Sudoku calculation method and system for children education

Abstract

The invention relates to the technical field of preschool education, and discloses a sudoku calculation method and a sudoku calculation system for children education, children are helped to learn addition and subtraction, especially carry addition and borrow subtraction, through concrete building block combination and sudoku modules, basic building blocks with numbers from 1 to 9 are combined into a fixed arrangement, and the sudoku calculation method and the sudoku calculation system for children education are provided. Through visual display of the Sudoku module, children are visually helped to understand the relationship between digits and the operation process of the digits. The system comprises a Sudoku module, basic building blocks, a ten-bit marking area, virtual auxiliary bits and an operation processing module, children can gradually master the basic principles of carry addition and borrow subtraction by combining digital building blocks, and the problem that abstract mathematics concepts are difficult to understand in traditional teaching is solved. Through a teaching strategy of removing auxiliary three steps, children can form a mathematical brain map in repeated practice, automatically master addition and subtraction within 10, and gradually transit to multi-digit calculation.

Description

Technical Field

[0001] This invention relates to the field of preschool education technology, specifically to a nine-square grid calculation method and system for children's education. Background Technology

[0002] In children's mathematics education, basic addition and subtraction are key skills for developing mathematical thinking. However, traditional mathematics teaching methods often suffer from a high degree of abstraction, especially in the learning of carrying addition and borrowing subtraction. Many children struggle to understand the essence of numbers and the basic rules of arithmetic when faced with numerical calculations. For young children, numbers themselves lack concrete representations, making it difficult for them to intuitively understand the relationships between numbers and the principles of their operations through abstract symbols. For example, the concepts of "making ten" in carrying addition and "borrowing 1 as 10" in borrowing subtraction often lead to difficulties in understanding and mastering these concepts due to a lack of intuitive teaching tools.

[0003] Most existing math education tools use methods like stacking blocks or arranging numbers. While these methods offer some assistance, they lack systematic guidance and standardized operational rules, failing to effectively help children understand the principles behind calculations. For example, some tools restrict the placement of blocks, leading to fragmented calculation processes and hindering children from forming complete mathematical logical structures. Furthermore, existing tools typically do not provide concrete demonstrations of carrying and borrowing concepts, preventing children from seeing the practical application of these rules in real-world operations, thus further obscuring their understanding. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a nine-square grid calculation method and system for children's education, solving the problem that the calculation methods in existing technologies are abstract and inconvenient to understand.

[0005] The first aspect of this invention provides a nine-square grid calculation method for children's education. This method combines the visual representation of numbers with building blocks, using a nine-square grid module to intuitively process basic mathematical operations. The method includes the following steps:

[0006] Provides a 3x3 grid module, where each cell can hold a basic block. The cells of the 3x3 grid module are used to arrange combinations of number blocks to form a visual representation of numbers.

[0007] The numbers 1 to 9 are combined into blocks using specific arrangements of basic building blocks. Each number has a fixed arrangement rule. For example, the number 1 is composed of 1 block, the number 9 is arranged in a 3x3 matrix, the number 6 is arranged in a 2x3 matrix, and the other numbers are combined in the same way.

[0008] Insert the basic building blocks into the 3x3 grid according to the rules described to create a visual representation of numbers. This step helps children understand the quantity of numbers and their role in addition and subtraction by changing the combinations of numbers within the 3x3 grid.

[0009] Addition and subtraction are performed by changing the combination of blocks within a 3x3 grid. In addition with carry, the "making ten" method is used. When the sum of two numbers exceeds 10, they are combined to form 10, and a basic block is placed in the carry area to represent the carry-over part. In subtraction with borrow, the tens digit block is split into two groups of complementary colors. When borrowing, the first group of blocks is removed, and the result is combined with the units digit to obtain the calculation result.

[0010] The steps of carrying addition and borrowing subtraction involve specific combinations of numbers. By breaking down and combining numbers in a 3x3 grid, each step has a clear execution process, enabling children to gradually master the basic logic of addition and subtraction.

[0011] A second aspect of the present invention provides a nine-square grid calculation system for children's education, the system comprising:

[0012] The 3x3 grid module consists of nine square cells arranged in a 3x3 grid, each of which can hold a basic building block. The 3x3 grid module uses these building blocks to represent and perform calculations, arranging the number blocks according to the needs of addition and subtraction operations.

[0013] The basic building blocks, numbered 1 through 9, consist of a certain number of blocks depending on their quantity and arrangement. Each number has a fixed arrangement rule to ensure its clear representation within the 3x3 grid.

[0014] The tens digit marker area, located on the outside of the 3x3 grid module, is used to display carry-over flags that may occur during the calculation process. The carry-over flags are indicated by basic building blocks to ensure accurate display of carry-overs in addition operations.

[0015] The virtual auxiliary bit, located on one side of the 3x3 grid module, helps handle carry-in addition and borrow-out subtraction. In borrow-out subtraction, the tens digit is split into two sets of complementary colored blocks for the borrow operation. After the borrow is completed, the remaining number blocks are combined with the units digit for calculation.

[0016] The calculation processing module is responsible for automatically performing addition or subtraction operations based on the number combinations within the 3x3 grid. This module identifies the block combinations and processes them according to the rules of carry-over addition or borrow-subtraction subtraction to ensure the correctness of the calculation results.

[0017] This invention provides a nine-square grid calculation method and system for children's education. It has the following beneficial effects:

[0018] This invention uses a combination of a 3x3 grid module and basic building blocks to achieve a concrete representation of numbers, helping children grasp the basic concepts of carrying in addition and borrowing in subtraction through visualization. This system provides children with a new way of learning mathematics through intuitive and simple number arrangement and calculation methods, avoiding the abstract problems of traditional teaching methods. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the assembly of the present invention;

[0020] Figure 2 This is a schematic diagram of the assembly of the present invention;

[0021] Figure 3 This is a schematic diagram of the assembly of the present invention;

[0022] Figure 4 This is a schematic diagram of the assembly of the present invention;

[0023] Figure 5 This is a schematic diagram of the assembly of the present invention;

[0024] Figure 6 This is a schematic diagram of the assembly of the present invention;

[0025] Figure 7 This is a schematic diagram of the assembly of the present invention;

[0026] Figure 8 This is a schematic diagram of the assembly of the present invention;

[0027] Figure 9 This is a schematic diagram of the assembly of the present invention;

[0028] Figure 10 This is a schematic diagram of the steps of the present invention. Detailed Implementation

[0029] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0030] This invention provides a teaching method that uses a 3x3 grid to help children learn addition and subtraction. This method utilizes a combination of 3x3 grid modules and building blocks, along with specific numbers combined with other numbers, to help children understand addition, subtraction, and the commutative and associative laws of arithmetic.

[0031] In this method, children first learn to combine the number 1 with other numbers (such as 5, 6, 7, etc.) to form new numbers. For example, the shape formed by combining the number 1 and the number 5 is actually the same as the shape of the number 6, and the shape formed by combining the number 1 and the number 7 is the same as the shape of the number 8. In this way, children can understand the relationships between numbers and avoid misunderstandings, such as simply memorizing 3+5=8 without understanding the commutative property of 5+3=8. In this process, the rules of number combination are gradually established.

[0032] Please see the appendix Figure 1 - Appendix Figure 5 The diagram illustrates the combination of N+n, where 6+n is simply the reverse of 4+n, and will not be elaborated upon here.

[0033] Except for the combinations of the numbers 4 and 5, which produce two different shapes, the combinations of other numbers maintain the same shape. Except for the number 1, the combinations of other numbers retain the original basic shape's structure. For example, when 5 is combined with other numbers, the resulting block combination still matches the basic shape. In this way, children can grasp the basic rules of addition and subtraction through these combinations.

[0034] Learning addition with carrying and subtraction with borrowing does not disrupt existing graphic patterns; both carrying and borrowing operations are extensions and decompositions of number combinations. After understanding these basic concepts, children can smoothly transition to more complex operations.

[0035] During the learning process, a three-step strategy of withdrawal and reinforcement was adopted. First, parents or teachers draw a combination shape frame for "10" on paper or other tools, placing each block in the correct position to help children understand the basic composition of numbers. Second, after the children understand the basic content of the shape frame, parents no longer provide actual blocks but instead show the combination shape frame, allowing children to determine the number combinations based on it. For example, when asked what numbers make up 8 in a combination of 1 + a number, the child should be able to find the answer using the shape frame. Third, after removing the shape frame, parents ask the same question again, requiring the child to answer independently based on what they have learned. For example, when asked what numbers make up 6 in a combination of 1 + a number, the child should be able to answer directly.

[0036] After children complete the learning of five sets of number combinations, they should be able to master addition and subtraction within 10 and gradually develop their own mathematical mind maps. These mind maps are thought frameworks that children form during the learning process through block combinations and numerical patterns. This mind map not only helps children complete simple addition and subtraction operations but also provides assistance when facing more complex multi-digit operations.

[0037] Many children struggle with carrying and borrowing. Traditional methods focus on algorithms while neglecting the underlying logic, which can cause children to get stuck in multi-digit operations. To overcome this challenge, this invention helps children understand the logic behind operations by breaking down and visualizing number combinations step by step, rather than simply memorizing the algorithms for addition and subtraction. This approach not only helps children master basic arithmetic skills but also lays a solid foundation for more complex mathematical learning later on.

[0038] Learn addition with carrying using the "making ten" method:

[0039] The "making ten" method proposed in this invention is a fundamental skill for children learning addition with carrying. During the teaching process, children are guided to memorize the method using nursery rhymes, such as "One nine, one nine, hand in hand; two eight, two eight, good friends; three seven, three seven, very close; four six, four six, walking together; five five, five five, making a pair of hands," thus helping children become familiar with and master the "making ten" method. Through this method, children can understand and skillfully apply addition within 10, especially in the process of carrying.

[0040] The teaching breakdown strategy breaks down learning objectives into multiple steps to enhance children's learning interest and effectiveness. In the initial learning phase, teachers guide children to understand number combinations by showing them the operational diagrams of multiples of ten. To help children better master addition with carrying, teachers can break down the teaching process into several stages: through games or questioning, children can understand the relationship between numbers and addition within the geometric shapes of building blocks. For example, after children grasp the concept that 1 and 5 combine to form 6, the teacher can further train their addition skills by asking, "What combinations make 10?" Through this repeated practice, children can quickly master the method of making ten.

[0041] Please see the appendix Figure 6 Recognizing the tens digit is a crucial part of the teaching process in this invention. Adults understand the number 12 as composed of 10 and 2, but many children new to mathematics, especially those just beginning to learn, mistakenly believe that the 1 at the beginning only represents the quantity of one object, not 10. This misunderstanding can cause difficulties in subsequent learning about carrying and borrowing. Therefore, teachers should use concrete block combinations to help children understand the concept of the tens digit.

[0042] The method of addition with carrying is illustrated using graphic representations of specific number combinations to help children understand. The following is a description of the calculation method based on a 3x3 grid:

[0043] 9+1: Combine the combination of 9 (a 3x3 matrix) with the fixed combination of the addend 1 to form 10 (9+1), then continue to calculate the remaining part to get the final result.

[0044] 8+something: By combining the combination of 8 (2 rows and 3 columns matrix + 2 stacked blocks) with the fixed combination of the addend 2, we can form 10 (8+2). Then we continue to calculate the remaining part to get the final result.

[0045] 7+something: Combine the combination of 7 (2 rows and 3 columns matrix + 1 stacked block) with the fixed combination of the addend 3 to form 10 (7+3), then continue to calculate the remaining part to get the final result.

[0046] 6+something: Combine the combination of 6 (2x3 matrix) with the fixed combination of the addend 4 to form 10 (6+4), then continue to calculate the remaining part to get the final result.

[0047] 5+something: Combine the combination of 5 (3 blocks side by side + 2 stacked blocks) with the fixed combination of the addend 5 to form 10 (5+5), then continue to calculate the remaining part to get the final result.

[0048] The subtraction with borrowing method is also taught using a 3x3 grid of number combinations. For subtraction without borrowing, simply remove the complete combination of numbers corresponding to the subtrahend; the remaining part is the final result. Subtraction with borrowing uses two sets of complementary colored blocks for the tens digit. The sum of each set of blocks is 10. By removing the first set of blocks, the remaining second set is combined with the units digit, and then the subtraction is performed.

[0049] The specific combination rules for borrowing subtraction are as follows:

[0050] A=9 (first color), B=1 (second color): By combining 9 and 1 to form the tens digit, learn the borrowing subtraction of 9.

[0051] A=8 (first color), B=2 (second color): By combining 8 and 2 to form the tens digit, learn the borrowing subtraction of 8.

[0052] A=7 (first color), B=3 (second color): By combining 7 and 3 to form the tens digit, learn the borrowing subtraction of 7.

[0053] A=6 (first color), B=4 (second color): By combining 6 and 4 to form the tens digit, learn the borrowing subtraction of 6.

[0054] A=5 (first color), B=5 (second color): By combining 5s to form the tens digit, learn the borrowing subtraction of 5.

[0055] For multi-digit borrowing subtraction, the minuend is split into a combination of "ten-digit numbers + teen-digit numbers". First, the "teen-digit numbers" are borrowed and subtracted. Then, the ten-digit numbers are reduced and combined with the result to obtain the complete result.

[0056] The 3x3 grid module structure consists of 9 square cells arranged in 3 rows and 3 columns, with a tens digit marking area and virtual auxiliary positions on the outside, serving as the basis for block arrangement and calculation identification. Each number's block combination has fixed characteristics. For example, the core combination characteristics (quantity, arrangement, and stacking relationship) of numbers 1 to 9 are unique, and their positions can be selected in any suitable area within the 3x3 grid, ensuring that children can quickly identify numbers through combination characteristics.

[0057] The virtual auxiliary position's number 1 block combined with the number 9 is equivalent to 10, providing the logical basis for carrying over to ten. During carry-over addition, the combinations of numbers 5 to 9 with their corresponding addends follow a fixed "making ten" rule, simplifying the calculation logic. Borrowing subtraction uses a two-color complementary combination of the tens digit, removing one block from the complementary combination and merging it with the units digit. Borrowing in multi-digit numbers is achieved by splitting the number into "ten-digit + teen-digit".

[0058] This system has a simple structure and intuitive operation, is adapted to children's concrete thinking characteristics, can stimulate children's interest in learning mathematics, and is widely applicable to scenarios such as family early education and kindergarten teaching.

[0059] In a preferred embodiment of the present invention, in order to further enhance children’s structural understanding of “10” in the decimal system, the system also provides a “concrete structural representation of ten”.

[0060] The concrete structural composition of the ten includes:

[0061] Several basic building blocks, wherein each basic building block is a single unit and each basic building block is used to represent the value "1";

[0062] And a ten-digit marker block, the ten-digit marker block having a splicing cavity for accommodating multiple basic blocks.

[0063] In practical operation, 10 basic building blocks can be combined through the splicing cavity to form a tens marker building block, and the number "10" is marked on the outer surface of the tens marker building block.

[0064] The ten-digit marker block can be used as a whole as a ten-digit counting unit, or it can be split and restored into 10 basic blocks according to the needs of the operation.

[0065] Through the above-mentioned detachable and combinable structural design, the concrete expression of "10 ones are equivalent to 1 ten" is realized, providing a unified physical operation basis for subsequent carry addition and borrow subtraction.

[0066] In another preferred embodiment, the nine-square grid calculation system of the present invention also supports multi-digit borrow subtraction operations based on digit partitioning.

[0067] The nine-square grid module or its outer extended area is divided into units digit area, tens digit area and higher digit area;

[0068] The units area is used to place the basic block representing the value "1", and the tens area is used to place the tens marker block. Each tens marker block represents one "10".

[0069] When performing a subtraction operation and the number of basic blocks in the units digit region is insufficient to complete the subtraction operation, the system executes the following borrowing process:

[0070] Select one tens digit marker block from the tens digit area;

[0071] The ten-digit marker block is split into 10 basic blocks;

[0072] Transfer the 10 basic blocks obtained from the splitting to the units area;

[0073] The subtraction operation continues based on the updated number of basic blocks in the units digit area.

[0074] Through the above structured decomposition process, the logic of "one ten is decomposed into ten ones" in borrowing operations is presented in a visual and operable way.

[0075] Correspondingly, in multi-digit addition operations with carry, when the number of basic blocks in the units digit region reaches or exceeds 10 after addition, the system executes the carry processing step:

[0076] Select 10 basic building blocks;

[0077] The 10 basic building blocks are combined and embedded into the splicing cavity of the ten-digit marker building block to form a complete ten-digit marker building block;

[0078] The tens digit marker block is transferred to the tens digit area as a carry counting unit;

[0079] The units digit region retains the remaining basic building blocks to complete the representation of the final calculation result.

[0080] Through the above carry-in combination operation, the concrete process of "combining 10 ones into 1 ten" in carry-in addition is realized.

[0081] The present invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0082] Example 1: Carry-based addition (7+5) Please refer to the appendix. Figure 7 - Appendix Figure 9 ;

[0083] Tools needed: a 3x3 grid module (including the ten-digit marker area on the right and virtual auxiliary positions), basic building blocks, and preset fixed combination features corresponding to the numbers 7 and 5;

[0084] Step 1: The combination feature of the number 7 is "2 rows and 3 columns matrix + 1 stacked block in the upper right corner". Select the top and middle rows of cells in the 3x3 grid to piece together this shape;

[0085] Step 2: The combination features of the number 5 are "3 consecutive side-by-side blocks + 1 stacked block each in the top left corner and the top center", prepare the complete shape;

[0086] Step 3: According to the principle of making ten, 7 needs to be combined with 3 to make 10. Take the fixed combination of 3 from the combination of 5 (3 consecutive side by side blocks).

[0087] Step 4: Combine the combination of the number 3 and the combination of the number 7 to trigger the "full 10" logic, and place a basic block in the tens place marking area as a carry-over indicator;

[0088] Step 5: The remaining part of the combination of the number 5 is a fixed combination of the number 2 (2 adjacent blocks side by side). Piece this shape together in the 3x3 grid and combine it with the carry symbol to form "12". The result of the calculation is 12.

[0089] Example 2: Borrowing subtraction operation (12-9)

[0090] Tools needed: a 3x3 grid module (including the tens digit marker area on the right), basic building blocks, and preset fixed combination features corresponding to the minuend 12 and the subtrahend 9;

[0091] Step 1: The tens digit of the minuend 12 is composed of the first color combination of 9 (3 rows and 3 columns of full grid) and the second color combination of 1 (single independent block), and the units digit is the combination of 2 (2 adjacent blocks side by side). Complete the assembly within the 3x3 grid.

[0092] Step 2: Determine the size of the units digit. If 2 < 9, the borrowing subtraction rule is triggered.

[0093] Step 3: Based on the complementary combination of the tens digit (9+1=10), remove the first color combination of the tens digit 9, leaving the second color combination of the tens digit 1;

[0094] Step 4: Combine the remaining 1s with the units digit 2s to form a fixed combination of 3. The result is 3.

[0095] Example 3: Borrowing subtraction operation (12-8)

[0096] Tools required: Same as in Example 2;

[0097] Step 1: The tens digit of the minuend 12 is composed of the first color combination of 8 (2 rows and 3 columns matrix + 2 stacked blocks) and the second color combination of 2 (2 adjacent side by side blocks), and the units digit is the combination of 2. Complete the piecing together in the 3x3 grid.

[0098] Step 2: The units digit 2 < 8, triggering the borrowing subtraction rule;

[0099] Step 3: Based on the complementary combination of the tens digit (8+2=10), remove the first color combination of 8 in the tens digit, leaving the second color combination of 2;

[0100] Step 4: Combine the remaining 2 combinations with the units digit 2 combinations to form a fixed combination of 4. The result of the operation is 4.

[0101] Example 4: Multi-digit borrowing subtraction operation (56-8)

[0102] Tools needed: a 3x3 grid module (including the tens digit marking area on the right), basic building blocks, and preset fixed combination features corresponding to the minuend 56 and the subtrahend 8;

[0103] Step 1: Divide 56 into “40+16”. Place 4 basic blocks in the tens digit marking area to mark 40. The tens digit of 16 is composed of the first color combination of 8 (2 rows and 3 columns matrix + 2 blocks side by side) and the second color combination of 2 (2 consecutive blocks side by side). The units digit is a combination of 6 (2 rows and 3 columns matrix). Complete the assembly within the 3x3 grid.

[0104] Step 2: The units digit 6 < 8, triggering the borrowing subtraction rule;

[0105] Step 3: Based on the complementary combination of the tens digits (2+8=10), remove the first color combination of 8 from the tens digit of 16, leaving the second color combination of 2;

[0106] Step 4: Combine the remaining 2 combinations with the units digit 6 combinations to form an equivalent combination of 8;

[0107] Step 5: Combine the combination of 8 with 40, keep 4 basic blocks in the tens place marking area, and combine the units digit with the combination of 8 to form 42. The result is 48.

[0108] Example 5: Carry-based addition (5+6)

[0109] Tools needed: a 3x3 grid module (including the tens digit marking area on the right), basic building blocks, and preset fixed combination features corresponding to the numbers 5 and 6;

[0110] Step 1: The combination feature of the number 5 is "3 consecutive side by side + 2 stacked blocks". Select the bottom row of the nine-square grid to piece together this shape;

[0111] Step 2: The combination feature of the number 6 is a "2-row, 3-column matrix", prepare the complete graphic;

[0112] Step 3: According to the principle of making ten, 5 needs to be combined with 5 to make 10. Take the fixed combination of 5 from the combination of 6 (3 consecutive side by side + 2 stacked blocks).

[0113] Step 4: Combine the combination of the number 5 with the original combination of 5 to trigger the "full 10" logic, and place a basic block in the tens place marking area as a carry-over indicator;

[0114] Step 5: The remaining part of the combination of the number 6 is a fixed combination of the number 1 (a single independent block). Piece this shape together in the 3x3 grid and combine it with the carry symbol to form "11". The result of the operation is 11.

[0115] Example 6: Borrowing Subtraction (23-8)

[0116] Place two tens digit marker blocks in the tens digit area of ​​the nine-square grid teaching board, and place three basic blocks in the ones digit area;

[0117] If the number of basic blocks in the units digit is less than the subtrahend 8, the borrowing rule is triggered.

[0118] Split one tens digit marker block in the tens digit area into 10 basic blocks and transfer them to the units digit area;

[0119] At this point, there are 13 basic blocks in the units digit area, and 1 tens digit marker block remains in the tens digit area;

[0120] Remove 8 basic blocks from the units area, leaving 5;

[0121] The final result is represented by one tens digit marker block in the tens digit area and five basic blocks in the units digit area, and the result is 15.

[0122] Example 7: Addition with carry (27 + 5)

[0123] Place two tens place marker blocks in the tens place area and seven basic blocks in the ones place area;

[0124] Add the addend 5 to the units place as 5 basic blocks;

[0125] If the number of basic building blocks in the unit area reaches 12, select 10 of them to combine.

[0126] Assemble the 10 basic blocks into one tens digit marker block and transfer it to the tens digit area;

[0127] Two basic blocks remain in the units digit area;

[0128] The final result is represented by three tens digit marker blocks in the tens digit area and two basic blocks in the units digit area, and the result is 32.

[0129] Modular Arithmetic System (MAS). "Modular" emphasizes the use of fixed modular building blocks in an arithmetic system. It embodies an approach of constructing and manipulating numbers using standardized building blocks, making the system both efficient and easy to understand. It highlights the cultivation of mental arithmetic skills and the application of these modular building blocks. By associating numbers with fixed combinations of blocks, one can quickly construct a block model of numbers in their mind, performing overall addition and subtraction operations without counting each number individually. This improves mental arithmetic speed and accuracy, especially for addition and subtraction within 100, making it a highly efficient mental arithmetic training tool.

[0130] I. Core Concepts:

[0131] 1. Fixed Block Arrangement Pattern: In MAS, each number has a specific and fixed block arrangement. For example, the number 5 is composed of 5 blocks arranged in a certain structure. This arrangement pattern is standardized and fixed, giving each number a unique and recognizable block shape. This fixed pattern provides a stable foundation for number manipulation and calculation, allowing students to intuitively see the composition and structure of numbers.

[0132] 2. Modular Construction: MAS views numbers as wholes constructed from building blocks. These blocks can be individual blocks or pre-assembled larger blocks, such as tens-digit structure blocks. For example, the number 10 can be represented by a dedicated tens-digit structure block instead of 10 individual blocks. This modular construction method simplifies the representation and manipulation of numbers, allowing complex numbers to be broken down into smaller, more manageable modules.

[0133] Systematic and Orderly

[0134] Structured Calculation Method: MAS emphasizes calculations following specific rules and steps, exhibiting strong systematicity and orderliness. When performing addition and subtraction, it doesn't simply add or remove blocks one by one; instead, it operates as a whole based on a fixed block arrangement pattern. For example, when calculating 9+5, it directly takes the fixed block combinations for 9 and 5, combines them, and then adjusts the overall result (such as carrying over) to obtain the final result. This method avoids the tediousness of counting one by one, improving calculation efficiency and accuracy.

[0135] The MAS operating procedure is logically clear, easy to understand and master. Each step has a clear purpose and method, allowing students to develop a deep understanding and proficiency in arithmetic operations through repeated practice. This systematic and structured approach not only helps students build clear logical thinking during the learning process but also lays a solid foundation for their future learning of more complex mathematical concepts.

[0136] 4. Efficiency and ease of understanding

[0137] High-efficiency computation: One of MAS's greatest strengths lies in its efficiency. By using a fixed block arrangement and modular construction, students can quickly combine and decompose numbers to perform addition and subtraction within 100. This efficiency is not only reflected in calculation speed but also in reducing errors and confusion during the calculation process. For example, when performing subtraction, the subtrahend's block combination can be directly removed from the minuend's block combination, without needing to subtract 1 from each block individually, greatly improving computational efficiency.

[0138] Intuitive and easy to understand: MAS uses intuitive block models to represent numbers and calculation processes, making abstract arithmetic concepts concrete, vivid, and easy to understand. Students can experience the combination and decomposition of numbers firsthand by manipulating the blocks, thereby gaining a deeper understanding of the meaning and principles of addition and subtraction. This intuitiveness is particularly suitable for children or beginners, stimulating their interest and enthusiasm for learning mathematics and enhancing learning outcomes.

[0139] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A nine-square grid calculation method for children's education, characterized in that, Includes the following steps: Provide a 3x3 grid, where each cell can hold a certain number of basic building blocks; The basic building blocks from 1 to 9 are combined into building blocks according to a specific arrangement rule, with each number corresponding to a fixed arrangement of building blocks; By inserting the combined number blocks into a 3x3 grid, a visual representation of numbers is formed; Addition or subtraction is performed by changing the combination of blocks within a 3x3 grid. During the calculation, carry and borrow are handled according to the rules of the combination of numbers. When adding with carry, the tens place is formed by combining the number blocks with the method of making ten, and the carry indicator is marked in the carry area; In subtraction with borrowing, the tens digit is split into two groups of complementary colors, borrowing is performed, and the remaining part is combined with the units digit to obtain the calculation result.

2. The nine-square grid calculation method for children's education according to claim 1, characterized in that: In step 1, each cell of the 3x3 grid is a square, and the outer side has a marking area for identifying carry and borrow in the tens place.

3. The nine-square grid calculation method for children's education according to claim 1, characterized in that: In step 2, the basic building blocks from 1 to 9 are combined to form different number representations according to their quantity and arrangement. The number 1 is one basic building block, and the number 9 is a combination of building blocks in a row of 3 rows and 3 columns.

4. The nine-square grid calculation method for children's education according to claim 1, characterized in that: In step 4, the addition operation is handled by the "making ten" method. When the sum of two numbers exceeds 10, they are combined into 10 and marked in the carry area. The remaining part is then combined with the other numbers for further calculation.

5. The nine-square grid calculation method for children's education according to claim 1, characterized in that: In step 5, the carry-in addition is performed by arranging the number blocks in a 3x3 grid, where the number 7 and the number 3 are combined to form 10, and the carry-in flag is placed in the tens carry-in area using the basic blocks.

6. The nine-square grid calculation method for children's education according to claim 1, characterized in that: In step 6, during borrowing subtraction, the tens digit is split into two groups of complementary colored blocks. The sum of the number corresponding to the first group of blocks and the second group of blocks is 10. During borrowing, the first group of blocks is removed and combined with the units digit.

7. A nine-square grid calculation system for children's education, comprising a nine-square grid calculation method for children's education according to any one of claims 1-6, characterized in that, include: A 3x3 grid module, comprising 9 square cells arranged in 3 rows and 3 columns, each cell containing a combination of building blocks; Basic building blocks: Each number corresponds to a fixed set of basic building blocks, which are used to combine the numbers. The tens digit marker area is used to identify the carry-over portion of a number; Virtual auxiliary bits are used to handle carry in addition and borrow operations in subtraction. The arithmetic processing module is used to perform addition or subtraction operations on the basic building blocks according to the arrangement rules within the nine-square grid, and to perform number combination and adjustment according to the requirements of carry addition or borrow subtraction.

8. A nine-square grid calculation system for children's education according to claim 7, characterized in that: The outer side of the 3x3 grid module is provided with a carry-in area for displaying the carry-in indicator during the calculation process.

9. A nine-square grid calculation system for children's education according to claim 7, characterized in that: The basic building blocks are detachable, making it easy to arrange and combine them according to different numbers, and to express the numbers through the cells in the nine-square grid.

10. A nine-square grid calculation system for children's education according to claim 7, characterized in that: The calculation processing module is used to automatically perform addition or subtraction operations based on the inserted block combination, and adjust the number combination according to the method of making ten or borrowing.

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