CN1299118A - Array of numeral demonstrator for education - Google Patents

Abstract

Both the teaching device and the learning device for mathematics have several display windows for the situation of combining or deviding, yes or no and amount in different digit positions and several digital wheels in the windows, the middle display axis as a calculating unit (K), upper number axis as a number times of K, and down axis as a k digital place and digital portion numbers. Using the devices can reveal the function relationship of y=KxX+B to solve various methematic questions.

Description

Array of numeral demonstrator for education

The present invention is a kind of mathematics teaching aid, learning aid, and it is synthetic by demonstration device and counter.Demonstration device has the beginning to arrange in an orderly manner to show unit of account (each amount), and counting, numeration are used to set up each relevant notion such as integer, decimal, mark: three kinds of modes that represent several synthetic and decomposition; Disclose manage (the row formula) of calculating according to several seats of data relation of putting.Counter to be representing the orderly arrangement of digit, the being and not being of reflection digit, what the variation of digit's number; Different digits gather and the variation of changing; Demonstrate the calculating of (examination question) plus-minus and multiplication and division with this.

This teaching aid relates to the progress to the theory of foundations of mathematics practice knowledge.1. with China traditionally the expression number what one, ten, hundred, thousand, ten thousand ... numeral be defined as the variant digit of integer, the present invention then represents different digits with 1 on different numerical digits of walking crosswise, and will, ten, hundred, thousand, ten thousand ... as the mark of distinguishing the variant digit of integer, be used for pronunciation to digit, with getting in touch of hint digit and number, integer digit is labeled as ... ten thousand, thousand, hundred, ten, individual: the decimal digit of invention is labeled as

, the digit of mark is labeled as

(when N is 10 be

When N is 100 be

), made things convenient for the calculating (vertical) and the understanding of logarithm so widely to calculating.2. determine the unit of number with ordered series of numbers.Each amount when 3. establishing new ideas one counting of unit of account has been set up mathematic(al) mode Y=K * X+B thus, and K be each amount, and X is that (part) of K is counted, and Y, B represent quantity, and corresponding relation is $\frac{Y\&PlusMinus;B}{X}=\frac{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="0010664600102.png,0010664600111.png"\; state="\{\{state\}\}">K</figure-callout>}}{1}$ 。4. data are divided into unit of account, quantity, quantitative relation three classes, foundation $\frac{y}{x}=K$ Data relationship, determine computing (row formula), disclose to calculate reason, simple, intuitive.

In the prior art, as Chinese patent 93212299X " miniature multi-function digital calculator ", it only can replace abacus bead to calculate with reading, and can not offer an explanation data sense and disclose data relationship; Patent 96233667X " permutation calculation exerciser " belongs to the not mature enough product of present technique, reason is digit's definition unclear, expression mode ambiguity, present technique not only theoretically, all solved the problems referred to above on the expression mode, it more mainly is the mark of having invented decimal, mark digit, no matter making integer, decimal, mark is the foundation of the notion of logarithm, the pronunciation and the literary style of number, or calculate and all organically combine together, be very easy to calculating, principle is calculated in reflection pellucidly.

The purpose of this teaching aid, be to provide a row numerical aperture arranged side by side, what manifest digit has (1) and does not have (0), what variation (1-9) its (part) count, poly-and the variation of changing of different digits, the calculating principle of showing plus-minus and multiplication and division pellucidly: the demonstration axle is set, there is the beginning to arrange in an orderly manner by each amount (K) mathematical problem, counting---following number axis, numeration---go up number axis, make each data all have unique several separately, according to several relations, disclose and calculate reason, determine computing (row formula).

Array of numeral demonstrator for education according to the design of this purpose, its structure is that the cuboid box internal upper part by hollow is provided with row's numerical digit wheel, each numerical aperture top all indicates mark---the counter of different digits: the bottom is set side by side with (individual or (part) number of record unit of account of number axis under the rotating rectangular parallelepiped from the case surface to being embedded in the cuboid box, last number axis (record quantity), three of number axis all have different data up and down, one side is blank, be provided with the cylinder rotatable unit of account up and down among the number axis and show axle, expression is to the arrangement of space things, be carved with and the corresponding equidistant sign of number axis up and down each corresponding array relation all in direct ratio---the demonstration device on the corresponding number axis up and down of one sign on the axial plane.

This product has following characteristics and effect:

1, to the understanding and the read-write of integer, decimal, mark: the list of numerical digit and figure place, digital value and positional value, counting and measurement unit and number should, the understanding of radix and notions such as quantity, ordinal number and number sequence, multiple and approximate number, the size comparison of two radixes.

2, the understanding and the calculating of the addition subtraction multiplication and division problem of integer, decimal, mark.

3, direct proportion and inversely proportional are understood and are calculated.

4, the different expressions and the calculating of algebraic expression and arithmetic formula.

5, the unit of geometrical body arranges and calculates.

6, showing that plus-minus is reciprocal, multiplication and division are reciprocal, as much and differ what, and intuitive is strong, the explanation that intensification comprises division to several several understandings and five equilibrium.

Accompanying drawing 1 is an enforcement structural representation of the present invention.

Fig. 2 is four face stretch-out views that go up number axis.

Fig. 3 is the double-colored plane outspread drawing that shows axle.

Fig. 4 is four face stretch-out views of following number axis.

Fig. 5 to Figure 11 is several teaching examples of this teaching aid.

Details are as follows below in conjunction with accompanying drawing enforcement:

Numerical digit axle on the rectangular parallelepiped top of hollow connects the cuboid box both sides, circular shaft is provided with and can takes turns 5. along the numerical digit of de-rotation, 4. the case surface has two rows numerical aperture arranged side by side, and each window can only appear a numeral on the numerical digit wheel, and the mark of different digits is arranged on the window.Lower box part embeds last number axis arranged side by side 3., 7. number axis is provided with unit of account up and down and shows axle 6. among the number axis down, and number axis and a surface that shows spool and case are surperficial up and down becomes a plane.1. number axis is rotated by turn-knob up and down, shows that 8. axle is rotated by turn-knob, and number axis is a rectangular parallelepiped up and down, its a, b, c three faces are evenly equipped with different data, and one side is blank, and a face of last number axis indicates the natural sequence of expansion, the b face is the multiple ordered series of numbers of a number, and the c face is the ordered series of numbers of the umber of a number.The a face of following number axis is that the number of digit is arranged, and the b face is the number ordered series of numbers of a number, and the c face is the umber ordered series of numbers of a number.Show that axle is a right cylinder, axial plane is carved with equidistant sign, then along the axle center to being divided into two kinds of colors, every kind of color is provided with the numbered card that can horizontally slip.

Several use-cases of this teaching aid are as follows: one, the calculating of counter and formula topic

Because each digit of decimal system digit, its maximum numbers are 9, and minimum number is 1 (digit), are not 0.

(1) 10 plus-minus method with interior number comes down to the plus-minus to digit's number.During teaching: each 9 abacus rhymes that is simple and easy to remember with " several several " or " several go several " substitute 10 with interiorly add, each 45 pithy formula of subtraction.As 3+2 (on two two

30+20 (on two two) (two go two to 5-2 50-20 (two go two)

(2) 20 with interior or whole 10, whole 100 ... the plus-minus method of (two or more digit), come down to between the plus-minus of the number of two or more digits and unit poly-with change the just variation of numerical digit.

During teaching: each 9 abacus rhymes that is simple and easy to remember with " several go several advance " or " several move back also several " on identical figure place substitute 20 and add, subtract respectively 45 pithy formulas with interior advance and retreat position.

As: 7+8 (eight go two the advance) 70+80 that extends (eight go two advance one)

15-8 (eight move back one goes back two) 150-80 (eight move back one goes back two)

(3) teaching of multiplication: utilize " multiplication table ' ' and the combination of rechoning by the abacus addition pithy formula, the change multiplication calculates into addition.

As 15 * 5 → (5 52 5) → (on five five)

(4) teaching of division: utilize the combination of " multiplication table " and rechoning by the abacus subtraction pithy formula, become division and calculate into subtraction.

75 ÷ 5=15

→ (" five go five ": go five) at 7 li (five or five go 25

Two, display and application topic is determined the calculation reason demonstration of operational method

Anything of space can take certain mode to measure with relevant measurement unit.---application topic, summary of relation---literal is inscribed, and concerns with data representation---formula topic that all arithmetic problem in the primary school mathematics all are to obtain relevant data by this things is measured, or these data are added the statement of plot.

With the production process (counting process) of display reflection data, just reproduce the process of things, intuitively obtain data relationship, disclose and calculate reason.Through facts have proved, an available formula is commanded quantitative relation, and two kinds of structures reflection mathematical materials are arranged reflection mathematical education rules for three kinds, thereby determined operational method, have embodied its simple, directly perceived, easy-operating characteristics.

1, mathematic(al) mode (Y ₁=K) (see Figure of description one)

Y = K × X

Quantity is amount amount number at every turn

2, mathematic(al) structure

Show the monochromatic demonstration of axle, show the component relationship of a things.

Show the double-colored demonstration of axle, the comparison of showing two things.

3, three kinds of arrangements

The mathematics self-service approach of the corresponding relation of upper and lower each corresponding array of number axis is:

Arrange one: integer adds, subtraction ()

Component relationship (show that axle is monochromatic, numbered card is displaced to another point from a bit)

The understanding of integer, read-write and plus-minus method (K=1, natural unit) (seeing explanation accompanying drawing two)

(1) numbered card moves right to the B point from the A point---ask sum: 4+5=9

(2) numbered card moves to the A point left from the B point---ask residue: 9-5=4

Brief summary: demonstration device has beginning, orderly, unlimited character and plus-minus reciprocal relation simple, intuitive disclosing natural number, is equally applicable to that mark, decimal add, subtraction.

Integer adds, subtraction (two)

Comparison (show that axle is double-colored, two numbered cards are determined 2 position respectively) (seeing Figure of description three)

(1) ask phase difference (2) to ask plurality (3) to ask than decimal

B A A B B A

9 -?4 =5 4?+ 5 =9 9 -5 =4

Size differs to differ for a short time and differs little greatly

Brief summary: demonstration device is being showed the as much part and is being differed part and the more few and few what part is clear, simple, directly perceived.

Sum up: when K is decimal unit or sub-multiple unit, this kind arrangement can to the understanding of decimal, mark, read-write and to decimal, mark add, the demonstration of subtraction.

Arrange two: the integer multiplication and division are with integer (one)

Component relationship (K＞1, the integer of X＞1)

The example: when K=3, (see Figure of description four) (1) ask several how many what are? (2) five equilibrium division (3) comprises the whole every part umber brief summary of the every part of division 3 * 5=15 15 ÷ 5=whole umber of 3 15 ÷, 3=5 part numbers: demonstration device is in the meaning that discloses the multiplication and division method, the reciprocal relation of multiplication and division method, the five equilibrium division with comprise in the resolution of division clear, simple, directly perceived.

It is multiple 3 * 5=15 15 ÷ 5=3 15 ÷, 3=5 criterion numeral comparand comparand criterion numeral comparand criterion numerals of decimal that the integer multiplication and division ask plurality (2) to ask to be asked big number than decimal (3) with integer (two) comparison (K＞1, the integer of X＞1) (seeing Figure of description five) (1)

Brief summary: demonstration device in the comparison that discloses comparative quantity (big number) and the quantitative relation of standard volume (decimal), to its (standard volume) as much, be its several times or Duo than it and to show absolutely clearly on several times the problem.

Sum up: when K is a decimal or a mark (not comprising decimal unit and sub-multiple unit), this kind arrangement promptly can be demonstrated the decimal multiplication and division and remove integer with integer and mark at every turn.

Arrange three: the integer multiplication and division are with mark (one)

Component relationship (integer of K＞1, the mark of 0＜X＜1)

Example: (1) portion of asking of (seeing Figure of description six) when K=15 always concerns that (2) ask part number (3) to ask whole number

The whole component relationship part of the whole component relationship of part part component relationship integral body

Brief summary: demonstration device is clear, simple, directly perceived in the demonstration that discloses meaning, component relationship and the calculation reason of integer multiplication and division with mark.

The integer multiplication and division are with mark (two)

Comparison (integer of K＞1, the mark of 0＜X＜1) (seeing Figure of description seven)

(1) asks comparison (2) to ask and ask plurality than decimal (3)

Than decimal plurality comparison plurality than the less several pluralities of decimal

Brief summary: demonstration device is disclosing comparative quantity (than decimal) and standard volume (plurality), and quantitative relation and its (plurality) as much are that its several of several branches show absolutely clearly.

Sum up: when K is a decimal or mark (K does not contain decimal unit and sub-multiple unit), this kind arrangement can demonstrate the decimal multiplication and division with mark and mark multiplication and division with mark, can also show in the quantitative relation than it and Duo the several of several branches and several problem of lacking several branches than it, show clearly, simple, directly perceived.

Claims (4)

1, a kind of mathematics teaching aid, learning aid mainly are applicable to the foundation of integer, decimal, each relevant notion of mark, show the combination of number and three kinds of modes of decomposition, strengthen the understanding and the computing power of plus-minus and each computing of multiplication and division.The cuboid box that it comprises hollow 1., the blackboard (case surface) of complying with one's wishes, it is characterized in that:

1. 5. the digital wheel shaft of connecting box internal upper part both sides is provided with several rotating digit wheels, uniform 0-9 0 numerals on each digit wheel periphery.

2. 4. digital window can only manifest a numeral on the digital wheel face, and each window top indicates the mark of different digits, and a left side is ... do a hundred or so The right side is ... do a hundred or so

Annotate note work when n is 10

Note is done when n is 100

Mark ..., Under the window, determine the number of digit wheel by the figure place of n.Digit's mark, replaceable is the measurement unit mark.

3. the bottom embeds corresponding side by side rectangular parallelepiped and rotates number axis in the case, 3. last number axis represents the multiple ordered series of numbers (tolerance is K) of unit of account, 7. following number axis represents the number or the umber ordered series of numbers (tolerance is 1) of unit of account, three of number axis all have different data up and down, and each corresponding array of number axis relation in direct ratio simultaneously is blank for the use that complies with one's wishes up and down.

4. up and down is provided with rotating unit of account (each amount) in the middle of the number axis and shows axle 6., be carved with on the axle and the corresponding equidistant sign of number axis up and down, axle is provided with the numbered card that can horizontally slip.

2, mathematics teaching aid as claimed in claim 1, it is characterized in that digit wheel be generally 10-12 be divided into about two groups.

3, as the described mathematics teaching aid of claim l, it is characterized in that showing that the axle pros and cons is a different colours, it can homochromy or double-colored corresponding the demonstration.Two kinds of existences with the reflection data relationship.

4, mathematics teaching aid as claimed in claim 1, it is characterized in that a face of number axis indicates the natural sequence of expansion, the a face of corresponding following number axis is that the number of digit is arranged: the b face of going up number axis is the multiple ordered series of numbers of a number, and the b face of corresponding following number axis is the number ordered series of numbers of a number; The c face of last number axis is the arrangement of number of the umber of a number, and the c face of corresponding following number axis is the arrangement of the umber of a number.

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