A mathematical abacus for enlightening number sense

Abstract

The utility model discloses a mathematical enlightenment number sense abacus, including the outer frame, the rod body of setting in the outer frame and the setting and can slide on the rod body, the cube bead of turning, the limiting structure for the positioning of one side of the bead is provided between the bead and the rod body, the utility model discloses a limiting structure is arranged between the rod body and the cube bead, guarantees one side of the cube bead to keep the state of going up, completes the positioning of one side of the cube bead, and various marks on each face on the cube bead are identified and calculated to the use personnel, and the operation is simple and flexible, to solve the abacus of existing not practical for the student in school, and the calculation principle is not intuitive, and the mental arithmetic operation skill is single, and the simple calculation can not be carried out, and the mathematical enlightenment mathematical plugboard or mathematical hole hole board learning aid, the difficult problem of scattering, scattering, losing, disorder in the operation process, and the difficult problem of not suitable for the addition and subtraction calculation of larger number.

Description

Technical Field

[0001] This utility model relates to the field of teaching aids technology, and in particular to an abacus for mathematical enlightenment and number sense. Background Technology

[0002] Many of the difficulties children encounter in learning mathematics can be explained through number sense, which has gradually become an internationally accepted concept. In China's mathematics curriculum standards, number sense is listed as one of the ten core concepts and is defined. Simply put, number sense is the ability to understand numbers and quantities, quantitative relationships, the relationship between abstract and concrete concepts, the ability to estimate the results of calculations, and the ability to use numbers flexibly.

[0003] Currently, the teaching tools used to cultivate children's number sense, teach counting, establish basic number concepts, and learn addition, subtraction, multiplication, and division are abacuses, mental arithmetic abacuses, and math enlightenment products such as math pegboards or math hole boards. However, all of the above teaching tools have certain shortcomings.

[0004] Abacus calculation requires memorizing a large number of formulas and extensive practice to become proficient. However, in math exams, without an abacus, calculations become impossible, and written calculations are still necessary. Furthermore, the period during which students use an abacus in their math textbooks is quite short. Using the abacus as a tool for early math education in preschool children is even less suitable.

[0005] With the help of mnemonic rhymes, after a lot of practice, users can operate the abacus skillfully. In addition to quickly finding the correct answer, they can also visualize the abacus's layout, levels, and the movement of the beads in their minds, which effectively solves the problem of students being unable to perform calculations without the abacus.

[0006] Disadvantage 1: Abacus mental arithmetic skills and calculation methods are limited, making it impossible to perform simplified calculations or achieve algorithmic diversity.

[0007] Disadvantage 2: It focuses too much on improving calculation speed, mechanically practicing calculations, and the calculation process and principles are not intuitive;

[0008] Disadvantage 3: It requires memorizing the formulas. Only by memorizing the correct formulas can the calculation be correct. If the formulas are memorized incorrectly, the calculation will be completely wrong.

[0009] The teaching method of abacus mental arithmetic involves memorizing a large number of formulas and then starting a large amount of calculation practice without understanding the principles behind the formulas. After a lot of repeated practice, students memorize single formulas for addition, subtraction, multiplication, and division. Mechanically using these formulas leads to a lack of perception of specific quantities and the development of number sense. It also lacks the analysis and understanding of the algorithmic principles and the learning and application of diverse algorithms.

[0010] Math learning products - math pegboards or math hole boards:

[0011] Disadvantage 1: When children manipulate learning materials, they often scatter, break, drop, or make a mess.

[0012] Disadvantage 2: It is less efficient and effective when performing addition, subtraction, multiplication, and division.

[0013] Because when calculating addition and subtraction within 10, 20, 100, etc., it is necessary to place each piece individually to perform addition, subtraction, multiplication, and division calculations. When encountering larger numbers, it takes a long time, so the calculation efficiency and effectiveness are low.

[0014] Disadvantage 3: The number of calculations is relatively small, and the usage period is relatively short.

[0015] This learning tool is primarily used for counting, perceiving quantity, and establishing number concepts in the early stages of early math education for young children. Because its calculation efficiency and effectiveness are relatively low, it can only perform addition and subtraction within 10 or 20, but is not suitable for addition and subtraction within 100 or for calculations involving larger quantities. Therefore, this tool is only suitable for preschool children and is not applicable to primary school students.

[0016] To address the aforementioned problems, this invention provides a mathematical abacus for early math education, thus resolving the issue of the impracticality of previous math education tools. Utility Model Content

[0017] The purpose of this invention is to provide a mathematical abacus for beginners, thereby improving its practicality and extending its lifespan. More importantly, it can significantly shorten the learning and practice time for beginners to learn addition and subtraction within 10,000 and multiplication and division within 100, cultivate number sense, and achieve teacherless teaching and intelligent self-learning.

[0018] To achieve the above objectives, this utility model provides the following solution:

[0019] A mathematical abacus for early math literacy includes an outer frame, a rod disposed within the outer frame, and cube beads that pass through the rod and can slide and flip on the rod. A limiting structure is provided between the beads and the rod for positioning one face of the beads upward.

[0020] Preferably, the abacus has a through hole inside, the rod passes through the through hole, the inner diameter of the through hole is larger than the outer diameter of the rod, and the limiting structure includes a horizontal contact surface of the abacus on the inner wall of the through hole and a horizontal contact surface of the rod on the rod that can match and overlap with the horizontal contact surface of the abacus.

[0021] Preferably, the through hole is located at the intersection of the diagonals of one of the faces. Both the through hole and the rod have square cross-sections. The side length of the through hole is greater than the side length of the rod. The four sides of the inner wall of the through hole are horizontal contact surfaces of the beads and can be rotated and limited as needed. The four sides of the outer wall of the rod are horizontal contact surfaces of the rod and can be limited to the horizontal contact surfaces of the beads as needed. The width of the horizontal contact surface of the beads is 90mm to 120mm, and the width of the horizontal contact surface of the rod is 80mm to 100mm.

[0022] Preferably, the other four faces of the abacus are respectively provided with numbers, fruit patterns, animal patterns and solid color patterns, and the numbers are 10, 100 or 1000.

[0023] Preferably, the outer frame is rectangular, and the interior of the outer frame is provided with horizontal and vertical partitions that intersect vertically. The horizontal and vertical partitions divide the outer frame into four regions, and each region is provided with two rods. The two ends of the rods are connected to the outer frame and the vertical partition, respectively.

[0024] Preferably, the two ends of the horizontal partition are respectively connected to the corresponding short sides of the outer frame, and the two ends of the horizontal partition are respectively connected to the midpoint of the short side. The vertical partition includes a lower short plate disposed below the horizontal partition and an upper short plate disposed above the horizontal partition. The two ends of the upper short plate and the lower short plate are respectively connected to the midpoint of the horizontal partition and the midpoint of the long side of the outer frame.

[0025] Preferably, the rod penetrates the upper short plate and is located at a position where the upper short plate is divided into three equal parts along its length, and the two rods penetrate the lower short plate and are located at a position where the lower short plate is divided into three equal parts along its length.

[0026] Preferably, the number of beads in each region is equal and not less than 5.

[0027] Preferably, the system also includes an auxiliary learning tool, which includes a telescopic rod and a cube-shaped abacus bead that passes through the telescopic rod and can slide and flip on the telescopic rod. A limiting structure is provided between the abacus bead and the telescopic rod to position one side of the abacus bead upward.

[0028] Preferably, the telescopic rod includes a hollow main rod and a secondary rod that passes through the hollow main rod and can slide inside the main rod, and the abacus beads are disposed on the outer walls of the main rod and the secondary rod.

[0029] Preferably, the abacus beads are cubes, and the other four non-through faces of the cube are respectively provided with animal patterns, fruit patterns and solid color patterns, wherein two faces are provided with different animal patterns.

[0030] Preferably, it also includes a display screen connected to the mathematical abacus for beginners, and the display screen and the mathematical abacus for beginners are foldably connected by a hinge.

[0031] Preferably, it also includes a number sense game card, which comprises several cards, each card having a marker for counting, the marker being a square color block, a circular color block, or an animal pattern.

[0032] Preferably, it also includes a small calculator with a display screen and buttons, which is connected to the mathematical introductory abacus via a plastic frame.

[0033] Preferably, it also includes a drawer for placing the mathematical learning abacus, the auxiliary learning tools, the number sense game cards, and the display screen.

[0034] The present invention achieves the following technical advantages over the prior art:

[0035] 1. This utility model, by setting a limiting structure between the rod and the cube abacus beads, ensures that one face of the cube abacus beads remains in an upward position, thus completing the positioning of one face of the cube abacus beads. This facilitates the user's identification and calculation of various markings on each face of the cube abacus beads, making the operation flexible and simple. It solves the problems of existing abacuses being impractical for school students, having an unintuitive calculation principle, limited mental arithmetic skills, and the problems of scattering, losing, and messing up during operation, as well as being unsuitable for calculating addition and subtraction of large numbers.

[0036] 2. This utility model has a through hole inside the abacus beads, and the rod body passes through the through hole. The inner diameter of the through hole is larger than the outer diameter of the rod body. The limiting structure includes a horizontal contact surface of the abacus beads set on the inner wall of the through hole and a horizontal contact surface of the rod body set on the rod body and matching and overlapping with the horizontal contact surface of the abacus beads. When one side of the abacus beads needs to be positioned, the abacus beads are lifted and flipped until the required side is facing up. Then the abacus beads are put down so that the horizontal contact surface of the abacus beads corresponding to that side contacts and fits against the horizontal contact surface of the rod body, thus completing the positioning of one side of the abacus beads. The operation is simple and convenient.

[0037] 3. In this invention, the other four faces of the abacus are respectively decorated with numbers, fruit patterns, animal patterns, and solid color patterns. The animal or fruit patterns are concrete and figurative, while the corresponding cubes or square color blocks are semi-abstract. The numbers are a symbolic representation with strong abstraction and logic. The combination of these three elements can effectively help preschool children transition from concrete image thinking to abstract logical thinking.

[0038] 4. This utility model also includes an auxiliary learning tool, which includes a telescopic rod and cubic beads that are threaded through the telescopic rod and can slide and flip on the telescopic rod. A limiting structure is provided between the beads and the telescopic rod to position one side of the beads upward. The flipping and positioning method of this auxiliary learning tool is the same as that of the abacus for mathematical enlightenment, but the telescopic rod has a telescopic function, which can reduce the space occupied by the auxiliary learning tool by shortening the length of the telescopic rod, making it convenient for users to carry.

[0039] 5. This utility model also includes a combination of a math-learning abacus and a small calculator, a small calculation display screen and button combination, the display screen and the math-learning abacus are combined by a plastic frame, the display screen can display the problem to be calculated, and the learner can perform calculation on the math-learning abacus according to the problem, realizing the integrated setting of question generation and answering.

[0040] 6. This utility model also includes a display screen connected to the math-learning abacus. The display screen and the math-learning abacus are foldable together via a hinge. The display screen can show App content, including animated demonstrations, basic knowledge, reinforcement exercises, assessments, and interactive number sense games. This allows learners to operate, practice, and learn counting, addition, subtraction, multiplication, and division calculations, and understand word problems on the math-learning abacus based on the App's demonstrations. This achieves teacherless teaching and intelligent self-directed learning. Furthermore, the foldable design makes it easy for users to fold and carry after use, making it simple and convenient.

[0041] 7. This utility model also includes a drawer for placing the mathematical learning abacus, the auxiliary learning tools, and the display screen.

[0042] 8. When learners use this invention to learn addition, subtraction, multiplication, and division, they can directly perceive the quantities by hand, personally operate the calculation process, and intuitively observe the changes and results of the calculation principle. Therefore, they can better learn and understand the algorithm's rationale and the process of simplified calculation, thereby realizing diverse applications of the algorithm and achieving better learning efficiency and results.

[0043] 9. The cube beads of this invention are arranged in groups of five, with two groups of ten cubes forming a grid shape, transforming the planar "ten-grid number array" into a three-dimensional, operable one. Therefore, when performing calculations by manipulating the beads, it better achieves a combination of number and shape, and is easier to visualize using a mental image compared to an abacus. Furthermore, there is no need to memorize formulas or rely on pen and paper; even without an abacus, efficient calculations can still be performed through mental imagery to obtain the result. This further improves learning efficiency, practice efficiency, and problem-solving efficiency.

[0044] 10. This utility model can be used by school-age children worldwide to learn mathematics, and it has significant commercial value.

[0045] 11. This utility model incorporates the advantages of abacus beads (which prevent beads from falling out or scattering during calculation); it also incorporates the advantages of mental arithmetic beads (which create mind maps); it further incorporates the advantages of math puzzle boards and pegboards (which feature animal, fruit, and number patterns); and it incorporates the shape of "ten-grid number arrays" (5 grids per row, 10 grids per row) and their concept of number-shape transformation. Simultaneously, it avoids the shortcomings of these four types of products and is more practical. Compared to these four types of products, this utility model is more suitable for use in conjunction with a matching app and can achieve intelligent, self-directed learning. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in this utility model or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this utility model. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a schematic diagram of the structure of this utility model;

[0048] Figures 2 to 25 A schematic diagram of the structure of the supporting embodiment of this utility model;

[0049] Figure 26 A schematic diagram showing the integration of a display screen and an abacus for introducing mathematical number sense.

[0050] Figures 27 to 32 This is a structural diagram of the learning aid;

[0051] Figures 33 to 35 This is a schematic diagram of the structure of a number sense game card;

[0052] Figure 36 A schematic diagram of a small calculator and an abacus for early math learning;

[0053] The components include: 1. Outer frame; 2. Rod body; 3. Abacus beads; 4. Vertical partition plate; 5. Horizontal partition plate; 6. Display screen; 7. Telescopic rod. Detailed Implementation

[0054] The technical solutions of the present utility model will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present utility model, and not all embodiments. Based on the embodiments of the present utility model, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present utility model.

[0055] The purpose of this invention is to provide a mathematical abacus for beginners, thereby improving its practicality and extending its lifespan. More importantly, it can significantly shorten the learning and practice time for beginners to learn addition and subtraction within 10,000 and multiplication and division within 100, cultivate number sense, and achieve teacherless teaching and intelligent self-learning.

[0056] To make the above-mentioned objectives, features and advantages of this utility model more apparent and understandable, the utility model will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] refer to Figure 1 A mathematical abacus for early math literacy includes an outer frame, a rod within the outer frame, and cubic beads that slide and rotate on the rod. A limiting structure is provided between the beads and the rod to position one side of the beads upwards. A through hole is formed inside the beads, and the rod passes through the through hole. The inner diameter of the through hole is larger than the outer diameter of the rod. The limiting structure includes a horizontal contact surface for the beads on the inner wall of the through hole and a horizontal contact surface for the rod that matches and overlaps with the horizontal contact surface of the beads. When one side of the beads needs to be positioned, the beads are lifted and... Flip the beads until the desired side is facing up, then place the beads down so that the horizontal contact surface of the beads corresponding to that side is in contact with the horizontal contact surface of the rod, thus completing the positioning of one side of the beads. The operation is simple and convenient. It allows users to identify and calculate various markings on each face of the cube-shaped beads. The operation is flexible and simple, solving the problems of existing abacuses being impractical for school students, the calculation principle being not intuitive, the mental arithmetic skills being limited, and the problems of scattering, losing, and messing up during operation, as well as the problem of not being suitable for calculating addition and subtraction of large numbers.

[0058] refer to Figure 1 The beads are cube-shaped, with a through hole located at the intersection of the diagonals of one of the faces.

[0059] refer to Figure 1The other four faces of the abacus are decorated with numbers, fruit patterns, animal patterns, and solid color patterns, respectively. The numbers are 10, 100, or 1000.

[0060] refer to Figure 1 The outer frame is rectangular, and horizontal and vertical partitions are arranged vertically inside the outer frame. The horizontal and vertical partitions divide the outer frame into four areas. Two rods are arranged in each area, and the two ends of the rods are connected to the outer frame and the vertical partition, respectively.

[0061] refer to Figure 1 The two ends of the horizontal partition are connected to the corresponding short sides of the outer frame, and the two ends of the horizontal partition are connected to the midpoint of the short side, respectively. The vertical partition includes a lower short plate disposed below the horizontal partition and an upper short plate disposed above the horizontal partition. The two ends of the upper short plate and the lower short plate are connected to the midpoint of the horizontal partition and the midpoint of the long side of the outer frame, respectively.

[0062] refer to Figure 1 The rod penetrates the upper short plate and is located at a position where the upper short plate is divided into three equal parts along its length. The two rods penetrate the lower short plate and are located at a position where the lower short plate is divided into three equal parts along its length.

[0063] refer to Figure 1 The number of beads in each region is equal and not less than 5.

[0064] Furthermore, the beads on adjacent rods maintain a corresponding distance and ensure that they do not affect each other during the bead flipping process.

[0065] The method of using this utility model is as follows:

[0066] For preschool children with no prior math knowledge, when learning to count, you can flip the cube beads so that the apple (or animal) pattern is facing up. Starting from the left (or right) area and moving towards the center (or the other side), move one apple bead at a time and count one number. You can also move several animal, solid-color, or number-patterned cube beads at a time to learn composition and decomposition, addition and subtraction, word problems, etc., thereby establishing basic mathematical concepts and achieving the effect of early math education.

[0067] When elementary school children are learning addition and subtraction within 10,000, simplified calculation, and multiplication and division within 100, they can refer to the following implementation methods.

[0068] by Figure 1 The following explanation uses the abacus as an example to illustrate mathematical initiation and arithmetic skills:

[0069] Example 1, Reference Figure 2 ,

[0070] When calculating 8+7

[0071] Method 1:

[0072] (1) First, flip the cube beads in the two areas above the horizontal divider so that the fruit side is facing up. Take out 8 beads from the left area (5 on the upper rod and 3 on the lower rod) to the rightmost side of the area where they are located. Then take out 7 beads from the right area (5 on the upper rod and 2 on the lower rod).

[0073] (2) First, flip the cube beads in the two areas below the horizontal divider so that the solid color faces up. Take out 8 beads from the left (5 on the upper rod and 3 on the lower rod) to the rightmost side of the area where they are located. Then take out 7 beads from the right area (5 on the upper rod and 2 on the lower rod).

[0074] The calculation method is as follows:

[0075] ① Observation method (decomposition calculation method): The number of fruit beads in the first row is 5 + 5 = 10, and the number of fruit beads in the second row is 3 + 2 = 5. Therefore, the total number is 15.

[0076] ② Making 10: The 8 on the left needs 2 more to make 10. Take 2 of the 7 on the right and add 2 more to the left to make 10. The remaining 5 on the right makes a total of 15.

[0077] ③ Making 10: The 7 on the right side needs 3 more to make 10. Remove 3 of the 8 from the left side and add 3 more to the right side to make 10. The remaining 5 on the left side makes a total of 15.

[0078] ④ Rounding method: See reference Figure 3 Treat 8+7 as an integer 10, then 10+7=17, which is 2 extra. Then subtract 2 from the result 17=15.

[0079] ⑤ Rounding method: Treat the 7 in 8+7 as the integer 10, 8+10=18, count 3 more, then subtract 3 from the result 18=15.

[0080] ⑥ Rounding method: Treat both 7 and 8 in 8+7 as integers 10, 10+10=20, count 2 and 3 more, then subtract 2-3=15 from the result.

[0081] ⑦ Observation method (splitting method): 8+7 can be split into 5+3+5+2=5+(3+2)+5=15.

[0082] Method 2:

[0083] (1) First, flip the beads in the two areas above the horizontal divider so that the fruit side is facing up. Then, pull out a total of 8 beads from the upper rod of the left and right areas, and then pull out a total of 7 beads from the lower rod.

[0084] (2) First, flip the beads in the two areas below the horizontal divider so that the solid color side is facing up. Then, pull out a total of 8 beads from the upper rod of the left and right areas, and then pull out a total of 7 beads from the lower rod.

[0085] refer to Figure 4 ,

[0086] ⑧ Observation method (splitting method): 8+7 observations can be split into 10+3+2=15.

[0087] ⑨ Rounding method: Treat 8+7 as an integer 20, count 5 more, then subtract 5 from the result 20 = 15.

[0088] ⑩ Making up identical numbers: Treat 8+7 as 7+7 and observe it. Figure 7 +7 = 14, then +1 = 15.

[0089] 11. Matching Identical Numbers: Treat 8+7 as 8+8 and observe the result. Figure 8 +8 = 16, then -1 = 15.

[0090] 12. Once you're familiar with it, you can think of it this way: since 7 + 8 = 15, then 8 + 7 = 15.

[0091] Method 3:

[0092] There are twelve main quantitative relationships in the existing preschool mathematics education content: 1 and many, correspondence, size and quantity, equality, conservation, reversibility, arithmetic progression, complementarity, commutation, transitivity, inclusion, and function.

[0093] Observe and operate Figure 5 This allows for a more intuitive understanding of the meaning of addition and subtraction, and the various quantitative relationships between the parts: 8+7=15, 7+8=15, 15-8=7, 15-7=8.

[0094] Equality relationships: 8+7=7+8=15=10+5=5+5+5=5+5+2=……;

[0095] Complementary relationship: 15 contains two parts, 8 and 7. 8 needs to be supplemented with 7 to form 15, and 7 also needs to be supplemented with 8 to form 15.

[0096] Interchange relationships: 8+7=15, 7+8=15, 8+7=7+8

[0097] Reciprocal relationship: Since 8 + 7 = 15, then 15 - 8 = 7; Since 15 - 8 = 7, then 8 + 7 = 15.

[0098] Example 2: The calculation method of the abacus for mathematical enlightenment is in line with the mathematical idea of ​​"combining numbers and shapes". It can cleverly transform quantities into shapes composed of square areas, realizing the mutual transformation between numbers and shapes.

[0099] refer to Figure 6 :

[0100] The result, 40, can be visually observed. The numerical equation 10 × 4 can also be represented as a rectangle with a length of 10 and a width of 5, having an area of ​​40. A rectangle with an area of ​​40 can also be represented as 10 × 4. Here, the "number" is transformed into the "shape," and the "shape" is transformed into the "number."

[0101] refer to Figure 7 The area of ​​a rectangle with a length of 5 and a width of 4 is 20, that is, 5 × 4 = 20.

[0102] This can be transformed into the following: the area of ​​a rectangle with a length of 10 and a width of 4 is 20, which can be calculated as 5×4. It can also be transformed into the calculation of 10×2=20.

[0103] Then we can get the "rectangle before and after cutting and patching": the area of ​​the rectangle with a length of 5 and a width of 4 is equal to the area of ​​the rectangle with a length of 10 and a width of 2 and they can be transformed into each other;

[0104] The comparison also shows that: if the length is doubled and the width is doubled, the area of ​​the rectangle remains unchanged.

[0105] We can also obtain the transformed numbers: the product of 5×4 and 10×2 is equal and can be converted into each other;

[0106] The comparison also yields the following result: if the first factor is doubled, and the second factor is halved, the product remains unchanged.

[0107] This allows students to intuitively perceive the mutual transformation between numbers and shapes under certain conditions, thereby enlightening them on the mathematical concept of "combining numbers and shapes."

[0108] Example 3: During operation, one can learn to carry over when the sum of ten is reached, and can learn to calculate addition and subtraction within 100, addition and subtraction within 1000, and multiplication and division within 40.

[0109] refer to Figure 8 The process of carrying over from ten is as follows: count from 9 to 10 or 9 + 1 = 10. When the quantity reaches 10, the 10 ones make up one ten. Therefore, 10 ones make up 10, which can be exchanged for one ten. The 10 ones are then moved back, the abacus beads are flipped to show 10, and one ten is moved out. The process of carrying over from ten tens to one hundred is the same, and so on.

[0110] refer to Figure 9 The calculation is 55+44, and the result 99 can be observed intuitively.

[0111] refer to Figure 10 For the calculation of 99+99, you can intuitively observe that the sum of the tens digits on the left is 90+90=180, and the sum of the units digits on the right is 9+9=18. Therefore, the result is 180+18=198. There is no need to memorize the formula or perform vertical calculation.

[0112] Calculate addition with carry up to 1000, for example: 777 + 177.

[0113] Method 1: Reference Figure 11 Starting from the hundreds place, add 777+100+70+7.

[0114] Method 2: Reference Figure 12 Starting from the units digit, add 777+7+70+100.

[0115] Calculate subtraction within 1000 with borrowing, for example: 954 - 177

[0116] Method 1: Reference Figure 13 Starting from the hundreds place, subtract 954-100-70-7.

[0117] Method 2: Reference Figure 14 Subtract 954-7-70-100 from the units digit.

[0118] Example 4:

[0119] Explain using 5×8, 8×5, 40÷8, and 40÷5.

[0120] observe Figures 15 to 17 From the horizontal rows, we can see that there are 10 in each row, and there are 4 rows. 5 × 8 = 40, 40 = 10 × 4, therefore, 5 × 8 = 10 × 4.

[0121] From the sequence, we can observe that there are 4 in each column, and there are 10 columns. 4×10=40=10×4=5×8=8×5.

[0122] For example, 4×6, 6×4 or 24÷4, 24÷6 are similar.

[0123] Example 5: Calculate two-digit addition without carrying: 52 + 52

[0124] refer to Figure 18 :

[0125] Move the beads in the two areas above the horizontal divider to represent the data 52. Flip the face of the beads marked with the number 10 on the upper left rod to face up, then move the 5 beads on that rod to the far left of the rod, and move the remaining beads to the far right. Move all the beads on the lower left rod to the far right of that rod. Flip the solid-color face of the beads on the rod in the right area to face up, then move the 2 beads on that rod to the far left of the rod, and move the remaining beads to the far right. Move all the beads on the lower right rod to the far right of that rod. At this point, the leftmost bead in the two areas above the horizontal divider represents 52.

[0126] Move the beads in the two areas below the horizontal divider to represent the data 52. Flip the face of the beads marked with the number 10 on the upper left rod to face up. Then move the 5 beads on that rod to the far left of the rod and the remaining beads to the far right. Move all the beads on the lower left rod to the far right of that rod. Flip the solid-color face of the beads on the rod in the right area to face up. Then move the 2 beads on that rod to the far left of the rod and the remaining beads to the far right. Move all the beads on the lower right rod to the far right of that rod. At this point, the leftmost bead in the two areas below the horizontal divider represents 52.

[0127] After moving the beads, observe the dial and count the number of beads marked with the number 10, then count the number of beads with solid color patterns. This will allow you to visually see the result 105 without needing to use formulas or perform vertical calculations.

[0128] Calculate two-digit addition with carry: 77 + 77

[0129] refer to Figure 19 Move the abacus beads.

[0130] Calculate two-digit subtraction without borrowing: 87 - 52

[0131] refer to Figure 20 Move the abacus beads.

[0132] Calculate two-digit subtraction with borrowing: 87 - 58

[0133] refer to Figures 21 to 22 Move the abacus beads.

[0134] Calculate three-digit addition with carry: 777 + 777

[0135] refer to Figure 23 Move the abacus beads.

[0136] Calculate three-digit subtraction with borrowing: 777 - 199

[0137] refer to Figures 24 to 25 Move the abacus beads.

[0138] The results of the above calculations can be seen intuitively, without the need for formulas or pen and paper calculations.

[0139] refer to Figure 27 It also includes auxiliary learning tools, which include a telescopic rod and a cube abacus bead that is threaded through the telescopic rod and can slide and flip on the telescopic rod. A limiting structure is provided between the abacus bead and the telescopic rod to position one side of the abacus bead upward.

[0140] refer to Figure 27 The telescopic rod includes a hollow main rod and a secondary rod that passes through the hollow main rod and can slide inside the main rod. The abacus beads are disposed on the outer walls of the main rod and the secondary rod.

[0141] refer to Figures 27 to 32 The abacus beads are cube-shaped, with various numbers, animal patterns, fruit patterns, and solid color patterns on the four non-through faces of the cube. Among these, combinations with number patterns include symbols such as +, -, ×, ÷, >, <, and =, as well as cube-shaped number array patterns. The number of cube beads can be in groups of 5, 10, 20, 40, 100, 3, 6, or 7, etc.

[0142] refer to Figure 32 , is an example diagram for calculating 10×10=100.

[0143] refer to Figures 33 to 35 Further auxiliary learning tools include cards in the form of ten-square number arrays, used for card games, flashcard games, etc.

[0144] refer to Figure 26 It also includes a display screen connected to the abacus for early math literacy, the display screen and the abacus being foldable together via a hinge. The display screen displays animated demonstrations of a teaching app.

[0145] Furthermore, it also includes a drawer for placing the mathematical learning abacus, the auxiliary learning tools, and the display screen.

[0146] refer to Figure 36 Furthermore, it also includes a display screen connected to the mathematical learning abacus. The display screen is similar to a calculator display screen, and the number buttons are assembled with the mathematical learning abacus to form a non-folding screen.

[0147] Any adaptive changes made according to actual needs are within the protection scope of this utility model.

[0148] It should be noted that, for those skilled in the art, it is obvious that this utility model is not limited to the details of the above exemplary embodiments, and that this utility model can be implemented in other specific forms without departing from the spirit or essential characteristics of this utility model. Therefore, the embodiments should be considered as exemplary and non-limiting in all respects, and the scope of this utility model is defined by the appended claims rather than the foregoing description. Therefore, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the utility model. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. An abacus for introducing mathematical concepts and number sense, characterized in that, It includes an outer frame, a rod disposed within the outer frame, and a cube-shaped abacus bead that passes through the rod and can slide and flip on the rod. A limiting structure is provided between the abacus bead and the rod to position one side of the abacus bead upward.

2. The abacus for mathematical initiation and number sense according to claim 1, characterized in that, The abacus has a through hole inside, and the rod passes through the through hole. The inner diameter of the through hole is larger than the outer diameter of the rod. The limiting structure includes a horizontal contact surface of the abacus on the inner wall of the through hole and a horizontal contact surface of the rod on the rod that can match and overlap with the horizontal contact surface of the abacus.

3. The abacus for mathematical initiation and number sense according to claim 2, characterized in that, The through hole is located at the intersection of the diagonals of one of the faces. Both the through hole and the rod have square cross-sections. The side length of the through hole is greater than the side length of the rod. The four sides of the inner wall of the through hole are horizontal contact surfaces of the beads and can be rotated and limited as needed. The four sides of the outer wall of the rod are horizontal contact surfaces of the rod and can be limited to the horizontal contact surfaces of the beads as needed. The width of the horizontal contact surface of the beads is 90mm to 120mm, and the width of the horizontal contact surface of the rod is 80mm to 100mm.

4. The abacus for mathematical initiation and number sense according to claim 3, characterized in that, The other four faces of the abacus are respectively decorated with numbers, fruit patterns, animal patterns, and solid color patterns, and the numbers are 10, 100, or 1000.

5. The abacus for mathematical initiation and number sense according to claim 1, characterized in that, The outer frame is rectangular, and horizontal and vertical partitions are arranged vertically inside the outer frame, dividing the outer frame into four areas. Two rods are arranged in each area, and the two ends of the rods are connected to the outer frame and the vertical partition, respectively.

6. The abacus for mathematical initiation and number sense according to claim 5, characterized in that, The two ends of the horizontal partition are respectively connected to the corresponding short sides of the outer frame, and the two ends of the horizontal partition are respectively connected to the midpoint of the short side. The vertical partition includes a lower short plate disposed below the horizontal partition and an upper short plate disposed above the horizontal partition. The two ends of the upper short plate and the lower short plate are respectively connected to the midpoint of the horizontal partition and the midpoint of the long side of the outer frame.

7. The abacus for mathematical initiation and number sense according to claim 6, characterized in that, The rod penetrates the upper short plate and is located at a position where the upper short plate is divided into three equal parts along its length. The two rods penetrate the lower short plate and are located at a position where the lower short plate is divided into three equal parts along its length.

8. The abacus for mathematical initiation and number sense according to claim 5, characterized in that, The number of beads in each area is equal and not less than 5.

9. The abacus for mathematical initiation and number sense according to claim 1, characterized in that, It also includes auxiliary learning tools, which include a telescopic rod and a cube-shaped abacus bead that is threaded through the telescopic rod and can slide and flip on the telescopic rod. A limiting structure is provided between the abacus bead and the telescopic rod to position one side of the abacus bead upward.

10. The abacus for mathematical initiation and number sense according to claim 9, characterized in that, The telescopic rod includes a hollow main rod and a secondary rod that passes through the hollow main rod and can slide inside the main rod. The abacus beads are disposed on the outer walls of the main rod and the secondary rod.

11. The abacus for mathematical initiation and number sense according to claim 10, characterized in that, The abacus beads are cube-shaped, and the other four non-through faces of the cube are respectively decorated with animal patterns, fruit patterns, and solid color patterns. Among them, two faces are decorated with different animal patterns.

12. The abacus for mathematical initiation and number sense according to claim 11, characterized in that, It also includes a display screen connected to the mathematical learning abacus, the display screen and the mathematical learning abacus being foldably connected via a hinge.

13. The abacus for mathematical initiation and number sense according to claim 12, characterized in that, It also includes number sense game cards, which consist of several cards, each card having a marker for counting, the marker being a square color block, a circular color block, or an animal pattern.

14. The abacus for mathematical initiation and number sense according to claim 13, characterized in that, It also includes a small calculator with a display screen and buttons, which is connected to the mathematical learning abacus by a plastic frame.

15. The abacus for mathematical initiation and number sense according to claim 13, characterized in that, It also includes a drawer for holding the mathematical learning abacus, the auxiliary learning tools, the number-sense game cards, and the display screen.

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