filling ball (8) is formed in the upper base plate (101);

the upper transparent plate (102) is arranged at the front end of the upper substrate (101), and the gap between the upper transparent plate (102) and the upper substrate (101) is equal to the diameter of the filling ball (8);

and a shutter plate (103) that is provided telescopically at the lower end of the upper substrate (101).

3. A calculus presentation device as claimed in claim 1,

the lower demonstration assembly (4) comprises:

the lower substrate (401) is arranged at the lower part of the bracket (2) in a vertically sliding manner, and a fixing clamping jaw (403) is arranged on the lower substrate (401);

and the transparent box (402) is detachably connected with the lower substrate (401).

4. A calculus presentation device as claimed in claim 1,

the upper base plate (101) is provided with a guide strip (105) penetrating through the support (2), a rotatable positioning rotating shaft (106) is arranged in the guide strip (105), and two positioning grooves used for being connected with the support (2) in a clamping mode are formed in the positioning rotating shaft (106).

5. A calculus presentation device as claimed in claim 1,

the utility model discloses a set up the infrabasal plate, including infrabasal plate (401) and support (2), articulated in proper order have first connecting rod (5) and second connecting rod (6) between the bottom of infrabasal plate (401) and support (2), first connecting rod (5) and second connecting rod (6) facial make-up are equipped with magnetism and inhale locating piece (7) mutually, and when first connecting rod (5) and second connecting rod (6) rotated to the collineation position, locating piece (7) actuation.

6. A calculus presentation device as claimed in claim 1,

the four corners of the middle base plate (304) are provided with middle guide wheels (305), the bracket (2) is provided with an annular guide groove, and the middle guide wheels (305) are arranged in the guide groove in a rolling manner.

7. A calculus presentation device as claimed in claim 2,

the four corners of the upper substrate (101) are provided with upper guide wheels (104), the bracket (2) is provided with guide grooves in the vertical direction, and the upper guide wheels (104) are arranged in the guide grooves in a rolling manner.

8. A calculus presentation device as claimed in claim 3,

lower guide wheels (404) are arranged at four corners of the lower base plate (401), guide grooves in the vertical direction are formed in the support (2), and the lower guide wheels (404) are arranged in the guide grooves in a rolling mode.

9. A calculus presentation method using the calculus presentation device as claimed in any one of claims 1-8, comprising the steps of:

a. a filling ball (8) is placed in the upper demonstration component (1);

b. a plurality of sliding columns (303) of the middle demonstration component (3) extend out to form a function curve;

c. the middle demonstration component (3) is turned for 180 degrees;

d. filling balls (8) in the upper demonstration assembly (1) enter the middle demonstration assembly (3) until an area enclosed by a function curve formed by the extending sliding columns (303) and the edge strips (302) is filled;

e. the middle demonstration component (3) is turned for 180 degrees;

f. the filling ball (8) in the middle demonstration component (3) enters the lower demonstration component (4).