The teaching content of the proportional teaching design for the sixth grade of People's Education Press: proportional quantity
Teaching objectives:
1. Make students understand the meaning of direct ratio and correctly judge the size of direct ratio.
2. Make students understand the image characteristics of the quantity expressed in direct proportion and solve simple problems according to the image.
Teaching emphasis: the significance of positive proportion.
Teaching difficulty: correctly judge whether the two quantities are proportional.
Teaching process: First, reveal the theme.
1. In real life, we often encounter two related quantity changes, one quantity change and the other quantity change. Can you give some examples?
Under the guidance of teachers, students will give some simple examples, such as:
(1) The class size has increased, and so have the desks and chairs; There are fewer people and fewer tables and chairs.
(2) The number of milk delivery packages is more, and the total quality of milk is also more; If the number of bags is less, the total mass will be less.
(3) When you go to school, you walk fast and spend less time; Slow speed and too much time.
(4) When queuing, the number of people in each line is small and the number of people in the queue is large; There are more people in each row. There are fewer lines.
2. What is the regularity of this change? What does it matter? Today, let's first learn about the proportional quantity. Blackboard writing: a proportional quantity
Second, explore new knowledge.
1. Teaching example 1 (1) Show the example situation diagram.
Q: What do you see?
Health: The cups are the same. The height of water in a cup is different, and the volume of water is also different. The higher the height, the larger the volume. The lower the height, the smaller the volume.
(2) Display form.
Height /2468 10 12
Volume/350100150200250300
Bottom area /2
Q: What did you find?
It is not difficult for students to find that the bottom area of the cup is 25㎝2.
Blackboard writing:
Teacher: The ratio of volume to height is certain.
(2) Explain the significance of direct proportion.
(1) On this basis, the teacher clearly explained the meaning of positive proportion.
Because the bottom area of the cup is fixed, the volume of water varies with the height. The height of water increases, so does its volume, and the height of water decreases, so does its volume. The ratio of water volume to height is certain.
Show it on the blackboard: in this way, two related quantities, one quantity changes and the other seed quantity changes. If the ratio of the corresponding two numbers in these two quantities is certain, these two theorems are called proportional quantities, and the relationship between them is called proportional relationship.
② Students read and talk about how you understand the proportional relationship.
Students are required to master three elements:
First, two related quantities;
Second, one of them has increased and the other has also increased; One quantity is reduced, and the other quantity is also reduced.
Third, the ratio of the two quantities is certain.
(3) Expressed in letters.
If the letters X and Y are used to represent two related quantities and K is used to represent their ratio (certain), the proportional relationship can be expressed by a positive formula:
(4) think about it:
Teacher: What other quantities are directly proportional to life?
Students illustrate with examples. For example:
The width of a rectangle is constant, and the area is proportional to the growth.
The quality of each bag of milk is certain, and the number of milk bags is directly proportional to the total quality.
When the unit price of clothes is irregular, the number of clothes purchased is directly proportional to the amount of money payable.
The floor tile area is certain, and the classroom area is directly proportional to the number of floor tiles.
2. Teaching example 2. (1) display the form (see this book)
(2) Track points according to the data in the table below. (See this book)
(3) What do you find in the picture?
These points are all on the same straight line.
(4) Look at the picture and answer the questions.
If the height of water in the cup is 7㎝, what is the volume of water?
Health: 175㎝3.
② What is the height of water in a cup with a volume of 225㎝3?
Health: 9㎝.
③ The height of water in the cup is 14㎝, so what is the volume of water? Is this corresponding point on a straight line?
Health: The volume of water is 350㎝3, and the corresponding point must be on this straight line.
(5) What other questions can you ask? What experience do you have?
Make students understand the image characteristics in direct proportion through communication.
Do it.
Process requirements:
(1) Read the data in the table, write down several groups of ratios of distance and time, and tell the meaning of the ratios.
The ratio indicates how many kilometers are driven per hour.
(2) Is the distance in the table proportional to the time? Why?
In direct proportion. Reason:
① Distance changes with time;
② With the increase of time, the distance increases, and with the decrease of time, the distance decreases;
(3) The ratio (speed) between planting process and time is constant.
(3) Draw points representing distance and time in the diagram and connect them. What did you find? The tracked point is in a straight line.
(4) How long does it take to drive120km?
(5) What other questions can you ask?
4. Course summary
Talk about the changing characteristics of the quantity that is said to be proportional.
Three consolidation exercises
Complete 1 ~ 5 in exercise 7.
The Application of Reflective Proportion in the Positive Proportion Teaching of Grade 6 of People's Education Press. This part of the textbook contains two examples of positive proportion and negative proportion, and its knowledge contains dialectical thinking to some extent, so that students can understand that in this lesson, I will guide students to analyze carefully, discuss the proportional relationship between invariants and variables, find out the equivalent relationship and list the equations.
Make full use of students' knowledge and basically compare the old and new methods. At the same time, let students fully understand the role and application of proportion in practical problems.
In class, I lead the students to analyze the relationship between the water consumption and water fee of Grandma Zhang's house, which is the total price. Quantity = unit price. Through the existing knowledge and life experience, we know that the price per ton of water is certain, so the water fee is directly proportional to the tonnage of water, that is to say, the ratio of water fee to tonnage of water of the two companies is equal. So ask:? With the proportion knowledge we have mastered before, will students solve it? What kind of knowledge are you going to use to answer the students? Prepare to answer in direct proportion, because the conditions in the question meet the requirements of direct proportion. ? A class allows students to participate in the whole process of experiencing and solving problems from beginning to end. According to the teacher's clever questions and enlightening guidance, students can quickly master the content of the new lesson through independent learning and cooperative communication. This course not only attaches importance to the teaching of problem-solving methods of proportional problem solving, but also encourages the diversification of problem-solving strategies to develop students' personality. The classroom structure is rigorous, students practice more and master it well. A stone stirs up a thousand waves, and students learn to interact; Communication is enthusiastic and successful.
The design of exercises can be closely combined with students' real life, and try to design some topics that arouse students' interest and attract them, so as to stimulate students' interest, improve students' enthusiasm for practice, overcome unattractive narratives and statements in old textbooks, and deepen students' understanding of the new curriculum.
Of course, there are still some shortcomings in this course: if students can't fully express the true meaning of the topic in mathematical language, although they can do the topic according to the textbook, they are still vague about the basic ideas and their meanings, and can't achieve higher teaching goals. In the future teaching process, we will pay attention to the idea of doing the problem and continue to work hard. One last question. It is less difficult to solve application problems in proportion and the correct rate is higher. But why do students prefer arithmetic to this method? Is it because of the trouble of setting unknowns or other reasons?
Guess you like:
Excellent teaching plan design in direct proportion to 1.
2. The sixth grade volume math proportion teaching plan
3. The first volume of the sixth grade mathematics proportion application problem teaching plan
4. Teaching plan for the application of mathematics proportion in the sixth grade of primary school.
5. Application teaching design of 5.PEP ratio
& gt& gt& gt More proportional knowledge points in the sixth grade mathematics on the next page?