JP6372893B2 - Math learning materials - Google Patents

Description

  The present invention relates to an arithmetic learning material for learning multiplication, addition, and subtraction, and an arithmetic education method using the same.

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

  Therefore, for example, Patent Document 1 discloses a building block whose height is proportional to log 10A with respect to a value A of 1 to 9. Using this building block, two blocks each representing the numbers A and B to be multiplied are stacked and experienced to experience the same height as the building block corresponding to the answer C of A × B. be able to. However, it does not allow the learner of the table (hereinafter referred to as “student”) to understand the concept of logarithm, and it is only an effect of learning, and does not promote the understanding of the student.

  Regarding addition and subtraction, Patent Document 2 discloses a teaching tool for arithmetic education that moves a sphere in an internal region designed so that five spheres are arranged. It is a teaching tool for math education that makes it easy to understand the carry-up and carry-down in decimal notation when five pieces become two pieces. However, there has not been known a learning material for math learning that promotes understanding of multiplication by utilizing the fact that 5 becomes 10 by 2.

JP 2005-305002 A JP 2012-058750 A

  The present invention provides an arithmetic learning material for experiencing learning of multiplication, addition, and subtraction, and an arithmetic education method using the same, and more particularly, an arithmetic learning material effective for the multiplication table, and the use of the same. It is an issue to provide a mathematical arithmetic method.

The teaching material for arithmetic learning of the present invention is:
Math learning material for learning multiplication,
A base card on which at least 81 square cells connected in a shape of at least 9 rows and 9 columns are drawn;
A work card having a unit of 10 having a shape formed by connecting ten squares having the same size as the square;
A work card having a unit of 5 having a shape formed by connecting five squares;
A work card with a unit of a fraction having a shape formed by connecting the squares in any number of 1 to 4;
With
The work card with the unit of 10 includes a work card with a unit of the first 10 having a shape in which the square is connected in 10 in 5 rows and 2 columns or 2 rows and 5 columns,
The work card having the unit of 5 includes a work card having a unit of the first 5 having a shape formed by connecting five of the squares in 5 rows and 1 column or 1 row and 5 columns,
The work card with the fraction as a unit includes a work card with a unit of 1 having one square.
It is characterized by that.

According to this feature, a student who learns multiplication by m × n is a working card whose unit is a rectangular area including m rows and n columns of the 81 cells drawn on the base card. And other work cards are filled side by side, the number of work cards in units of 10 used to fill the rectangular area (in principle, the tenth place of the product), and the squares of the other work cards By knowing the number of squares contained in the rectangular area from the number of (in principle, the one's place of product), mxn multiplication can be learned in decimal notation. In addition, since it becomes the same only if the vertical and horizontal sides of the rectangular area are reversed in the case of n rows and m columns, it will be described as m rows and n columns.
The work card having the first 10 as a unit and the work card having the first 5 as a unit are unified to have a width or height of 5, and can be arranged neatly and arranged easily. It is not preferable that the work of filling up side by side has a puzzle-like difficulty because the student's thinking is away from learning of multiplication. It is preferable that it can be filled easily.
A work card having a fraction as a unit is “connected by any number of 1 to 4”, but “worked by only 1” has one square.

The teaching material for arithmetic learning of the present invention is:
The work card having the unit of 10 includes two second 10 work cards having a shape formed by connecting five of the squares in 5 rows and 1 column or 1 row and 5 columns. It is characterized by.

  According to this feature, two rectangular regions in 5 rows and 1 column or 1 row and 5 columns can be combined and arranged as a region having 10 as a unit. Specific methods and effects will be described later.

The teaching material for arithmetic learning of the present invention is:
The work card having the unit of 10 includes a work card having a unit of 10 having a shape formed by connecting the squares in 4 rows and 3 columns or 3 rows and 4 columns. To do.

  According to this feature, work cards in units of 10 can be arranged in a rectangular area having no width and no height. Specific methods and effects will be described later. Here, “within 4 rows and 3 columns or within 3 rows and 4 columns” means that the width and height are determined when the squares are drawn every 5 rows and every 5 columns as described later. A rectangular area of less than 5 and including 10 or more cells is of 4 rows 3 columns, 3 rows 4 columns, and 4 rows 4 columns, but within 4 rows 3 columns or 3 rows 4 columns It is because it can respond to any.

The teaching material for arithmetic learning of the present invention is:
The work card having the unit of 5 includes a work card having a second unit of 5 having a shape in which five squares are connected in four rows and three columns or three rows and four columns. And

  According to this feature, work cards in units of 5 can be arranged in a rectangular area having no width and height of 5. Specific methods and effects will be described later.

The teaching material for arithmetic learning of the present invention is:
The work card with the fraction as a unit is
A work card having a unit of 2 having a shape formed by connecting two of the squares;
A work card with a unit of 3 having a shape formed by connecting the three squares;
A work card having a unit of 4 having a shape formed by connecting four of the squares;
Is further provided.

  According to this feature, the last remaining fractional area can be filled with a small number of cards. The effort of filling up is reduced, and it becomes easier for students to concentrate on the learning of multiplication.

The teaching material for arithmetic learning of the present invention is:
The work card with the unit of 10, the work card with the unit of 5 and the work card with the fraction as a unit have a pattern drawn inside each of the connected squares. Features.

  According to this feature, the student can visually recognize the pattern drawn on the work card and intuitively understand or count it to easily grasp the number of squares included in the rectangular area. .

The teaching material for arithmetic learning of the present invention is:
The work card having the unit of 10 includes two sets of work cards in which the design is drawn using the first and second colors,
The work card having the unit of 5 has the design drawn using a third color,
The work card having the fraction as a unit is characterized in that the symbol is drawn using a fourth color.

  According to this feature, the design of the work card in units of 10 and the work card in units of 5, and the work card in units of fractions have different colors. In addition, many work cards with a unit of 10 may be used, but they can be color-coded in units of cards. The student can visually recognize 10 units in units divided by color, and can visually recognize less than 10 units. Note that the work card with a unit of 5 has a different color from the work card with a fraction as a unit. When two work cards with a unit of 5 are used, the work card has a total of 10 It can be visually recognized as.

The teaching material for arithmetic learning of the present invention is:
One of the squares located at the four corners included in the 81 square is set as a reference square,
The 81 squares are drawn on the base card, divided into 5 rows and 5 columns with reference to the reference square.

  According to this feature, it is possible to easily arrange work cards having 10 as a unit with the section as a mark.

The teaching material for arithmetic learning of the present invention is:
The base card is characterized in that for each of the 81 cells, a number of values obtained by multiplying m and n in the m-th row and n-th column of the reference cell is drawn. To do.

  According to this feature, the product value can be shown to the student. Students can check the result of multiplication not only by the number of work cards but also by numbers. In particular, when there is no teacher and learns, there is an effect of answering together.

The teaching material for arithmetic learning of the present invention is:
In the base card, numbers 1 to 9 are drawn next to the first row of the 81 cell, corresponding to the first to ninth columns based on the reference cell. Next to the first column of cells, numbers 1 to 9 are drawn corresponding to the first to ninth rows with reference to the reference cells.

  According to this feature, two numbers (multiplier and multiplicand) to be multiplied by the student can be indicated. The student can visually check the multiplier and the multiplicand in the work of filling the grid, and never forgets what kind of multiplication is being learned.

The teaching material for arithmetic learning of the present invention is:
Among the 81 cells of the base card, at least the m rows and n columns of the remaining cells excluding the m rows and n columns including the reference cells and the m rows and n columns. It further comprises an auxiliary card that covers the cells adjacent to the eyes.

  According to this feature, it is possible to emphasize and represent the m-by-n columns related to the target m × n multiplication using the auxiliary card. A rectangular area of m rows and n columns is clearly shown, and the student's work becomes easy.

The arithmetic education method of the present invention is:
A mathematical education method for teaching m × n multiplication using the above-mentioned arithmetic learning material,
A work card whose unit is the m row and n column rectangular area including the reference cell and the m row and n column cell among the 81 cells of the base card, Filling the work card with the unit of 5 and the work card with the fraction as a unit;
The number of work cards in units of 10 used to fill the rectangular area to students, the work cards in units of 5 and the squares included in the work cards in units of fractions And grasping the number of squares included in the rectangular area from the number of
It is characterized by including.

  According to this feature, it is possible to allow a student to experience sensible learning by multiplying m × n by a decimal system.

The arithmetic education method of the present invention is:
In filling it up,
When the rectangular area includes a sub-rectangular area having a width or height of 5 drawn by dividing the rectangular area, the work card with the first 10 as a unit and the work with the second 10 as a unit Arranging the sub-rectangular areas with the width or height of 5 as much as possible,
When the sub-rectangular area having a fractional width other than the sub-rectangular area having the width or height of 5 in the rectangular area includes ten or more cells, the work card having the third 10 as a unit. Arranging the sub-rectangular regions of the fraction width or height as much as possible;
Arranging the work cards in units of 5 and arranging the remaining areas as much as possible;
Arranging work cards in units of the fractions to fill all the rectangular areas;
It is characterized by including.

  According to this feature, the procedure for filling the squares is standardized, and many students can surely perform it. In addition, taking advantage of the fact that 2 becomes 10 by 2 makes it possible to easily learn bodily sensation in decimal notation.

The teaching material for arithmetic learning of the present invention is:
The work card with the unit of 10, the work card with the unit of 5, and the work card with the fraction unit, the pattern is drawn inside each of the connected squares,
It is a teaching material card in which the symbol is printed on the base card with respect to a state after the rectangular area is completely filled by the arithmetic education method.

  According to this feature, a learning material for arithmetic learning that visually promotes an understanding based on the decimal system is provided without the student performing an operation to fill the grid.

The teaching material for arithmetic learning of the present invention is:
Math learning material for learning addition and subtraction,
A base card on which at least 54 square cells connected in a shape of at least 3 rows and 18 columns are drawn;
A first work card formed by connecting a square of the same size as the squares in a number i of 1 to 9 in one direction;
A second work card formed by connecting a square having the same size as the squares to a number j of 1 to 9, in one direction;
A third work card formed by connecting a square of the same size as the squares to a number k of 2 to 18 in the one direction;
It is characterized by providing.

  According to this feature, addition and subtraction can be learned by the same work card as that for learning the above-mentioned table. Since students learn addition and subtraction before multiplication, they can become familiar with the work card. It becomes easy to attach when learning the multiplication table.

The teaching material for arithmetic learning of the present invention is:
The third working card has a third working card A formed by connecting 10 squares having the same size as the squares in the one direction, and 1 to 9 squares having the same size as the squares. And a third work card B connected in several directions.

  According to this feature, 11 or more third work cards can be a combination of two cards, and since one of them is 10, an understanding according to the decimal system is possible.

The teaching material for arithmetic learning of the present invention is:
The first work card has a pattern drawn on the inside of each of the connected squares using a first color,
The second work card has a pattern drawn on the inside of each of the connected squares using a second color,
The third work card is characterized in that a pattern is drawn inside each of the connected squares using a third color.

  According to this feature, the student can visually recognize and understand the symbol. In addition, in both the addition of i + j = k and the subtraction of k−i = j, the color of the third work card representing k is fixed, so that it is easy to understand the sum and difference.

The arithmetic education method of the present invention is:
An arithmetic education method for teaching the addition of i + j = k using the arithmetic learning material described above,
Placing the first work card on the first row of the 54 squares of the base card in alignment with the end of the first row of cells;
Allowing the student to place the second work card on the second row of the 54 squares of the base card in alignment with the end of the first work card;
Placing the third work card on the third row of the 54 squares of the base card in alignment with the end of the third row of cells;
It is characterized by including.

  According to this feature, addition sensation learning can be performed.

The arithmetic education method of the present invention is:
An arithmetic education method for teaching subtraction of k−i = j using the above-described arithmetic learning material,
Placing the third work card on the first square of the 54 squares of the base card in alignment with the end of the first square;
Placing the first work card on the second row of the 54 squares of the base card in accordance with the end of the second row of squares;
Allowing the student to place the second work card on the third row of the 54 squares of the base card in alignment with the end of the first work card;
It is characterized by including.

  According to this feature, subtraction experience learning is possible.

  According to the teaching material for arithmetic learning and the arithmetic teaching method using the same according to the present invention, it is possible to experience and learn multiplication, addition and subtraction easily. In particular, it is effective for studying multiplication tables.

FIG. 1 is a diagram illustrating a base card included in an arithmetic learning material. (Examples 1 and 2) FIG. 2 is a diagram showing a work card having 10 as a unit included in the arithmetic learning material. Example 1 FIG. 3 is a diagram showing a work card having a unit of 5 included in the arithmetic learning material. (Examples 1 and 2) FIG. 4 is a diagram showing a work card with a fraction included in the arithmetic learning material. (Examples 1 and 2) FIG. 5 is a diagram illustrating an example of an auxiliary card included in the arithmetic learning material. Example 1 FIG. 6 is a diagram illustrating an example of an answer card included in the arithmetic learning material. (Examples 1 and 2) FIG. 7 is a diagram showing a procedure of a method for teaching m × n multiplication using an arithmetic learning material. Example 1 FIG. 8 is a diagram showing a procedure of a method of teaching m × n multiplication using arithmetic learning materials. Example 1 FIG. 9 is a diagram illustrating a procedure of a method of teaching m × n multiplication using a learning material for arithmetic learning. Example 1 FIG. 10 is a diagram showing a procedure of a method of teaching m × n multiplication using arithmetic learning materials. Example 1 FIG. 11 is a diagram showing a learning material card. Example 1 FIG. 12 is a diagram showing a base card included in the arithmetic learning material. (Example 3) FIG. 13 is a diagram showing a first work card included in the arithmetic learning material. (Example 3) FIG. 14 is a diagram showing a second work card included in the arithmetic learning material. (Example 3) FIG. 15 is a diagram illustrating a third work card included in the arithmetic learning material. (Example 3) FIG. 16 is a diagram showing another third work card included in the arithmetic learning material. (Example 3) FIG. 17 is a diagram illustrating an example of an answer card included in the arithmetic learning material. (Example 3) FIG. 18 is a diagram showing a procedure of a method for teaching the addition of i + j = k using the arithmetic learning material. (Example 3) FIG. 19 is a diagram illustrating a procedure of a method for teaching subtraction of k−i = j using an arithmetic learning material. (Example 3) FIG. 20 is a diagram illustrating a division auxiliary card. Example 4

  Examples of the present invention will be described below.

  In this embodiment, multiplication is learned.

  The learning material 1 for arithmetic learning is a teaching material set for experiencing learning by multiplication in decimal notation, and work cards 30, 25, which are based on the base cards 10, 10, and work cards 30, 1, which are based on the base cards 10, 10. A work card 40, an auxiliary card 50, and an answer card 60 are provided.

  FIG. 1 shows a base card 10. The base card 10 is made of, for example, sheet-like paper, plastic, or the like, and is composed of an image (hereinafter referred to as “tablet image”) displayed on a tablet-type display in accordance with the size of a work card described later. There may be. On the surface of the base card 10, there are drawn 100 squares 11 of a square shape including at least 9 rows and 9 columns, and in this embodiment, connected in a shape of 10 rows and 10 columns. Here, the term “continuous” means that square-shaped squares are connected to each other on one side (that is, overlapped). One of the squares located at the four corners included in the 100 squares 11, in this embodiment, the lower left square is set as the reference square (that is, the first row and first column square) 11 a. It is assumed that the first to tenth rows are arranged from left to right and the first to tenth columns are arranged from bottom to top with reference grid 11a as a reference.

  On the left side of the first row of the 100th cell, numbers 1 to 10 are drawn corresponding to the first to tenth columns, respectively, with reference to the reference cell 11a. These numbers from 1 to 10 are called the index 12a. Further, below the first column of the 100 squares 11, numbers 1 to 10 are drawn corresponding to the first to tenth lines, respectively, with reference to the reference square 11a. These numbers from 1 to 10 are called the index 12b. These indexes 12a and 12b allow the student to recognize two numbers (multiplier and multiplicand) of multiplication to be learned.

  In each of the 100 cells 11, numbers of values obtained by multiplying m and n by m cells in the nth column are drawn. For example, the number “21” is drawn in the cell in the third row and the seventh column.

  The 100 squares 11 are partitioned using a thick solid line every five rows and every five columns with reference to the reference square 11a.

  FIG. 2A and FIG. 2B show work cards 20 and 25 in units of 10, respectively. The work cards 20 and 25 in units of 10 are sets of cards each having a shape formed by connecting ten squares of the same size as the grid 11.

  The work card 20 in units of 10 includes work cards 21, 22, 23a, 23b, 24a, and 24b as an example.

  The work card 21 (work card having the first 10 as a unit) has a rectangular shape formed by connecting 10 squares in 5 rows and 2 columns.

  The work card 22 (work card with the second 10 as a unit) includes two cards having a shape formed by connecting five squares in five rows and one column. Depending on the shape of the rectangular area of the base card 10, when the rectangular area includes ten or more cells but the work card 21 cannot be overlapped with the rectangular area, the two work cards 22 are separated to form a rectangular area. By overlapping in different regions, 10 can be arranged in units.

  The work cards 23a, 23b, 24a, and 24b (work cards having the third 10 as a unit) have a shape formed by connecting 10 squares in 4 rows and 3 columns. More specifically, the work card 23a has a shape in which nine squares connected in the form of 3 rows and 3 columns are connected to one square on the upper right square. The work card 23b has a symmetrical shape with the work card 23a. The work card 24a has a shape in which two squares are connected to two squares on the upper right on eight squares connected in a form of four rows and two columns. The work card 24b has a symmetrical shape with the work card 24a.

  Note that the work cards 21, 22, 23a, 23b, 24a, and 24b can be used by being rotated in units of 90 degrees, and thus include the illustrated cards rotated by 90 degrees, 180 degrees, and 270 degrees.

  In the work cards 21, 22, 23a, 23b, 24a, and 24b, symbols are drawn using the first color in each of the ten squares. Here, in this embodiment, the symbol is a circle and the first color is red.

  Using these work cards 21, 22, 23a, 23b, 24a, and 24b, the cells drawn on the base card 10 can be arranged to be filled in 10 units as described later.

  The work card 25 with the unit of 10 is the same as the work card 20 with the unit of 10 except that the design is drawn using a second color different from the first color. To do. Here, in this embodiment, the second color is blue.

  By including two sets of work cards 20 and 25 in which the design is drawn using the first and second colors as work cards in units of 10, as will be described later, the student is given 10 units. The number of squares included in the rectangular area can be easily grasped.

  FIG. 3 shows a work card 30 in units of 5. The work card 30 in units of 5 is a set of cards having a shape formed by connecting five squares having the same size as the grid 11. The work card 30 in units of 5 includes work cards 31, 32a, 32b, 33a, 33b, and 34 as an example.

  The work card 31 (work card having the first 5 as a unit) has a shape formed by connecting five squares in five rows and one column.

  The work cards 32a and 32b (work cards having the second 5 as a unit) have a shape in which five squares are connected in four rows and two columns. More specifically, the work card 32a has a shape in which four squares connected in the form of 4 rows and 1 column are connected to one square on the rightmost square. The work card 32b has a symmetrical shape with the work card 32a.

  The work cards 33a and 33b (work cards having the second 5 as a unit) have a shape in which five squares are connected in three rows and two columns. More specifically, the work card 33a has a shape in which three squares connected in a form of three rows and one column are connected to two squares on the two right squares. The work card 33b has a symmetrical shape with the work card 33a.

  The work card 34 (work card having the second 5 as a unit) has a shape formed by connecting five squares in three rows and three columns. More specifically, the work card 34 has a shape in which three squares connected in the form of 3 rows and 1 column are vertically connected to two squares on the leftmost square.

  In the work cards 31, 32a, 32b, 33a, 33b, and 34, a symbol is drawn using a third color in each of the five squares. Here, in this embodiment, the symbol is a circle and the first color is green.

  Note that the work cards 31, 32a, 32b, 33a, 33b, and 34 can be used by being rotated in units of 90 degrees, and therefore include the illustrated ones rotated by 90 degrees, 180 degrees, and 270 degrees.

  Using these work cards 31, 32a, 32b, 33a, 33b, 34, as will be described later, the squares drawn on the base card 10 can be arranged to fill in 5 units.

  FIG. 4 shows a work card 40 with a fraction as a unit. The work card 40 with a fractional unit is a set of cards having a shape in which one to four squares having the same size as the grid 11 are connected. The work card 40 in units of 1 and the like includes work cards 41, 42, 43a, 43b, 44a, 44b, and 44c as an example.

  The work card 41 (work card with 1 as a unit) is a work card with 1 as a unit having a shape including one square.

  The work card 42 (work card in units of 2) is a work card in units of 2 having a shape formed by connecting two squares in two rows and one column.

  The work cards 43a and 43b (work cards in units of 3) are work cards in units of 3 having a shape formed by connecting three squares. The work card 43a has a shape formed by connecting three squares in three rows and one column. The work card 43b has a shape formed by connecting three squares in two rows and two columns. More specifically, the work card 43b has a shape in which two squares connected in the form of 2 rows and 1 column are connected to one square on the right square.

  The work cards 44a, 44b, and 44c (work cards in units of 4) are work cards in units of 4 having a shape formed by connecting four squares. The work card 44a has a shape formed by connecting four squares in four rows and one column. The work card 44b has a shape formed by connecting four squares in three rows and two columns. More specifically, the work card 44b has a shape in which three squares connected in the form of 3 rows and 1 column are connected to one square on the rightmost square. The work card 44c has a shape formed by connecting four squares in two rows and two columns.

  In the work cards 41, 42, 43a, 43b, 44a, 44b, and 44c, a symbol is drawn using a fourth color in each of one to four squares. Here, in this embodiment, the symbol is a circle and the fourth color is black.

  The work cards 41, 42, 43a, 43b, 44a, 44b, and 44c can be used by being rotated in units of 90 degrees, and therefore include the illustrated ones rotated by 90 degrees, 180 degrees, and 270 degrees. .

  Using these work cards 41, 42, 43a, 43b, 44a, 44b, and 44c, as will be described later, a rectangular area including the m-th row and n-th column of the cells drawn on the base card 10 is displayed. Of these, the work cards 20 and 25 in units of 10 and the work card 30 in units of 5 cannot be filled up, and the remaining area can be filled up.

  FIG. 5 shows the auxiliary card 50. The auxiliary card 50 is an L-shaped concealment of the remaining squares except for the squares of the m-th row and the n-th row, including the reference square 11a and the m-th row and the n-th row of the 100 squares 11 of the base card 10. Set of cards. The auxiliary card 50 includes, for example, an auxiliary card 51 in which 10 squares having the same size as the grid 11 are connected horizontally and 9 squares are connected vertically below the rightmost square.

  The auxiliary card 50 may include a card having a shape other than the auxiliary card 51. In addition, for example, two cards of 9 rows and 10 columns and 10 rows and 9 columns may be combined and used as the auxiliary card 50 as long as the squares not involved in the learning purpose multiplication can be hidden.

  FIG. 6 shows the answer card 60. The answer card 60 is made of, for example, sheet-like paper, plastic, a tablet image, and the like. On the surface of the answer card 60, the value 1 to 9 is multiplied by the value 1 to 9, and the result of the multiplication, that is, a list of tables is drawn. It is. This allows the student to use the work cards 20, 25 in units of the base cards 10, 10 and the work card 30 in units of 5, and the work card 40 in units of 1 etc. After learning the multiplication, the answer can be confirmed from the answer card 60.

  A method of teaching mxn multiplication using the arithmetic learning material 1 will be described with reference to FIGS. As an example, consider multiplication by 9 × 9 = 81.

  First, as shown in FIG. 7A, the auxiliary card 51 is arranged on the 10th row and 10th column of the 100 cells drawn on the base card 10. As a result, only the 9th and 9th column which is related to the target 9 × 9 multiplication is shown, and the remaining cells which are not related to the target multiplication are hidden.

  FIG. 7B shows the arrangement of the auxiliary cards 51 when considering multiplication of 8 × 7 = 56. Thus, the cells to be filled with the auxiliary card 51 become clear. However, the auxiliary card 51 may not be used. For example, an auxiliary card whose unit is 1 may be used as a mark in a cell of m rows and n columns.

  Next, among the 9th row and 9th column of the base card 10 represented by the auxiliary card 51, on the 9th row and 9th column rectangular area 19 including the reference cell 11a and the 9th row and 9th column square 19x. The work cards 20 and 25 in units of 10 are arranged, and the work cards 30 and 40 in units of 1 to 5 are arranged in the remaining cells to fill the rectangular area 19. The number of squares contained in the work cards 20 and 25 in units of 10 used in this case and the number of squares included in the work cards 30 and 40 in units of 1 to 5 is decimal. To be grasped based on.

  Here, the work cards may be arranged in any way, but many students can be surely arranged by instructing as follows.

  As shown in FIG. 8A, the rectangular area 19 is divided into the following three sub-rectangular areas divided by sections 13a and 13b. (1) a sub rectangular area 19a having a width of 5 on the left side, (2) a sub rectangular area 19b having a height of 5 on the lower side (rotated by 90 degrees), (3) a rectangular area 19 to a sub rectangular area 19a, A rectangular area 19c having a width and height less than 5 remaining after removing 19b. Here, the sub-rectangular regions 19a, 19b, and 19c may not exist depending on the values of m and n. If n <5, the sub rectangular area 19a does not exist, if m <5, the sub rectangular area 19b does not exist, and if m = 5 or n = 5, the sub rectangular area 19c does not exist. In any case, as long as the sub-rectangular areas 19a, 19b, and 19c exist, in principle (the only exception is the case where work cards in units of 10 are arranged in the sub-rectangular area 19c as described later). Place work cards in order and fill them up.

  First, as shown in FIG. 8B, work cards 21 and 26 having the first 10 as a unit are alternately arranged as much as possible in the sub-rectangular area 19a. If m is an even number, the rectangular area 19a is completely filled. If m is an odd number, an area of 1 row and 5 columns remains.

  If the 1-row and 5-column area remains, and if the sub-rectangular area 19b exists, as shown in FIG. 9A, the remaining 1-row and 5-column area and the sub-rectangular area 19b (part) The work cards 22 and 27 having the second 10 as a unit are arranged.

  Thereafter, as shown in FIG. 9B, the work cards 21 and 26 having the first 10 as a unit are alternately arranged and arranged in the sub rectangular area 19b as much as possible. If m + n is an odd number, the sub-rectangular area 19b is completely filled. When m + n is an even number, an area of 5 rows and 1 column remains.

  The procedure for arranging the work cards 20 and 25 in units of 10 in the sub rectangular areas 19a and 19b is simple and easy to understand. In addition, since cards of different colors are used alternately, the number of cards can be easily grasped visually after being arranged.

  Next, when the work cards 20 and 25 in units of 10 are arranged in the sub-rectangular area 19c, they are arranged (see FIG. 9B). Since the sub-rectangular area is less than 5 in both width and height, the work cards 21 and 26 in units of the first 10 and the work cards 22 and 27 in units of the second 10 cannot be arranged. The work cards 23, 24, 28, 29 with the third 10 as a unit are arranged. The sub-rectangular area 19c has a maximum of 16 squares, and there is only one work card 20 or 25 in units of 10.

  Thus, the operation of arranging the work cards 20 and 25 in units of 10 is finished, and the cards are arranged in the remaining area.

  When an area of 5 rows and 1 column (or 1 row and 5 columns) remains in the sub rectangular area 19b (or the sub rectangular area 19a when the sub rectangular area 19b does not exist), as shown in FIG. The work cards 31 having the first 5 as a unit are arranged there.

  When five or more squares remain in the sub-rectangular area 19c, the work cards 32 having the second 5 as a unit are arranged there (see FIG. 10A).

  Thus, the operation of arranging the work cards 30 in units of 5 is finished, and the cards in units of fractions are arranged in the remaining area as shown in FIG. At this time, the number of remaining squares is less than 5, and all squares can be filled with the work card 40 (41, 42, 43, 44) in any one of 1 to 4. .

  Finally, the product value is determined based on the card used.

  The tenth place of the product value is the number of work cards 20 and 25 in units of 10 in principle. As an exception, when the work card 31 having the first unit of 5 is used for the sub-rectangular area 19b (19a) and the work card 32 having the second unit of 5 is used for the sub-rectangular area 19c. Only. In this case, a value obtained by adding 1 to the number of work cards 20 and 25 in units of 10 is a value of the order of 10. The design of the work card 30 in units of 5 is a different color from the other work cards, and the design of the work card 31 in units of the first 5 and the work card 32 in units of the second 5 Are of the same color, the student will easily notice that two work cards 30 with a unit of 5 have been used. The total of two cards is counted as 10, and a value obtained by adding 1 to the number of work cards 20 and 25 in units of 10 can be derived.

  The one's place of the product value is the number of squares of the work card 40 with a fraction as a unit, or when only one work card 30 with a unit of 5 is used, 5 is added to it. It is a number. Students can easily enumerate.

  Here, the student, except for all work cards arranged on the rectangular area 19, has the number of squares included in the rectangular area 19 counted above (81 in this embodiment) as the upper right square of the rectangular area. It can be confirmed that it matches the number drawn on the eye. Further, it can be confirmed from the answer card 60. Realizing that the values obtained through experience are correct, the learning effect is high.

  FIG. 11 shows a learning material card. A teaching material card 70 shown in FIG. 11A is obtained by printing a design in the state shown in FIG. 10B on a base card. It is also possible to learn by looking at the educational material card 70 without performing the operation of arranging the work cards. This is because the units of 10, 5 and fraction are clear depending on the color of the design.

  The educational material card 70 shown in FIG. 11B is for multiplication of 8 × 7 = 56. An effect similar to that of the educational material card 70 shown in FIG.

  When the learning material card 70 shown in FIG. 11B is compared with the learning material card 70 shown in FIG. 11A, the following can be understood. This also applies to the case where the students arrange work cards. (1) Since m is an even number, work cards 22 (27) having the second 10 as a unit are not arranged. (2) Since m + n is an odd number, the first 5 is added to the sub-rectangular area 19b. The work cards 31 in units of are not arranged.

  Depending on the values of m and n, there may be cases where the work cards 32 having the second 5 as a unit are arranged in the sub-rectangular area 19c (1) and (2). In any case, mxn multiplication can be learned by the decimal system.

  As described above in detail, the arithmetic learning material 1 according to the present embodiment is the same size as the base card 10 in which 81 square squares connected in the shape of at least 9 rows and 9 columns are drawn. 10 working cards 20, 25, and 5 working cards 30 having a shape formed by connecting ten squares, and 1 working card having a shape including one square. A work card 40 including 1 to 4 including 41 is provided. As a result, a student who learns multiplication of m × n has a work card 20 having a rectangular area including m squares and n square squares out of 81 squares drawn on the base card 10 as units. Included in the rectangular area based on the working card used to fill the rectangular area by filling the rectangular area with the working card 30 in units of 25, 5 and the working card 40 in units of 1 etc. By knowing the number of cells, it is possible to experience learning by multiplying m × n in decimal.

  In the present embodiment, work cards with units of 2 to 5 are used, but work cards with units of 1 are used (instead of work cards with units of 2 to 5 It is also possible to use only the work card 20 in units of 10 and the work card 41 in units of 1.

  In this embodiment, the principle of multiplication is learned. The same arithmetic learning material as in Example 1 is used, but the operations by the students are different.

  In the present embodiment, it is assumed that 7 × 6 = 42 multiplication is learned. The student uses six work cards 31 each having the first 5 as a unit and six work cards 42 each having a unit of 2.

  When the work card 31 having the first 5 as a unit and the work card 42 having a unit of 2 are used one by one, they are arranged in seven squares. In the first row of the base card 10, a work card 31 having the first 5 as a unit and a work card 42 having a unit of 2 are arranged one by one. “7” is written in the rightmost square, and the student learns that 7 × 1 = 7.

  Next, in the second row of the base card 10, the work cards 31 having the first 5 as a unit and the work cards 42 having 2 as a unit are arranged one by one. In the upper right corner, “14” is entered, and the student learns that 7 × 2 = 14.

  Thereafter, the operation is similarly performed up to the sixth line. Thereby, it is possible to learn up to 7 × 6 = 42.

  Unlike the first embodiment, since the work cards 20 and 25 in units of 10 are not used, it is difficult to learn the idea of the decimal system. On the other hand, since each row is stacked, it is possible to experience multiplication by 7 × n while increasing n by 1. Thus, it can be easily understood that 7 is increased each time, and it can be easily noticed that the product of multiplication of 7 × n increases as an arithmetic sequence when n is increased.

  As described above in detail, the arithmetic education method of the present embodiment can experience multiplication while increasing the multiplier by one, and it is easy to notice that the product of multiplication increases as an arithmetic sequence.

  In this embodiment, addition and subtraction are learned.

  The arithmetic learning material 101 is a learning material set for experiencing addition and subtraction, and includes a base card 110, a first work card 120, a second work card 130, a third work card 140, and An answer card 160 is provided.

  FIG. 12 shows the base card 110. The base card 110 is made of, for example, an image of sheet-like paper, plastic, a tablet, and the like, and on the surface thereof, square square cells connected in a shape of at least 3 rows and 18 columns are drawn. Here, the term “continuous connection” means that square squares are connected at least in the horizontal direction with one side being in contact with each other (that is, overlapping), and may be connected vertically or separated. In the present embodiment, three rows of 18 squares connected horizontally, that is, the first row 111, the second row 112, and the third row 113 are drawn side by side in the vertical direction.

  On the first column 111, numbers from 1 to 18 are drawn corresponding to each of the 18 cells, with the leftmost cell being the first cell. Using these numbers as the index 114, the student can recognize three numbers in the addition or subtraction to be learned.

  The first to third columns 111, 112, and 113 are partitioned using a thick solid line every five with reference to the leftmost square. Accordingly, the work cards 120, 130, and 140 can be arranged on the base card 110 with the section 115 as a mark.

  FIG. 13 shows the first work card 120. The first work card 120 is a set of cards having a shape in which a square having the same size as the square is connected in the horizontal direction by a number i of 1 to 9. The first work card 120 includes work cards 121 to 129 each including one to nine squares. The first work card 120 has a pattern drawn inside each of the connected squares using the first color. In this embodiment, the symbol is a circle and the first color is blue.

  FIG. 14 shows the second work card 130. Similar to the first work card 120, the second work card 130 is a set of cards having a shape in which a square having the same size as the grid is connected in the horizontal direction by a number j of 1 or more and 9 or less. is there. The second work card 130 includes work cards 131 to 139 each including one to nine squares. The second work card 130 has a pattern drawn inside each of the connected squares using the second color. In this embodiment, the symbol is a circle and the second color is green. This allows the student to visually distinguish the second work card 130 from the first work card 120.

  FIG. 15 shows a third work card 140. The third work card 140 is a set of cards having a shape in which a square having the same size as the square is connected in the horizontal direction by a number k of 2 to 18. Third work card 140 includes work cards 141-140i that each include from 2 to 18 squares. The third work card 140 has a pattern drawn inside each of the connected squares using the third color. In this embodiment, the symbol is a circle and the third color is red. This allows the student to visually distinguish the third work card 140 from the first and second work cards 120 and 130.

  FIG. 16 shows another third work card 150 that is another example of the third work card 140. Another third work card 150 has 10 squares that are the same size as the squares, a work card 150a that is connected in the horizontal direction, and squares that are the same size as the squares. Work cards 151 to 159 connected in the direction are included. Accordingly, any one of the work cards 151 to 159 can be used alone as a work card representing 1 to 9 and used in combination with the work card 150a as a work card representing 11 to 18. Can do.

  FIG. 17 shows the answer card 160. The answer card 160 is made of, for example, a sheet-like paper, plastic, tablet image, and the like. The upper side of the answer card 160 adds 1 to 9 to the value of 1 to 9, the result of the addition, and 2 to 18 on the lower side. The subtraction of 1 to 9 and the result of this subtraction are depicted. As a result, the student learns the addition of i + j = k or the subtraction of k−i = j using the first to third work cards 120, 130, and 140 and confirms the answer from the answer card 160. Can be made.

  A method for teaching the addition of i + j = k using the arithmetic learning material 101 will be described with reference to FIG. In this embodiment, an addition of 6 + 8 = 14 is considered as an example.

  First, as shown in FIG. 18A, work included in the first work card 120 on the grid of the first row 111 on the base card 110 so as to be aligned with the left end of the grid of the first row 111. A work card 126, here a work card 126 representing 6, is placed.

  Next, as shown in FIG. 18 (B), the work card 126 is included in the second work card 130 with its left edge aligned with the right edge of the second row 112 on the base card 110. A work card, here a work card 138 representing 8 is arranged.

  Next, as shown in FIG. 18C, the third work card 140 is included on the grid in the third row 113 on the base card 110 so as to align with the left end of the grid in the third row 113. A work card, here a work card 140e representing 14, is arranged.

  The work card 140e represents that the right end position of the work card 140e matches the right end position of the work card 138, that is, the work card 138 adds 8 to the 6 represented by the work card 126. Can be confirmed. Further, since 138 is decomposed into 4 and 4 on the extension line 115 on 111, the number of one's place after the carry can be confirmed.

  The student can also confirm the answer of the addition of 6 + 8 = 14 experienced from the answer card 160.

  As described above, it is possible to experience and experience the addition of i + j = k. Note that the combination of work cards to be used is an example, and a plurality of work cards can be arbitrarily combined and used for any addition of i + j.

  A method for teaching subtraction of k−i = j using the arithmetic learning material 101 will be described with reference to FIG. 19. In this embodiment, a subtraction of 14−6 = 8 is considered as an example.

  First, as shown in FIG. 19A, work included in the third work card 140 on the grid of the first row 111 on the base card 110 so as to be aligned with the left end of the grid of the first row 111. A work card, here a work card 140e representing 14, is placed.

  Next, as shown in FIG. 19B, the work cards included in the first work card 120 on the squares in the second row 112 on the base card 110 are aligned with the right end of the work card 140e. Here, a work card 126 representing 6 is arranged.

  Next, as shown in FIG. 19C, the work card 126 is included in the second work card 130 with its right end aligned with the left end of the work in the third row 113 on the base card 110. A work card, here a work card 138 representing 8 is placed.

  The work card 138 represents that the left end position of the work card 138 matches the left end position of the work card 140e, that is, the work card 138 represents 8 by subtracting 6 represented by the work card 126 from 14 represented by the work card 140e. Can be confirmed. Moreover, since 126 is decomposed into 4 and 2 on the extension line 115 on 113, the carry-down calculation can be confirmed as a number obtained by dividing 10 into 2 and 8.

  The student can also check the answer of the subtraction of 14−6 = 8 experienced from the answer card 160.

  As described above, the subtraction of k−i = j can be learned. Note that the combination of work cards to be used is an example, and a plurality of work cards can be arbitrarily combined and used for any k-j subtraction.

  As described in detail above, the arithmetic learning material 101 of the present embodiment is the same size as the base card 110 in which the square-shaped 54 squares connected in the shape of at least 3 rows and 18 columns are drawn. The first working card 120 is connected in one direction to a number i of 1 to 9 in a square, and the number j is 1 to 9 and connected in one direction to a square having the same size as the square. 2 working cards 130, and a third working card 140 formed by connecting squares of the same size as the squares to a number k of 2 to 18 in one direction. Thereby, among the 54 squares drawn on the base card 110, the first work card 120 is arranged on the square of the first row in accordance with the end of the square, and the square of the second row is over. The second work card 130 is arranged in accordance with the end of the first work card, and the third work card 140 is arranged on the third row in accordance with the end of the square. , I + j = k, and the third work card can be learned and added to the end of the square of the first row of the 54 squares drawn on the base card 110. 140 is arranged, the first work card 120 is arranged in accordance with the end of 140, and the second work card 130 is arranged in accordance with the end of the first work card 120 on the third row of cells. By arranging, you can experience subtraction of k-i = j

  In this embodiment, students who have mastered multiplication and subtraction according to Embodiments 1 to 3 learn division.

  In the division by writing, a quotient for one digit is set, the quotient is multiplied by the divisor, and the result is subtracted from the dividend (together with the digits). This refers to both the remainder obtained as a result of the calculation.) For students who are proficient in multiplication and subtraction, there is only difficulty in creating a quotient. If the divisor is 1 digit, it is relatively easy to derive the correct quotient using the multiplication table, but if the divisor is 2 digits or more, it is difficult to establish a quotient. This is because the multiplication of the quotient and the divisor cannot be performed by mental arithmetic.

  FIG. 20 shows a division auxiliary card. In the division auxiliary card 200, a value obtained by multiplying a 2-digit divisor by a number from 1 to 9 (candidate for quotient) is rounded to 10 units, and is shown on the right side. The figure shows that the divisor is 17, but the same division auxiliary card 200 is used for divisors from 11 to 99 (excluding multiples of 10). Note that the last digit is always 0 due to rounding. This 0 may be omitted.

  The student can easily compare the number on the right side of the division assistance card 200 with the number of higher digits of the dividend, and select the largest one whose right side does not exceed the number of higher digits of the dividend from the quotient candidates. Can make a quotient. A quotient may be established while looking at the division assistance card 200, or a quotient may be established by memorizing the contents of the division assistance card 200.

  The value obtained by rounding off is shown on the right side, and the number of digits is small and judgment is easy. In addition, since the value of the quotient set up is approximated by rounding off, there is a high probability that it is a correct value. Multiply and subtract to obtain the dividend. If it is negative, subtract 1 from the quotient, and if it is greater than the divisor, add 1 to the quotient.

  As described in detail above, according to the division auxiliary card 200 of the present embodiment, in the case of a divisor of two digits or more, the quotient is set up with an error range of 1 even in the case of being accurate in many cases even in the case of an error. It becomes possible. A student who has sufficiently mastered multiplication and subtraction according to Examples 1 to 3 is effective in performing division.

  Although the divisor has been described as being two digits, when it is three digits or more, it can be approximated by the upper two digits.

  The teaching material for arithmetic learning for experiencing learning of multiplication, addition, and subtraction, and the arithmetic teaching method using the same, particularly the teaching material for arithmetic learning effective for the multiplication table and the arithmetic teaching method using the same. It can be used by many educators.

1 Math learning material 10 Base card 11 cell 11a reference cell 12a index 12b index 13a partition 13b partition 19 rectangular region 19a subrectangular region 19b subrectangular region 19c subrectangular region 19x cell 19y cell 20 Work card 21 Work card in units of first 10 22 Work card in units of second 10 23 Work card in units of third 10 24 Work card in units of fourth 10 Card 25 Work card in units of 10 26 Work card in units of 1 10 27 Work card in units of 2 10 28 Work card in units of 3 10 29 4th Work card in units of 10 Work card in units of 5 31 Work card in units of the first 5 32 Working card with second 5 as unit 33 Working card with third 5 as unit 34 Working card with fourth 5 as unit 40 Working card 41 with fraction as unit Work card 422 work card 43 unit of work card 43 unit of work card 44 unit of work card 44 unit of work 51 auxiliary card 60 answer card 70 teaching material card 101 arithmetic learning material 110 base card 111 1st column 112 2nd column 113 3rd column 114 Index 115 Partition 120 1st work card 130 2nd work card 140 3rd work card 150 Another 3rd work card 160 Answer card 200 Division assistance card

Claims (11)

Math learning material for learning multiplication,
A base card on which at least 81 square cells connected in a shape of at least 9 rows and 9 columns are drawn;
A work card having a unit of 10 having a shape formed by connecting ten squares having the same size as the square;
A work card having a unit of 5 having a shape formed by connecting five squares;
A work card with a unit of a fraction having a shape formed by connecting the squares in any number of 1 to 4;
With
The work card having the unit of 10 has a work card having a unit of the first 10 having a shape in which the square is connected in 10 in 5 rows and 2 columns or 2 rows and 5 columns , and the square. Including a work card having a unit of a third 10 having a shape formed by connecting 10 in 4 rows and 3 columns or 3 rows and 4 columns ,
The work card having the unit of 5 includes a work card having a unit of the first 5 having a shape formed by connecting five of the squares in 5 rows and 1 column or 1 row and 5 columns,
The work card with the fraction as a unit includes a work card with a unit of 1 having one square.
A learning material for math learning. The work card having the unit of 5 includes a work card having a second unit of 5 having a shape in which five squares are connected in four rows and three columns or three rows and four columns. The learning material for arithmetic learning according to claim 1 . The work card with the fraction as a unit is
A work card having a unit of 2 having a shape formed by connecting two of the squares;
A work card with a unit of 3 having a shape formed by connecting the three squares;
A work card having a unit of 4 having a shape formed by connecting four of the squares;
And further comprising a teaching material for mathematics learning according to claim 1 or 2. The work card with the unit of 10, the work card with the unit of 5 and the work card with the fraction as a unit have a pattern drawn inside each of the connected squares. The learning material for arithmetic learning according to any one of claims 1 to 3 , wherein the learning material is characterized. The work card having the unit of 10 includes two sets of work cards in which the design is drawn using the first and second colors,
The work card having the unit of 5 has the design drawn using a third color,
Working card in units of the fraction is characterized in that the symbols are drawn using a fourth color, materials for arithmetic learning of claim 4. One of the squares located at the four corners included in the 81 square is set as a reference square,
The 81 cells are drawn on the base card, divided into 5 rows and 5 columns on the basis of the reference cells. 6 . Teaching material for arithmetic learning according to one item. The base card is characterized in that for each of the 81 cells, a number of values obtained by multiplying m and n in the m-th row and n-th column of the reference cell is drawn. The teaching material for arithmetic learning according to claim 6 . In the base card, numbers 1 to 9 are drawn next to the first row of the 81 cell, corresponding to the first to ninth columns based on the reference cell. next to the first row of squares, wherein the respectively corresponding to the ninth row from the first row on the basis of the said reference grid numbers 1 to 9 are depicted, in claim 7 Teaching materials for math learning as described. Among the 81 cells of the base card, at least the m rows and n columns of the remaining cells excluding the m rows and n columns including the reference cells and the m rows and n columns. The learning material for arithmetic learning according to any one of claims 6 to 8 , further comprising an auxiliary card that covers a grid adjacent to the eyes. Math learning material for learning addition and subtraction,
A base card in which at least 54 square squares connected in a shape of at least 3 rows and 18 columns are drawn, and is divided using a thick solid line every 5 with reference to the leftmost square ;
A first work card formed by connecting a square of the same size as the squares in a number i of 1 to 9 in one direction;
A second work card formed by connecting a square having the same size as the squares to a number j of 1 to 9, in one direction;
A third work card formed by connecting a square of the same size as the squares to a number k of 2 to 18 in the one direction;
Teaching material for arithmetic learning characterized by comprising. The first work card has a pattern drawn on the inside of each of the connected squares using a first color,
The second work card has a pattern drawn on the inside of each of the connected squares using a second color,
The arithmetic learning material according to claim 10 , wherein the third work card has a pattern drawn inside each of the connected squares using a third color.