Teaching objectives of the second volume of fourth grade mathematics "Chickens and Rabbits in the Same Cage" (1);
1, understand the structural characteristics of the problem of "chickens and rabbits in the same cage", master the list method, hypothesis method and problem-solving method, and initially form a general strategy to solve this kind of problem.
2. Through independent exploration and cooperative communication, cultivate students' cooperative consciousness and logical reasoning ability, realize the diversity of problem-solving strategies, and infiltrate the idea of simplifying the complex.
3. Feel the interest of ancient math problems and improve the interest in learning math. Teaching emphasis: understand and master different ideas and methods to solve problems with different methods. Difficulties in teaching: solving practical problems in different ways. Preparation of teaching AIDS: multimedia courseware, study list, etc. Teaching process:
First, create a situation and reveal the topic.
1, Teacher: Students, today the teacher is very happy to have a lively and interesting class with you. Are the students confident to do this course well? Great! Please take your confidence and enthusiasm to have a math wide angle with your teacher. Let's learn a very famous interesting math problem in ancient China. "Today, chickens and rabbits are in the same cage, with 35 heads above and 94 feet below. What are the geometric figures of chickens and rabbits? " (PPT projection shows the original problem. ) What do these four sentences mean? Take a student to answer. There are some chickens and rabbits in the cage, counting from the top, there are 35. It's 94 feet from the bottom. How many chickens and rabbits are there? PPT explains the meaning. )
2. What should I call this kind of question? (the problem of "chickens and rabbits in the same cage". ) blackboard writing. In fact, the problem of chickens and rabbits in the same cage is recorded in Sun Tzu's Art of War. As early as 1500 years ago, the ancients were studying it, and we modern people are still studying it, and many foreigners are also studying it. So what is the charm of this problem that has been circulating for thousands of years, so that so many people take pains to solve this problem? I believe that after learning this lesson, you will uncover the secret. The teacher asked everyone again: Do you have the confidence to learn the content of this lesson well?
Second, cooperate in exploration and learn new knowledge.
Activity 1: Explore how to solve the problem of "chickens and rabbits in the same cage" by guessing the list.
In order to facilitate learning, we can start with simple problems and discuss how to solve such problems, ok? Example 1
1, Teacher: Please look at the questions. Thinking: From the top, there are 8 heads, and from the bottom, there are 26 feet. What do you mean? What's the problem?
Health: 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? .
Health: A chicken has two legs, and a rabbit has four. Chickens and rabbits have eight heads. Chickens and rabbits have 26 legs. How many? Teacher's comment: He also found hidden conditions, and he was really careful in examining the questions.
2. List method
(1) conjecture
How many chickens and rabbits do you need? Let's guess, shall we? (Students guess)
(2) Verification:
Who guessed right? Let's verify it. To solve the problem, you should be reasonable and well-founded, and you can't guess at will. What conditions should we seize to verify whether our guess is correct? First of all, we should know that there are 8 chickens and rabbits, and then the legs of chickens and rabbits are 26, so we must add up the legs of chickens and rabbits to see if they are equal to 26. These two conditions must be met at the same time to be the correct answer.
Now, please take out your form, fill in the guessing data in the form in order, and find the correct answer. Students complete the form independently, then communicate the completion and display the form on the big screen.
Listing our guesses in a certain order like this is called tabulation. Look at this table. Did you find the answer? What is the answer?
Activity 2: Explore the hypothetical method to solve the problem of "chickens and rabbits in the same cage".
Teacher: list method can solve the problem of chickens and rabbits in the same cage, but what if the data is very large? (cumbersome). Is there any other way to solve it? Please discuss in groups of four whether there are other solutions.
Suppose all chickens have two feet, and each chicken has 2×8= 16 (strips). How many feet do eight chickens have? What does 26- 16= 10 (bar) mean? 4-2=2 (bars) What is 2 for all rabbits? Every rabbit has fewer feet.
10÷2=5 (rabbit) means 10 feet, and two feet on each chicken become rabbits, so * * * five chickens become rabbits, so 8-5=3 (chicken) has five rabbits, which means that the total number of rabbits is equal to the number of chickens.
Some students may be a little confused. Let's use drawing to understand intuitively. ?
(1) Please draw 8 circles to represent chickens. Each chicken has 2 legs, and one * * * has 16 feet.
(2) Without 10 feet, two feet of each chicken will become rabbits. * * * Five chickens will become five rabbits.
(3) The last three are chickens.
Is everyone clear now? Guide the students to review it again. What comes to mind first? Assuming that all chickens are chickens, you can find them by subtracting the number of chickens from the total number of feet.
The difference is 10, and then divide the difference by the difference between the two feet of each chicken to get the number of rabbits. Finally, subtract the number of rabbits from the total to get the actual number of chickens. Is this a good method? Give this method a name. What should I call it? Hypothesis method.
②: If all rabbits were assumed, would you understand? Well, I'll leave this method to you to finish after class.
Conclusion: Students, we have just solved the same problem in many ways. What do you think is the core idea of these methods? (suppose. Therefore, the problem of chickens and rabbits in the same cage is also called hypothetical problem. )?
Think in multiple ways to deepen understanding;
Can we use the above methods to solve the problems handed down by the ancients now? Display: Chicken and rabbit are in the same cage, with 35 heads and 94 feet. How many chickens and rabbits are there? Students do it independently.
Conclusion: Now can you sum up the advantages and scope of application of these methods? When the quantity is small, the list method is used. When the number is relatively large, the list method is large, limited and troublesome. It is best to use the hypothesis method. Special attention should be paid when using the hypothesis method: if it is a chicken, find the rabbit first, if it is a rabbit, find the chicken first, and vice versa.
Third, consolidate the practice.
Textbook 1 and 2 "Doing" on page 105.
Fourth, class summary.
Teacher: What did you gain from today's study?
Verb (abbreviation for verb) assignment
Exercise the first question of 24 questions on page 106 of the textbook.
The teaching plan of the second volume of the fourth grade mathematics "Chickens and Rabbits in the Same Cage" (2) Teaching objectives;
1, knowledge and skills
Understand the interesting mathematical problems of chickens and rabbits in the same cage, and understand the relevant mathematical history. We can use list method and drawing method to solve related practical problems, and use graphic method and understanding hypothesis to solve the problem of chickens and rabbits in the same cage.
2. Process and method
Through drawing analysis, citing examples, hypothetical calculation and other methods, we can understand the quantitative relationship, experience the convenience of combining numbers and shapes, experience the diversity of problem-solving methods, and improve the ability to solve practical problems.
3. Emotions, attitudes and values
Cultivate students' cooperative consciousness, let students feel the connection between the application of mathematical thinking methods and solving practical problems, improve students' ability and self-confidence, be influenced by various mathematical thinking methods, and let students realize the value of mathematics.
Teaching emphasis: using drawing method and list method to solve related practical problems.
Teaching difficulties: to realize the diversity of problem-solving strategies and cultivate students' ability to analyze and solve problems.
Teaching preparation: courseware.
Teaching process:
(A) the introduction of questions to reveal the theme
Teacher: (showing the theme map) About 1500 years ago, Sun Tzu recorded such an interesting question in his calculation. The book says, "There are pheasant rabbits in the same cage today, with 35 heads on the top and 94 feet on the bottom. What is the geometric figure of pheasant rabbit? "
Q: What does this passage mean? Who can talk about it? (biological test)
Teacher: This passage means that there are a number of chickens and rabbits in a cage, counting from top to bottom, with 35 heads. It's 94 feet from the bottom. How many chickens and rabbits are there in the cage? This is what we usually call the problem of chickens and rabbits in the same cage. How to solve this mathematical problem raised by the ancients 1500 years ago is what we will study in this lesson. (blackboard title: chicken and rabbit in the same cage)
(2) Actively explore, cooperate and exchange, and learn new knowledge.
Teacher: For the convenience of research, let's simplify the conditions of the topic first.
Example 1: A chicken and a rabbit live in the same cage, with 8 heads and 26 legs. How many chickens and rabbits are there?
Teacher: Let's discuss it first and see if we can provide you with one or several ideas to solve this problem, so that other students can understand it easily. (Students discuss)
Students' initial communication and teachers' refinement: drawing, listing and hypothesis are all acceptable.
Teacher: Please think carefully first, discuss and communicate in groups, and see what method your group should choose to solve this problem. Then record your thoughts and your thinking process in your own way.
Students think, analyze and explore, and then discuss and communicate in groups.
After the group activities are full, enter the stage of group report and collective communication.
Teacher: Who can tell us about the inquiry process of your group and how did you come to the conclusion? How many chickens and rabbits are there?
Methods and conclusions of student reports and surveys;
1, drawing method:
Draw two legs for each animal (that is, they are all regarded as chickens), so that a * * * uses 16 legs and leaves 10 legs. Add two legs at a time and a chicken becomes a rabbit. To finish drawing 10, five chickens will become rabbits.
Summary: The painting method is very easy to observe and understand.
2. List method: (display student list)
Methods and steps for students to explain the list:
Student Report: Suppose there are eight chickens, then a * * * has 16 legs, which is obviously incorrect. Then subtract a chicken, add a rabbit, try one by one, tabulate the results, and finally get three chickens and five rabbits.
Teacher: The students' exploration spirit and methods are very good, and they can successfully solve the problem of "chickens and rabbits in the same cage" in their own way. But the teacher still thinks that the above two methods are more troublesome, drawing and listing. Is there a more convenient and concise way to solve this problem?
3. Hypothesis method: (according to whether students will have this situation, show it as a maneuver)
Teacher's Guidance: Looking at the table above, we find that. If all eight are chickens, one * * * has only 16 legs, which is less than 26 legs 10 legs, because each rabbit actually has two more legs than each chicken. A * * * has 10 legs, so the rabbit has 10÷2=5 (only), so we can also think like this:
Write it on the blackboard: Method 1: Suppose all 8 are chickens, then the rabbit has:
(26-8×2)÷(4-2)=5 (only)
Chickens have 8-5=3 (only)
Similarly, if eight rabbits are rabbits, then a chicken has only 32 legs, which means six more legs than 26, because each chicken actually has two fewer legs than each rabbit. A * * * has six more legs, so a chicken has 6÷2=3 (only), so we can also think like this:
Write on the blackboard: Method 2: Assuming that all 8 rabbits are rabbits, then the chicken has:
(4×8-26)÷(4-2)=3 (only)
Rabbits have 8-3=5 (only)
Summary method: We have just solved the problem of chickens and rabbits in the same cage with so many methods. Which method do you like best? Tell me your reasons.
Now let's sum up these methods: when the number is small, it is faster to draw a list, and when the number is large, it is better to use the hypothesis method.
(3) Solve practical problems and extend the classroom.
1. Try to solve the problem of chickens and rabbits in the same cage, and put it forward before class. The book says, "Today, chickens and rabbits are in the same cage, with 35 heads above and 94 feet below. What are the sizes of chickens and rabbits? "
See how ancient China people solved this problem.
2. Bicycles and tricycles *** 10, with a total of * * * 26 wheels. How many bicycles and tricycles are there?
(4) class summary
What did you gain from today's study?
Teacher's summary: In this lesson, we solved the famous problem of "chickens and rabbits in the same cage" in ancient China by drawing, listing and assuming. In fact, since 1500, our mathematicians in China have been studying and exploring this problem, and they have also come up with many methods to solve the problem of "chickens and rabbits in the same cage", from which they have gained many mathematical ideas. I hope that students will be good at thinking, discovering and summarizing methods in their future study.