Teaching objectives:
1. With specific examples, we have gone through the process of solving the simple proportional distribution problem.
2. Understand the meaning of proportional distribution, you will answer the known proportion and total amount, and find the simple proportional distribution problem of some quantities.
3. Feel the wide application of proportional distribution in production and life, and stimulate students' interest in learning mathematics.
Teaching focus:
Master the structural characteristics and solving ideas of proportional distribution problem.
Teaching difficulties:
Correctly analyze and flexibly solve the practical problems of proportional distribution.
Preparation before class: Put the pictures of eggplant and tomato on the blackboard.
Teaching plan:
Teaching link
Design intent
Teaching presupposition
First, create a situation
1, the dialogue between teachers and students leads to the content to be learned in this lesson.
Second, the problem of growing vegetables.
1. Show the schematic diagram on the blackboard. Ask the teacher to dictate the questions. Ask the students to observe the pictures and talk about the information and problems mentioned in the pictures.
2. Explain the method of proportion and ask the question of "discussion": What do you mean by 3: 5 kinds of eggplant and tomato? Organize students to discuss and communicate. The teacher explained: this kind of problem is called
The problem of proportional distribution.
3. Question: How many square meters of eggplant and tomato are planted? Let the students solve it independently.
4. Teachers communicate the methods in the book purposefully, and teachers complete the corresponding blackboard writing according to the students' answers.
5. Encourage students to exchange other methods.
6. Ask whether the calculation is correct, and encourage students to say different inspection methods and actually test them.
one
two
Sanwu
Third, specific issues.
1, showing the topic of concrete preparation in the construction site. Let the students read the questions and say the mathematical information in the questions.
2. What do you mean by mixing cement, sand and stone in the ratio of 2: 3: 5? Let the students explain in their own words and organize the students to communicate.
3. Question: How many kilograms of cement, sand and stones do you need to prepare 2000 kilograms of concrete? Encourage students to answer independently. Then the whole class communicates.
4. Teachers and students * * * summarize the ideas and methods to solve the problem of proportional distribution.
Fourth, classroom exercises.
1, practice 1, let the students read the questions, find out the meaning of the questions, answer them independently, and then communicate and correct them. When communicating, let students focus on what they think.
2, practice the second question, let students read the question, understand the meaning of the question, answer independently, and then communicate and correct.
3. Practice the third question. After reading the questions, ask the students to say what "45 sawdust, 4 rice bran and corn flour 1 serving" means. Then let the students answer independently.
4. Practice the fourth question, let the students answer it independently, and exchange and correct it.
5, expand the practice
Exercise 5. Read the questions, let the students understand the relationship between the sides of a cuboid 192 cm and 12, and then encourage the students to solve it by themselves. For students who have spare time to study.
Through dialogue, let students know what they have learned in this class, feel the close connection between mathematics knowledge and actual production and life, and stimulate students' interest in learning mathematics.
Present the problem situation with the help of direct diagram, let students use the existing knowledge to explain the problem and pave the way for learning new methods.
Linking existing knowledge with new knowledge, let students experience the development process of knowledge and deepen their understanding of the practical significance of "proportional distribution".
Let students understand the meaning of "3: 5 kinds of eggplant and tomato" through discussion, and pave the way for solving the following problems correctly.
Let students experience the process of solving the simple problem of proportional distribution on the basis of understanding the significance of proportional distribution.
Under the guidance of teachers, students can communicate and discuss purposefully, so as to master the general methods to solve the problem of proportional distribution.
While mastering the basic methods, experience the diversification of problem-solving methods.
Inspection can not only improve students' ability of self-inspection, but more importantly, let students realize the significance of inspection and form a good habit of self-inspection.
Let students fully understand the mathematical information in solving problems and prepare for solving them.
Understanding the meaning of 2: 3: 5 is the key to answering the question correctly. Explain the meaning of 2: 3: 5 with your own understanding, paving the way for correct problem solving.
Let the students personally experience the simple process of solving and communicating the proportional distribution problem, so as to further learn the general methods to solve the proportional distribution problem.
By summing up, let students master the characteristics of proportional distribution problems and general problem-solving methods.
The basic problem of proportional distribution, to examine the degree of mastery of students.
Let students further feel the close relationship between mathematics and life.
Let students further feel the wide application of proportional distribution in life.
The basic problem of proportional distribution, to examine the degree of mastery of students.
Under the guidance of teachers, we can complete challenging problems, so that students can further experience the strategies and methods to solve the problem of proportional distribution, improve their ability of comprehensive application of knowledge and develop mathematical thinking.
Teacher: Students, we learned some knowledge about competition in the last few classes. In this class, we will use what we have learned to solve some practical problems.
Blackboard writing: the application of comparison, showing the schematic diagram with a small blackboard.
Teacher: The farmer's uncle is going to grow eggplant and tomatoes in a rectangular vegetable field of 984 square meters. This is a schematic diagram drawn by the farmer's uncle. What did you learn from the pictures?
Student: The farmer's uncle divided this rectangular vegetable field into eight parts on average, among which, 3 parts planted eggplant and 5 parts planted tomato.
Teacher: Good. What other questions can you ask according to the information reflected in the picture?
Health: Eggplants account for 3/8 of the whole land, and tomatoes account for 5/8 of the whole land.
Teacher: How clever. These questions are all based on previous fractional knowledge. After learning to compare, this question can be expressed as follows: a rectangular vegetable field is 984 square meters. Plan 3: 5 Planting eggplant and tomato respectively.
Blackboard: We plan to plant eggplant and tomato at 3: 5.
Teacher: Who can explain: What do you mean by 3: 5 eggplant and tomato?
The default student may say:
Divide the 984-square-meter vegetable field into 8 parts on average, including 3 eggplant and 5 tomato.
Eggplants account for 3/8 of the whole land, and tomatoes account for 5/8 of the whole land.
Eggplants account for 3/8 of the total area of rectangular vegetable fields, and tomatoes account for 5/8 of the total area of rectangular vegetable fields.
Teacher: The students' understanding is reasonable. "Plant eggplant and tomatoes in a ratio of 3: 5" means dividing this vegetable field into eight parts on average, of which three are planted with eggplant and five with tomatoes. This distribution method is usually called proportional distribution.
Blackboard writing: proportional distribution
Teacher: The students have understood the meaning of "3: 5 kinds of eggplant and tomato", so can you find out the planting area of eggplant and tomato in square meters? Please find a way to find out for yourself.
Students try, teachers patrol and guide, understand students' methods and prepare for communication.
Teacher: XXX students introduce your method and results to everyone.
Communicate the following methods purposefully:
984×3/8=369 (square meter)
984×5/8=6 15 (square meter)
Teacher: Whose algorithm is the same as this one? Who can say what they think?
Health: Eggplants and tomatoes account for 3/8 and 5/8 of the rectangular vegetable fields respectively. According to the score of a number, we can calculate it by multiplication, and then we can calculate how many square meters eggplant and tomato are listed as 984×3/8 and 984×5/8 respectively.
Teacher: That makes sense. The teacher has a question. How do you know this 8?
Health: As you can see from the picture, this vegetable field is divided into eight pieces on average.
Teacher: If you don't give me a picture, just tell me the 3: 5 eggplant and tomato, how can you work it out? Why?
Health: 3+5=8. Because eggplant accounts for 3 parts of this land and tomatoes account for 5 parts of this land, 3 plus 5 is the total number of this land.
Teacher: Yes! Calculate the total number of copies according to the number of copies of eggplant and tomato, and then calculate.
Complete the blackboard writing.
3+5=8
984×3/8=369 (square meter)
984×5/8=6 15 (square meter)
Teacher: Just now, we exchanged a method. Who has another way? Let me introduce you.
If students come up with other methods, give them affirmation if it is reasonable. such as
3+5=8
984×3/8=369 (square meter)
984-369=6 15 (m2)
Teacher: The students solved the problem. How do you know if your answer is correct? Please try to test it.
Students may ask:
Add up the area of eggplant and tomato to see if it is equal to the total area of this vegetable field.
123+369=984 square meters
Write down the area number of eggplant and tomato in the form of ratio, and then have a look to see if it is 3: 5 after simplification.
123:369=3:5
Teacher: Just now, the students solved the problems in planting. Now let's solve the problems from the construction site together. Please read 19 and read the following questions. What mathematical information did you learn from them?
Students may say:
The worker's uncle wants to mix 2000 kilograms of concrete with cement, sand and stone in a ratio of 2: 3: 5.
The concrete used in the construction of workers' uncles is made of cement, sand and stone. The ratio of cement, sand and stone is 2: 3: 5. Now, 2000 kilograms of such concrete will be produced.
The worker's uncle wants to mix 2 parts of cement with 3 parts of sand and 5 parts of stone to prepare 2000 kilograms of concrete.
Teacher: Who can explain what it means to make concrete with cement, sand and stone in a ratio of 2: 3: 5?
Students may say:
Concrete is made of 2 parts cement, 3 parts sand and 5 parts stone.
Divide the concrete into (2+3+5) 10 parts, including 2 parts of cement, 3 parts of sand and 5 parts of stones.
In the prepared concrete, cement accounts for 2/ 10, sand accounts for 3/ 10 and stone accounts for 5/ 10.
Teacher: What is the relationship between the expression order of cement, sand and stone and 2: 3: 5?
Health: Yes, they are corresponding. Let's talk about cement first. The first number in the proportion represents cement, then sand, and the middle number represents sand.
Teacher: It seems that the students have made clear the meaning of "mixing concrete with cement, sand and stone in a ratio of 2: 3: 5". So how many kilograms of cement, sand and stone do you need to prepare 2000 kilograms of concrete? Can you answer that? Please find a way to find out for yourself.
Students answer, teachers patrol guidance.
Teacher: Who can tell us how you calculated it and what was the result?
Possible ways for students to appear:
(1) Count the number of copies of a * * * first.
2+3+5= 10
(2) Calculate how many kilograms each.
2000×2/ 10=400 (kg)
2000×3/ 10=600 (kg)
2000×5/ 10= 1000 (kg)
Teacher: Like the above, we allocate a quantity according to a certain proportion, and then find out how many of these parts are. This is called the proportional distribution problem. The problem of proportional distribution is the practical application of ratio in life. So what are the general ideas and methods to solve the problem of proportional distribution?
Student: First, find out how many copies a * * * will be divided into, and then find out how many copies according to the distribution ratio.
Teacher: Please look at 1 practice. Look at the questions first and observe the situation map. What mathematical information did you learn from the question? What's the problem?
Health: The ratio of an insecticide to water is 1: 14, and a barrel of insecticide is 1500ml. The question is how many milliliters of pesticide and water are there?
Teacher: OK, please do the math problem.
After the students finish the calculation, the whole class communicates.
Answer: 100 ml of medicine and 1400 ml of water.
Teacher: Please read the second question and see what mathematical information you can learn from it. How do you solve problems based on this information?
Students answer independently, and teachers patrol for guidance. When communicating, let students focus on what they think.
Teacher: Question 3. Who said "45 portions of sawdust, 4 portions of rice bran and corn flour 1 portion"?
After the roll call students answer, let them answer independently. The teacher will patrol and guide them, and then correct them. Let students focus on what they think.
Teacher: Please finish Question 4 independently in your exercise book.
Students answer independently, teachers patrol and guide, and then organize students to exchange and revise.
Teacher: Please read question 5 and discuss the relationship between the sides of a cuboid 192 cm and 12.
Health: The sum of 12 sides of a cuboid is equal to 192 cm.
Teacher: What is the relationship between 192 cm and the length, width and height of a cuboid?
Health: 192 cm divided by 4 equals the sum of the length, width and height of a cuboid.
Teacher: What does it mean that the ratio of the length, width and height of a rectangle is 3: 2: 1?
Health: Divide the length, width and height of a cuboid into 6 parts on average, with the length accounting for 3 parts, the width accounting for 2 parts and the height accounting for 1 part.
Teacher: Try to answer it yourself.
Reference answer:
192÷4=48 (cm)
3+2+ 1=6
48×3/6=24 cm
48×2/6= 16 (cm)
48× 1/6=8 (cm)
Volume: 3072 cm.