Elementary School Mathematics Profits and Losses Problem Solution Strategy Research Thesis
** Title: A Study on the Strategy to Solve the Breakeven Problem in Elementary Mathematics ** ** abstract: ** This thesis aims to study the profit-loss problem in primary school mathematics and its solution strategy. Through the analysis of various types of profit-loss problems, the corresponding solution ideas and methods were explored to help primary school students better understand and solve such problems and improve their mathematical thinking ability. ##I. Introduction The profit-loss problem was an important type of elementary math problem. It involved distributing a certain number of items to a certain number of people or objects according to different distribution methods, resulting in a surplus or loss. Mastering the solution strategy of the profit-loss problem is of great significance for primary school students to improve their mathematical application ability and logical thinking ability. ##2. Type of Breakeven Problem 1. ** One profit and one loss type ** - In this type of allocation, there would be a surplus (surplus) and a deficit (deficit). For example, if each person gets three apples, there will be 11 more apples (profit), and each person gets four apples, there will be one less apple (loss). 2. ** Two-in-one ** - There were more than enough people for both assignments. For example, three people sitting on each bench were nine more people, and four people sitting on each bench were three more people. 3. ** Two-loss Type ** - Both assignments were insufficient. For example, if each person was given 3 candies, they would be short of 4 candies, and if each person was given 5 candies, they would be short of 16 candies. 4. ** One full and one flat (just finished)** - One of them had just been distributed, and the other had a surplus. 5. ** One loss and one draw (just finished distributing)** - One of them had just been distributed, and the other had suffered a loss. ##3. Solution Strategy 1. ** Basic Formula Method ** - For the one-profit-one-loss type, the number of people =(profit + loss)/(the difference between the two distribution numbers). For example, if each person gets 3 apples, 11 more apples, and each person gets 4 apples, 1 less. The number of people =(11+1)/(4 - 3)=12 people. The number of apples can be calculated based on the number of people and one of the distribution methods, such as 12×3+11 = 47. - For the two-win type, the number of people =(big winning-small winning-small winning-small For example, the number of people sitting on the bench in front =(9 - 3)/(4 - 3)=6 people. - For the two-loss type, the number of people =(big loss-small loss)/(the difference between the two distribution numbers). For example, the number of people =(16 - 4)/(5 - 3)=6 people. 2. ** Analyzing the relationship between quantity and quantity ** - First of all, the key to solving the problem was to determine the total number of items and the number of objects to be distributed. When analyzing the profit and loss problem, it was necessary to carefully compare the changes in the number of people allocated in the two distribution methods and the resulting changes in profit or loss. For example, in the problem of a rope winding around a tree, two circles would be five meters more, and five circles would be seven meters less. Through analysis, it could be seen that five circles would be three more circles than two circles, and the corresponding length of these three circles was the sum of the extra five meters and the less seven meters. Thus, the length of one circle was (5 + 7) × (5 - 2)=4 meters, and then the length of the rope was calculated. - In some complicated profit-loss problems, such as the problem of repairing roads, if 260 meters were repaired every day, the total length of the road would be extended by 8 days. If 300 meters were repaired every day, the total length of the road would be extended by 4 days. He needed to first find out the relationship between the speed difference between the two road repairs and the time difference, calculate the number of days of the original plan to repair the road, and then find the total length of the road. 3. ** Line-segment diagram auxiliary method ** - The line graph could directly represent the quantity relationship in the profit and loss problem. For example, in the problem of splitting apples, the total number of apples could be represented by line segments, and it could be divided according to different distribution methods to clearly show the profit or loss parts to help students better understand the problem. In the problem of a rope winding around a tree, the length of the rope could be represented by drawing a line segment. It could be seen that the relationship between the number of circles and the number of circles was more or less, which was helpful in the formation of the solution. ##4. The conclusion The profit-loss problem in primary school mathematics has a certain degree of difficulty, but through the accurate judgment of its type, using the basic formula method, the analysis of the relationship between quantity and the line diagram auxiliary method to solve the problem, primary school students can gradually master the method to solve the profit-loss problem, improve the ability to solve mathematical application problems, and also help to cultivate logical thinking and mathematical accomplishment. In the teaching process, teachers should focus on guiding students to understand the nature of the profit-loss problem and flexibly use the solution strategy to better deal with this kind of problem. Read more exciting novels for free
Elementary Mathematics Research Report
The following is an example of a research report on elementary school mathematics: ** 1. Research background ** (I) Education Competition In modern society, science and technology were developing rapidly. The economic competition had turned into a competition for talents, which then evolved into a competition for education. Education innovation and teaching reform have become the core theme of education. Mathematics education is an important part of basic education, and its teaching reform is essential to cultivate talents to adapt to modern society. (II) Mathematics teaching reform and development background 1. Changes in teaching philosophy The new mathematics curriculum standards required students to acquire the mathematical knowledge, thinking methods, and application skills needed to adapt to future social life and further development, to experience the connection between mathematics, nature, and human society, to learn to use mathematical thinking to solve problems, and to form a scientific spirit. The current mathematics curriculum reform focuses on reflecting the basic mathematical thinking methods, presenting the content in a popular and life-oriented way, so that students can master mathematics in activities and real life. 2. Traditional teaching situation There were many problems in traditional mathematics teaching: - In terms of goals, they focused on imparting knowledge and achieving skills, ignoring the cultivation of students 'practical ability and innovative spirit. - In terms of content, they relied too much on textbooks and were out of touch with student life. - In terms of learning activities, students 'learning methods were monotonous and passive, lacking opportunities for practice, exploration, and cooperation. - In terms of evaluation, it paid more attention to book knowledge, calculation and reasoning skills, and paid less attention to students 'learning attitude, emotions and practical ability. ** 2. Main Research Questions ** (I) Teaching content reform It solved the problem of traditional mathematics teaching content being separated from the reality of life. It made the mathematics content full of life and let the students experience the close connection between mathematics and nature, society and life. (II) Homework problems 1. The Status of Homework in Teaching Homework was as important as classroom teaching. Both domestic and foreign teaching theories pay attention to homework problems. With the deepening of teaching reform and the promotion of the "double reduction" policy, homework problems need to be analyzed and studied from a multi-dimensional perspective. Homework reform is an important way to reduce the burden of students 'homework and reflect the students' learning initiative. 2. The Present Situation and Disadvantages of Mathematics Homework in Primary Schools - Our school's sample survey found that primary school mathematics homework generally has boring content, monotonous form, uneven distribution of quantity, ignoring students 'potential, paying attention to independent homework and neglecting cooperative homework, etc., which leads to students' disgust and affects students 'physical and mental health development. - In the current mathematics teaching, due to the influence of examination scores, there are drawbacks such as ignoring the differences between students, the imbalance of practice "quantity" and "quality", emphasizing concept theorem and neglecting the use of skills, resulting in ineffective or inefficient homework for students. Therefore, constructing a student-centered primary school mathematics homework model has become an important topic. ** 3. Theoretic basis ** (I) Constructionist Theory Knowledge included objective and subjective knowledge. Obtaining objective knowledge required the participation of subjective experience. Students should take the initiative to construct knowledge on the basis of their original cognition, rather than simply accepting the teacher's transmission. Multiple Intelligence Theory ** IV. Strategy in Teaching Practice ** (I) Large unit teaching strategy 1. total planning The teacher planned the teaching of mathematics as a whole, defined the goal and content, and connected the knowledge points to form a logical structure system to help the students form an overall understanding. 2. create situations Create situations based on the reality of life, guide students to use mathematics to solve practical problems, cultivate applied and innovative thinking, and stimulate interest and curiosity. 3. inquiry learning Guide the students to explore the knowledge of the unit, provide space and time for exploration, let the students experience the mathematical thinking process, and cultivate the ability of exploration and independent learning. 4. exchanges and interactions Through group discussions and other means, students can communicate and cooperate, inspire each other, and stimulate their thinking and innovation potential. 5. Evaluation and Reflection It uses a variety of evaluation methods to evaluate the learning results and process, guiding students to reflect, focusing on comprehensive quality and development potential. (II) Exploration homework design strategy 1. Exploration of the theoretical basis of homework. 2. To analyze the causes of ineffective and inefficient homework. 3. In order to promote the healthy and effective development of students, this paper explored the ways and methods to cultivate students 'positive feelings of loving mathematics, to comprehensively apply mathematical knowledge, to accumulate mathematical experience, and to improve their scattered and creative thinking in the learning activities inside and outside the mathematics subject. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
The Research of Primary School Mathematics Cooperation Strategy
The primary school mathematics cooperation strategy research mainly involves the following aspects: ** 1. In terms of rational grouping ** 1. ** Number of people and expression ** - Each group should have 4 - 6 people. This would ensure that each team member could express their thoughts within the specified time, and there would be enough time to discuss and exchange ideas, which would be beneficial for thinking. 2. ** Principle of Member Constitution ** - Follow the principle of "in-group heterogeneities, in-group homologies". The members of the group were determined according to the students 'academic performance, learning ability, gender, hobbies, and family background. Students with different mathematics foundations, genders, and personalities were grouped together to learn from each other, learn from each other's strengths, and improve their mathematics results together. There should be no obvious differences between the groups to promote fair competition. ** 2. Team Leader Selection and Training ** 1. ** Team Leader Selection ** - Students with strong self-control and organizational skills were selected as group leaders. 2. ** Team Leader Training ** - Carry out "pre-job training" for the team leader and clarify the responsibilities of the team leader, such as being responsible for the cooperation and communication organization of the team, inspection and supervision, praise and criticism, etc., so that the team leader can play a role in developing team cooperation and enhancing the competitiveness of the team. ** 3. Teacher guidance ** 1. ** Seize the opportunity to intervene ** - In the process of group teaching, the teacher could not interfere with the students 'discussion and learning at will. He had to think of ways to deal with possible situations in advance. When the student group discussion could not go on, the teacher would give guidance to help the students get out of the bottleneck and let the group cooperation proceed smoothly. 2. ** Ask questions are encouraged ** - Teachers should encourage students to ask questions, which helps to cultivate students 'thinking ability and creativity. 3. ** Character Change ** - When the students were engaged in cooperative exchanges, the teacher was the catalyst and collaborator. Sometimes, according to the difficulty of the learning task and the actual situation of the students, the teacher would act as a guide. They had to observe the group activities, including the individual participation and cooperation of the students. They had to go deep into the group to understand the completion of the learning tasks, analyze the solutions, find mistakes in time, provide hints or correction, and answer the students 'questions. In group communication, teachers were also collaborators. They had to adjust the students 'learning content, time, and emotions in time to achieve mutual learning and mutual promotion. When guiding the cooperation team to complete the summary and application of new knowledge, the teacher was more of a mentor. ** 4. Learning content selection ** - Teachers had to make sufficient preparations before class, make clear which content was suitable for the group teaching mode, and think about what methods to use to motivate students in order to carry it out smoothly. Not everything was suitable for group teaching. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school mathematics electric meter application problem
The following are some examples of elementary school math electric meter application questions: 1. Wonderful Imagination's electricity consumption in July was 95 kWh. Given the electricity meter reading in July, find the electricity meter reading at the end of June. 2. Wondrous Imagination's monthly electricity meter reading for the second half of the year is known. How many kWh will be used in the second half of the year? 3. Xiao Hong's family's electricity meter reading from January to July last year was known. They calculated the electricity consumption in February, March, April, May, June, and July, as well as the total electricity consumption from February to July. 4. Mengmeng's house used 32 kWh of electricity in March, which was 14 kWh less than in February. How many kWh of electricity did she use in the past two months? 5. At the end of February, Xiaoxiao's electricity meter reading was 360 kWh. At the end of March, the electricity meter reading was 580 kWh. The electricity price per kWh was 0.6 yuan. 6. The Zhang family used 456 kWh of electricity in August and 367 kWh of electricity in September. How many kWh of electricity were used in August and September, and how many kWh were saved in September compared to August? <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school mathematics, train crossing the bridge problem
The train crossing the bridge problem was a classic problem in primary school mathematics. The following are the key points and typical questions of this type of problem. ** 1. Basic Concept Understanding ** 1. ** Calculating the distance of the train crossing the bridge ** - When a train crossed the bridge, the distance traveled by the train was the length of the bridge and the length of the train. This was because the train had a certain length, and one could not simply consider the length of the bridge. For example, when the train's head drove onto the bridge, the train only passed the length of the bridge, but the train's tail was still on the bridge. The complete process of crossing the bridge was to leave the bridge at the tail, so the total distance was the length of the bridge plus the length of the train. 2. ** Formula ** - The total length of the bridge car = the speed of the car x the time it took to cross the bridge. This formula was the basic formula for solving the problem of a train crossing a bridge. It could calculate the unknown quantity according to the known conditions. ** 2. Classic Questions and Solution ** 1. ** Find the length and speed of the train ** - For example, it took a train 12 seconds to pass through a 420-meter-long cave, and it took 22.5 seconds to pass through a 1050-meter-long bridge at the same speed. What was the speed and length of this train? - Solution 1 (equation method): - Let the length of the train be (x) m. Since the speed of the train did not change, according to speed = distance/time, the equation could be obtained as: <(420 + x)> 12=(1050 + x)> 22.5> - First, he simplified the two sides of the equation: - \((420 + x)×22.5=(1050 + x)×12\)。 - The expansion is [9450+22.5x = 12600+12x]. - Transferring the entries will yield a result of {22.5x -12x =12600 - 9450}. - That is,<10.5x = 3150>, the solution is <x = 300> meters. - The train's speed was given as [(420 + 300) div12 = 60] m/s. - Solution 2 (Arithmetic): - First, find the train speed. According to the difference between the two journeys, it is the product of the time difference and the time. The train speed is [(1050 - 420)]/(22.5 - 12)=60 m/s. - Then find the length of the train. The length of the train is [60×12 - 420 = 300] meters. 2. ** Combined questions on the train crossing the bridge and other questions ** - For example, 122 Young Pioneers lined up in two neat rows to go to the Children's Palace. The speed of the team was 60 meters per minute, and the distance between the two people was 1 meter. Now, the team had to cross a 600-meter-long wooden bridge. How long would it take for the team to get on the bridge and leave? - Solution: - First, find the length of the team. The 122 Young Pioneers were arranged in two columns. Each column had {122 × 2 = 61} people, and the number of intervals was {61 - 1 = 60}. Because the distance between the two people in front and behind was 1 meter, the length of the team was {60×1 = 60} meters. - The distance traveled by the entire team from the bridge to the bridge was the length of the team plus the length of the bridge, which was {600+60 = 660} meters. - According to the time = distance/speed, the required time is (660/60 = 11) minutes. 3. ** The problem of two trains crossing each other ** - For example, if two trains were moving in opposite directions, the speed of car A was 40m/s, and the speed of car B was 25m/s. When the two trains crossed each other, the passengers on car B saw the front of car A and the back of car A. It took a total of 10 seconds. How long was car A? - Solution: - From the time the two cars passed each other to the time the passengers saw the back of car A, the sum of the distance between the two cars was the length of car A. - The sum of the speed of the two vehicles is [40 + 25 = 65] m/s. According to the distance = speed x time, the length of vehicle A is [65×10 = 650] m. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school students 'mathematics problem solving skills
The following are some elementary school math problem solving techniques: 1. Drawing Strategy: Translate the words of a difficult problem into a picture. It can quickly sort out your thoughts and find a solution. In the process of solving a problem, by drawing a diagram related to the meaning of the problem, the diagram was used to help reasoning and thinking. This was especially common when solving problems such as geometry, proportions, or scores. 2. ** Transformation Strategy **: Transform a complex problem into a simple problem, and turn an unknown problem into a known problem. This is one of the common methods used to solve problems in primary school mathematics. 3. ** List Strategy (Enumeration Strategy)**: List the condition information of the problem in the form of a table. This makes it easy to find the problem and analyze the quantitative relationship, thereby eliminating the interference of non-mathematical information. At the same time, it also helps to find a solution to the problem. When using it, one must pay attention to not repeating or missing anything. 4. ** Enumeration Strategy **: When solving some special problems that cannot be calculated, it can list all possible situations of the research object, so that the problem can be solved more easily. When listing, you have to think in an orderly manner to ensure that you don't miss anything. 5. ** Substitution Strategy **: Used to solve the problem of the relationship between several quantities and the total quantity. By using this strategy, the relationship between two quantities could be simplified into one, which would help to solve the problem. 6. ** Comparing Method **: According to the meaning of the mathematics question, compare the meaning and essence of concepts, properties, laws, rules, formulas, terms, and terms. Relying on the understanding, memory, recognition, reproduction, and transfer of mathematical knowledge to solve the question. This would help train the child to have a correct understanding of mathematics knowledge, a firm memory, and accurate identification. 7. ** Comparisons **: By comparing the similarities and differences of mathematical conditions and problems, you can study the reasons for the similarities and differences and find a solution to the problem. When using it, you need to pay attention to the completeness of the comparison, find the connection and difference, compare under the same relationship, and grasp the main content to compare carefully. 8. Formula Method: Use laws, formulas, rules, and rules to solve problems, reflecting deductive thinking from the general to the special. However, it was necessary to ensure that the child had a correct and profound understanding of formulas, laws, rules, and rules, and could use them accurately. 9. ** Analysis Method **: To break down the whole into parts, to break down complex things into various parts or elements, and to study and derive these parts or elements. The idea was to start from the problem to be solved, choose the two conditions needed correctly, and deduce them one by one until the problem was solved, which was "tracing the cause from the effect." 10. ** Holistic approach **: For some calculations, when a certain part cannot be calculated directly, this part can be regarded as a whole and solved step by step. For example, when solving an equation, if there were multiple calculation steps on one side of the equal sign and a certain part could not be calculated, one could first treat this part as a whole to solve it. 11. ** Using Aptitudes **: When you encounter complex calculation problems, you can use approximate numbers to help with quick calculations. 12. ** logical reasoning method **: When solving some reasoning or logic questions, use logical reasoning to get the correct answer. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school mathematics reasoning problem solving skills
The following are some elementary math reasoning questions: * * 1. Calculation and Derivation ** Calculation was the basic method of reasoning. He had been exposed to computing since elementary school, but he had to understand its uses in depth. When solving problems using algebra, calculations could reveal hidden information, expose the nature of the problem, and draw reliable conclusions. When calculating and deducing, he had to consider all situations to avoid missing out. * * 2. Deductive Reasoning ** 1. This was a way of reasoning from the general to the specific. The premise and the conclusion were connected. If the premise was true, the conclusion must be true. 2. Derivation was a special method in deductive reasoning. Using the connection between the research subjects, the previous conclusion could be deduced into the next conclusion, just like dominoes, which could simplify the problem. * * 3. Induction and classification ** 1. This was a method of reasoning from the individual to the general, and the conclusion might not be completely correct (except for the complete induction reasoning). When a complete induction and reasoning examined all the objects of a thing, the conclusion must be true. * * 4. Analogies ** By analogy with simple examples, he could find similar patterns to solve the problem. For example, when finding a two-digit number with an additional 0 added to the end of the two-digit number, one could make an analogy inference from the similar change law of simple numbers such as 2 and 3. * * 5. Comparisons ** By comparing the mathematical conditions and the similarities and differences of the problem, he could study the reasons for the similarities and differences and find the solution. * * 6. Comprehensive Method ** He treated the known content as parts, analyzed the internal connections between the parts, and gradually deduced the requirements of the question. * * 7. Method of parameters ** Use letters or numbers that only participate in formulas and calculations but do not need to be solved to represent the relevant quantities, and list the formulas according to the meaning of the questions. * * 8. Elimination Method ** The logical principle was that everything had its opposites. Among many outcomes (right and wrong), the wrong outcome was eliminated, and the remaining outcome was the right outcome. * * 9. Think flexibly and draw inferences from one instance ** 1. When doing questions, you should think flexibly to avoid rigid thinking and think divergently. 2. They learned to draw inferences from one instance and use their existing solutions when they encountered similar problems. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school fifth grade mathematics distribution stamp problem
There were many problems in fifth-grade mathematics. For example, if Xiao Ming bought x stamps, 1.5x - 3 = x + 3, then x = 12 stamps, 1.5x = 18 stamps, which means that Xiao Ming bought 12 stamps and Xiao Hong bought 18 stamps. Also, Xiao Hong and Xiao Ming had a total of 126 stamps. Xiao Hong had twice as many stamps as Xiao Ming. If Xiao Ming had y stamps, then Xiao Hong had 2y stamps. Y+2y = 126, 3y = 126, y = 42, Xiao Ming had 42 stamps, Xiao Hong had 84 stamps, and so on. These problems were mainly solved by setting unknown numbers and establishing equations based on the quantitative relationships in the questions. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school fourth grade mathematics reading problem solving
The fourth grade mathematics reading questions could be solved from the following aspects: First, he had to understand the problem. Before reading the question, read it carefully to ensure that you fully understand the meaning of the question. You can break the question into small parts and clearly understand the answers and related conditions. Secondly, if the question involved a chart, a chart analysis was required. Carefully observe the data in the chart, such as reading the values, comparing the data, or finding the patterns in it to help solve the problem. Furthermore, he had to use logical reasoning. Mathematics reading questions often needed to analyze the logical relationships, find patterns and laws, and infer the answers through the observation of the development trend and laws of things. Then, he could use the method of illustration. When answering questions, use specific examples to help you understand. These examples can be familiar to you or constructed according to the conditions given by the question. In addition, he had to think from many angles. When reading a mathematical problem, you can't be limited to one way of thinking. Try to think from different angles and use different methods to solve the problem. Use the mathematical knowledge you have learned to find a better solution. Finally, he summarized the problem. When reading, try to summarize the problems and find out the common points and rules by summarizing the problems that have been solved, so as to better solve similar problems. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school mathematics class efficiency research project design case
The following is a case study of an efficient primary school mathematics classroom exploration project: ** 1. Research purpose and significance ** 1. ** Reality needs it ** - In primary school mathematics teaching, there are many teachers who have problems in understanding and implementing the new curriculum standard, which affects the classroom teaching effect. In the current education environment, improving classroom teaching efficiency was the key to improving the quality of primary school mathematics teaching. 2. ** Theoretically significant ** - Through effective classroom teaching evaluation, the ideas of curriculum reform can be transformed into concrete actions of teachers. It has positive significance for the improvement of teachers 'teaching level, teaching quality and teachers' professional development. At the same time, clear classroom teaching evaluation standards are related to whether it can promote the professional development of teachers. For example, different classroom real-time evaluations reflect different teaching cultures, and it is of great theoretical significance to study whether teachers are based on student development. 3. ** Practicality ** - Based on the demands of the new curriculum for mathematics classroom teaching, such as "the generation of classroom teaching", this paper studies the "immediate evaluation" behavior of junior mathematics teachers, providing reference, reference and operational tools for mathematics teachers to grasp the generation of classroom and realize the growth of classroom teaching. ** 2. Research content ** 1. ** Research object ** - The research could be conducted on primary school students in the lower grades (such as first and second grade). Of course, it could also cover the entire primary school stage. 2. ** Research Range ** - It included addition, deduction, multiplication, division, verbal calculation, written calculation, estimation, and so on. - It started from all aspects of classroom teaching, such as teachers 'teaching methods, students' learning habits, classroom interaction, etc. 3. ** Ability Cultivation related content ** - They had strict teaching requirements, such as ensuring that students had a high accuracy rate in their calculations. - Cultivate good study habits, such as writing habits, calculating habits, patiently checking habits, etc. - Seeking reasonable and flexible algorithms, cultivating the flexibility of thinking and improving the efficiency of calculation, thus strengthening the cultivation of students 'good learning habits and improving their ability to solve practical problems. ** 3. Research goal ** 1. ** Overall goal ** - While reducing the burden on the students, it also improved their computational ability and cultivated their oral, mental, and pen-based arithmetic abilities. This would make the students interested in mathematics, improve their academic performance, and lay the foundation for subsequent studies. 2. ** Target ** - From the student's point of view, it will help the students set up the correct learning goals, correct their attitudes, and develop good learning habits. ** 4. Research Method ** 1. ** Observation Method ** - Observe the teacher's classroom teaching behavior, such as the use of teaching methods, interaction with students, etc. - Observe the students 'performance in class, including their learning status, participation, and mastery of knowledge. 2. ** Investigation Method ** - Teachers and students could be investigated through interviews and other means. For example, he could ask the teachers about the problems they encountered in teaching and their understanding of efficient classrooms. He could also ask the students about their interest in mathematics and learning difficulties. 3. ** Experimental Method ** - In some classes, new teaching methods or strategies were used, such as the use of situated teaching methods, group cooperative learning methods, etc., and compared with traditional teaching classes to observe the differences in students 'learning effects and classroom efficiency. ** 5. Research Steps ** 1. ** Preparing Stage ** - Search for relevant information to understand the domestic and foreign research status of the efficient classroom of primary school mathematics. - Set up a research team and clarify the division of labor. - To formulate a research plan, determine the research object, content, methods, etc. 2. ** Execution Stage ** - Carry out research activities according to the research plan, such as implementing new teaching methods in classroom teaching, conducting observation and investigation activities, etc. - Regular discussions and exchanges were conducted to analyze and solve the problems that appeared in the research process. 3. ** Summing Stage ** - To organize and analyze the research data and summarize the research results. - Write a research report and propose strategies and suggestions for the construction of an efficient primary school mathematics classroom. ** VI. Anticipated Achievement ** 1. ** Research Report ** - It also elaborated on the construction strategy and influencing factors of the efficient classroom of primary school mathematics. 2. ** Teaching Resources ** - Form a set of teaching case collections, teaching design collections, etc. that are suitable for the efficient classroom of primary school mathematics. 3. ** The growth of teachers and students ** - The teaching level of teachers has been improved, and they are able to skillfully use effective teaching methods. The students 'learning ability and interest in mathematics had improved, and their academic performance had improved. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary School Mathematics Square Matrix Problem-solving Skills and Methods
The square matrix problem was divided into a solid square matrix and an empty square matrix. The following were the techniques and methods to solve the problem: ** 1. The relationship between the number of people on each side and the number of people around the square matrix ** 1. ** Knowing the number of people on each side, please ask for the number of people in four weeks ** - Number of people around =(number of people on each side- 1)×4. For example, if there were five people on each side, the number of people around =(5 - 1)×4 = 16 people. This was because the people at the four corners of the square matrix would be counted again, so they had to subtract 1 and multiply by 4. 2. ** Knowing the number of people around, please ask for the number of people on each side ** - The number of people on each side = the number of people in all four weeks divided by 4+1. For example, if there were 20 people in a square formation, the number of people on each side =20 div4 + 1=6 people. ** 2. Calculating the total number of people in the square matrix ** 1. ** Solid Square Matrix ** - Total number of people = number of people on each side x number of people on each side. For example, if there were six people on each side, the total number of people =6×6 = 36 people. 2. ** Hollow Square Array ** - ** Method 1: Subtract the small solid square matrix from the large solid square matrix (Hollow Method)** - Total number of people =(number of people outside) × (number of people outside)-(number of people inside) × (number of people inside), where number of people inside = number of people outside-number of floors ×2. For example, a three-layer hollow square array, the outermost layer has 10 people on each side, the number of people on the inner side =10 - 3×2 = 4 people, the total number =10×10 - 4×4 = 84 people. - ** Method 2: Accumulate each level ** - First, find out the number of people on each floor. For every floor in the square matrix, the number of people on each side will decrease by 2. Then, he added up the number of people on each floor. For example, if there were 14 people on each side of the outermost layer, the outermost layer would have 52 people, the second layer would have 12 people on each side, and the third layer would have 10 people on each side. The total number of people would be 52+44+36 = 132. - ** Method 3: Average substitution method ** - The number of people in each layer could be seen as an arithmetic progression with a difference of 8. The total number of people in the hollow square matrix was equal to the number of flower pots in the second layer from the outside (assuming it was the middle layer) x the number of layers. For example, the three-layer hollow square array mentioned above, counting from the outside, the second layer has 12 people on each side, the number of people =(12 - 1)×4 = 44 people, the total number of people =44×3 = 132 people. - ** Method 4: Extending with four blocks ** - If the hollow square matrix was divided into four equal squares, the total number of people =(number of people on each side-number of floors) x number of floors x 4. For example, if there were 14 people on each side of the outermost layer, the total number of people would be (14 - 3)×3×4 = 132 people. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>