In the revised curriculum standard, the simple estimation of "estimation" and "selecting appropriate units" has been strengthened. How to understand the simple estimation of "choosing the right unit"

For example, the school organized 987 students to play in the park. If each ticket in the park is in 8 yuan, will it be enough to bring 8000 yuan?

The appropriate method to solve this problem is to regard 987 people as 1000 people, so the appropriate unit is "1000 people". Combining with the specific situation, choosing the right unit is the core of the first phase estimation. When estimating large numbers, it is also important to choose appropriate units. How far is the classroom from the school gymnasium? You should choose the meter as the unit. And how far is it from home to school, you must choose kilometers as the unit. The distance from the sun to the earth is measured in light years.

The estimation of the first phase emphasizes the selection of suitable units under specific circumstances. The example just now was that 1000 people were selected as the unit. Generally speaking, when estimating the length of a classroom, it is usually in meters; When estimating the length of a book, it is usually in centimeters. You can also take the length of familiar objects around you as a unit, such as step size and arm length. In teaching, students should be familiar with some commonly used measurement units, truly understand their length, size and weight, and establish corresponding representations in their minds.

Second, how to grasp the content and requirements of estimation teaching

(1) Why teach?

Estimation is widely used in daily life.

It is helpful for people to grasp the range of operation results in advance and is an important aspect of developing students' sense of numbers.

It provides a basis for judging whether the results of calculator, oral calculation and written calculation are reasonable.

Estimation in specific situations is beneficial to students' judgment and choice ability.

It is estimated that it is conducive to the planning of cultivating students.

Estimation plays an important role in students' subsequent mathematics learning.

(2) What to teach

As for "what to teach", we should start teaching according to the requirements in the new curriculum standard. At least the teaching should involve "estimation methods" and "estimation strategies".

Estimation method:

(1) rounding method. If you add up to an integer of ten or one hundred.

② Take the middle number. For example, when the four numbers 32, 37, 30 and 39 are added together, they are all close to 35, some are a little more than 35, and some are a little less than 35. Take an intermediate number 35, and directly use 35×4 to roughly calculate the result of adding these numbers.

③ Use special data features to estimate the quantity. For example, 126 × 8, it can be thought that 125 × 8 and 125 are 8 times, and 1000 is obtained.

4 looking for intervals. That is to say, it is called finding its scope, and it is also called going to the tail and entering one. Going to the end means only looking at the first place, so when you only look at the first place, what is the estimated result at least; Entering one is the first place plus one. If we say 278, we will see it as 300, and the first place will add one, so it may be like this at most. So we can get an interval, that is, we can find its interval range.

⑤ Size coordination. Two figures, one is estimated to be larger, the other is estimated to be smaller, or the other is estimated not to be estimated.

⑥ Estimate first and then adjust.

⑦ Use multiplication formula to make up the numbers. This method is usually used for the estimation of division. Generally speaking, the divisor is multiplied by an integer, an integer or an integer. If the product is closest to the dividend, this number is the quotient of the division estimate. For example, 358÷6, multiply the divisor 6 by the integer 60, and the product 360 is closest to the dividend 358, so the integer 60 is the quotient.

(3) How to teach?

Estimation teaching is not simply to teach students to remember an estimation method, but through our classroom teaching, to make

Students gradually understand the significance and value of estimation and cultivate the awareness of estimation. In this process, we should increase some students' experience, constantly enrich students' experience in this field and gradually accumulate it.

Teaching suggestions:

1. Take estimation teaching as a whole, and take cultivating estimation consciousness as an important teaching goal.

The so-called overall grasp of estimation teaching is to grasp the knowledge structure and position of estimation teaching part and know the position of estimation knowledge part in the whole primary school stage. What role can it play in future estimation learning? What kind of goal do you want to achieve in teaching? In this way, you can be comfortable and know well in teaching.

The initial stage of learning estimation may be difficult for students, which may affect the teaching progress or calculation speed. At this time, teachers should not rush to catch up with the progress, but should give students space and time to fully understand. You know, the initial "slow" is only for the recent "fast" and "good".

In teaching, we should first consider the estimated teaching objectives. If the goal is only to make an estimate, or to estimate when you see an appointment, and do some mechanical training, it may form a wrong stereotype for students. In estimation teaching, the most important thing is how to cultivate students' approximate consciousness, which is a problem that mathematics teaching itself should attach importance to and should be implemented as an important teaching goal.

Guide students to choose estimation or accurate calculation in the comparison of problem situations, and constantly accumulate experience in this field. As a math teacher, we should try our best to collect or capture some good materials so that students can feel them in specific problem situations. What kind of problem-solving needs approximation, that is, we need to estimate and what kind of problem-solving needs to calculate accurate values. For example, the cost of "family dinner" is around 200 yuan, which is what we need to estimate. There is no need for accurate calculation. But as a cashier in a hotel, it needs accurate calculation, which is obviously not possible.

2. Choose a good topic and ask questions, so that students can understand the significance and value of estimation.

As a teacher, in teaching design, we should first choose a good topic and ask questions with predictive value. For example, if three digits are divided by two digits, how many digits is its quotient? This question is valuable. In addition, only by choosing good topics and asking good questions can students consciously realize the value of estimation, and after students have this experience of estimating value, their awareness of estimation can be continuously enhanced.

In addition, students are encouraged to use estimates to verify the calculation results and form good habits. In the teaching of estimation, students should be aware of the significance and value of estimation in combination with specific problem situations, and put forward appropriate questions in combination with students' reality, especially their existing knowledge level and life experience, so that students can deeply understand the significance of estimation. More importantly, students should be given enough time and space to communicate and explain the calculation process through students' communication.

Faced with different formulas, students sometimes use calculators and sometimes use accurate pens to calculate. Whether the result is correct, especially whether the number of digits of the product sum quotient is accurate, the approximate range can be determined by estimation method first, which can help students verify the calculation results. The cultivation of estimation consciousness should start from dribs and drabs, so that students can gradually develop a habit. After forming this good habit, he will consciously estimate.

3. Encourage diversification of methods, attach importance to the process of communication and explanation, and let students make reasonable estimates.

Because students have different degrees of mastery of relevant mathematical knowledge and skills, different ways of thinking and different levels, there are many ways to estimate China. Teachers should actively encourage students to diversify estimation methods, let students fully communicate, express their ideas, understand other people's algorithms, let students realize that there are different methods to solve the same problem, and promote students' optimization.

There are various estimation results, so we should pay attention to whether the estimation results are reasonable. Let students exchange estimation methods in estimation teaching.

Method is particularly important, as long as it meets the purpose of estimation or the need of solving problems, it is a good method. So different scenarios will choose different estimation methods.

Teachers should strengthen the awareness of estimation in teaching and do a good job of estimation demonstration in combination with the teaching content. This kind of demonstration is not an arrangement, but an appropriate guidance for students to estimate in a scientific range, while emphasizing good methods and making reasonable estimates.

4. Evaluate the estimate effectively.

(1) assessment awareness assessment

First look at a case, taken from TIMSS's test:

Paul spent $5 on milk, bread and eggs. When he arrived at the store, he found the prices of these three kinds of food as shown in the following figure:

In which of the following cases, using estimation is more meaningful than accurate calculation?

A. When Paul tries to confirm whether $5 is enough;

B. When the salesperson inputs the price of each food into the cash register;

C. When Paul was told how much he had to pay;

D. When the salesman counted the expenses paid by Paul.

This topic is cleverly designed. Through a specific question, this paper examines whether students can judge whether it is necessary to calculate and estimate in a specific situation, that is, whether students have a certain awareness of estimation. The biggest inspiration of this question is that estimation consciousness can also be examined. Therefore, we should also pay attention to the investigation of estimation consciousness when estimating and evaluating.

(2) Evaluation of evaluation strategy

Estimation is divided into: one is to estimate according to actual problems, and the other is to estimate by pure formula without actual problems.

According to the actual problem, choose a reasonable estimation strategy, and the reasonable result is correct.

As long as students can solve practical problems, this estimate should be reasonable, which is aimed at solving practical problems. Teachers need to realize that the estimation result is not as close to the actual situation as possible, as long as it is reasonable, it is correct. What is reasonable? It is reasonable as long as the estimated results can effectively solve the problem.

The estimation of pure test questions is correct as long as the results fall within a certain range; But it should be evaluated according to the cognitive reality of students of different ages.

Some topics, divorced from actual problems, belong to pure formula estimation. In this case, we propose that whether the estimation result is closest to the exact value cannot be simply taken as the only criterion, as long as it falls within the interval, it is considered reasonable. This interval, that is, its value range.

At the same time, students of different ages should have different evaluation criteria. If junior students are new to estimation, its estimation results fall within a relatively large range, and we think it is ok. Senior three students already have some estimation experience, so we should guide them to constantly reflect and adjust. For example, what is the product of 78 × 365? At the beginning of learning, students may estimate 70 × 300, 80 × 300 or 80 × 400 in this way, which we can all consider reasonable. With certain calculation skills, teachers should guide students to reflect constantly, which can be estimated as 80 × 350. At this time, the scope is much smaller than before.

In mathematics, more attention is paid to whether the estimated results fall in the appropriate order of magnitude.

The order of magnitude is ten, one hundred, one thousand, ten thousand ... In other words, how many times can 10 be used? For example, the alternative answer to a question in the TIMSS test mentioned above is very interesting. "The Smiths' water consumption is 6000 liters per week. How many liters of water does his family use a year? " Ask the students to choose from the following answers.

A.30000 B.240000 C.30 million D.240 million e.3 million

This is precisely to examine students' understanding of the order of magnitude. 52 weeks a year, 52 × 6000, the result is100000 orders of magnitude, plus it must be more than 300000, so the result is C.

Regarding the evaluation and estimation strategies, we think that students' estimation strategies are different. As long as it is reasonable, it should be reasonable.

Encourage them to try boldly, and encourage them to actively expound their views and exchange their views. In this process, many valuable things will certainly emerge in the classroom. Teachers should be careful to protect students' spirit of inquiry, and don't deny a method easily in one or two sentences. Teachers should not rush to judge, give children a relaxed atmosphere, let children learn to constantly adjust and reflect, and improve their judgment ability.

Question 4: How to help students understand common quantities by relying on realistic situations?

1. What is the requirement of "public quantity" in Curriculum Standards?

In primary school, the "commonly used quantity" basically appeared in the first period, mainly including monetary unit, time unit and weight unit. This part of the revised curriculum standard has not changed much. However, in the past teaching, some teachers did not fully implement the specific requirements of "understanding common quantities" in the curriculum standards. For the teaching of this part of the content, some teachers just stay to let students know these common quantities and can convert them between simple units. Then, in view of this problem, how should we accurately implement the specific goal of "understanding common quantities" in classroom teaching?

Second, how to help students understand common quantities

(A) relying on real life situations to help students understand common quantities.

Mathematics curriculum standards advocate students to feel mathematics in life situations. Professor Geng Shuang's grams and kilograms, and Professor Zhu Jie's cognition time, the first primary school affiliated to Beijing Xuanwu Normal University, can help students reflect and understand common quantities according to real life.

In the lesson of "grams and kilograms", Mr. Geng pays attention to relying on real life situations and introduces learning from the life situations that students are familiar with (all kinds of goods bought from supermarkets and common situations related to grams and kilograms in life), which reveals the learning content of this lesson. This introduction can better stimulate students' interest, at the same time give children the opportunity to discover math problems, and also let students feel the close connection between "grams and kilograms" and daily life.

In the lesson of "Knowing Time", Mr. Zhu combines knowing time with students' work and rest time at school, arouses students' existing and familiar life experience, and helps them to know clocks and watches and understand common time units.

(B) relying on real activity situations to help students understand common quantities.

Practice is the best teacher, and students will be more impressed only by personal experience. Therefore, in addition to relying on realistic life situations, we can also rely on realistic activity situations to help students understand common quantities and establish a correct concept of quality and time.

For example, it is difficult for students to learn "grams and kilograms". Although students have come into contact with quality problems in their lives and feel that they are too light and too heavy, they have seen kilograms and grams on commodity labels, but most students do not know that they are quality units, nor do they know the progress between them, let alone the weight of 1 gram or 1 kg. And people's perception of quality is not strong, the same things are weighed and lifted, left hand and right hand, everyone's tolerance and so on. And I feel the result is different. At the same time, the volume and mass of an object are not necessarily uniform, which makes it difficult for students to understand the unit of mass. In the process of teaching grams and kilograms, Mr. Geng, the first primary school affiliated to Xuanwu Teachers College, prepared a large number of operable items for students, leaving room for students to explore, so that students can know grams and kilograms through weighing and weighing activities in the process of feeling 1 kg and 1 kg, and at the same time help students establish a correct quality concept.

For another example, the understanding of time unit is a very abstract concept for students. Without visible and tangible shapes and colors, they are invisible and intangible, so it is difficult for them to grasp the abstract concept of time. Therefore, the development of children's sense of time must be related to specific events in daily life, so as to have practical content. What can students do after 1 minute in the course of "Knowing Time"? (You can bounce the ball a few times, jump rope a few times, and write a few times), so that students can experience, feel and understand how long 1 minute is, and help them establish the concept of time.

Third, the teaching suggestions about "common quantity"

(1) Strive for the cooperation and support of parents, let students learn "common quantity" in advance, and accumulate life experience.

Because the content of "common quantity" is abstract for the students in the first period, whether they have enough life experience will affect the learning of this part of knowledge. If students can often come into contact with relevant knowledge in their daily life, they can learn well in this respect. For example, if students have the experience of shopping with their parents, it will be much easier to learn RMB. On the contrary, the lack of life experience will make it difficult for students to understand and cause learning difficulties.

(B) the use of a variety of teaching strategies, the "common quantity" and real life organically.

In teaching, we should pay attention to the use of various teaching strategies to make the study of "common quantity" closer to students. We should pay attention to providing students with a variety of learning materials, making full use of learning tools, mobilizing students' multiple senses to participate in learning, providing students with opportunities for hands-on practice, independent exploration, observation and thinking, discovery and expression, stimulating students' participation consciousness and enthusiasm, and letting students learn to use what they have learned to solve practical problems in practice.