Percentage application teaching reflection

Part 1: Percentage of teaching reflection

The "Percentage Application" unit is based on the students' understanding of the meaning of the percentage, the learning of the four-score hybrid operation, and the ability to solve some practical problems with the fractional four arithmetic. How to apply the meaning of percentage to solve related practical problems, how to communicate the internal relationship between mathematical knowledge and methods such as percentage and score, and improve the cognitive structure of students, has become the goal of this unit. Reviewing the learning content of this module can be summarized into the following two key points:
First, take the meaning of the percentage as a breakthrough, analyze the relationship between the numbers, and explore the algorithm.
A percentage is a number indicating that a number is a few percent of another number, and the essence is to express a multiple relationship between two quantities in a specific form. Whether it is to find a number is a few percent of another number or to ask for a number more than a few percent of the other number, the key is to understand the meaning of the percentage, to correctly judge what amount to consider as the standard, that is, we usually Said the unit "1". For example: What is the percentage of B for A? It is a direct comparison between A and B, with B as the standard, column: A÷B; how much is A more than B? It can be understood that the portion where A is more than B is equivalent to a few percent of the standard amount B, and either ÷B or A÷B-1 can be used. In fact, the two algorithms and the two ideas are ultimately to find that A is more than a few percent of B. As for the number of one less than the other, it involves solving the actual problem of "increasing a few percent", "reducing a few percent", etc., as long as the students understand these concepts. The meaning and the way to solve the problem are the same.
Second, take the meaning of the fractional multiplication as the main line, clarify the relationship between the numbers, and choose the algorithm.
The meaning of fractional multiplication - "How many fractions of a number can be calculated by multiplication" is a main line for solving the actual problem of fractions and percentages. Whether it is a practical question about taxation, interest, discounts, or solving a slightly more complex percentage problem, it is inseparable from the analysis and understanding of the basic quantitative relationship. If the number of female students is 80% of male students, it can be concluded that “the number of male students × 80% = the number of female students”; “the water consumption in October is 20% less than that in September”, it can be concluded: “Water consumption in September – September 20% = water consumption in October." From these key sentences, we must find the unit "1", that is, the percentage in the comprehension question is a few percent of what is expressed, and then the equality between the numbers in the question is clarified.
In order to reduce the difficulty of understanding, students should first strengthen the understanding of the meaning of scores and percentages when analyzing the meaning of the questions, and make full use of the basic quantitative relationship of "how many percent of a number is used", and rationally choose the formula or column equation to solve the problem. .
In the teaching of this unit, I strive to achieve a close connection between mathematics and real life, and focus on cultivating students' awareness of applying mathematics. Special attention is paid to correcting the boring and abstract appearance of the teaching of the set of questions, and borrowing the existing knowledge and life experience of the students, effectively helping the students to understand the quantitative relationship and practical value of the percentage of the set of questions. Pay special attention to changing the expression of the set of questions and enriching the way information is presented. In the teaching process, when the sample questions and exercises are presented, the presentation form should be diverse and lively, so that students can participate in various senses to attract students' attention and cultivate interest in mathematics.
The shortcomings in the teaching of this unit are mainly: due to the relatively tight time, the cultivation of the solution to the problem of the application of the problem, and the ability of students to choose the algorithm and the rational selection of the algorithm are not enough. There are also fewer open exercises and deeper practice training for the percentage of questions. Some students have to improve their ability to carefully examine questions, analyze quantitative relationships, and use appropriate methods to correctly answer questions.

Part 2: Percentage application teaching reflection

In this lesson, the knowledge point seems to be simple, that is, "one number is a few percent of another number" and "percentage." But there is nothing that is easy to get out of, and naturally it does not appeal to students. I took the percentage of life in the example, and the students reached a small climax in this session. Answering questions is also reasonable and the ideas are very creative. Breaking through the key points and difficulties.
First, be good at excavating the bright spots of students.
When students talk about the percentage of their lives, they have the correct rate, excellent rate, attendance rate, shooting rate, and pass rate of the mid-term exam. Therefore, I seized the opportunity to name the student's oral teacher's book: the rate of compliance = the number of students in the standard, the total number of students × 100%; the pass rate = the number of passers, the number of the whole class × 100%; the survival rate, germination rate, attendance rate of the seedlings. Teachers are encouraged at the right time and have a pertinent evaluation of their responses. Students have a sense of accomplishment that further motivates their potential.
Second, give play to the subjectivity of students, let students develop in autonomy, cooperation and inquiry.
When teaching, we should proceed from the reality of the students, respect the students, and trust the students, so that the main role of the students can be fully exerted. In teaching percentage, I should adopt a group cooperative approach, group communication, give them enough time, say the percentage in life, say their meaning, and better understand the concept of percentage. And let them feel the mathematics of life. Knowing that mathematics comes from life, there are many mathematical knowledge in life to promote their better study of mathematics.
Third, carefully design the practice session, so that students feel the joy of learning mathematics.
In the practice session, an open exercise designed to allow students to compile a percentage of questions based on the classmates' class is very active. The students' questions are no longer seen in many textbooks or extracurricular exercises. “Males account for a few percent of the class and girls account for a few percent of the class.” Some students say that they first investigate the number of students participating in the interest group in the class, and then count the number of people participating in the interest group. A few percent of the class size, some said that there are countless classmates in the class who have cows in their homes. Counting the number of families who raise cattle accounts for a few percent of the total number of families in the class, and some say that the only child in my class is counted. The number of women, counted as a percentage of the class in the class. It does reflect that when mathematics and life are combined, it will rejuvenate the vitality of life, and students will truly enjoy the joy of mathematics.

Part 3: Percentage application teaching reflection

In this self-prepared presentation class, I taught the percentage of the first lesson. This example looks very simple. It seems that the scores I have learned before are expressed in percentages, but I think: the percentage of the questions here is not It is as simple as adding a few points to "increasing a few percent". The content of this lesson needs to understand its true meaning in combination with specific life situations, which is difficult for most students. Let's share some of the sentiments after teaching.
First, the system reviews, highlights the key points, and breaks through the difficulties.
The main content of the percentage application is "to increase or decrease the number of one number by another." The difficulty in this lesson is to help students understand the meaning of “increasing or decreasing a few percent”. If this problem can be solved, it is much easier to find the percentage. How to highlight the key points, the difficulty is the big problem in front of me. In order to complete the teaching of this class well, according to the actual situation of the students in my class, I did not take the method of going straight to the theme, but adopted the connection method. Although it took nearly 10 minutes in the review period, the results received were very good. For example, when students are asked to use the two mathematical information to ask questions about the percentages, there will be a review of the content of the review. Students will naturally think of such a percentage application that “increased a few percent”. The students will not feel suddenly. The solution to the problem naturally has a direction.
Second, with the help of the line segment map, find the unit "1", seek and understand the problem-solving ideas.
How do you understand that “the volume of frozen water is increased by a few percent more than the volume of water?” The problem that students can easily think of is the first method of the book. First, find the volume and then remove the unit by “1”. For the second method students, one is hard to think of, and the second is the understanding of "-100%", that is, the plan should be regarded as 1 minus, which may be understood by students who do not understand the meaning of the score. A little understanding. In order to understand the second method well, the key is to use the previous line segment diagram to directly use two quantities to find the volume of the frozen volume is a few percent of the volume of water, and then combine with the familiar thinking to find more reductions, think of With the current subtraction of the original, combined with the figure to think of the original amount is the unit "1", that is 100%, and then use the reduction to find the problem. From the actual process of the classroom, in the analysis of the "increasing a few percent" is also said to be "reduced by a few percent", the students disagree, I am not eager to give students a conclusion, but to let students According to the example, draw a line segment diagram and analyze it independently. Let the students also understand the common points and subtle differences between the two questions in the drawing: the common point is to draw the unit "1" quantity first, and then draw the comparison quantity. The difference is that the example first draws the volume of water, and this time The first is the frozen volume. The position of the unit "1" marked in the two figures is different. This is also the difficulty of teaching in this lesson. The visual representation in the picture greatly helps more students to understand the solution.

Part 4: Percentage application teaching reflection

The school's "361" happy classroom "in-class than teaching" activities are in full swing. According to the arrangement of teaching progress, I just put "percentage application", "percentage application" is a key and difficult problem in the problem solving of mathematics. According to past experience, whether it is eugenics or poor students, this class is the most difficult for students to understand, and it is also the most error-prone part of students. Logically speaking, the percentages are solved by using equations. It is the best way to use the line graph to understand the problem. But for students, one. Students don't like to draw line segments, nor do they have the habit of drawing line segments. 2. Many students do not like to use equations to solve problems. It is too cumbersome to use equations to solve problems. Another point is that finding quantitative relationships is a key to solving such problems. This is in turn the support of the column equation. However, what students often dislike most is the quantitative relationship. It seems that many common senses in life are mathematically an esoteric problem. Therefore, the habit of the students throughout the process is to directly list the formulas. Is there a direct and useful way for students to think and learn? Can you find a solution to the problem that they want in their minds? After thinking about it, I will determine the teaching ideas of this chapter as follows:
One. Focus on solving the student's understanding of the topic's meaning of “increasing a few percent”. Use the line graph to understand and understand in the sense of percentage.
two. Find the quantitative relationship
three. Column equation or division formula
My idea is: In the teaching of the new lesson, try to let the students understand each method and lay the foundation for the follow-up learning.
After the completion of the "Percentage Application", I added a set of contrast questions for the students to answer. The comparison questions are as follows:
The school has 20 footballs, basketball is 25% more than football, and how many basketballs are there?
The school has 20 footballs, 25% more football than basketball, and how many basketballs?
The school has 20 footballs. Basketball is 25% less than football. How many basketballs are there?
The school has 20 footballs. Football is 25% less than basketball. How many basketballs are there?
Let the students do it first. If students use very few equations, they use arithmetic methods. And no matter how good or bad, there are only a few people who are right. Then let the students return to the topic: 1. Use the method of drawing line segments to help students understand the problem and find the quantitative relationship
2. Write a quantitative relationship
3. Make a correct answer to the known and problematic questions in the title. Then go to reflect on where your problem is and then let the students compare the differences between these topics. Students can still find the differences in the title:
1. I know more than the percentage, I want the number of basketballs, the number of football is known.
2. Sometimes it is possible to think of the number of units "1", and some are not. After the difference is found, the arithmetic method of each topic is written on the blackboard. An important question is thrown in the appropriate encouragement: Can you find the flaws in solving the scores? Students must be observed that the form of the formula is very similar. The mathematics formula is as follows:
20×
20÷
20×
20÷
Students from the blackboard book can quickly sort out the thinking and find the law of using the mathematical formula to solve the problem:
One. As a whole, we can know: To list mathematical formulas, it is to find out when to use ×, ÷, when to use "+", "-".
two. When there are many problems in the title, use "+" instead of "-"
three. After judging who the unit "1" is, if the amount regarded as the unit "1" is a known condition, "x" is used, and "÷" is used instead.
I feel that students are looking for the rules of solving the arithmetic method as if they are as skilled and interested in finding the rules of the game. This is another gain I have tried. Moreover, in the review of the percentage, the students encountered another problem that could not be clearly distinguished, and the problem could be solved smoothly. The topics are as follows:
The school has 20 footballs, basketball is 25% of football, and how many basketballs are there?
The school has 20 footballs, football is 25% of basketball, and how many basketballs are there?
Excellent students can also use this rule to help them distinguish between when to use "X, ÷". Most students can feel from the law, but it is actually simpler than the previous ones. You don't have to determine "+" or "-".
Of course, using the equation method is also a very good method. I think the reason why the new textbook pays more attention to the solution of the equation is for the connection of mathematics learning in middle school. The ideas and methods of the middle school equation are used very frequently. Therefore, we should also strengthen the teaching of solving problems with equations, so that students can learn more ways to let students choose the right method. I want to think about the students and carry out the teaching according to the actual situation of the students. Under the support of this teaching concept, I have tried this content as above.

Part 5: Percentage application teaching reflection

For students, the percentage of students should not be particularly unfamiliar, and they have been exposed to a higher percentage in the fifth grade. And in order to allow students to better apply the percentage of previous studies, a special percentage of exercises were prepared for students last weekend. It should be said that the basis of the students is there, but a large number of students have forgotten. This requires the teacher to integrate the existing knowledge in the teaching, so that the knowledge is more organized and systematic.
Today's teaching solves the problem that a number is increased by a few percent more than the other. For the problem of water freezing, combined with the weather in these days, the weather is particularly hot, and the problem is caused by the phenomenon of the ice in the life of the bottle. 180 cubic meters The centimeter of water is formed into an ice volume of 200 cubic centimeters. What questions can you ask based on these two conditions? Trying to ask students to increase the volume of frozen water compared to the volume of water? What is the frozen volume that is a few percent of the volume of water? This makes it easier for students to solve the problem of a few percent increase in the volume of frozen water than the volume of water? However, the student's situation is not particularly good, and few students ask questions. And for the key issue: the volume of the frozen is a few percent more than the volume of the water, and the students are not particularly well understood.
Analyze the reason, the situation that may be created in the beginning of the class. After the student’s interest comes up, it will be immediately stumped by the first question. The student’s interest will disappear at once, and on the other hand, the thinking time and discussion time for the key issues will be lost. Not enough, the students did not have a deep understanding of the meaning of “increasing a few percent” in the classroom, which made students have difficulties in solving problems. In response to this problem, take the students directly to the problem: how much does the frozen volume increase by a few percent more than the volume of water? In thinking and discussing, will you put more time for thinking into the problem of solving the meaning of the percentage? Let students learn how to solve in the process of thinking about meaning? And put this open question in the second lesson or in the review class to open up thinking and enhance the depth of students' learning. In the first lesson, we must focus on the key issues to discuss and solve, which needs attention in future teaching.