CN203085019U

CN203085019U - Multifunctional plane area exploration instrument

Info

Publication number: CN203085019U
Application number: CN 201320080921
Authority: CN
Inventors: 李祖源; 苏文建
Original assignee: Individual
Current assignee: Individual
Priority date: 2013-02-21
Filing date: 2013-02-21
Publication date: 2013-07-24
Anticipated expiration: 2023-02-21

Abstract

The utility model discloses a multifunctional plane area exploration instrument which relates to a mathematical teaching tool, and provides a multifunctional plane area exploration instrument which can help students to understand the deduction processes of various geometric figure areas and can be used for building graphics such as rectangles, parallelograms, triangles, trapezoids and the like. The instrument is provided with a bottom plate and at least three straight rods, wherein grids are arranged on the front side of the bottom plate; at least one first magnet is arranged on the bottom plate; and a second magnet or an iron sheet is arranged on each straight rod. The bottom plate and the plastic rods are ingeniously utilized to combine rectangles, parallelograms, triangles and trapezoids, and a plurality of grids, a cut and complement method and other modes are adopted to analyze and deduct the area formulas of the rectangles, parallelograms, triangles and trapezoids. The instrument has strong comprehensiveness, and can also have a good intuitive demonstration function in a teaching process as well as good application value and meaning; and the instrument can be used as a teaching tool or a learning tool.

Description

Multi-functional area of plane exploring instrument

Technical field

The utility model relates to a kind of mathematical education tool, especially relates to a kind of multi-functional area of plane exploring instrument.

Background technology

In primary school mathematics study, the student exists relevant rectangle, parallelogram, triangle and trapezoidal area formula understood and problem such as does not obscure thoroughly, easily.Utilize base plate and sticking plaster that they are combined into rectangle, parallelogram, triangle and trapezoidal dexterously by Self-made Realia, and utilize number grid and mode analytical derivations such as cutting reinforcing method to go out their area formula.This teaching aid has had very strong comprehensive, also can play good ocular demonstration function in teaching process, has also possessed good using value and meaning.

Summary of the invention

The purpose of this utility model is to provide a kind of student of help to understand the derivation of multiple geometric figure area, can be used for building the multi-functional area of plane exploring instrument of rectangle, parallelogram, triangle and trapezoidal figures.

The utility model is provided with base plate and at least 3 straight rods, and the front of described base plate is provided with grid, and described base plate is provided with at least 1 the 1st magnet, and described straight rod is provided with the 2nd magnet or iron plate.

Described base plate can adopt square poly (methyl methacrylate) plate or square plastic plate etc., and length can be 40～80cm, and width can be 40～80cm; Described grid can be square net, and the length of each grid can be 1cm.The 1st magnet of being located on the base plate can be established 4.The 2nd magnet or the iron plate be located on the straight rod can be established 4.

The utility model utilizes base plate and sticking plaster that they are combined into rectangle, parallelogram, triangle and trapezoidal dexterously, and utilizes number grid and mode analytical derivations such as cutting reinforcing method to go out their area formula.Simultaneously, in this process, also solved two difficult points in study: the first, same rectangle girth in becoming the process of parallelogram not to become, but area is diminishing, and the area of the parallelogram that is become is determined by its height; The second, no matter how how triangle, trapezoidal shape change, as long as satisfy with being equal to height, their area size is identical.In a word, the utlity model has very strong comprehensively, in teaching process, also can play good ocular demonstration function, also possessed good using value and meaning.

The utility model can be used as teaching aid or learning aid.

Description of drawings

Fig. 1 is that the structure of the utility model embodiment 1 is formed synoptic diagram.

Fig. 2 is that the structure of the utility model embodiment 2 is formed synoptic diagram.

Fig. 3 is that the structure of the utility model embodiment 3 is formed one of synoptic diagram.

Fig. 4 is that the structure of the utility model embodiment 3 is formed two of synoptic diagram.

Embodiment

Embodiment 1: the derivation demonstration of rectangular area formula

As shown in Figure 1, the utility model embodiment is provided with base plate 1 and 4 straight rods 2, the front of described base plate 1 is provided with grid 11, and described base plate 1 is provided with at least 1 the 1st magnet (not drawing in the drawings), and described straight excellent 2 are provided with the 2nd magnet or iron plate (not drawing in the drawings).

Described base plate 1 can adopt square poly (methyl methacrylate) plate or square plastic plate etc., and length can be 40～80cm, and width can be 40～80cm; Described grid 11 can be square net, and the length of each grid can be 1cm.The 1st magnet of being located on the base plate 1 can be established 4.The 2nd magnet or the iron plate be located on straight excellent 2 can be established 4.

On base plate 1, risk a rectangle with 4 straight rod (can adopt sticking plaster) 2, can know rectangular area by the method for number grid 11, this just verified well rectangular area equal long * wide, utilize the method for number grid 11 to derive rectangular area formula.

Embodiment 2: the derivation demonstration of parallelogram area formula

As shown in Figure 2, the rectangle of Fig. 1 is carried out simply moving just having become parallelogram, can know the area of parallelogram, find that the area of this parallelogram is littler than the rectangular area of Fig. 1 by the method for number grid 11.By demonstration, known that rectangle area in becoming the process of parallelogram diminishes, and the parallelogram area size that becomes is to be determined by the high of it.Therefore, the area formula that utilizes the mode of number grid 11 can derive parallelogram is: the end * height.

Embodiment 3: the derivation demonstration of triangle area formula

As shown in Figure 3, on rectangular diagonal line, add a sticking plaster, just rectangle can be divided into two duplicate right-angle triangles, so the area of this right-angle triangle just equals half of rectangular area.Find that also the end of right-angle triangle is rectangular length, the height of right-angle triangle is rectangular wide.Be the right-angle triangle area equal the end * height/2.So, whether is this also applicable to oxygon and obtuse triangle? further probe into and verify.

As shown in Figure 4, utilizing two sticking plasters to tell an oxygon Δ ABC, know that by the mode of number grid its area is 6 square decimeters, is half of its place rectangular area just.Change a kind of thinking thinking, make the height of oxygon, find by analyzing: the height of this oxygon Δ ABC is rectangular wide just, is the same with rectangular length at the bottom of the oxygon.So, the area of oxygon also equal the end * height/2.

By analyzing relatively three kinds of difform triangle areas, can find that their area all equates, further reaches a conclusion by the mode of number grid: with being equal to high triangle area size is identical.

If on the rectangular diagonal line of Fig. 2 parallelogram, add a sticking plaster, just it can be divided into two duplicate obtuse triangles, so the area of this obtuse triangle just equals half of rectangular area.The end of also finding obtuse triangle is the length of parallelogram, and the height of obtuse triangle is the wide of parallelogram.Be the obtuse triangle area equal the end * height/2.

In sum, ingeniously utilize rectangle or parallelogram area to derive leg-of-mutton area formula to be: the end * height/2.Simultaneously, found also how no matter how leg-of-mutton shape changes, as long as satisfy with being equal to height, their area size is identical.

Embodiment 4: the derivation demonstration of trapezoidal area formula

Utilize sticking plaster on base plate, to risk an isosceles trapezoid, right-angle triangle or generally trapezoidal.At this moment, can know trapezoidal area by the method for number grid, wait the contour trapezoidal area in the end to equate, this has verified that well trapezoidal area equals (upper base+go to the bottom) * high/2.Can so, derive trapezoidal area with modes such as cutting reinforcing method? further analyze and probe into.

1. utilize triangle area derivation of equation trapezoidal area

On diagonal line, add a sticking plaster, just can be divided into two triangles trapezoidal.Can know by analyzing: two leg-of-mutton areas are respectively: (going to the bottom * high/2) and (upper base * height/2), and these two leg-of-mutton height equate.So trapezoidal area can be these two triangle area sums, that is: (upper base+go to the bottom) * high/2.Like this, can utilize leg-of-mutton area formula to derive trapezoidal area formula.

2. utilize parallelogram area formula derivation trapezoidal area

Trapezoidal going to the bottom prolonged upper base length, and upper base then prolongs the length of going to the bottom, so just by two trapezoidally constituted a parallelogram, promptly trapezoidal area is half of this this parallelogram area just.The length of this parallelogram is the trapezoidal upper base+sum of going to the bottom, and wide also is trapezoidal height, so, by at the bottom of the parallelogram area * as can be known wide: trapezoidal area formula also can write: (upper base+go to the bottom) * high/2.Like this, can utilize the area formula of parallelogram to derive trapezoidal area formula.

In a word, can derive trapezoidal area with cutting reinforcing method from the area of triangle, parallelogram by ingenious land productivity: (upper base+go to the bottom) * high/2.How no matter how trapezoidal shape changes, as long as satisfy with being equal to height, their area size is identical.

Claims

1. multi-functional area of plane exploring instrument is characterized in that being provided with base plate and at least 3 straight rods, and the front of described base plate is provided with grid, and described base plate is provided with at least 1 the 1st magnet, and described straight rod is provided with the 2nd magnet or iron plate.

2. multi-functional according to claim 1 area of plane exploring instrument, the length that it is characterized in that described base plate is 40～80cm, width is 40～80cm.

3. multi-functional according to claim 1 area of plane exploring instrument is characterized in that described grid is a square net.

4. multi-functional according to claim 1 area of plane exploring instrument, the length that it is characterized in that described grid is 1cm.

5. multi-functional according to claim 1 area of plane exploring instrument is characterized in that the 1st magnet on the described base plate is established 4.

6. multi-functional according to claim 1 area of plane exploring instrument is characterized in that the 2nd magnet or the iron plate on the described straight rod established 4.