WO2020194747A1 - Arithmetic learning material - Google Patents

Arithmetic learning material Download PDF

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WO2020194747A1
WO2020194747A1 PCT/JP2019/013875 JP2019013875W WO2020194747A1 WO 2020194747 A1 WO2020194747 A1 WO 2020194747A1 JP 2019013875 W JP2019013875 W JP 2019013875W WO 2020194747 A1 WO2020194747 A1 WO 2020194747A1
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displayed
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square
column
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明子 直井
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明子 直井
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B42—BOOKBINDING; ALBUMS; FILES; SPECIAL PRINTED MATTER
    • B42D—BOOKS; BOOK COVERS; LOOSE LEAVES; PRINTED MATTER CHARACTERISED BY IDENTIFICATION OR SECURITY FEATURES; PRINTED MATTER OF SPECIAL FORMAT OR STYLE NOT OTHERWISE PROVIDED FOR; DEVICES FOR USE THEREWITH AND NOT OTHERWISE PROVIDED FOR; MOVABLE-STRIP WRITING OR READING APPARATUS
    • B42D15/00—Printed matter of special format or style not otherwise provided for
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B19/00—Teaching not covered by other main groups of this subclass
    • G09B19/02—Counting; Calculating
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B23/00—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
    • G09B23/02—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics

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  • the present invention relates to teaching materials for learning arithmetic for learning multiplication.
  • the multipliers are 1, 2, 3, ... .. .. It is important for students to understand the arithmetic progression (n, 2n, 3n 7) that increases with.
  • a card in which the value of m ⁇ n is displayed in the squares of m rows and n columns as shown in Patent Document 1 students can get closer to understanding arithmetic progressions.
  • the sequence of n 7, 7, 14, 21. .. .. It cannot be said that it is easy to grasp that it is an arithmetic progression by looking only at the sequence.
  • An object of the present invention is to provide a teaching material for arithmetic learning capable of learning multiplication for a large value of a multiplicand n based on an understanding of a value of a small multiplicand n.
  • mn 5m + (n-5) m.
  • 5m it is the 5th step that is easy to remember in 99, and for (n-5) m, (n-5) is less than 5, so it is easy to understand.
  • process 5 in the 1st place of 5m. As will be described later, various methods can be considered for this process depending on the ability of the students to add.
  • the teaching material for arithmetic learning of the present invention is It is a teaching material for learning arithmetic for learning multiplication.
  • the base card is characterized in that a number indicating a value of m ⁇ p is displayed in the square of m row and p column, and no number is displayed in the square of m row and v column (v ⁇ p).
  • v ⁇ p the teaching material for arithmetic learning of the present invention
  • the teaching material for arithmetic learning of the present invention is In the base card, for one n where n> p, a number indicating the value of m ⁇ n is displayed in the square of the m row and nth column, and the m row and wth column (w> p and w ⁇ n). The feature is that the number is not displayed in the square of).
  • the base card displays only the numbers indicating the value of m ⁇ p and the numbers indicating the value of m ⁇ n, and is not aware of other values.
  • the teaching material for arithmetic learning of the present invention is In the base card, for one n where n> p, a number indicating a value of m ⁇ (n ⁇ p) is displayed in the square of m row nth column (n> p), and m row w column. It is characterized in that no number is displayed in the square of the eye (w> p and w ⁇ n).
  • the teaching material for arithmetic learning of the present invention is
  • the base card is characterized in that, for all n where n> p, a number indicating a value of m ⁇ n is displayed in the square of the m row and nth column.
  • one base card can be shared for learning about many multiplicands n.
  • the teaching material for arithmetic learning of the present invention is The base card is characterized in that, for all n where n> p, a number indicating a value of m ⁇ (n ⁇ p) is displayed in the square of the m row and nth column. Teaching materials for learning mathematics described in 1.
  • one base card can be shared for learning about many multiplicands n.
  • FIG. 1 is a diagram showing a base card.
  • FIG. 2 is a diagram showing the use of a work card.
  • FIG. 3 is a diagram showing the use of a base card and a work card.
  • FIG. 4 is a diagram showing the use of a base card and a work card.
  • FIG. 5 is a diagram showing the use of a base card and a work card.
  • FIG. 6 is a diagram showing a base card.
  • FIG. 7 is a diagram showing the use of a work card. (Example 4)
  • FIG. 1 is a diagram showing a base card.
  • the base card 1 is composed of rectangular squares arranged in a matrix.
  • a multiplicand display frame 11 is provided at the lower end, a multiplier display square 12 is provided at the left end, and the other parts are squares 13 divided in a grid pattern.
  • the multiplicand display frame 11 displays the multiplicand n.
  • the base card 1 is for one multiplicand n, and one multiplicand n in a rectangle having a shape in which the lowermost squares are connected without being divided into squares (6 in FIG. 1A, FIG. 7 is displayed in B), 8 is displayed in FIG. 1 (C), and 9 is displayed in FIG. 1 (D).
  • the multiplier display square 12 displays the multiplier m.
  • the base card 1 is related to a plurality of multipliers m (1 to 10 in this embodiment) for one multiplier n, and each line is related to one multiplier m. Therefore, each line is divided into squares. The value of m is displayed in the square.
  • the square 13 is a blank space in which a number indicating a value of m ⁇ n is displayed or a number is not displayed in the square m row and nth column.
  • the values of m and n when referred to as the m row and nth column count the squares on the base card 1 without including the multiplier display frame 11 and the multiplier display square 12.
  • the number indicating the value of m ⁇ n is displayed in which square and which square is not displayed according to the following criteria.
  • a number indicating a value of m ⁇ n is displayed in the n-th column (n-th column 13b).
  • No numbers are printed on other squares.
  • FIG. 2 is a diagram showing the use of a work card. The procedure for learning multiplication using the base card 1 will be described below.
  • u n-p.
  • the student adds the value "20" displayed in the p-column cell 13d adjacent to the top row on which the work card 2 is placed to 12, and the product value (m ⁇ n) is 32. To guide.
  • m is an even number (4), but when m is an odd number, it is necessary to process the value displayed in the p-column cell 13d adjacent to the top row by 5 in the 1st place. is there.
  • m 5
  • the product value (m ⁇ n) is 40, as in the case of even m. Can guide you.
  • This embodiment describes another form of base card 1.
  • the display of the n-row squares 13b is different from that of the first embodiment, and the others are the same as those of the first embodiment. A detailed description of the same parts as in the first embodiment will be omitted.
  • FIG. 3 is a diagram showing the use of a base card and a work card.
  • FIG. 3A shows an example of the base card 1.
  • the multiplicand is 8, which corresponds to FIG. 1 (C). The same applies to other multiplicands.
  • nth column 13b a number indicating a value of m ⁇ n was displayed in the first embodiment, but in this embodiment, a number indicating a value of m ⁇ (np) is displayed.
  • FIG. 3B shows the use of a work card. The number of squares covered by the work card is displayed in the n-row squares 13b.
  • the student adds the value "20" displayed in the p-column cell 13d adjacent to the top row on which the work card 2 is placed to 12, and derives that the product value (m ⁇ n) is 32. ..
  • the number 12 to be added is displayed in the nth column 13b.
  • This embodiment describes another form of base card 1.
  • the point that the integrated n-row square 13c is used instead of the n-row square 13b and the display of the multiplicand display frame 11 are different from those of the first embodiment, and the other points are the same as those of the first embodiment. A detailed description of the same parts as in the first embodiment will be omitted.
  • FIG. 4 is a diagram showing the use of a base card and a work card.
  • FIG. 4A shows the base card 1.
  • the position of the n-column square 12b differs depending on the value of n.
  • the entire cell on which these numbers are displayed is defined as the integrated n-column cell 13c.
  • Figure 4 (B) shows the use of work cards. Students learn by looking at the numbers displayed in the squares of the base card 1 at the right end of the work card 2.
  • n 6,7,8,9. Therefore, in the multiplicand display frame 11, all of 6, 7, 8, and 9 are displayed at positions corresponding to n (6, 7, 8, 9) in the integrated n-column square 13c.
  • the number indicating the value of m ⁇ (n ⁇ p) may be displayed in the integrated n-column square 13c as in the second embodiment.
  • the use of the base card and the work card in this case is shown in FIG.
  • Example 1 This embodiment describes another form of base card 1.
  • Others are the same as in Example 1. A detailed description of the same parts as in the first embodiment will be omitted.
  • FIG. 6 is a diagram showing a base card.
  • FIG. 7 is a diagram showing the use of a work card.
  • the base card 1 and the work card 2 it is considered that paper ones are used. However, it may be made of other materials, such as wood or plastic.
  • the base card 1 and the work card 2 may be displayed on the display screen by a computer program, and the display position of the work card 2 may be moved by operating the mouse or the touch panel.
  • a separate base card 1 and work card 2 are used for each multiplicand. Therefore, by designating the multiplicand, the base card 1 and the work card 2 corresponding to the multiplicand are displayed. Then, the combination of the base card 1 and the work card 2 is automatically and correctly selected, which is convenient. Further, also in the third embodiment, since the work card 2 is used separately for each multiplicand, it is convenient in that the work card can be automatically selected.
  • various base cards 1 can be considered, and it is also possible to selectively use them according to the proficiency level of the students. It is effective to select the type of base card 1 to be used by a computer program.
  • the teaching material for arithmetic learning of the present invention it is possible to learn multiplication for a large n value based on an understanding of a small n value by using a value obtained by subtracting 5 or 10 from a multiplicand n, and multiplying. You can improve the learning effect of. It can be used by many cram schools and individuals.
  • Multiplicand display frame 12 Multiplier display square 13 square 13a p row square 13b n row square 13c Integrated n row square 2 Work card

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Abstract

[Problem] To provide an arithmetic learning material that allows a learner to learn multiplication with a multiplicand n that has a large value on the basis of understanding multiplication with the multiplicand n having a small value. [Solution] Provided is an arithmetic learning material for learning multiplication, provided with a base card 1 whereon s × t sections 13 connected in the form of s rows and t columns (5≤s) (p<t<2p), are drawn for p which is 5 or 10, and a work card 2 of 1 row and u columns, which is formed by connecting u (u<p) squares having the same size as the sections in one direction; a number indicating the value of m × p is displayed in a section 13a in the m-th row and the p-th column on the base card 1, whereas no number is displayed in the section 13 in the m-th row and the v-th column (v<p).

Description

算数学習用教材Teaching materials for math learning
　本発明は、掛け算を学習するための算数学習用教材に関する。 The present invention relates to teaching materials for learning arithmetic for learning multiplication.
　小学校低学年の算数教育において、掛け算、足し算、及び引き算を学習する。ここで、掛け算の学習は、いわゆる九九を基礎とする。しかし、九九は、通常、暗記による学習であることから、掛け算の概念を習得する機会に乏しい。 Learn multiplication, addition, and subtraction in mathematics education in the lower grades of elementary school. Here, the learning of multiplication is based on the so-called multiplication table. However, since multiplication tables are usually learned by rote learning, there are few opportunities to learn the concept of multiplication.
　ここで、九九の暗記によらずに掛け算の考え方を学習することを検討すると、被乗数がｎである場合に、乗数が１、２、３、．．．と増加していく等差数列（ｎ、２ｎ、３ｎ．．．）を生徒が理解することが重要である。この点、特許文献１に示すようにｍ行ｎ列のマス目にｍ×ｎの値を表示したカードを用いれば、生徒を等差数列の理解に近づけることができる。 Here, when considering learning the concept of multiplication without memorizing multiplication tables, when the multiplier is n, the multipliers are 1, 2, 3, ... .. .. It is important for students to understand the arithmetic progression (n, 2n, 3n ...) that increases with. In this regard, by using a card in which the value of m × n is displayed in the squares of m rows and n columns as shown in Patent Document 1, students can get closer to understanding arithmetic progressions.
　ここで、数列を見た生徒が「等差数列である」と確実に把握できるのは、ｎの値が小さい場合である。例えば、ｎ＝１の数列１，２，３．．．、ｎ＝２の数列２，４，６．．．については、等差数列であることが容易に把握できる。一方、例えばｎ＝７の数列７，１４，２１．．．についてその数列のみを見て等差数列であると把握することが容易であるとは言えない。 Here, the student who sees the sequence can surely grasp that it is an arithmetic progression when the value of n is small. For example, a number sequence of n = 1, 1, 2, 3. .. .. , N = 2 sequence 2, 4, 6. .. .. Can be easily grasped as an equal difference number sequence. On the other hand, for example, the sequence of n = 7, 7, 14, 21. .. .. It cannot be said that it is easy to grasp that it is an arithmetic progression by looking only at the sequence.
　してみれば、小さなｎの値についての理解に基づいて大きなｎの値についての掛け算を学習することのできる算数学習用教材が期待される。 If you try, you can expect a teaching material for arithmetic learning that can learn multiplication for a large n value based on an understanding of a small n value.
特開２０１７－１３４２９９号公報Japanese Unexamined Patent Publication No. 2017-134299
　本発明は、小さな被乗数ｎの値についての理解に基づいて大きな被乗数ｎの値についての掛け算を学習することのできる算数学習用教材を提供することを課題とする。 An object of the present invention is to provide a teaching material for arithmetic learning capable of learning multiplication for a large value of a multiplicand n based on an understanding of a value of a small multiplicand n.
　被乗数ｎが、５＜ｎ＜１０である場合、乗数をｍとすると、積ｍｎは、ｍｎ＝５ｍ＋（ｎ－５）ｍと表すことができる。５ｍについては九九の中でも覚えやすい５の段であり、（ｎ－５）ｍについては、（ｎ－５）が５未満となるので、容易に理解できる。 When the multiplier n is 5 <n <10 and the multiplier is m, the product mn can be expressed as mn = 5m + (n-5) m. For 5m, it is the 5th step that is easy to remember in 99, and for (n-5) m, (n-5) is less than 5, so it is easy to understand.
　ここで、５ｍと（ｎ－５）ｍを加算する点については、ｍが偶数であれば５ｍが１０の倍数となり、１の位を考えずに１０の位のみを考えればよく容易である。九九で学ぶ範囲のｍ＜１０であれば、１０の位は繰り上がりのない１桁の数の加算となり容易である。 Here, regarding the point of adding 5m and (n-5) m, if m is an even number, 5m is a multiple of 10, and it is easy to consider only the tens place without considering the ones place. If m <10, which is the range learned in multiplication tables, the tens place is an addition of single-digit numbers without carry, which is easy.
　ｍが奇数の場合には、５ｍの１の位の５の処理をする。この処理は、後述するように、生徒の足し算の力量によって各種の方法が考えられる。 If m is an odd number, process 5 in the 1st place of 5m. As will be described later, various methods can be considered for this process depending on the ability of the students to add.
　以上のように、本発明の算数学習用教材は、ｍｎ＝５ｍ＋（ｎ－５）ｍとして取扱い、５以下の被乗数ｎの値についての理解に基づいて６以上の被乗数ｎの値についての掛け算を学習することを可能にする。 As described above, the teaching material for arithmetic learning of the present invention is treated as mn = 5m + (n-5) m, and the value of the multiplicand n of 6 or more is multiplied based on the understanding of the value of the multiplicand n of 5 or less. Allows you to learn.
　なお、ｍｎ＝１０ｍ＋（ｎ－１０）ｍとして取扱い、１０以下の被乗数ｎの値についての理解に基づいて１１以上の被乗数ｎの値についての掛け算を学習することを可能にすることも、同様に可能である。 Similarly, it is treated as mn = 10m + (n-10) m, and it is possible to learn multiplication for the value of the multiplicand n of 11 or more based on the understanding of the value of the multiplicand n of 10 or less. It is possible.
　本発明の算数学習用教材は、
　掛け算を学習するための算数学習用教材であって、
　５又は１０であるｐについて、
　ｓ行ｔ列（５≦ｓ）（ｐ＜ｔ＜２ｐ）列の形に連接されたｓ×ｔのマス目が描かれたベースカードと、
　前記マス目と同大の正方形を１方向にｕ個（ｕ＜ｐ）連接してなる１行ｕ列の作業用カードとを備え、
　前記ベースカードは、ｍ行ｐ列目のマス目にｍ×ｐの値を示す数字が表示され、ｍ行ｖ列目（ｖ＜ｐ）のマス目には数字が表示されていないことを特徴とする。 The teaching material for arithmetic learning of the present invention is
It is a teaching material for learning arithmetic for learning multiplication.
For p, which is 5 or 10,
A base card with s × t squares connected in the form of s rows and t columns (5 ≦ s) (p <t <2p) columns,
It is equipped with a 1-row, u-column work card formed by connecting u (u <p) squares of the same size as the squares in one direction.
The base card is characterized in that a number indicating a value of m × p is displayed in the square of m row and p column, and no number is displayed in the square of m row and v column (v <p). And.
　この特徴によれば、ｎ＞ｐである被乗数ｎについて、乗数ｍとの積をｍｎ＝ｐｍ＋（ｎ－ｐ）ｍとして学習することが容易となる。ベースカードにはｍ×ｐの値を示す数字が表示され、ｖ×ｐの値を示す数字が表示されていないので、ｍ×ｐの値を示す数字に意識が集中するからである。 According to this feature, it becomes easy to learn the product of the multiplier m, which is n> p, as mn = pm + (n−p) m. This is because the number indicating the value of m × p is displayed on the base card, and the number indicating the value of v × p is not displayed, so that the consciousness is concentrated on the number indicating the value of m × p.
　本発明の算数学習用教材は、
　前記ベースカードは、ｎ＞ｐである１つのｎについて、ｍ行ｎ列目のマス目にはｍ×ｎの値を示す数字が表示され、ｍ行ｗ列目（ｗ＞ｐかつｗ≠ｎ）のマス目には数字が表示されていないことを特徴とする。 The teaching material for arithmetic learning of the present invention is
In the base card, for one n where n> p, a number indicating the value of m × n is displayed in the square of the m row and nth column, and the m row and wth column (w> p and w ≠ n). The feature is that the number is not displayed in the square of).
　この特徴によれば、ｍｎ＝ｐｍ＋（ｎ－ｐ）ｍとして学習することが容易となる。ｍ×ｐの値を示す数字及びｍ×ｎの値を示す数字のみが表示されたベースカードとなり、他の値を意識することがない。 According to this feature, it becomes easy to learn as mn = pm + (n−p) m. The base card displays only the numbers indicating the value of m × p and the numbers indicating the value of m × n, and is not aware of other values.
　本発明の算数学習用教材は、
　前記ベースカードは、ｎ＞ｐである１つのｎについて、ｍ行ｎ列目（ｎ＞ｐ）のマス目にはｍ×（ｎ―ｐ）の値を示す数字が表示され、ｍ行ｗ列目（ｗ＞ｐかつｗ≠ｎ）のマス目には数字が表示されていないことを特徴とする。 The teaching material for arithmetic learning of the present invention is
In the base card, for one n where n> p, a number indicating a value of m × (n−p) is displayed in the square of m row nth column (n> p), and m row w column. It is characterized in that no number is displayed in the square of the eye (w> p and w ≠ n).
　この特徴によっても、ｍｎ＝ｐｍ＋（ｎ－ｐ）ｍとして学習することが容易となる。ｍ×ｎの値に替えてｍ×（ｎ―ｐ）の値を示す数字が表示されている。積ｍｎの値ではないが、ｍ×ｐの値を加算することで積ｍｎとなる値なので、容易に理解できる。 This feature also makes it easy to learn as mn = pm + (n-p) m. Instead of the value of m × n, a number indicating the value of m × (n−p) is displayed. Although it is not the value of the product mn, it can be easily understood because it is a value obtained by adding the value of m × p to obtain the product mn.
　本発明の算数学習用教材は、
　ｎ＝ｔであり、ｕ＝ｎ－ｐであることを特徴とする。 The teaching material for arithmetic learning of the present invention is
It is characterized in that n = t and u = n−p.
　この特徴によれば、被乗数ｎを超える箇所のマス目がない。被乗数をｎに限定して設計されたベースカードとなる。 According to this feature, there are no squares where the multiplicand n exceeds. It is a base card designed by limiting the multiplicand to n.
　本発明の算数学習用教材は、
　前記ベースカードは、ｎ＞ｐである全てのｎについて、ｍ行ｎ列目のマス目にはｍ×ｎの値を示す数字が表示されていることを特徴とする。 The teaching material for arithmetic learning of the present invention is
The base card is characterized in that, for all n where n> p, a number indicating a value of m × n is displayed in the square of the m row and nth column.
　この特徴によれば、１枚のベースカードを、多くの被乗数ｎについての学習に共用することができる。 According to this feature, one base card can be shared for learning about many multiplicands n.
　本発明の算数学習用教材は、
　前記ベースカードは、ｎ＞ｐである全てのｎについて、ｍ行ｎ列目のマス目にはｍ×（ｎ－ｐ）の値を示す数字が表示されていることを特徴とする、請求項１に記載の算数学習用教材。 The teaching material for arithmetic learning of the present invention is
The base card is characterized in that, for all n where n> p, a number indicating a value of m × (n−p) is displayed in the square of the m row and nth column. Teaching materials for learning mathematics described in 1.
　この特徴によっても、１枚のベースカードを、多くの被乗数ｎについての学習に共用することができる。 With this feature as well, one base card can be shared for learning about many multiplicands n.
　本発明の算数学習用教材によれば、被乗数ｎから５又は１０を減算した値を用いて、小さなｎの値についての理解に基づいて大きなｎの値についての掛け算を学習することができ、掛け算の学習効果を上げることができる。 According to the teaching material for arithmetic learning of the present invention, it is possible to learn multiplication for a large n value based on an understanding of a small n value by using a value obtained by subtracting 5 or 10 from a multiplicand n, and multiplying. You can improve the learning effect of.
図１は、ベースカードを示す図である。（実施例１）FIG. 1 is a diagram showing a base card. (Example 1) 図２は、作業用カードの使用を示す図である。（実施例１）FIG. 2 is a diagram showing the use of a work card. (Example 1) 図３は、ベースカード及び作業用カードの使用を示す図である。（実施例２）FIG. 3 is a diagram showing the use of a base card and a work card. (Example 2) 図４は、ベースカード及び作業用カードの使用を示す図である。（実施例３）FIG. 4 is a diagram showing the use of a base card and a work card. (Example 3) 図５は、ベースカード及び作業用カードの使用を示す図である。（実施例３）FIG. 5 is a diagram showing the use of a base card and a work card. (Example 3) 図６は、ベースカードを示す図である。（実施例４）FIG. 6 is a diagram showing a base card. (Example 4) 図７は、作業用カードの使用を示す図である。（実施例４）FIG. 7 is a diagram showing the use of a work card. (Example 4)
　以下、本発明の実施例について説明する。 Hereinafter, examples of the present invention will be described.
　図１は、ベースカードを示す図である。ベースカード１は、マトリクス状に配置された矩形状のマス目から構成されている。下端に被乗数表示枠１１、左端に乗数表示マス目１２を備え、他の箇所は格子状に区分されたマス目１３である。 FIG. 1 is a diagram showing a base card. The base card 1 is composed of rectangular squares arranged in a matrix. A multiplicand display frame 11 is provided at the lower end, a multiplier display square 12 is provided at the left end, and the other parts are squares 13 divided in a grid pattern.
　被乗数表示枠１１は、被乗数ｎを表示する。ベースカード１は、１つの被乗数ｎについてのものであり、マス目に区切らずに下端のマス目を結合した形状の長方形の中に１つの被乗数ｎ（図１（Ａ）では６、図１（Ｂ）では７、図１（Ｃ）では８、図１（Ｄ）では９が表示されている。 The multiplicand display frame 11 displays the multiplicand n. The base card 1 is for one multiplicand n, and one multiplicand n in a rectangle having a shape in which the lowermost squares are connected without being divided into squares (6 in FIG. 1A, FIG. 7 is displayed in B), 8 is displayed in FIG. 1 (C), and 9 is displayed in FIG. 1 (D).
　乗数表示マス目１２は、乗数ｍを表示する。ベースカード１は、１つの被乗数ｎについて複数の（本実施例では１～１０の）乗数ｍに係るものであり、各々の行が１つの乗数ｍに係る内容なので、マス目に区切った各行のマス目にｍの値が表示されている。 The multiplier display square 12 displays the multiplier m. The base card 1 is related to a plurality of multipliers m (1 to 10 in this embodiment) for one multiplier n, and each line is related to one multiplier m. Therefore, each line is divided into squares. The value of m is displayed in the square.
　マス目１３は、ｍ行ｎ列目のマス目に、ｍ×ｎの値を示す数字を表示し、又は、数字を表示しない空白のものである。ここで、ｍ行ｎ列目と言う時のｍ及びｎの値は、被乗数表示枠１１及び乗数表示マス目１２を含まずにベースカード１上のマス目をカウントしたものとする。 The square 13 is a blank space in which a number indicating a value of m × n is displayed or a number is not displayed in the square m row and nth column. Here, it is assumed that the values of m and n when referred to as the m row and nth column count the squares on the base card 1 without including the multiplier display frame 11 and the multiplier display square 12.
　ここで、いずれのマス目にｍ×ｎの値を示す数字を表示し、いずれのマス目に表示しないかについて、以下の基準による。（１）ｐ列目（ｐは５又は１０、本実施例ではｐ＝５とする）のマス目（ｐ列マス目１３ａ）にはｍ×ｐの値を示す数字を表示する。（２）ｎ列目のマス目（ｎ列マス目１３ｂ）にはｍ×ｎの値を示す数字を表示する。（３）他のマス目には、数字を印字しない。 Here, the number indicating the value of m × n is displayed in which square and which square is not displayed according to the following criteria. (1) A number indicating the value of m × p is displayed in the squares (p row squares 13a) in the p-th column (p is 5 or 10, p = 5 in this embodiment). (2) A number indicating a value of m × n is displayed in the n-th column (n-th column 13b). (3) No numbers are printed on other squares.
　図２は、作業用カードの使用を示す図である。以下、ベースカード１を用いて掛け算を学習する手順を説明する。 FIG. 2 is a diagram showing the use of a work card. The procedure for learning multiplication using the base card 1 will be described below.
　生徒は、１行ｕ列の作業用カード２を、下から順に（図２において、作業用カード２ａ、２ｂ、２ｃ、２ｄの順に）置いていく。図２は被乗数ｎが８であり、乗数ｍが４の場合（８×４＝３２）を学ぶものである。他の被乗数ｎ、乗数ｍについても同様である。 Students place work cards 2 in 1 row and u columns in order from the bottom (in the order of work cards 2a, 2b, 2c, and 2d in FIG. 2). FIG. 2 learns the case where the multiplier n is 8 and the multiplier m is 4 (8 × 4 = 32). The same applies to the other multipliers n and m.
　ここで、ｕ＝ｎ－ｐとする。本実施例では、ｕ＝８－５＝３である。生徒は、４行目まで置いた時に、作業用カードによって覆われたマス目の数が、３×４＝１２個であることを理解している（被乗数ｎが３である掛け算は、問題なく行えるものとする）。 Here, u = n-p. In this embodiment, u = 8-5 = 3. The student understands that the number of squares covered by the work card is 3 × 4 = 12 when placed up to the 4th line (multiplication with a multiplicand n of 3 is fine. It should be possible).
　そこで、生徒は、作業用カード２が置かれた最上行に隣接するｐ列マス目１３ｄに表示された値「２０」を１２に加えて、積の値（ｍ×ｎ）が３２であることを導く。 Therefore, the student adds the value "20" displayed in the p-column cell 13d adjacent to the top row on which the work card 2 is placed to 12, and the product value (m × n) is 32. To guide.
　ここで、２０＋１２＝３２との加算については、２０が１０の倍数であるので、１の位を考えずに１０の位のみを考えればよく容易である。 Here, regarding the addition of 20 + 12 = 32, since 20 is a multiple of 10, it is easy to consider only the tens place without considering the ones place.
　上例ではｍが偶数（４）であったが、ｍが奇数の場合には、最上行に隣接するｐ列マス目１３ｄに表示された値について、１の位の５の処理をする必要がある。例えばｍ＝５の場合、生徒が２５＋１５＝４０との足し算を容易に行えるくらいに足し算に習熟していれば、ｍが偶数の場合と同様に、積の値（ｍ×ｎ）が４０であることを導くことができる。 In the above example, m is an even number (4), but when m is an odd number, it is necessary to process the value displayed in the p-column cell 13d adjacent to the top row by 5 in the 1st place. is there. For example, in the case of m = 5, if the student is proficient in addition enough to easily add 25 + 15 = 40, the product value (m × n) is 40, as in the case of even m. Can guide you.
　生徒が足し算に習熟していない場合には、（ｍ－１）が偶数であるので、（ｍ－１）×５を加え、後に５を加えることもできる。２０＋１５＝３５を先に計算し、後に３５＋５＝４０を計算する。 If the student is not proficient in addition, (m-1) is an even number, so (m-1) x 5 can be added, and 5 can be added later. 20 + 15 = 35 is calculated first, and 35 + 5 = 40 is calculated later.
　本実施例は、別形態のベースカード１を説明するものである。ｎ列マス目１３ｂの表示が実施例１と相違し、他は実施例１と同様である。実施例１と同様の部分については、詳細な説明を省略する。 This embodiment describes another form of base card 1. The display of the n-row squares 13b is different from that of the first embodiment, and the others are the same as those of the first embodiment. A detailed description of the same parts as in the first embodiment will be omitted.
　図３は、ベースカード及び作業用カードの使用を示す図である。図３（Ａ）にベースカード１の一例を示す。被乗数が８であり、図１（Ｃ）に対応するものである。なお、他の被乗数についても同様である。 FIG. 3 is a diagram showing the use of a base card and a work card. FIG. 3A shows an example of the base card 1. The multiplicand is 8, which corresponds to FIG. 1 (C). The same applies to other multiplicands.
　ｎ列マス目１３ｂには、実施例１ではｍ×ｎの値を示す数字が表示されていたが、本実施例では、ｍ×（ｎ―ｐ）の値を示す数字を表示する。図３（Ｂ）に作業用カードの使用を示す。ｎ列マス目１３ｂには、作業用カードによって覆われたマス目の数が表示されていることとなる。 In the nth column 13b, a number indicating a value of m × n was displayed in the first embodiment, but in this embodiment, a number indicating a value of m × (np) is displayed. FIG. 3B shows the use of a work card. The number of squares covered by the work card is displayed in the n-row squares 13b.
　生徒は、作業用カード２が置かれた最上行に隣接するｐ列マス目１３ｄに表示された値「２０」を１２に加えて、積の値（ｍ×ｎ）が３２であることを導く。加える数字１２がｎ列マス目１３ｂに表示されている。 The student adds the value "20" displayed in the p-column cell 13d adjacent to the top row on which the work card 2 is placed to 12, and derives that the product value (m × n) is 32. .. The number 12 to be added is displayed in the nth column 13b.
　本実施例は、また別形態のベースカード１を説明するものである。ｎ列マス目１３ｂに替えて統合ｎ列マス目１３ｃである点、及び被乗数表示枠１１の表示が実施例１と相違し、他は実施例１と同様である。実施例１と同様の部分については、詳細な説明を省略する。 This embodiment describes another form of base card 1. The point that the integrated n-row square 13c is used instead of the n-row square 13b and the display of the multiplicand display frame 11 are different from those of the first embodiment, and the other points are the same as those of the first embodiment. A detailed description of the same parts as in the first embodiment will be omitted.
　図４は、ベースカード及び作業用カードの使用を示す図である。図４（Ａ）にベースカード１を示す。ｎ列マス目１２ｂの位置は、ｎの値によって相違する。本実施例では、ｎ＝６，７，８，９に対応する全てのｎ列マス目１２ｂの位置に、ｍ×ｎの値を示す数字を表示する。これらの数字が表示されたマス目の全体を、統合ｎ列マス目１３ｃとする。 FIG. 4 is a diagram showing the use of a base card and a work card. FIG. 4A shows the base card 1. The position of the n-column square 12b differs depending on the value of n. In this embodiment, numbers indicating the value of m × n are displayed at the positions of all n-column squares 12b corresponding to n = 6, 7, 8, 9. The entire cell on which these numbers are displayed is defined as the integrated n-column cell 13c.
　図４（Ｂ）に作業用カードの使用を示す。生徒は、作業用カード２の右端におけるベースカード１のマス目に表示された数字を見て、学習を行う。 Figure 4 (B) shows the use of work cards. Students learn by looking at the numbers displayed in the squares of the base card 1 at the right end of the work card 2.
　本実施例のベースカード１は、１枚のカードを、ｎ＝６，７，８，９の全ての学習に使うことができる。そのため、被乗数表示枠１１には、６，７，８，９の全てが、統合ｎ列マス目１３ｃのｎ（６，７，８，９）に対応する位置に表示されている。 As the base card 1 of this embodiment, one card can be used for all learning of n = 6,7,8,9. Therefore, in the multiplicand display frame 11, all of 6, 7, 8, and 9 are displayed at positions corresponding to n (6, 7, 8, 9) in the integrated n-column square 13c.
　なお、統合ｎ列マス目１３ｃには、ｍ×ｎの値を示す数字に替えて、実施例２のようにｍ×（ｎ―ｐ）の値を示す数字を表示してもよい。この場合のベースカード及び作業用カードの使用を、図５に示す。 Note that, instead of the number indicating the value of m × n, the number indicating the value of m × (n−p) may be displayed in the integrated n-column square 13c as in the second embodiment. The use of the base card and the work card in this case is shown in FIG.
　本実施例は、さらに別形態のベースカード１を説明するものである。実施例１では、ｐ＝５としたが、ｐ＝１０とするものである。他は実施例１と同様である。実施例１と同様の部分については、詳細な説明を省略する。 This embodiment describes another form of base card 1. In Example 1, p = 5, but p = 10. Others are the same as in Example 1. A detailed description of the same parts as in the first embodiment will be omitted.
　図６は、ベースカードを示す図である。ベースカード１は、ｐ＝１０であり、１１以上の被乗数ｎに対応するものである。図はｎ＝１３（＝ｐ＋３）の場合を示し、ｎ＝ｐ＋３である点で、実施例１において図１（Ｃ）に示したものと同等である。なお、ｎ＝１１，１２、ｎ＝１４．．．においても同様である。 FIG. 6 is a diagram showing a base card. The base card 1 has p = 10 and corresponds to a multiplicand n of 11 or more. The figure shows the case of n = 13 (= p + 3), and is equivalent to that shown in FIG. 1 (C) in Example 1 in that n = p + 3. In addition, n = 11,12, n = 14. .. .. The same applies to.
　図７は、作業用カードの使用を示す図である。このように、１行ｕ列（ｕ＝ｎ－ｐ＝１３－１０＝３）の作業用カード２を置き、１３×４＝５２を学ぶ。他の被乗数ｎ、乗数ｍについても同様である。 FIG. 7 is a diagram showing the use of a work card. In this way, the work card 2 of 1 row and u column (u = n-p = 13-10 = 3) is placed, and 13 × 4 = 52 is learned. The same applies to the other multiplicands n and m.
　生徒は、作業用カードによって覆われたマス目の数が３×４＝１２個であることを理解しており、作業用カード２が置かれた最上行に隣接するｐ列マス目１３ｄに表示された値「４０」を１２に加えて、積の値（ｍ×ｎ）が５２であることを導く。 The student understands that the number of squares covered by the work card is 3 × 4 = 12, and is displayed in the p-column square 13d adjacent to the top row where the work card 2 is placed. The value "40" is added to 12 to derive that the product value (m × n) is 52.
　ここで、４０＋１２＝３２との加算については、４０が１０の倍数であるので、１の位を考えずに１０の位のみを考えればよく容易である。本実施例においては、ｍが奇数であってもマス目１３ｄに表示された値が１０の倍数となる。１の位の５の処理をする必要はない。 Here, regarding the addition of 40 + 12 = 32, since 40 is a multiple of 10, it is easy to consider only the tens place without considering the ones place. In this embodiment, even if m is an odd number, the value displayed in the square 13d is a multiple of 10. It is not necessary to process 5 in the 1st place.
　なお、本実施例は、実施例１を基礎としてｐ＝１０としたが、ｐ＝５でなくｐ＝１０とすることは、ｐ＝５の場合とｐ＝１０の場合とでベースカード１の設計は同一なので、実施例２のようにｎ列マス目１３ｂの表示をｍ×（ｎ―ｐ）の値を示す数字とする場合にも、実施例３のように統合ｎ列マス目１３ｃを設ける場合にも可能である。 In this embodiment, p = 10 is set based on the first embodiment, but setting p = 10 instead of p = 5 means that the base card 1 is set to p = 5 and p = 10. Since the design is the same, even when the display of the n-th column 13b is a number indicating the value of m × (n-p) as in the second embodiment, the integrated n-th column 13c is used as in the third embodiment. It is also possible to provide it.
　以上、４つの実施例で詳細に説明したように、本発明の算数学習用教材は、ｍｎ＝ｐｍ＋（ｎ－ｐ）ｍとして、（ｎ－ｐ）を被乗数とした掛け算の知識に基づいて、被乗数ｎについての掛け算を学習することが容易となる、ｐを５又は１０とすることで、効率的な学習が可能となる。 As described in detail in the above four examples, the teaching material for arithmetic learning of the present invention is based on the knowledge of multiplication with (n-p) as a multiplicand, with mn = pm + (n-p) m. Efficient learning is possible by setting p to 5 or 10, which makes it easy to learn multiplication for the multiplicand n.
　ベースカード１及び作業用カード２については、紙製のものを用いると考えられる。しかし、他の材質、例えば木製やプラスチック製のものであってもよい。 As for the base card 1 and the work card 2, it is considered that paper ones are used. However, it may be made of other materials, such as wood or plastic.
　また、コンピュータプログラムによってベースカード１及び作業用カード２をディスプレイ画面に表示し、マウスやタッチパネルの操作によって作業用カード２の表示位置を移動させてもよい。 Alternatively, the base card 1 and the work card 2 may be displayed on the display screen by a computer program, and the display position of the work card 2 may be moved by operating the mouse or the touch panel.
　実施例１，２，４においては、被乗数毎に別々のベースカード１及び作業用カード２を使用するので、被乗数を指定することによってその被乗数に対応したベースカード１及び作業用カード２が表示されると、ベースカード１と作業用カード２との組み合わせが自動的に正しく選択され、便利である。また、実施例３においても、作業用カード２は被乗数毎に別々のものを使用するので、自動的に作業用カードの選択ができる点で、便利である。 In the first, second, and fourth embodiments, a separate base card 1 and work card 2 are used for each multiplicand. Therefore, by designating the multiplicand, the base card 1 and the work card 2 corresponding to the multiplicand are displayed. Then, the combination of the base card 1 and the work card 2 is automatically and correctly selected, which is convenient. Further, also in the third embodiment, since the work card 2 is used separately for each multiplicand, it is convenient in that the work card can be automatically selected.
　また、４つの実施例で示したように、多様なベースカード１が考えられ、生徒の習熟度に応じて選択的に用いることも考えられる。使用するベースカード１の種類をコンピュータプログラムによって選択することが有効である。 Also, as shown in the four examples, various base cards 1 can be considered, and it is also possible to selectively use them according to the proficiency level of the students. It is effective to select the type of base card 1 to be used by a computer program.
　本発明の算数学習用教材によれば、被乗数ｎから５又は１０を減算した値を用いて、小さなｎの値についての理解に基づいて大きなｎの値についての掛け算を学習することができ、掛け算の学習効果を上げることができる。多くの学習塾や個人における利用が考えられる。 According to the teaching material for arithmetic learning of the present invention, it is possible to learn multiplication for a large n value based on an understanding of a small n value by using a value obtained by subtracting 5 or 10 from a multiplicand n, and multiplying. You can improve the learning effect of. It can be used by many cram schools and individuals.
　１　　　ベースカード
　１１　　被乗数表示枠
　１２　　乗数表示マス目
　１３　　マス目
　１３ａ　ｐ列マス目
　１３ｂ　ｎ列マス目
　１３ｃ　統合ｎ列マス目
　２　　　作業用カ―ド 1 Base card 11 Multiplicand display frame 12 Multiplier display square 13 square 13a p row square 13b n row square 13c Integrated n row square 2 Work card

Claims (6)

  1. 　掛け算を学習するための算数学習用教材であって、
    　５又は１０であるｐについて、
    　ｓ行ｔ列（５≦ｓ）（ｐ＜ｔ＜２ｐ）列の形に連接されたｓ×ｔのマス目が描かれたベースカードと、
    　前記マス目と同大の正方形を１方向にｕ個（ｕ＜ｐ）連接してなる１行ｕ列の作業用カードとを備え、
    　前記ベースカードは、ｍ行ｐ列目のマス目にｍ×ｐの値を示す数字が表示され、ｍ行ｖ列目（ｖ＜ｐ）のマス目には数字が表示されていないことを特徴とする、算数学習用教材。     It is a teaching material for learning arithmetic for learning multiplication.
    For p, which is 5 or 10,
    A base card with s × t squares connected in the form of s rows and t columns (5 ≦ s) (p <t <2p) columns,
    It is equipped with a 1-row, u-column work card formed by connecting u (u <p) squares of the same size as the squares in one direction.
    The base card is characterized in that a number indicating a value of m × p is displayed in the square of m row and p column, and no number is displayed in the square of m row and v column (v <p). Teaching materials for learning mathematics.
  2. 　前記ベースカードは、ｎ＞ｐである１つのｎについて、ｍ行ｎ列目のマス目にはｍ×ｎの値を示す数字が表示され、ｍ行ｗ列目（ｗ＞ｐかつｗ≠ｎ）のマス目には数字が表示されていないことを特徴とする、請求項１に記載の算数学習用教材。 In the base card, for one n where n> p, a number indicating the value of m × n is displayed in the square of the m row and nth column, and the m row and wth column (w> p and w ≠ n). The teaching material for arithmetic learning according to claim 1, wherein the number is not displayed in the square of).
  3. 　前記ベースカードは、ｎ＞ｐである１つのｎについて、ｍ行ｎ列目（ｎ＞ｐ）のマス目にはｍ×（ｎ―ｐ）の値を示す数字が表示され、ｍ行ｗ列目（ｗ＞ｐかつｗ≠ｎ）のマス目には数字が表示されていないことを特徴とする、請求項１に記載の算数学習用教材。 In the base card, for one n where n> p, a number indicating a value of m × (n−p) is displayed in the square of m row nth column (n> p), and m row w column. The teaching material for arithmetic learning according to claim 1, wherein a number is not displayed in the square of the eye (w> p and w ≠ n).
  4. 　ｎ＝ｔであり、ｕ＝ｎ－ｐであることを特徴とする。請求項２又は３に記載の算数学習用教材。 It is characterized in that n = t and u = np. The teaching material for math learning according to claim 2 or 3.
  5. 　前記ベースカードは、ｎ＞ｐである全てのｎについて、ｍ行ｎ列目のマス目にはｍ×ｎの値を示す数字が表示されていることを特徴とする、請求項１に記載の算数学習用教材。 The base card according to claim 1, wherein a number indicating a value of m × n is displayed in the square of the m row and the nth column for all n where n> p. Teaching materials for learning math.
  6. 　前記ベースカードは、ｎ＞ｐである全てのｎについて、ｍ行ｎ列目のマス目にはｍ×（ｎ－ｐ）の値を示す数字が表示されていることを特徴とする、請求項１に記載の算数学習用教材。 The base card is characterized in that, for all n where n> p, a number indicating a value of m × (n−p) is displayed in the square of the m row and nth column. Teaching materials for learning mathematics described in 1.
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