Content 1:
Such a simple question simply does not reflect the advantages of the equation method. The purpose of this section is only to let students master the general steps of equation method: setting, listing, solving and answering. The content is so simple that you can pave the way for infiltration in arithmetic methods. When you are behind the word than, the amount you want to see is just the opposite. You need to see more-see less+,so it is much easier to find a number after knowing how many times it is more or less.
The second content:
The problem equation method in this section does not see much advantage, and the purpose is still to further consolidate the general steps of the equation method.
The third content 1 class:
The equation method in this section has advantages, but under the premise that the equation method is not explicitly required, children still prefer the arithmetic method first, so the arithmetic method is the main one, supplemented by the equation method.
More scientific and efficient teaching concept;
Teaching ideas: from basic type to new type-with tail type. Example 1 summary after example 2: the tail with tail should be reversed first and then divided by multiple. Then it is quickly consolidated through a series of exercise groups, only the formula is not counted. Finally, the exercise or homework of self-made questions. For the convenience of marking, the layout of the questions is better: there are boys and girls, 27 and 6 and 3, and write two answers to questions with tails, one more and one less.
It is worth noting that after the exercise, I did the following questions, and only 23 people got it right.
If you are talking about the equation method, you can practice with reference to the following design:
As for the following ideas, we should resolutely abandon them, because the quantitative relationship behind them is precisely the weakness of students, so the equation method is only introduced as an auxiliary method, so that we can better understand them and not forget them!
The third content, the second lesson:
The first difficulty to be solved is the design problem:
Deepen the understanding through the line segment diagram, and then carry out special training on the design.
Compare the difference between equation method and arithmetic method: reverse thinking is more-less+,positive thinking is more+less-. (Don't mention the reciprocal of multiples for the time being, otherwise the burden on students will be too heavy, and 1 class will be consolidated. After all, there are very few students with wrong multiples, so it is unnecessary).
Next, I asked my classmates to do two problems that had been done by arithmetic in their homework last night by equation method. When giving feedback, the teacher must finally write it on the blackboard. Some students just say no. They are not auditory thinking, but visual thinking.
The fourth content, the problem of differential magnification on the right side of the blackboard:
Several aspects that need to be improved and their reasons:
1. Let's talk about the difference multiple first, because it is more difficult. When calculating another quantity after calculating the weight of 1, we should use unified multiplication, because whoever uses less addition and subtraction in the problem of difference multiple is more likely to make mistakes. And practice in a single class until you are proficient.
2. Slow out the formula. After explaining the solution to the time difference problem, let the students repeat it first, deepen their understanding, form a complete train of thought, and practice and speak more until the students are familiar with it and it is not too complicated.
3. After summarizing the formula, guide students to describe it with structured requirements and form a complete idea with the formula. Write the structure on the blackboard first, so that students can grasp the structure as a whole.
4. Special training for key and difficult points. First, train to find out the weight of 1 under the condition of doubling, and present it intuitively with graphics. Draw the weight 1 under the condition of doubling in the above picture with a red pen! (Just like finding "1" in fractional problem-solving training, it can't be underestimated, so special training must be carried out, otherwise the consequences will be unimaginable), but the situation that the multiple is a decimal will only appear after students master it skillfully, otherwise it will be too difficult for students to learn.
Then solve the first difficulty, the poor number of copies, as shown below. Students imitate the red pen part of oral narration.
Then ask the students to add up the differences between the conditions in the two exercises, and the students can answer them completely in this book.
Distinguishing the difference condition is the second difficulty, even more difficult than the difference of copy number. In my teaching practice, quite a few children mistake difference for sum, which is not only the main reason for learning first and then turning over, but also related to the diversity of poor conditions, such as design age, height, quality, speed and so on. Therefore, homework should also leave such questions with poor conditions to guide students to grasp the nature and diversity of poor conditions.
Challenge: Variant of Differential Time Problem
The fifth content: the problem of doubling.
The following questions may have higher accuracy by using the equation method:
The sixth content, lesson 65438 +0, the arithmetic method of sum and difference problem:
The sixth content, the second kind, the arithmetic method of sum-difference problem:
Note: Make clear the method at the beginning:
Students can't distinguish three kinds of questions, so they can make up their own questions: for example, boys and girls, 60 and 4, and answer them.
Equation method of sum and difference problem;
The problem of sum and difference is to set the sum column with difference, and set the compared quantity as X. The training is as follows:
The seventh content: the equation method of sum multiple problem and difference multiple problem.
Method: Set the sum or difference of times, and set the weight of 1 as x.
You can also compare it through review and poor questions:
Perhaps it can be summarized more simply: set one condition and list another; If there is a multiplier, let the quantity of 1 be X. If there is no multiplier, let the quantity be X.
It's hard to work out the damn equation and list it. Train first. As for Liege, go to since the enlightenment consciously!
Everything is difficult at the beginning, and the key of equation method is to grasp the setting of the beginning. The training content is as follows:
Several good extension problems:
1.
It is good because it can be transformed into a sum multiple problem, and it can also be solved by knowing how many times a number is or how many times it is. The most powerful weapon is the line chart.
2.
3.
The eighth content, the arithmetic method of meeting problems:
Give an example and two exercises to learn a formula.
This section focuses on the speed and the figure below.
The idea of 60×3+80×3 is very simple, and the blackboard diagram on it has been erased.
The latter two formulas can be derived from the term 1, 2. Question 2: If Xiaoming's speed is 80 meters per hour, what is Xiaohong's speed? Make it clear after communication: one speed = speed and-the speed of the other.
If you directly calculate Xiaohong's speed, there will be another way of thinking: first, calculate Xiaohong's distance, and make it clear that the encounter problem is one car distance = encounter distance-another car distance.
Outward bound training:
Students' learning is a process from romantic perception to accurate learning, that is, first forming a complete thinking method, and then carrying out special training for the difficulties in thinking methods.
The ninth content, the arithmetic method of inverse problem:
1. Arithmetic has two ideas, and it is necessary to explain the quantitative relationship under the following two different ideas.
It can be seen that arithmetic will bring a lot of things, and the law of equations only needs to remember that slow road+posterior road = fast road. If the equation method is used, because it is different from the encounter, it is suggested that this type should be independent first, and then compared with the encounter problem. It is pointed out that the sum of two kinds of questions is equal to the sum of a large paragraph, which can be summarized as one sentence: the sum of two small paragraphs is equal to the sum of a large paragraph, and the problem behind it is that slow road+posterior road = fast road. The teacher was asked to imitate the painting before moving on to the next step.
3. The significance of introducing speed difference lies in the subsequent problem modeling, which can be used to solve both the problem of water inflow and outflow and the problem of cattle grazing, and can be pointed out to students in time during the teaching process.
Negative:
Because of the questions reviewed above, I was shaken by the arithmetic method and wrote a bunch of reasons as follows:
1. After using arithmetic method, it leads to more questions, more difficulty in understanding and more class hours.
2. It's really not worth the trouble just for the convenience of applying arithmetic to a doubling problem and a meeting problem. It is entirely possible to introduce the algorithms of these two kinds of problems after students have fully mastered the equation method.
3. The following teaching will focus on the equation method, supplemented by the arithmetic method. Specifically, in teaching, if the arithmetic method is affirmed or acquiesced, it will not be explained in detail, but the problems of doubling and finding the meeting time should be explained and practiced in detail.
4. There are two ways for me to solve the equation. One is to solve the equation with the relationship between the parts, and the other is to adopt the strategy of only listing the questions and highlighting the method of solving the equation when doing exercises.
4. In the future, the lesson of "Solving Problems by Fractions and Percentages" can also consider the idea of giving priority to equations, supplemented by arithmetic.
Negation of negation:
1. For the following two questions, there is no evidence that the equation method is more accurate, just guessing. If the equation method is used, can these children who have made mistakes do it right?
2. For the problem that the difference times increase with age, can the equation method be used to prevent children from misjudging it as sum times?
This is the reason for the exam, not the method.
In a word, if our children can't even know the formula, how can we be sure that they can use it well? Unless there are data from homogeneous comparative experiments to illustrate this point.
The new situation, ***6 such children:
Thinking: Is it because the equation is supplemented? If they focus on equations, they can do it, right? Not exactly.
I'm afraid this is related to the variety of fill-in-the-blank questions and the lack of practice. At the end of the term, we should strengthen the practice of filling in the blanks.
Negative again:
1. It's really not worth the trouble just for the convenience of applying arithmetic to a multiplication problem and a chance encounter. I think it will be convenient in the future, but it will increase the burden on students. There is really no need to introduce arithmetic.
2. As for the tail shape and the problem of falling behind, we must use the equation method, especially the tail shape is too difficult to reverse, and I am taking the most difficult road.
All equation teaching should pay attention to finding equivalence relations from key sentences. First, special training should be carried out: only key sentences should be given to train students' ability to find, speak and write.
The key to problem-solving teaching by equation method is that teachers should have the idea of losing weight, that is, first remove the details and give only key sentences, first train students to find the equivalent relationship in key sentences after losing weight, and then solve problems in the completely obese version.
For example, "Instructional Design with Tails" foreshadows special training on finding equal relations:
Key sentences: There are four times more men than women.
Teacher: If you want a boy, what do you want?
Student: female ×4+2= male.
Teacher: This is an equivalent relationship. In an equal relationship, why multiply women by a multiple of 4?
Student: Women are four times as many as women, so women should be multiplied by four.
Special exercise: Write the equivalence relation in the following questions.
There are seven times more desks than chairs and three fewer.
There are four more football than basketball.
Another example is the special training on finding equal relations in the foreshadowing part of the teaching design of "Meeting and After":
Both passenger and freight vehicles set off from the two places where they met at 150 km, and the two vehicles met after a period of time.
Both Party A and Party B start from a certain place and travel in the same direction at the same time. After a period of time, Party A lags behind Party B 150km.
3. In order to unify the problem of sum and difference times, the equation is also used. For this double-condition problem, it is necessary to clarify a set of ideas, one column, one calculation and one test. The difficulty is that both quantities are unknown. Which quantity should be set to x? There is a tail-shaped foreshadowing in front. Here, students will set the double quantity as x by intuition and experience, and will also try to solve this problem. We need to deepen our understanding through the following questions: Under what conditions? On what terms? What are the conditions for finding another quantity? Under what conditions was the inspection carried out? Suggestion: After the question is put forward, first make clear what kind of equal relationship exists between boys and girls, so as to deepen the understanding of the conditions.
4. Don't talk about the sum times as soon as you finish talking about the sum times and the difference times, because you try to be confusing, and the strategy is to put them back and go back to school after learning the distance problem.
Review remedial measures:
1. Comparing the teaching of encounter and late-onset equation method, it is pointed out that the arithmetic relation of these two kinds of problems is that the sum of two short paragraphs is equal to the sum of a large paragraph, which can be summarized as one sentence: the arithmetic relation of encounter and late-onset equation method is that the sum of two short paragraphs is equal to the sum of a large paragraph, and the late-onset problem is slow road+posterior road = fast road. The teacher was asked to imitate the painting before moving on to the next step.
2. The problem with the tail can't be reworked. Only the person who mispronounced its name can make it say the solution and formula of the problem with the tail.