JP6719675B1 - Math learning materials - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a teaching material for arithmetic learning capable of learning multiplication for a value of a large multiplicand n based on an understanding of a value of a small multiplicand n. SOLUTION: This is a learning material for arithmetic learning for learning multiplication, in which p of 5 or 10 is connected in the form of s rows and t columns (5≦s) (p<t<2p) columns. A base card 1 on which a square 13 of ×t is drawn, and a work card 2 of 1 row and u column formed by connecting u (u<p) squares having the same size as the square in one direction, In the base card 1, a number indicating the value of m×p is displayed in the square 13a in the mth row and the pth column, and no number is displayed in the square 13 in the mth row and the vth column (v<p). Provide teaching materials for math learning.

Description

The present invention relates to an arithmetic learning material for learning multiplication.

Learn multiplication, addition, and subtraction in lower secondary school arithmetic education. Here, the learning of multiplication is based on the so-called multiplication table. However, since multiplication tables are usually learned by memorization, there is little opportunity to learn the concept of multiplication.

Here, considering learning the concept of multiplication without relying on memorization of multiplication tables, when the multiplicand is n, the multipliers are 1, 2, 3,. ． ． It is important for students to understand the progression of arithmetic progressions (n, 2n, 3n... ). In this respect, using a card in which the value of m×n is displayed in the cell of the m-th row and the n-th column as shown in Patent Document 1, it is possible to bring the students closer to understanding the arithmetic progression.

Here, it is when the value of n is small that the student who sees the number sequence can surely grasp that it is “equal number sequence”. For example, a sequence of n=1, 1, 2, 3. ． ． , N=2, 2, 4, 6. ． ． Can be easily understood as an arithmetic progression. On the other hand, for example, a sequence of numbers 7, 14, 21,. ． ． It can not be said that it is easy to understand that it is an arithmetic sequence by looking at only the sequence of.

If so, it is expected that the teaching material for arithmetic learning can learn the multiplication for the large value of n based on the understanding of the small value of n.

JP, 2017-134299, A

An object of the present invention is to provide a teaching material for arithmetic learning capable of learning multiplication for a large value of the multiplicand n based on an understanding of the value of the small multiplicand n.

When the multiplicand n is 5<n<10, the product mn can be expressed as mn=5m+(n-5)m, where m is the multiplier. 5m is the 5th step that is easy to remember in the multiplication table, and (n-5)m has (n-5) less than 5, so it can be easily understood.

Here, regarding the point of adding 5m and (n-5)m, if m is an even number, 5m becomes a multiple of 10, and it is easy to consider only the tens place without considering the ones place. If m<10 in the range learned in multiplication table, it is easy to add a single digit without adding a carry to the tens digit.

When m is an odd number, the processing of 5 in the 1s place of 5m is performed. As this processing, various methods can be considered depending on the ability of the student to add, as described later.

As described above, the teaching material for arithmetic learning of the present invention handles mn=5m+(n-5)m, and multiplies the value of the multiplicand n of 6 or more based on the understanding of the value of the multiplicand n of 5 or less. Allows you to learn.

Note that it is also possible to treat as mn=10m+(n-10)m, and to learn the 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.

The teaching material for math learning of the present invention is
A learning material for arithmetic learning for learning multiplication,
For p that is 5 or 10,
a base card in which s×t squares are drawn connected in the form of s rows and t columns (5≦s) (p<t<2p) columns;
A work card of 1 row and u column, which is formed by connecting u (u<p) squares having the same size as the square in one direction,
The base card is characterized in that a number indicating the value of m×p is displayed in the mth row and the pth column, and no number is displayed in the mth row and the vth column (v<p). And

According to this feature, it becomes easy to learn the product of the multiplicand n with n>p and the multiplier m 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 attention is focused on the number indicating the value of m×p.

The teaching material for math learning of the present invention is
In the base card, for one n with n>p, a number indicating the value of m×n is displayed in the mth row and the nth column, and the mth row and the wth column (w>p and w≠n). ) The numbers are not displayed in the squares.

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 does not consider other values.

The teaching material for math learning of the present invention is
In the base card, for one n with n>p, a number indicating a value of m×(n−p) is displayed in the cell at the mth row and the nth column (n>p), and the mth row and the wth column. It is characterized in that no numbers are displayed in the squares of the eyes (w>p and w≠n).

This feature also facilitates learning as mn=pm+(n−p)m. A number indicating the value of m×(n−p) is displayed instead of the value of m×n. Although it is not the value of the product mn, it is a value that becomes the product mn by adding the values of m×p, so it can be easily understood.

The teaching material for math learning of the present invention is
It is characterized in that n=t and u=n−p.

According to this feature, there are no squares where the multiplicand n is exceeded. The base card is designed by limiting the multiplicand to n.

The teaching material for math learning of the present invention is
The base card is characterized in that a number indicating a value of m×n is displayed in a cell in the m-th row and the n-th column for all n where n>p.

According to this feature, one base card can be shared for learning many multiplicands n.

The teaching material for math learning of the present invention is
The base card is characterized in that a number indicating a value of m×(n−p) is displayed in a cell in an m-th row and a n-th column for all n where n>p. Material for math learning described in 1.

This feature also makes it possible to use one base card for learning many multiplicands n.

According to the teaching material for arithmetic learning of the present invention, it is possible to learn multiplication for a large value of n based on an understanding of a small value of n by using a value obtained by subtracting 5 or 10 from the multiplicand n. The learning effect of can be improved.

FIG. 1 is a diagram showing a base card. (Example 1) FIG. 2 is a diagram showing the use of the work card. (Example 1) FIG. 3 is a diagram showing the use of the base card and the work card. (Example 2) FIG. 4 is a diagram showing the use of the base card and the work card. (Example 3) FIG. 5: is a figure which shows use of a base card and a work card. (Example 3) FIG. 6 is a diagram showing a base card. (Example 4) FIG. 7 is a diagram showing the use of the work card. (Example 4)

Examples of the present invention will be described below.

FIG. 1 is a diagram showing a base card. The base card 1 is composed of rectangular cells arranged in a matrix. The multiplicand display frame 11 is provided at the lower end, the multiplier display grid 12 is provided at the left end, and the other areas are grids 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 (6 in FIG. 1A, FIG. 7 is displayed in B), 8 is displayed in FIG. 1C, and 9 is displayed in FIG.

The multiplier display cell 12 displays the multiplier m. The base card 1 relates to a plurality of multipliers m (in this embodiment, 1 to 10) m for one multiplicand n, and since each line is a content related to one multiplier m, each of the lines divided into squares The value of m is displayed in the square.

The cell 13 is a blank cell that displays a number indicating the value of m×n on the cell of the m-th row and the n-th column, or does not display the number. Here, the values of m and n in the m-th row and the n-th column are assumed to be the squares on the base card 1 not including the multiplicand display frame 11 and the multiplier display squares 12.

Here, the following standard is used to indicate which square the number indicating the value of m×n is displayed and which square is not displayed. (1) A number indicating the value of m×p is displayed in the cell of the p-th column (p is 5 or 10, p=5 in the present embodiment) (p-th cell 13a). (2) A number indicating the value of m×n is displayed in the n-th cell (n-th cell 13b). (3) No numbers are printed on the other squares.

FIG. 2 is a diagram showing the use of the work card. Hereinafter, a procedure for learning multiplication using the base card 1 will be described.

The student places the work cards 2 of 1 row and u column in order from the bottom (in order of work cards 2a, 2b, 2c, 2d in FIG. 2). FIG. 2 is for learning the case where the multiplicand n is 8 and the multiplier m is 4 (8×4=32). The same applies to other multiplicands n and multipliers m.

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 row (multiplication of the multiplicand n is 3 is no problem) It should be possible).

Therefore, the student must add the value "20" displayed in the p-column square 13d adjacent to the uppermost row on which the work card 2 is placed to 12, and the product value (m×n) is 32. Guide.

Here, for addition with 20+12=32, since 20 is a multiple of 10, it is easy to consider only the tens place without considering the ones place.

In the above example, m is an even number (4), but when m is an odd number, it is necessary to perform the processing of 5s in the 1s place for the value displayed in the p-column square 13d adjacent to the top row. is there. For example, when m=5, the value (m×n) of the product is 40, as in the case where m is an even number, if the student is proficient in addition such that 25+15=40 can be easily added. I can guide you.

If the student is not familiar with the addition, (m-1) is an even number, so (m-1)*5 can be added and 5 can be added later. 20+15=35 is calculated first and then 35+5=40.

The present embodiment describes another form of the base card 1. The display of the n-th cell 13b is different from that of the first embodiment, and the rest is the same as that of the first embodiment. Detailed description of the same parts as those in the first embodiment will be omitted.

FIG. 3 is a diagram showing the use of the base card and the work card. An example of the base card 1 is shown in FIG. The multiplicand is 8, which corresponds to FIG. The same applies to other multiplicands.

In the first embodiment, the number indicating the value of m×n is displayed in the n-th cell 13b, but in the present embodiment, the number indicating the value of m×(n−p) is displayed. FIG. 3B shows the use of the work card. The number of cells covered by the work card is displayed in the n-th cell 13b.

The student adds the value “20” displayed in the p-th column 13d adjacent to the uppermost 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 n-th cell 13b.

The present embodiment describes another form of the base card 1. The integrated n-th column 13c is replaced with the n-th column 13b, and the display of the multiplicand display frame 11 is different from that of the first embodiment, and the other points are the same as those of the first embodiment. Detailed description of the same parts as those in the first embodiment will be omitted.

FIG. 4 is a diagram showing the use of the base card and the work card. The base card 1 is shown in FIG. The position of the n-th cell 12b differs depending on the value of n. In the present embodiment, a number indicating the value of m×n is displayed at the position of all the n-th cells 12b corresponding to n=6, 7, 8, 9. The whole square in which these numbers are displayed is the integrated n-th row square 13c.

FIG. 4B shows the use of the work card. The student learns by looking at the numbers displayed on the squares of the base card 1 at the right end of the work card 2.

The base card 1 of this embodiment can use one card for all learning of n=6, 7, 8, 9. Therefore, in the multiplicand display frame 11, all 6, 7, 8, 9 are displayed at positions corresponding to n(6, 7, 8, 9) of the integrated n-th column grid 13c.

It should be noted that, in the integrated n-th column cell 13c, a number indicating the value of m×(n−p) may be displayed instead of the number indicating the value of m×n, as in the second embodiment. The use of the base card and work card in this case is shown in FIG.

The present embodiment describes a base card 1 of another form. In the first embodiment, p=5, but p=10. Others are the same as in the first embodiment. Detailed description of the same parts as those in the first embodiment will be omitted.

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 a case of n=13 (=p+3), and is the same as that shown in FIG. 1C in the first embodiment in that n=p+3. In addition, n=11, 12, n=14. ． ． The same is true for.

FIG. 7 is a diagram showing the use of the 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 other multiplicands n and multipliers m.

The student understands that the number of squares covered by the work card is 3×4=12, and is displayed in the p-row square 13d adjacent to the top row on which the work card 2 is placed. The added value “40” is added to 12 to derive that the product value (m×n) is 52.

Here, for addition with 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 grid 13d is a multiple of 10. It is not necessary to perform the processing of the ones digit 5.

In this embodiment, p=10 is set on the basis of the first embodiment. However, setting p=10 instead of p=5 means that p=5 and p=10 Since the design is the same, even when the display of the n-th cell 13b is changed to a number indicating the value of m×(n−p) as in the second embodiment, the integrated n-th cell 13c is changed as in the third embodiment. It can also be provided.

As described above in detail in the four examples, the teaching material for arithmetic learning of the present invention is based on the knowledge of multiplication with mn=pm+(n−p)m, where (n−p) is the multiplicand. It becomes easy to learn multiplication with respect to the multiplicand n. By setting p to 5 or 10, efficient learning becomes possible.

The base card 1 and the work card 2 are considered to be made of paper. However, other materials such as wood and plastic may be used.

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.

In Examples 1, 2, and 4, the base card 1 and the work card 2 which are different for each multiplicand are used. 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 selected correctly, which is convenient. Further, also in the third embodiment, the work card 2 is different for each multiplicand, which is convenient in that the work card can be automatically selected.

Further, as shown in the four examples, various base cards 1 are conceivable, and it is also conceivable that they are selectively used according to the proficiency level of the student. It is effective to select the type of base card 1 to be used by a computer program.

According to the teaching material for arithmetic learning of the present invention, it is possible to learn multiplication for a large value of n based on an understanding of a small value of n by using a value obtained by subtracting 5 or 10 from the multiplicand n. The learning effect of can be improved. It can be used in many private schools and individuals.

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)

A learning material for arithmetic learning for learning multiplication,
For p that is 5 or 10,
a base card in which s×t squares are drawn connected in the form of s rows and t columns (5≦s) (p<t<2p) columns;
A work card of 1 row and u column, which is formed by connecting u (u= t−p ) squares having the same size as the square in one direction,
On the base card, a number indicating a value of m×p is displayed in a cell on the m-th row and the p-th column, a number indicating a value of m×t is displayed on a cell on the m-th row and the t-th column, and m-row v A learning material for math learning, which is characterized in that numbers are not displayed in the cells in the column (v<p). In the base card, for one or more (including t) of n>p (including t) , a number indicating a value of m×n is displayed in the cell in the m-th row and the n-th column, and the m-th row and the w-th column ( 2. The teaching material for math learning according to claim 1, wherein a number is not displayed in a cell of w>p and w≠n). A learning material for arithmetic learning for learning multiplication,
For p that is 5 or 10,
a base card in which s×t squares are drawn connected in the form of s rows and t columns (5≦s) (p<t<2p) columns;
A work card of 1 row and u column, which is formed by connecting u pieces (u=tp) of squares having the same size as the square in one direction,
On the base card, a number indicating the value of m×p is displayed in the cell in the m-th row and the p-th column, and a number indicating the value of m×(tp) is displayed in the cell in the m-th row and the t-th column. , A mathematics learning material characterized in that a number is not displayed in the square at the m-th row and the v-th column (v<p) . In the base card, for one or more (including t) n for which n>p, a number indicating a value of m×(n−p) is displayed in the mth row and nth column, and the mth row is displayed. 4. The teaching material for math learning according to claim 3, wherein numbers are not displayed in the cells in the w-th column (w>p and w≠n) . A learning material for arithmetic learning for learning multiplication,
For p that is 5 or 10,
a base card in which s×t squares are drawn connected in the form of s rows and t columns (5≦s) (p<t<2p) columns;
A work card of 1 row and u column, which is formed by connecting u pieces (u≦tp) of squares having the same size as the square in one direction,
On the base card, a number indicating a value of m×p is displayed in a cell on the m-th row and the p-th column, a number indicating a value of m×t is displayed on a cell on the m-th row, and the m-th row. No number is displayed in the cell in the v-th column (v<p), and a number indicating the value of m×n is displayed in the cell in the m-th row and the n-th column for all n with n>p. A teaching material for math learning that is characterized by A learning material for arithmetic learning for learning multiplication,
For p that is 5 or 10,
a base card in which s×t squares are drawn connected in the form of s rows and t columns (5≦s) (p<t<2p) columns;
A work card of 1 row and u column, which is formed by connecting u pieces (u≦tp) of squares having the same size as the square in one direction,
On the base card, a number indicating the value of m×p is displayed in the cell of the m-th row and the p-th column, a number indicating the value of m×t is displayed in the cell of the m-th row and the t-th column, and the m-row v No number is displayed in the cell in the column (v<p), and for all n with n>p, a number indicating the value of m×(n−p) is displayed in the cell in the m-th row and the n-th column. A teaching material for math learning that is displayed.

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