mathematical contest in modeling 2022

Alright, I can try to answer the mathematical modeling " Air Evolution Problem ". The air evolution problem was a classic example of mathematical modeling. It involved many fields of knowledge such as aeromechanics, biology, and ecology. The problem described the growth and spread of a population of organisms and their effects on the environment, such as the effects of air dynamics and climate factors. There are many factors to consider in this problem, such as the size and number of each population, the growth rate of each population, the effects of the atmosphere, climate factors, competition and symbiosis. Through mathematical modeling, we can transform these factors into equations and use mathematical methods to solve these problems. Mathematical modeling can help us better understand this problem and provide useful tools and methods for solving it. In addition, mathematical modeling could also provide the foundation for other related applications such as environmental science, urban planning, and traffic management.

The following is an example of an elementary school mathematical modeling activity plan: ** 1. Event theme ** "Mathematical Modeling in Life" ** 2. Activity Target ** 1. To help students understand the concept of mathematical modeling and cultivate their ability to use mathematical thinking to solve practical problems. 2. To enhance the students 'awareness of linking mathematics knowledge with the reality of life, and to increase their interest in mathematics learning. 3. Through group cooperation, students 'teamwork and communication skills were cultivated. ** 3. Event Target ** [X] grade student ** IV. Event Time and Place ** 1. ** Time **: The specific date of the event can be determined according to the school's curriculum. For example, the time slot for math class from Monday to Friday of a certain week. 2. ** Location **: Classroom ** 5. Event preparation ** 1. teacher preparation - Collect and design suitable mathematical modeling problems according to the students 'knowledge level and life experience, such as price calculation in shopping, itinerary problems, calendar making, etc., and make them into task cards. - Prepare relevant teaching materials, such as cube models (for problems such as calendar production), pictures, paper, etc. - Divide into activity groups, with [X] students in each group to ensure that the members of the group complement each other. 2. students prepare - To review the knowledge of mathematics that he had learned, such as the operation of the four rules, the recognition of graphs, the calculation of time, etc. ** 6. Activity process ** 1. Introduction (1 class hour) - Teachers would show pictures or videos of mathematical phenomena in their lives, such as supermarket promotional price tags, bus schedules, etc., to guide students to think about the mathematical knowledge hidden behind these phenomena, thus leading to the concept of mathematical modeling. 2. Explanation of modeling knowledge (1 class hour) - Mathematical modeling was the process of using mathematical thinking, methods, and knowledge to solve practical problems. For example, he could simplify a practical problem into a mathematical problem, establish the relationship between variables and parameters, and solve and verify the results. - For example, if Xiao Ming had 10 yuan and bought 3 pens, each pencil would cost 2 yuan. How much money was left? In this problem, 10 yuan is the initial amount (variable A), 3 is the number of pens (variable B), 2 yuan is the price of each pencil (variable C), and the remaining amount (variable D). Then, the mathematical model D = A - B×C can be established. Substituting the numerical solution, D = 10 - 3×2 = 4 yuan. 3. Group activities (3 - 5 lessons) - They distributed the task cards, and each group drew a mathematical modeling task. - Task example: - [Shopping Task: Design a family shopping list. The number of people in the family is known to be [X]. Each person needs to drink [X] bottles of milk every day. Each bottle of milk is [X] yuan. Each bread is [X] yuan. Each person eats [X] pieces of bread every day. Fruit is [X] yuan per catty. The family's weekly spending on fruits does not exceed [X] yuan. The total shopping expenses for a week are calculated. According to the budget of 100 yuan, the shopping list is adjusted.] - [Mission: The distance from home to school is [X] meters. Xiao Ming's walking speed is [X] meters per minute. His bicycle speed is [X] meters per minute. If Xiao Ming wants to reach school in [X] minutes, should he choose to walk or ride a bicycle?] If there was a road repair on the way and he needed to take a detour of [X] meters, what should he choose? - [Calendar Creation Task: Use 4 small cubes to create an activity calendar that can represent the month, day, and week. Think about how each cube should be marked with numbers or dates.] - The members of the group worked together to analyze the problem, find the key information (variables and parameters) in the problem, try to establish a mathematical model, and then solve and verify the results. - The teachers patrolled each group and provided timely guidance and inspiration to guide the students to correctly establish mathematical models and solve the difficulties they encountered. 4. Achievement presentation and exchange (2 - 3 class hours) - Each group would send a representative to present the modeling results of the group to the class, including the problem analysis, the established mathematical model, the solution process, and the results. - The other groups could ask questions, express opinions, or make suggestions for improvement. - The teacher commented on the results of each group, affirming the advantages, pointing out the shortcomings, and emphasizing the key points and difficulties in the mathematical modeling process. 5. Activity summary (1 class hour) - The teacher guided the students to review the entire activity process, summarize the steps and methods of mathematical modeling, and emphasize the importance of mathematics in solving practical problems in life. - Students were encouraged to actively use mathematical modeling to solve problems in their future studies and lives. ** 7. Event Evaluation ** 1. Group Evaluation (70%) - Rationally established model (30%): Whether the mathematical model correctly reflects the numerical relationship in the actual problem, and whether the variables and parameters are set accurately. - The accuracy of the solution process (30%): Whether the calculation process is correct and the result is in line with the actual meaning. - Teamwork (10%): Whether the division of labor between the team members is reasonable, whether the cooperation is tacit, and whether they can solve the problems together. 2. Personal evaluation (30%) - [Degree of participation (15%): Enthusiasm in group activities, number of speeches, contribution to group tasks, etc.] - Understanding of mathematical modeling concepts (15%): Through personal performance in activities, such as analysis of problems, explanation of models, etc., determine the degree of mastery of mathematical modeling concepts. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

The application of mathematical modeling in primary school mathematics had the following principles: 1. ** Considering the actual situation of the students and the principle of gradual progress **: Considering the characteristics of the primary school students 'young age and simple way of thinking, mathematical modeling must be combined with their actual situation and carried out step by step to make it consistent with their cognitive level. 2. ** Principle of combining life experience **: It should be combined with the life experience of primary school students so that they can connect the problem with real life, so as to effectively stimulate their interest and initiative in learning, so that they can use their own experience to actively perceive the effectiveness of the mathematical model. 3. ** Make students experience the modeling process **: Although the mathematical modeling process in primary school is relatively simple, students can only form a preliminary concept of mathematical modeling after experiencing the modeling process and then apply the model to solve problems. When teaching and demonstrating, teachers should pay attention to the clear, detailed, and easy to understand modeling process so that students can imitate and learn. 4. The principle of paying attention to cultivating students 'modeling awareness: A core goal of primary school mathematical modeling teaching is to cultivate students' initial modeling awareness. Teachers should implement it in classroom teaching, starting from the textbook content and connecting it with the reality of life, writing related modeling problems or adapting the textbook topics, so that students can think more about how to build models to solve problems, thus strengthening their modeling awareness. 5. ** Make the students form the basic principles of modeling thinking **: In primary school, mathematical modeling ideas are rooted in the practical problems around them. Teachers should start from specific event materials to the mathematical level, guide the students to summarize the essence through various thinking activities, build models to solve problems, and apply the models to a wider range of content. Let the students form the basic modeling ideas through repeated modeling and application of the model. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

The characters included the male lead, Fang Zhou, the female lead, Wei Lai, the female lead, Wang Sida, and the female supporting character, Gao Ge. "A Top Student Begins From Mathematical Modeling" Author: I'm Really Zhang Deshuai. It's a sci-fi/super science novel with academic, academic, and student elements. User recommendation: wake up in the middle of the night, do not open your eyes, slowly sit up to recall the quiet fall asleep, the dream will continue. Dream like the life of the previous life, or do good deeds, or kill, or play music, or suffer, remember their traces, experience the state of mind to observe the reality, with me to observe me and I know myself, I know that I am in the noisy world to stand on my own feet. Ark, who had been muddleheaded in university, had seen thousands of different lives in his sleep. By the time he was able to access his memories from other dimensions, he had already gone on the path of a top student. From the shadow of the sun to man-made flares, from school papers to man-made laws, he relied on himself to achieve the highest. This was a story about a top student, and a group of top students. This book is based on a real thesis, but not a real person. I hope you will like this book.

The mathematical modeling competition required a variety of abilities, and these abilities were also reflected in English thesis writing: * * 1. Mathematics Ability ** 1. * * Solid foundation in mathematics ** - He had to master a variety of mathematical knowledge fields, such as differential equations, graph theory, linear programming, non-linear programming, probability theory, mathematical statistics, and so on. In mathematical modeling, whether it was building a model or solving a model, these basic knowledge were indispensable. For example, when dealing with practical problems involving random factors, probability theory and mathematical statistics knowledge could help determine the probability distribution of events and build a reasonable model. 2. * * Mathematical thinking ability ** - Able to think logically and transform practical problems into mathematical problems. In a mathematical modeling competition, one needed to use logical reasoning to analyze the variable relationships in the problem and establish a mathematical model in the face of complex real-life scenarios. For example, the traffic flow problem was transformed into a network flow problem in graph theory, and a suitable relationship model between nodes and edges was constructed through logical analysis. - The ability to think abstractedly was also crucial. He could abstract mathematical concepts and models from concrete phenomena. For example, he could abstract a functional relationship model from the phenomenon of supply and demand in the economic market for quantitative analysis. * * Two, programming ability ** 1. * * Master programming language ** - Proficiency in at least one programming language, such as Python, matlab, etc. In mathematical modeling, programming languages were used to solve mathematical models and process data. For example, Python's Numpy and Scipy libraries could easily perform numerical calculations, the Panda library could perform data processing and analysis, and the MatplotLib and Seaborn libraries could perform data visualization. 2. * * Realization of algorithm ** - Able to program mathematical algorithms. For example, when solving an optimization problem, it might be necessary to implement a linear programming algorithm or a genetic algorithm. The programming of these algorithms could effectively solve the model and obtain the optimal solution or near-optimal solution. * * 3. Writing ability ** 1. * * Ability to express oneself in English ** - When writing an English thesis, you must have a good foundation in grammar and vocabulary. Use English vocabulary to describe mathematical concepts, models, and results. For example, using professional mathematical terms such as "derivative" and "integral", and being able to construct sentences correctly to make the thesis clear. 2. * * Thesis structure and organization skills ** - The content was organized according to the structure of a scientific paper. Generally, it included abstract, foreword, model construction, result analysis, conclusion, and so on. In the abstract part, the problem, method, and main results should be summarized concisely. In the preface part, the background and research significance of the problem should be described. In the model construction part, the mathematical model and its assumptions should be described in detail. In the result analysis part, the calculation results and data analysis should be presented. In the conclusion part, the research results should be summarized and the prospects should be put forward. - The logic must be coherent, and there must be a clear logical connection between the various parts. For example, the analysis of the results had to correspond to the model construction part, and the conclusion had to be based on the analysis of the results. 3. * * Data visualization ability (related to writing)** - In the thesis, the data and results needed to be presented in an intuitive way, such as making charts. For an English thesis, one had to be able to correctly add titles, coordinate labels, and other English annotations to the charts, and accurately describe the contents of the charts and their relationship with the research content in the thesis. * * 4. Teamwork Ability ** 1. * * Communication Skills ** - Able to clearly express their thoughts and opinions in the team. Whether it was the construction of mathematical models, programming solutions, or the framework of thesis writing, members needed to communicate effectively. For example, when discussing model construction, he could accurately describe his thoughts on variable selection and relationship setting, and understand other people's views to communicate effectively. 2. * * Division of labor and cooperation ability ** - According to the different specialties of the team members, a reasonable division of labor was carried out. For example, members with good mathematical foundations were mainly responsible for model construction, members with strong programming skills were responsible for programming the model, and members with good English writing skills were responsible for writing papers. At the same time, the members had to cooperate with each other and integrate and improve on the basis of their respective tasks. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

The following is an example of the feelings and gains of mathematical modeling in primary school (third grade): ** 1. Feelings ** 1. ** Interesting and challenging ** - When I was studying mathematical modeling in primary school, I found it to be like an interesting game. We can describe many problems in life in mathematical terms, just like turning real things into small mathematical models. However, this was also a challenge. Sometimes, it took a long time to express things in life using mathematical formulas or graphs. For example, when doing some problems about dividing things, we have to figure out how to use numbers and symbols to express how much each person can get. It's like how our group discussed how to divide a pile of small blocks evenly among everyone. At this time, we have to use a lot of brains. 2. ** Finding mathematics everywhere ** - I used to think that mathematics was just numbers and calculations in textbooks, but through mathematical modeling, I see that mathematics is everywhere around us. When we make handwritten reports, we have to combine mathematics knowledge with drawing and writing. At this time, we will find that mathematics can make our handwritten reports more content. For example, if I draw a scene of a small supermarket, the prices and quantities of the goods inside can be expressed in mathematics. This way, my handwritten newspaper will be like a small mathematical world. Moreover, in real life, things like counting the number of stairs and calculating the distance from home to school were all shadows of mathematical modeling. 3. ** Teamwork is very important ** - When we did some small mathematical modeling projects together, such as discussing how to solve a problem about the combination of graphs, I learned that teamwork was very useful. Some students could quickly think of what shapes to use to combine, and some students could accurately calculate how many small shapes were needed. It was much faster for everyone to think of a way together than to think alone. We can share our ideas with each other and learn new ways of thinking from others. ** 2. Harvest ** 1. ** Increases mathematical thinking ability ** - Mathematical modeling has made my thinking more flexible. In the past, I used to do math problems according to the method taught by the teacher. Now, I will think about how to turn a problem into math and then find a solution. For example, when solving some problems with numbers, I would try to find the law first and then use mathematical formulas to express it. This way, my logical thinking ability improved a lot. In the process of doing mathematical modeling, my understanding of numbers, graphs, and calculations also deepened. 2. ** Enhances the ability to solve practical problems ** - Now I can use math knowledge to solve small problems in life. For example, if Mom and Dad asked me to help calculate the money to buy things, or to calculate how many things our family needed to bring on a trip, I could solve it by building a small mathematical model. I knew that I had to find the important information in the question first, then choose the appropriate mathematical method, such as addition, substitution, or multiplication, and finally get the answer. 3. ** More interested in mathematics ** - Because mathematical modeling makes math more interesting, I especially like math classes now. I always look forward to what kind of new problems the teacher will bring us and what kind of new methods I can use to solve them. I would also find some small problems to do mathematical modeling after class, just like setting my own questions. This way, my enthusiasm for learning mathematics became higher. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

The following is a summary of a case study on mathematical modeling in primary school: ** I. Title ** The title should reflect the core content of the article concisely and clearly, for example,"Primary school mathematical modeling case summary and analysis". ** 2. Introduction ** 1. ** Explain the importance of mathematical modeling in primary school ** - It was mentioned that primary school mathematics was a basic subject, and its modeling ideas helped students understand the connection between mathematical knowledge and real life. Through the infiltration of modeling ideas, it could enhance students 'mathematical expression ability, comprehensive analysis ability, improve students' mathematical logical thinking, and build a suitable mathematical learning model for students. 2. ** Draw out the case ** - The case studies that were about to be summarized were selected from actual teaching situations. These cases could well demonstrate the application of mathematical modeling ideas in primary schools. ** 3. Case presentation and analysis ** 1. ** Case 1: Diagram and geometry ** - ** Description of the case ** - For example, in the teaching of the triangle concept, the teacher designed a series of activities to build a concept model. First, let the students draw a triangle and say its components. The students draw a triangle based on their existing knowledge and experience and point out that it has three sides, three angles, and three apices. Then, the teacher used three small rods (representing line segments) to let the students try to circle a triangle. The first student failed. By analyzing the reasons for the failure (the short and long lines could not be connected together), the teacher came to the conclusion that the three line segments of the triangle had to be connected together, thus deepening the understanding of the concept of the triangle. - ** Modeling Thought Analysis ** - In this case, the teacher guided the students to abstract the concept model of the triangle from the actual operation (drawing the triangle, surrounding the triangle). Through their own activities, the students experienced the process from the specific graphic operation to the abstract concept of the triangle. This process reflected the modeling ideas from the real world (stick, triangle) to the mathematical concept (triangle definition). 2. ** Case 2: Number and Algebra ** - ** Description of the case ** - For example, if the sum of two numbers was 2016, and one of the numbers had a single digit of 0, then removing 0 would be exactly twice the number of the other number. The teacher guided the students to analyze the relationship between the two numbers. After removing 0, one number was 10 times the other number, and because the number after removing 0 was 2 times the other number, it was 20 times the other number. Then, according to the sum of the two numbers, 2016, one of the numbers was 2016/21 = 96, and the other was 20×96 = 1920. - ** Modeling Thought Analysis ** - In this case, the student transformed the actual numerical relationship problem into a mathematical model. First, the relationship model between two numbers was established according to the characteristics of the numbers (the multiple relationship of a number after removing 0), and then the equation model was constructed using the relationship between and (although it may be based on the calculation of the multiple relationship in primary school, it was essentially a simple equation idea). Finally, the answer was obtained, which reflected the modeling process of transforming the actual problem into a mathematical model and solving it. 3. ** Case 3: Modeling Thoughts in Comprehensive Practice ** - ** Description of the case ** - For example, in the teaching activity of using A4 paper to cut the largest circle, the teacher created such a problem situation: First, let the students take out the largest circle that had been cut on the A4 paper, ask questions, and find the relationship between the diameter of the circle in their hands and the A4 paper. Then, under the condition that the A4 paper was 30 centimeters long and 20 centimeters wide, calculate the circumference and area of the circle. - ** Modeling Thought Analysis ** - Here, the students thought about the relationship between the circle and the rectangular paper (A4 paper) from the actual operation (circle trimming) and constructed the geometric relationship model between the circle and the rectangular paper. When calculating the circumference and area of a circle, the formula model of the circumference and area of the circle was applied. This process combined practical operation with mathematical formula model, reflecting the process from practical problems to the establishment of mathematical models and the application of models. ** IV. Summing Up ** 1. ** Inductive modeling in primary school mathematics ** - From the above cases, it could be seen that the mathematical modeling ideas of primary school could be reflected through hands-on operation, problem situation creation, and analysis of quantitative and graphic relationships. In this process, students would transform real-world problems or phenomena into mathematical problems and then establish mathematical models to solve them. 2. ** To emphasize the significance of modeling ideas to primary school mathematics teaching and student learning ** - The emphasis on modeling helped to make abstract mathematical knowledge more intuitive and easy to understand. It could stimulate students 'interest in learning because they could see the role of mathematics in solving practical problems. At the same time, it would help to cultivate students 'innovative thinking and the ability to solve practical problems. It would lay a foundation for students' future mathematics studies and mathematics applications in their lives. ** 5. conclusion ** 1. ** The Future of Mathematical Modeling in Primary Schools ** - It is pointed out that the idea of modeling should be further strengthened in the future primary school mathematics teaching. Teachers could continue to dig out more teaching resources and life examples, and design more creative teaching activities to better cultivate students 'modeling ability. 2. ** The need for continuous research and practice is emphasized ** - It was mentioned that with the continuous development of educational concepts and the innovation of teaching methods, the research and practice of mathematical modeling in primary schools also needed to be deepened to meet the needs of student development and educational reform. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

You mentioned a book called Mathematics Modeling by the United States. B Brown. The book contained four volumes, each of which discussed different mathematical modeling problems.

The characters included the male lead, Fang Zhou, the female lead, Wei Lai, the female lead, Wang Sida, and the female supporting character, Gao Ge. "A Top Student Begins From Mathematical Modeling" Author: I'm Really Zhang Deshuai. It's a sci-fi/super science novel with academic, academic, and student elements. User recommendation: wake up in the middle of the night, do not open your eyes, slowly sit up to recall quietly fall asleep, dream again. Dream like the life of the previous life, or do good deeds, or kill, or play music, or suffer, remember their traces, experience the state of mind to observe the reality, with me to observe me and I know myself, I know that I am in the noisy world to stand on my own feet. Ark, who had been muddleheaded in university, had seen thousands of different lives in his sleep. By the time he was able to access his memories from other dimensions, he had already gone on the path of a top student. From the shadow of the sun to man-made flares, from school papers to man-made laws, he relied on himself to achieve the highest. This was a story about a top student, and a group of top students. This book is based on a real thesis, but not a real person. I hope you will like this book.