Primary school mathematics second volume knowledge points sorting
The main knowledge points of the second volume of the first grade: - Subtraction within 20: There are methods such as leveling ten, breaking ten, adding and deducting if you want. For example, 13 - 9, the method of leveling ten first calculated 13 - 3 = 10, then calculated 10 - 6 = 4; the method of breaking ten first calculated 10 - 9 = 1, then calculated 1 + 3 = 4; if you want to add or subtract, because 4 + 9 = 13, so 13 - 9 = 4. For application questions, the known part of the total number was calculated by addition (keywords such as total, total, etc.), the known total and part of the other part was calculated by deduction (keywords such as remaining, etc.), and the deduction table needed to be memorized. - ** Know the shape **: Understanding Rectangle (Two long sides and two short sides, long sides equal, short sides equal), square (four sides equal), triangle (three sides), and circle; Able to draw three different cuboids with a cuboid, and draw the same square with a cube; In terms of placing patterns, at least four small rods for one square, at least seven for two squares, at least three for one triangle, at least five for two triangulars', at least six for one rectangular, and at least ten for two rectangular; A square piece of paper can be folded into a rectangular or triangular shape once, and folded twice can be folded into a rectangular, square, or triangular shape. - ** Know the numbers within 100 **: One by one, from 1 to 99, 99 plus 1 is 100; Ten times ten numbers, 10 times ten is 100. Although the second volume of knowledge was not fully presented in the second year and above, some of them were mentioned: - ** Sum-and-difference problem **: If the sum of two numbers is 81 and the difference between two numbers is 19, it can be solved by drawing a line diagram. First, find the decimals as (81 - 19) div2 = 31, and the large numbers as 31 + 19 = 50. - ** Special equation solution thinking **: For example, A + B = 50, A/3 + B/4 = 14, which can be solved by combining numbers and shapes. For example, if the sum of two squares in three squares is 17, 18, and 25 respectively, it can be solved by using hypothesis thinking (setting different symbols) and global thinking (adding the left side of the equation as a whole, adding the right side of the equation, and then finding a single value). On the whole, primary school mathematics also paid attention to the cultivation of mathematical thinking, such as the use of hypothesis thinking, overall thinking, and mathematical combination thinking when solving problems. Read more exciting novels for free
The most comprehensive question type in the collection of primary school mathematics knowledge points
The collection of primary school mathematics knowledge points covered a wide range of questions, including the following common questions: 1. ** Questions related to the four operations **: - Two-digit addition and substitution, for example, when calculating two-digit addition, one had to follow the rules of the same digit alignment, adding from the one digit, and adding 1 from the ten digits when the one digit was full; when calculating two-digit substitution, one had to follow the same digit alignment, deducting from the one digit, deducting from the ten digits if the one digit was not enough, adding 10 from the one digit, and then deducting. - For mixed operations, if there were only addition and division or multiplication and division in the formulas without parenthesis, the operations would be done from left to right. If there were multiplication and division, the multiplication and division would be done first before the addition and division. If there were parenthesis in the formulas, the operations in the parenthesis would be done first. - Multiply a single digit by a multi-digit number. Starting from the single digit, multiply each digit in the multi-digit number by the single digit number. The multiplied digit would be multiplied by dozens and then moved forward a few times. - Divisor is a division of one digit. Divide from the high digit of the dividends. Each time, divide the first digit of the dividends with the divinator. If it is smaller than the divinator, then divide the first two digits. Write the quotient on the digit where the divinator is divided. For each quotient, the remaining digits must be smaller than the divinator. - The factor was a two-digit multiplication. First, the number on the two-digit digit place was multiplied by another factor, and the last digit of the resulting number was aligned with the two-digit place. Then, the number on the tenth digit of the two-digit place was multiplied by another factor, and the last digit of the resulting number was aligned with the tens of digits of the two-digit place. Then, the two multiplied numbers were added together. 2. ** Questions related to understanding numbers **: - The smallest composite number was 4, the smallest prime number was 2, the smallest even number was 0, the smallest odd number was 1, the smallest factor was 1, the smallest single-digit number was 1, the smallest natural number was 0, the largest fraction unit was 1/2, the largest two-digit number was 99, the smallest two-digit number was 10, the largest single-digit number was 9, and so on. 3. ** Reading and writing questions related to mathematics **: - The four-digit numbers were read in order from the highest digit. For the thousand-digit number, it was read as a few thousand, for the hundred-digit number, it was read as a few hundred, and so on. If there was a zero or two zeros in the middle, only a "zero" would be read. No matter how many zeros there were at the end, it would not be read. - Four-digit numbers were written in order from the highest digit. If there were thousands of digits, write the number in the thousand digits. If there were hundreds of digits, write the number in the hundred digits, and so on. If there was no one in the middle or at the end, write a "0" in the middle or at the end. 4. ** Problem solving questions **: - For example, the sum of two numbers was 2016, and one of the numbers had a single digit of 0. If the 0 was removed, it was exactly twice the other number. The two numbers could be solved by analyzing the relationship between the numbers. - There were also the fourth-grade questions such as counting line segments, finding the law, crossing the bridge by train, sailing in flowing water, and encountering each other. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
The key points of making the primary school mathematics coursewares
The key points of making the primary school mathematics lesson are as follows: ** 1. Teaching content presentation ** 1. ** Question background ** - The source of the chicken and rabbit in the same cage problem was clearly shown, just like the records in ancient mathematical works, to increase the interest of the problem. He could use a story to draw out the problem, such as the scene where chickens and rabbits were raised together on an ancient farm and the number of them had to be calculated. 2. ** Concept explanation ** - The key to solving the problem was to highlight the differences in characteristics between chickens and rabbits, especially the number of legs (chickens had two legs and rabbits had four legs). You can use pictures or animations to show the appearance of chickens and rabbits and the number of legs. 3. ** Various solutions are displayed ** - ** Assuming Method ** - He explained in detail what he would think if he were to assume that they were all chickens or rabbits. For example, if they were all chickens, the difference between the number of legs and the actual number of legs would be calculated. Then, according to the principle that every rabbit was considered a chicken, the number of legs would be calculated. This part could be demonstrated with an animation. - ** Formula Method ** - Guide the students to find the relationship of equal amounts and set the unknown number (set the number of chickens or rabbits as the unknown number). For example, if there are x chickens and y rabbits, the equation (set) is listed according to the total number of heads and legs. In the course, the known conditions and unknown quantities could be listed in a table form, followed by the equation, and the steps to solve the equation could be shown step by step. - ** Other methods (such as grouping, packing, etc.)** - If he wanted to introduce these methods, the main point was to explain the basis for grouping or packing. Using the grouping method as an example, it was necessary to show how to reasonably group the chickens and rabbits according to the number of relationships. For example, in the case of the monk eating steamed buns, which was a variation of the chicken and rabbit in the same cage, the group was divided according to the number of steamed buns eaten by the big monk and the small monk. Then, the number of groups was calculated, and the number of people in each group was calculated. The process of grouping could be illustrated in the class. ** 2. Reflection of teaching objectives ** 1. ** Knowledge and Skill Target ** - Students should be allowed to intuitively understand the structure of the chicken and rabbit cage problem through the course, and learn to use different methods to solve this kind of problem. The practice questions in the class had to be targeted, from simple to complex. For example, the number of chickens and rabbits should be calculated from the total number of chickens and rabbits and the total number of legs. Then, some of the questions would be changed, such as the number of chickens and rabbits had a multiple relationship. 2. ** Course, Method, and Target ** - The focus was on the cultivation of students 'logical thinking ability. In the class, a flow chart could be used to show the thought process of solving a problem. From analyzing the problem, choosing a method, to getting the result, every step had to be clear and clear. For example, in the hypothesis method, the entire logical link from the hypothesis to the adjustment calculation had to be completely presented. 3. ** Emotions, attitudes, values, goals ** - It emphasized the fun and practicality of mathematics. Some pictures or videos of real life problems like chickens and rabbits in the same cage could be inserted into the class, such as the calculation of the number of cars and motorcycles in the parking lot, so that students could feel that mathematics knowledge was everywhere. You could also set up some encouraging words or interesting math challenges at the end of the lesson to stimulate students 'interest in mathematics. ** 3. Breakthrough in teaching difficulties ** 1. ** Establishing mathematical model ** - For the difficulty of understanding the mathematical model of the chicken and rabbit in the same cage problem, the tutorial could use a comparison method, such as comparing the actual problem with an abstract equation or formula. For example, put the actual scene of chickens and rabbits in a cage together with the equations listed by the hypothesis method, and use arrows to indicate the connection between the meaning of each step in the equation and the actual scene. 2. ** Ways to understand abstract thoughts ** - When explaining more abstract solution ideas, such as the idea of setting unknowns in the equation method, they had to be guided by simple and easy-to-understand examples. He could set up an interaction segment in the class, such as letting the students try to set up unknown numbers and list equations, then show the correct answers for comparison and explanation, so as to deepen the students 'understanding of abstract thinking methods. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school mathematics third grade equation knowledge points
1. ** The definition of an equation **: An equation that contains an unknown is called an equation. An equation is an equation, but an equation is not necessarily an equation. Only an equation that contains an unknown is an equation. 2. ** Solution of an equation **: The value of the unknown number that equals the left and right sides of the equation is called the solution of the equation. 3. ** Solution of the equation **: The process of solving the equation is called solving the equation. This is a calculation process. When solving the equation, you must satisfy the properties of the equation. You can't do random calculations. The result of each step satisfying the properties of the equation is the solution of the equation. The properties of an equation included adding or deducting the same number from both sides of the equation, and multiplying or dividing both sides of the equation by a number that was not equal to zero. 4. ** Use letters to indicate numbers. - When multiplying numbers and letters, or letters and letters, the multiplication sign could be written as "·" or omitted. The number had to be written in front of the letter. - When 1 is multiplied by any letter, 1 is omitted. - In a problem, different quantities were represented by different letters, and sometimes the range of the letters needed to be explained, such as (a = 0). At the same time, letters could be used to represent numerical relationships, calculation formulas, operational laws, and calculation rules. It could also be used to calculate the value of an algebra formula. That was, the value of a given letter could be substituted into the formula to obtain the value of the formula. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school students 'mathematics knowledge points are easy to understand
1. ** Understanding and Calculating Numbers ** - ** Intents **: Intents are composed of positive, zero, and negative numbers. They can be added, deducted, multiplied, and divided. - ** Two-digit addition by pen **: The same digits are aligned, starting from the one digit. If the one digit reaches 10, then the ten digits will be added by 1. - ** Two-digit Subtraction **: If the same digits are aligned, subtract from the first digit. If the first digit is not enough, subtract from the tenth digit by 1. Add 10 to the first digit and then subtract. - ** Mixed calculation rule ** - When there were no parenthesis, only addition and division or only multiplication and division were used, and the operations were done in order from left to right. If there were multiplication and division and addition and division, the multiplication and division were calculated first, and then the addition and division were calculated. - If there were calculations in parenthesis, the contents in parenthesis would be calculated first. - ** Reading and writing four-digit numbers ** - Reading: Reading in order from the highest position, thousands of digits read thousands, hundreds of digits read hundreds, etc. There is one or two zeros in the middle, only one "zero" is read, and the last zero is not read. - Write: Write it in order from the highest position. If there are thousands of numbers, write a few in the thousands. If there are no numbers in the middle or at the end, write "0". - ** Four-digit Subtraction **: The same digits are aligned, starting from the first digit. If one digit is not enough, the previous digit will be deducted by 1, and the original digit will be added by 10. - ** Multiplication rule of one-digit numbers multiplied by multi-digit numbers **: Starting from the single digit, multiply the multi-digit numbers by the one-digit numbers in turn, and then proceed forward when the number reaches dozens. - ** Divider is a one-digit number division rule **: Divide from the high digit of the dividends, first try to divide the first digit of the dividends with the divinator. If it is small, then try to divide the first two digits. The quotient is written on the digit where the divinator is divided. The remainder is smaller than the divinator. 2. ** Multiplication related ** - The second grade focused on multiplication and division calculations. They had to memorize the 99 multiplication table. Not only would they memorize it in order, but they also had to be clear about the source of the numbers. Children who had the ability to learn could gradually memorize the 99 multiplication table. 3. ** Formula related ** - When solving an equation, if the equation was complicated, one could treat part of the equation as a whole and solve it as an unknown number first. For example, 80 -(x +2) div3 = 76, one could first treat (x + 2) div3 as a whole and calculate the value of the whole before further solving x. 4. ** First Grade Learning Focus ** - He knew how to count and calculate simple addition and substitution. Subtraction was difficult for some children. Learning methods could be guided in life, such as shopping in the supermarket to calculate the price of goods, doing mental calculation cards every day and checking the accuracy rate at times. 5. ** Data and Chart **: An important tool for understanding and analyzing information. It can be used to organize data and draw charts. 6. ** Word problems **: By applying mathematical knowledge to practical problems, solving word problems can improve the ability to solve problems. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
The content arrangement of the second volume of mathematics for the first grade of primary school
The second volume of the first grade mathematics textbook included the knowledge of plane figures, abdication and substitution within 20, classification and sorting, the knowledge of numbers within 100, the understanding of RMB, addition and substitution within 100 (oral arithmetic), finding rules, solving problems with mathematics, and comprehensive and practical themed activities. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
How to teach the first lesson of the second volume of mathematics in primary school
Since it was not clear which part of the content corresponded to the first lesson of the specific textbook, the following was a common second-year mathematics division (1) in the average score (first lesson) as an example to provide teaching ideas. ##1. Knowledge Introduction 1. ** Introduction of the situation ** - They could start from the scenes that the students were familiar with, such as preparing food for the spring outing. He asked the students,"Students, if we want to divide some snacks equally among the students in the group, how should we divide them?" This would arouse the students 'interest and lead to the concept of average marks. 2. ** Initial Perception ** - Show some physical objects, such as small wooden sticks or small cards. For example, he took out six small wooden sticks and said,"Now the teacher has six small wooden sticks. He wants to give them to two children. How can we divide them?" There might be many ways to divide the points by guiding the students to do the operation. For example, one child would have one piece and another child would have five pieces; one child would have two pieces and another child would have four pieces; or each child would have three pieces. ##2. Concept Explanation 1. ** Draw out the concept ** - After the students were done with the operation, they would focus on explaining the method of dividing three sticks per child. They would emphasize the concept of "average score", which meant that each child would get the same number of sticks. He told the students to divide the six wooden sticks equally among the two children. Each child would get three sticks, which was the average score. 2. ** Strengthening Concept ** - Let's give some examples. For example, divide 8 apples equally among 4 children. Ask the students to use the learning tools (which can be small cards representing apples) to divide one point. Then ask the students to explain how they divided it. To further understand, the average score is the same number of apples. ##3. Class Practice 1. ** Simple Practice ** - Give some simple questions about the average score, such as dividing 10 balloons evenly among 5 children. How many balloons will each child get? Ask the students to draw or calculate the answer. 2. ** Expansion Practice ** - The format could be changed, such as giving some combinations of numbers to let the students judge whether it was an average score. For example, if three children were given two candies each, a total of six candies. Was this an average score? Through such exercises, the students could deepen their understanding of the concept of average marks. ##4. Class summary 1. ** Knowledge Review ** - At the end of the class, review the concept of average marks with the students and emphasize that the same amount of points per portion is the average mark. 2. ** To encourage thinking ** - He could assign some reflective homework, such as asking the students to go home and think about what other examples of average grades they had in their lives and share them in the next class. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Reflection on the teaching of the second volume of mathematics in the fourth grade of primary school
The following are some reflections on the fourth grade mathematics teaching: ** In terms of the first and fourth operations ** - ** Strengths ** - When teaching the order of the four operations, examples could be used to guide the students, such as the scenes of shopping and accounting in life, so that the students could understand the rules of multiplication and division before addition and addition, as well as calculating the parenthesis first. If he could successfully get the students to connect with reality, this would be a very good teaching strategy. - As for the simple arithmetic of the four arithmetic operations, it would be a good idea to guide students to observe the characteristics of numbers and explore them independently, so as to cultivate their sense of numbers and computational ability. - ** Not enough ** - There might be some students who were easily confused about the order of the four mixed operations. This might be due to insufficient practice or the lack of emphasis on confusing points in the teaching. - In the teaching of simple calculations, the explanation of some special number combinations (such as calculations close to the whole ten or hundred) might not be in-depth enough, causing some students to be unable to flexibly use simple calculations. ** 2. Observing objects (2)** - ** Strengths ** - Physical models or animations could be used to show the shapes of objects seen from different directions, which would help students understand intuitively. If such a teaching method was used, it could enhance the teaching effect. - ** Not enough ** - This part was difficult to teach. Some students might have poor spatial imagination and could not accurately identify the shapes of objects seen from different directions. Students with weak spatial imagination might lack sufficient targeted training and guidance methods. ** 3. Laws of Operations ** - ** Strengths ** - If they could explore the laws of addition and multiplication through group cooperation and let the students discover the laws themselves, it could improve their independent learning and cooperation ability. - If he could explain the law of calculation with real life examples (such as different algorithms for calculating the total price when shopping), it would deepen the students 'understanding. - ** Not enough ** - As for the reverse operation of the calculation law, it might not be emphasized enough in the teaching, resulting in some students only using the law to perform simple calculations and not being able to perform reverse operations flexibly. - Some students might just memorize the formulas and did not really understand their meaning, so they were prone to making mistakes in practical application. ** 4. The significance and nature of decimals ** - ** Strengths ** - When explaining the meaning of decimals, one could start with the concept of fraction and use graphs (such as a square divided into 10, 100, etc.) to directly represent decimals. This method of combining numbers and shapes would help students understand. - For the teaching of the property of decimals (adding or removing 0 at the end of the decimals, the size of the decimals remains the same), if a comparison example was used (such as the comparison of 2.3 and 2.30 in terms of numerical values), the students could clearly understand this property. - ** Not enough ** - In the teaching of reading and writing decimals, some students might make mistakes when reading and writing decimals, especially when there were many decimals. This might be the result of not practicing carefully enough. - When teaching the comparison of decimals, some students might not have a deep understanding of some special cases (such as the comparison between 0.9 and 0.900) and have vague concepts. ** 5. Triangle ** - ** Strengths ** - When teaching the classification of a triangle, if the students were to measure the sides and angles of the triangle by themselves, it would enhance their hands-on ability and understanding of the characteristics of the triangle. - For the teaching of a triangle with 180 degrees of internal angles, the method of puzzle experiment (putting the three angles of the triangle together) was used to help students understand this concept intuitively. - ** Not enough ** - In the teaching of the three-sided relationship of a triangle (the sum of any two sides is greater than the third side), some students may only remember this conclusion, but when they actually judge whether the three line segments can form a triangle, they cannot flexibly use this relationship. - When teaching complex triangular combinations, it might be difficult for students to accurately identify the triangular relationship and lack sufficient comprehensive analysis ability. ** 6. Adding and Subtracting Decimals ** - ** Strengths ** - It would be a good teaching method to emphasize the importance of decimal point alignment in teaching and to let students understand arithmetic through examples (such as the addition and substitution of decimals involved in shopping change). - Allowing students to calculate decimals vertically and verify them could cultivate their calculation accuracy and test habits. - ** Not enough ** - There might be some students who made mistakes in the number alignment when calculating the addition and substitution of decimals, especially when the number of digits in the integral part and the decimal part were different. - When solving the practical application of decimals, there might be students who could not correctly analyze the meaning of the question and list the wrong calculations. ** 7. Movement of the graph ** - ** Strengths ** - When teaching the translation and axis-symmetrical graphs, the students could use the grid paper to make the students operate the translation and complete the axis-symmetrical graphs themselves, which could improve their hands-on operation ability and space concept. - ** Not enough ** - For the determination of the distance of the figure translation and the determination of the symmetrical axis of the axis-symmetrical figure, some students might have difficulty understanding it, and there might be a lack of sufficient step-by-step guidance in the teaching. - In the teaching of translation and axis-symmetrical transformation of complex figures (including many basic figures), students might have difficulty accurately grasping the transformation of the overall figure. ** 8. Average and Bar Chart ** - ** Strengths ** - If he explained the meaning and calculation method of the average through specific life data (such as the test results of the students in the class), he could let the students feel the practical value of the average in life. - When teaching bar charts, students could draw their own charts to deepen their understanding of the structure and data representation of the charts. - ** Not enough ** - Some students might misunderstand the concept of the average due to the influence of extreme data. - When comparing different bar charts, students might lack the ability to analyze the information behind the data. ** 9. Mathematics (Chicken and Rabbit in the Same Cage)** - ** Strengths ** - If a variety of solution methods (such as the list method, the hypothesis method, etc.) were used to explain the chicken and rabbit in the same cage problem, it could broaden the students 'solution ideas. - By introducing the topic through the story of the ancient chicken and rabbit cage problem, it could stimulate the students 'interest in learning. - ** Not enough ** - The chicken and rabbit in the same cage problem was more difficult for some students. It might be difficult to understand the solution of the hypothesis method, and the tutoring for these students might not be enough. - Students might lack the ability to draw inferences from one example when they applied the solution to the chicken and rabbit in the same cage problem to other similar problems. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Primary School Mathematics Hebei Education Version Key Knowledge Summing Up
The following is a summary of some of the key knowledge of primary school mathematics in each grade: ** First grade ** - [Comparing: Cultivate interest in mathematics learning, master the method of enum, technical problems, finding patterns, and interesting math problems, and form the habit of active learning and thinking.] - ** Understanding the number within 10 ** and many other basic contents. ** First Grade ** - ** Position **: Cultivate interest in mathematics, master specific mathematical methods, form good study habits, and connect them to real life. - ** Understanding numbers within 100 ** and other knowledge, including understanding the RMB, addition and deduction within 100, etc. ** Second grade ** - ** Observing objects **: Experience the different shapes of objects observed from different positions. Able to identify the planar images of different surfaces of three-dimensional objects. - ** Add and Subtract Mixed Operations **: Continuous addition, continuous deduction, and addition and subtract mixed operations are done in a written and verbal order from left to right. If there are small parenthesis, do it in the small parenthesis first. Can add and subtract estimations. Master the steps to solve application questions. Can choose addition or substitution calculations according to different relationships. Can ask related mathematical questions. - [Multiplication in the Table (1): Understand the meaning of multiplication is a simple algorithm to find the sum of several identical addenda. Master the reading method of the multiplication formula, the names of each part, and the meaning of each part. Remember the multiplication formula from 2 to 6.] - ** Understanding of angles **: An angle has one apex and two sides. The size of the angle has nothing to do with the length of the side, but it is related to the size of the side. Master the drawing method of the angle, recognize the right angle in the triangle, square, and rectangular, and use the triangle to determine whether the angle is a right angle. ** Second Grade ** - ** centimeter, decimeter, meter **: Understand the units of length and strengthen your understanding in real life. - ** Division with remainder ** Knowledge, including understanding the unit of mass, reading, writing, addition and substitution of numbers within 1000, knowledge of quadrilateral, etc. ** Third grade ** - [** Big Numbers in Life **: Master reading and writing big numbers.] - ** Multiply two or three digits by one digit **, ** divide two or three digits by one digit **: Master calculations and solve practical problems. - [The movement of graphs (1)] and other knowledge, including the use of formulas to find the circumference of a rectangular square, four mixed operations. ** Third Grade ** - ** Year, Month, Day **: Proficient in multiplying two-digit numbers by two-digit numbers and solving practical problems, using the area formula to find the area of a rectangular and square, preliminary understanding of decimals and scores and combining them with reality, mastering different units and distinguishing them. ** Fourth grade ** - ** Liters and milliliters **: Accurately calculate the division of three-digit numbers by two-digit numbers and solve practical problems. Understand the classification of straight lines, rays, angles, and angles, and draw angles. Distinguish between multiple and factor, judge the least common multiple and the greatest common factor. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school sixth grade first volume mathematics knowledge point three
The following is a summary of the sixth grade mathematics knowledge points: ** 1. Concepts related to numbers ** 1. ** Intents ** - The concept of positive and negative numbers needed to be grasped. It was clear that positive numbers were numbers greater than 0, and negative numbers were numbers less than 0. - The rules of addition and substitution of the whole numbers included the addition and substitution of the same symbols, as well as the addition and substitution of different symbols. - For the multiplication and division operations of an integral number, one had to understand that multiplication was a simple operation of the same addend, while division was the inverse operation of multiplication. At the same time, one had to pay attention to the symbol rules in the operation. 2. ** Points ** - The concept and basic nature of scores. Scores represented the division of a whole into several parts, one or several parts. The basic property of a fraction was that the numerator and the numerator were multiplied or divided by the same number (except for 0), and the size of the fraction remained unchanged. - To add and subtract a fraction, one had to add and subtract a fraction with the same Denominator. If the Denominator did not change, the Numerator would be added and deducted. If one added and deducted a fraction with a different Denominator, one had to first divide it into a fraction with the same Denominator before calculating. - The multiplication and division of scores. Multiplying a fraction by an integral was a simple operation to find the sum of several identical scores. The numerator and the integral were multiplied, and the numerator remained unchanged. Multiplying a fraction by a fraction was to use the product of the numerator as the numerator, and the product of the numerator as the numerator. Fraction division was the inverse of fraction multiplication. Dividing by a fraction was equal to multiplying by its inverse. - The relationship between a fraction and an entire number was that an entire number could be regarded as a fraction with 1 as the Denominator. 3. ** Decimals ** - The concept and representation of decimals. The decimals were a special representation of real numbers, consisting of an integral part, a decimals part, and a decimals point. - To add and subtract decimals, one had to calculate them in line with the decimal point. - For multiplication and division of decimals, the multiplication of decimals was calculated according to the rule of multiplication of whole numbers. Then, the number of decimals in the factor was counted from the right side of the product, and the decimals were marked. For division of decimals, when the division was an integral number, it was calculated according to the rule of division of whole numbers. The decimals of the quotient should be aligned with the decimals of the dividends. When the division was a decimals, the division should be converted into an integral number before calculation. - The relationship between decimals and scores was that decimals could be converted into scores, and scores could also be converted into decimals. 4. ** Multiple and Subordinate of Numbers ** - The concept of multiple and common multiple was that if one whole number could be divided by another whole number, the whole number would be a multiple of the other whole number. The common multiple referred to two or more natural numbers, and if they had the same multiple, the multiple would be their common multiple. - Divisors are also known as factors. If the quotient of an integral a divided by an integral b(b = 0) is an integral without a remainder, we say that b is a quotient of a. A common quotient refers to an integral that can be divided by several integral numbers at the same time. - The greatest common factor and the least common multiple. The greatest common factor referred to the largest common factor of several numbers, and the least common multiple referred to the smallest common multiple of several numbers except for 0. ** 2. Fraction multiplication ** 1. ** Meaning of fraction multiplication ** - The meaning of multiplying an integral by a fraction was the same as multiplying an integral. It was a simple operation to find the sum of several identical addenda. The second factor must be an integral. - The meaning of multiplying a number by a fraction was to find the fraction of a number. The second factor must be the fraction. 2. ** Multiplication Method for Fraction ** - The algorithm for multiplying a fraction by an integral was to multiply the numerator by the integral, with the numerator unchanged. If it was possible to reduce the fraction, then calculate it. - The algorithm for multiplying a fraction by a fraction was to use the product of the numerator multiplied by the numerator as the numerator and the product of the numerator multiplied by the numerator as the numerator. If the formula contained a fraction, the fraction had to be converted into a fake fraction before the calculation. 3. ** Relationship between product and factor ** - A number (except 0) multiplied by a number greater than 1, the product is greater than this number. - A number (except 0) multiplied by a number less than 1, the product is less than this number. - A number (excluding 0) multiplied by 1, the product is equal to this number. 4. ** Mixed fraction and multiplication ** - The order of the mixed operations of fraction multiplication was the same as that of the whole numbers. Multiply first, divide first, then add and subtract. If there were any parenthesis, then calculate the ones inside the parenthesis first, and then calculate the ones outside the parenthesis. ** 3. Knowledge Points related to application questions ** 1. ** Itinerary problem ** - To understand the relationship between speed, time, and distance, distance = speed x time. When solving the travel problem, he could flexibly use this formula to solve the unknown quantity according to the known conditions. 2. ** Diagram Area Calculation ** - For simple shapes such as rectangular, square, triangular, quadrilateral, and echelon, you must remember the area calculation formula. - For complex combination graphs, they could be cleverly divided and reorganized into simple graphs that had been learned, and then the corresponding geometric formulas could be used to solve the area. In this process, one must pay attention to the observation and thinking of the characteristics and laws of the graph, and cultivate the ability of spatial imagination and logical thinking. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school fourth grade mathematics first volume knowledge point collection
The following is a collection of knowledge points in the first volume of fourth grade mathematics: 1. ** Conversion of length units **: 1 meter = 10 decimeters, 1 decimeter = 10 centimeters, 1 centimeter = 10 millimeters, 1 kilometer = 1000 meters, 1 decimeter = 100 centimeters, 1 meter = 100 centimeters. 2. ** Area unit conversion **: 1 square meter = 10000 square centimeters, 1 hectares = 1000 square meters, 1 square meter = 100 square decimeters, 1 square decimeter = 100 square centimeters, 1 square kilometer = 100000 square meters = 100 hectares. 3. ** The classification of angles **: acute angle (greater than 0° but less than 90°), right angle (90°), obtuse angle (greater than 90° but less than 180°), flat angle (180°), and peripheral angle (360°). 1 peripheral angle = 2 flat angles = 4 right angles. The relationship between the sizes is acute angle <right angle <obtuse angle <flat angle <peripheral angle. 4. ** Four operations related **: Multiplying 0 by any number will result in 0; dividing 0 by any number that is not 0 will result in 0. 5. ** Formula related to economic problems **: Unit price × quantity = total price, total price/unit price = quantity, total price/quantity = unit price. 6. ** Formula for the itinerary problem **: Distance/time = speed, distance/speed = time, speed × time = distance. 7. ** Rectangle and square area formula **: Rectangle area = length x width (length = area/width), square area = side length x side length. 8. The smallest composite number is 4, the smallest prime number is 2, the smallest even number is 0, the smallest odd number is 1, the smallest factor is 1, the smallest single-digit number is 1, the smallest natural number is 0, and the largest unit of fraction is 1/2. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>