Mathematics Wide Angle —— Teaching Design of "Chickens and Rabbits in the Same Cage" Teaching Content: The content of page115 in the first volume of the sixth grade of the curriculum standard experimental textbook published by People's Education Press. Teaching objective: 1. Understand the problem of "chickens and rabbits in the same cage" and feel the interest of ancient mathematical problems. 2. Try to solve the problem of "chickens and rabbits in the same cage" in different ways, so that students can realize the generality of algebraic methods. 3. Cultivate students' logical reasoning ability in the process of solving problems. Teaching emphasis: try to solve the problem of chickens and rabbits in the same cage in different ways, so that students can understand and master the problem-solving method of "chickens and rabbits in the same cage". Teaching difficulty: the understanding and application of "hypothesis method". Teaching process: 1 Creating situations leads to problems 1. Teacher: Our great motherland has a history of 5,000 years of civilization, and has made great contributions to the innovation and development of scientific knowledge in the long river of history, especially in the field of mathematics, such as Nine Chapters of Arithmetic, The Art of War and other ancient masterpieces, such as 1500 years ago. 2. Show me the original question: Today, there are pheasants and rabbits in the same cage, with 35 heads above and 94 feet below. What are the geometric shapes of pheasant rabbits? Teacher: Can you tell me what this question means? (Description: Pheasant) Show me: There are some chickens and rabbits in the cage. From the top, there are 35 heads. From the bottom, there are 94 feet. How many chickens and rabbits are there? 3. Reveal the topic: This is the problem we are going to study today, the problem of "chickens and rabbits in the same cage". (blackboard writing) Second, explore independently and solve problems 1. Teacher: In order to facilitate students to explore problems in various ways, let's first study a problem of "chickens and rabbits in the same cage" with small data. Example 1: There are some chickens and rabbits in the cage. From the top, there are 8 heads. From the bottom, there are 26 feet. How many chickens and rabbits are there? 2. To understand the meaning of the question, students should read the question first, then analyze the meaning of the question and find out two quantitative relations from the question. Teacher: Please read the questions freely. Do you think it's weird (1) that a chicken and a rabbit have eight heads? Chickens and rabbits have 26 legs. How many? Teacher: Do you have anything to add? There are two hidden conditions. Who looked for it carefully? . A chicken has two legs, and a rabbit has four. Teacher's comment: He also found hidden conditions, and he was really careful in examining the questions. 3. Guess Master: Just now, everyone said that there are eight chickens and rabbits. Let's guess how many chickens and rabbits there are, shall we? Teacher: Who guessed right? Let's verify it. (Teachers and students count the number of feet) 4. Try the list method (1). Teacher: Actually, everyone's guesses just now can be guessed in a certain order. Display: list method: chicken number 8765432 10. The number of rabbits is 0 12345678 * * The number of legs is16182022426283032 Teacher: What do you find by looking at this table? (Because the number of chickens and rabbits is fixed, the total number of legs will increase by two for each rabbit added and one chicken reduced. On the contrary, it remains the same. ) teacher: "like you, write all possible answers by list, without repetition or omission." This enumeration method is also called "enumeration method" in mathematics. 5. Hypothesis method (1). Look at the first column and ask: What do 8 and 0 mean? How many feet does this * * * have? (Pointing at the sixth column with an arrow) How many feet are missing? Whose foot is missing? How many feet are missing from each rabbit? How many rabbits are there? That is to say, the number of rabbits is obtained by dividing the number of feet per rabbit by the number of feet per rabbit, right? How many chickens are there? Teacher: Can you use an equation to express the process we just talked about? (Students list and name the blackboard) Guide the students to test. Blackboard writing: Suppose they are all chickens: 2×8= 16 (strips) 26- 16= 10 (strips) 10÷2=5 (only) ... Rabbits 8-5=3 (only) (2) Observe the ninth column and ask: What do 0 and 8 mean? (Assuming the cage is full of rabbits) How many feet does this * * * have? How many extra feet do you have? Whose feet are too many? How many feet does each chicken have? How many chickens are there? How did you get it? How many rabbits are there? Can you list the formulas based on this assumption? (Student list, name acting) Guide students to say that all hypotheses are rabbits, 8×4=32 (strips) 32-26=6 (strips) 6÷(4-2)=3 chickens 8-3=5 (rabbits only) Comprehensive formula chicken (8× 4-26) ÷ (. (3) Teacher: Can you give these two methods a name? (Hypothetical) 6. Try Algebra Master: Can you use other methods? (Equation solution) Students do it independently, and students are required to check when revising collectively. Solution: Suppose there are x chickens and 8-X rabbits, 2×X+(8-X)*4=26 Teacher: Who will explain what this equation means? What quantitative relationship did he use? Health: number of chicken feet+rabbit feet = total feet. Teacher: The explanation is really clear. Students who understand will explain again. Teacher: Please raise your hand if you understand. Thank this classmate for bringing us a simple idea, which can be understood at once. Teacher: Just set the chicken as X, and now set the rabbit as X. Please list the equations and don't calculate them. Teacher: Who will say? Student: 4X+(8-X)*2=26 Teacher: Does anyone know what quantitative relation his equation uses? Teacher: The idea of solving problems is really simple. This is the "column equation" method on the blackboard. 6. Summarize the communication and summarize the Methodist Church: What problems have we solved today? How did we solve the problem of "chickens and rabbits in the same cage" just now? Comparing these methods, which one do you prefer? Why? Which method do you think is generally applicable? The teacher concluded that there are many ways to solve this kind of problem. Problems can be solved by guessing and listing, but when the amount of data is large, the process is very complicated. Hypothesis method and equation method are universal and can be used regardless of data size. Third, the application method of solving problems 1, Teacher: Can you answer the questions in Sun Tzu's The Art of War with the hypothesis method or the equation method? (Exchange correction, students introduce their own algorithms) 2. Consolidation exercise (1) Page 65438 +0 15 1: "Turtle crane" (2) Page 65438 +0 15 Question 2: "Chartering" (3) Please read p/kloc-. Teacher: Who can understand the methods of the ancients? Health: Lift half a foot first. The remaining half foot. Teacher: At this time, a chicken has an extra foot and a rabbit has an extra foot. There are 12 rabbits and 12 feet. The formula is 26÷2-8=5 (only) 8-5=3 (only) Teacher: The ancient method: the number of feet ÷2- the number of heads = the number of rabbits-the number of rabbits = the number of chickens (2), application. Teacher: Do you want to try the methods of the ancients? Please solve the example. That was quick. Calculation formula. Do you agree? Teacher: Do you have anything to say? (simple. Teacher: It's easy) Teacher: Do you want to try again? To answer the second question on page 1 17. Who would say? Teacher: Why are the results inconsistent? Teacher: It seems that this method of the ancients is still not perfect. There are limitations. Suitable for solving the problem of chickens and rabbits. Teacher: Assumptions and equations are universal and general. Teacher: Why not? Interested students can try to study after class. Teacher: can ancient methods solve the problem of chickens and rabbits in the same cage and similar math problems? Those who are interested can go home and think. Fourth, report and exchange and summarize 1. What have you gained from this lesson? What experience do you have? Health 1: Knowing that mathematics is an ancient subject, our ancestors can solve some practical problems with simple mathematical knowledge, which shows that they are hardworking and smart ... In the long history of China, ancient Ceng Wenming's mathematics is famous all over the world, and we should be proud as descendants of the Chinese people, which also inspires us to study hard for the growing strength of our motherland. Student 2: Master the general steps and methods of solving ancient mathematical problems by using equations. Teacher: Students, in this lesson, we studied the problem that chickens and rabbits are in the same cage. Everyone actively used their brains, spoke boldly, and answered the same question in different ways, which was excellent. In fact, there are very few cases in life where chickens and rabbits live in the same cage. We should focus on mastering mathematical ideas and methods to help us solve similar problems. (5) expand and improve.

1. A team of hunters and a team of dogs, two teams walk together in a line, with 360 heads and 890 feet. How many hunters and dogs are there? 2. 100 monk eats 100 steamed stuffed bun. One big monk eats three, and three little monks eat one. How many monks are there? Sixth, blackboard design: mathematical wide-angle chicken rabbit cage enumeration method assumes that the normal equation 7 1 18 assumes that all rabbits have solutions: the number of rabbits is x and the number of chickens is (8-X). The second lesson: practical lesson on the problem of chicken and rabbit cages. Teaching content: book P 1 16-65438. Teaching objective: 1. Review various methods to solve the problem of "chickens and rabbits in the same cage", analyze and compare various methods, and let students feel the universality of algebraic method and hypothesis method; 2. Through different exercises, help students build models to solve such problems, so that students can more skillfully solve the problem of "chickens and rabbits in the same cage" in life; Teaching emphasis: modeling teaching process: First, review several methods to solve the problem of "chickens and rabbits in the same cage", and find their characteristics and appropriateness through comparison. List method is suitable for the problem of small data; 2. Hypothetical method; Generally appropriate, the quantitative relationship is easy to understand; 3. Algebraic method; Generally, understanding is suitable for teaching abstraction; 4. Leg lifting method; It is only used when the number of legs of two animals is different by "2", which has limitations; Second, help students to establish a model to solve the problem of "chickens and rabbits in the same cage" (taking 11of p/kloc-6 as an example). 2. Explore solutions through assumptions: (1) Students discuss in groups; (2) The group reports the discussion results; (3) explain collectively to help students build models to solve this kind of problems with hypothetical methods. 3. Complete the third question P116 with the hypothesis method; Third, exercise 1, complete the fourth question of this book p 1 16: The fourth question is the problem of "chickens and rabbits in the same cage" in the knowledge contest. If you use the "hypothesis method" to solve a problem, you should pay attention to correctly answering a question 10+6 = 16, not 10-6 = 4. Getting one question wrong is less than getting one question right 16 points. 2. Finish the sixth question in the book P 1 17: The sixth question is a game activity, much like the cage problem of chickens and rabbits. In practice, coins with 5 cents and 2 cents can also be replaced with other convenient teaching AIDS, such as coins with 5 cents and 1 cent. 3. Complete the thinking question: The thinking question arranges another interesting question similar to ancient mathematics, "100 monks eat 100 steamed buns", which can also be solved by "hypothesis method" or equations. You can also know that 1 big monk and three little monks eat four steamed buns according to the meaning of the question, that is, every four steamed buns are just given to 1 big monk and three little monks. So we might as well divide every four steamed buns in 100 into one group. A * * can be divided into 100÷4=25 (groups), and 100 monks are exactly divided into 25 groups. Each group should have 1 big monk and 3 little monks, so that we can make it clear. Four. Summary 5. Homework: Question 2 of P 1 16, Questions 5 and 7 of P 1 17. & lt/B& gt；