Shanghai Suanli
Publish: 2021-04-15 11:14:23
1. Introction: Qiantong bit (Shanghai) Information Technology Co., Ltd. is a company mainly committed to blockchain services, realizing the digital asset of computer computing power, so that every investor can participate in the operation of computing power
legal representative: Lin Meihua
time of establishment: February 8, 2018
registered capital: RMB 100 million
business registration number: 310115003604701
enterprise type: limited liability company (invested or controlled by natural person)
address: room 141-24, building 3, 2111 Beiyan highway, Chongming District, Shanghai (Chongming forest tourism park, Shanghai)
legal representative: Lin Meihua
time of establishment: February 8, 2018
registered capital: RMB 100 million
business registration number: 310115003604701
enterprise type: limited liability company (invested or controlled by natural person)
address: room 141-24, building 3, 2111 Beiyan highway, Chongming District, Shanghai (Chongming forest tourism park, Shanghai)
2. In the twinkling of an eye, I taught from grade one to grade four. Every time I finish a unit, I have to do a small exercise. Originally, the problem of hands-on operation has always been a difficult point for students, and they generally do not master it well. This time, however, the reverse happened. Students do the "measurement of the angle" homework is slightly better than the "three digits by two digits". This may have something to do with my usual training of students' practical ability, but at the same time, it makes me realize the importance of calculation again. So, I calm down, decided to improve the students' computing ability to a new height. Through the later training, students seldom make mistakes in unit 5 division by two digits
first, create a situation for students to pay attention to their thoughts and fully realize the importance of calculation.
I created such a situation: "students, have you ever seen building houses“ Some said "yes."“ What should be the first place to build a house? " At this time, basically no one knows. So, I went on to say, "to build a house, you need to build the foundation first." At the same time, with video, let the children know the process of building houses“ What will happen if the foundation is not firmly laid? " Next, a 13 story building under construction collapsed in Jingyuan community on the Bank of Lianhua River in Shanghai on June 27, 2009. After reading, I continued to talk: "students, the consequences of not laying a solid foundation are serious?"“ Serious. "“ In fact, the calculation in our mathematics is the same as that of the foundation. If we don't do the calculation well, our kingdom of mathematics will collapse just like the building in the picture just now. Therefore, we must do the calculation well, so that our kingdom of mathematics will become more and more brilliant. "< The great scientist Einstein said: "interest is the best teacher." It shows that as long as a person has a strong interest in something, he will take the initiative to seek knowledge, explore and practice, and proce ability in the process of seeking knowledge, exploring and practice, so as to turn low efficiency into high efficiency
(1) to stimulate students' interest in calculation by telling stories about mathematicians when they were young
it is almost common for children to like listening to stories. Among them, I told the students a famous story of Gauss hour: one day when school was about to end in the afternoon, many students in a class were not very disciplined. The teacher intended to punish these children gently, so he put forward a question (natural number from 1 to 100): 1 + 2 + 3 + 4... + 97 + 98 + 99 + 100 = (), and then he went home from school“ Students, can you calculate this problem? " Many children shook their heads“ Then let's listen to the story. " The students quickly took out the paper and pen to calculate, but one child did not do it, as if thinking. Soon the child worked out the answer. The method he used is to sum 50 pairs of sequences (1 + 100, 2 + 99, 3 + 98...) of construction sum 101, and get the result: 5050. The child's name was Gauss, and he was only nine years old that year. Later, Gauss became a famous German mathematician, physicist, astronomer, geometer and geodesist. After listening, the students adore Gauss and have a strong interest in calculation
(2) to stimulate students' interest in calculation by using one problem to do more calculation
in the usual calculation teaching, we should be good at training students' computational thinking ability. For example, when learning multiplication and addition calculation in grade two, there is a problem: it's a calculation problem of looking at the diagram, drawing four plates of peaches, six in each of the first three plates, and five in the fourth plate. How many peaches are there in total? Almost all the children are like this × 3 + 5 = 23 × 3 = 18, then 18 + 5 = 23. At this point, I asked, "is there any other algorithm?" The children are trying slowly. Finally, there are children and a new algorithm: 6 × 4-1 = 23 (pieces). If you take the last set as 6, there will be 4 6, and you will get 24. If you calculate one more, you will lose one, and you will get 23. Then, I asked the students to compare, which one is faster? Students quickly understand that the second algorithm is much faster, which stimulates students' interest in computing< Third, strengthen the cultivation of oral calculation ability
the "Primary School Mathematics Syllabus" points out: "to cultivate students' calculation ability, we should pay attention to basic oral calculation training. Oral calculation is not only the basis of written calculation, estimation and simple calculation, but also an important part of calculation ability." If the ability of oral calculation is strong, the speed of written calculation will be fast, and the accuracy of calculation will be improved. From the first grade, we should pay attention to the practice of addition and subtraction. If we can skillfully calculate the addition and subtraction within 20, it will be of great help to the calculation of multiplication and division. For example, when students learn the unit of "three digits multiplied by two digits", some students make mistakes when they encounter this problem: 389 × 28, the first step is 389 × 8 was originally equal to 3112, but some got 3002, 3222... The problem is that 7 + 4 is not right< Fourth, cultivate good habit of calculation.
French scholar Bacon said: "habit is the master of life, people should strive to pursue good habit." So, to some extent, good habits can determine our destiny. Good calculation habits directly affect students' calculation ability. Often some students can correctly understand and master the calculation rules, but they still make mistakes. The main reason is that they don't form a good habit of calculation< In the first grade, I purposely put out a few questions on the blackboard for students to in the book. The students are required to proofread the copied topics carefully, ranging from numbers and symbols, so as to make sure they are good
2. Develop the habit of examining questions
I ask students to see clearly every data and operation symbol in the questions, determine the operation order, and choose a reasonable operation method< (2) develop the habit of checking calculation
I let the students learn the checking method of addition, subtraction, multiplication and division, and make strict requirements on checking calculation as an important part of the calculation process, and advocate using estimation to check the correctness of the answers
in a word, it's not a matter of a day to improve the fourth grade students' computing ability. We should take it as a long-term work. As long as teachers and students make unremitting efforts together for a long time, the students' computing ability will reach a new level.
first, create a situation for students to pay attention to their thoughts and fully realize the importance of calculation.
I created such a situation: "students, have you ever seen building houses“ Some said "yes."“ What should be the first place to build a house? " At this time, basically no one knows. So, I went on to say, "to build a house, you need to build the foundation first." At the same time, with video, let the children know the process of building houses“ What will happen if the foundation is not firmly laid? " Next, a 13 story building under construction collapsed in Jingyuan community on the Bank of Lianhua River in Shanghai on June 27, 2009. After reading, I continued to talk: "students, the consequences of not laying a solid foundation are serious?"“ Serious. "“ In fact, the calculation in our mathematics is the same as that of the foundation. If we don't do the calculation well, our kingdom of mathematics will collapse just like the building in the picture just now. Therefore, we must do the calculation well, so that our kingdom of mathematics will become more and more brilliant. "< The great scientist Einstein said: "interest is the best teacher." It shows that as long as a person has a strong interest in something, he will take the initiative to seek knowledge, explore and practice, and proce ability in the process of seeking knowledge, exploring and practice, so as to turn low efficiency into high efficiency
(1) to stimulate students' interest in calculation by telling stories about mathematicians when they were young
it is almost common for children to like listening to stories. Among them, I told the students a famous story of Gauss hour: one day when school was about to end in the afternoon, many students in a class were not very disciplined. The teacher intended to punish these children gently, so he put forward a question (natural number from 1 to 100): 1 + 2 + 3 + 4... + 97 + 98 + 99 + 100 = (), and then he went home from school“ Students, can you calculate this problem? " Many children shook their heads“ Then let's listen to the story. " The students quickly took out the paper and pen to calculate, but one child did not do it, as if thinking. Soon the child worked out the answer. The method he used is to sum 50 pairs of sequences (1 + 100, 2 + 99, 3 + 98...) of construction sum 101, and get the result: 5050. The child's name was Gauss, and he was only nine years old that year. Later, Gauss became a famous German mathematician, physicist, astronomer, geometer and geodesist. After listening, the students adore Gauss and have a strong interest in calculation
(2) to stimulate students' interest in calculation by using one problem to do more calculation
in the usual calculation teaching, we should be good at training students' computational thinking ability. For example, when learning multiplication and addition calculation in grade two, there is a problem: it's a calculation problem of looking at the diagram, drawing four plates of peaches, six in each of the first three plates, and five in the fourth plate. How many peaches are there in total? Almost all the children are like this × 3 + 5 = 23 × 3 = 18, then 18 + 5 = 23. At this point, I asked, "is there any other algorithm?" The children are trying slowly. Finally, there are children and a new algorithm: 6 × 4-1 = 23 (pieces). If you take the last set as 6, there will be 4 6, and you will get 24. If you calculate one more, you will lose one, and you will get 23. Then, I asked the students to compare, which one is faster? Students quickly understand that the second algorithm is much faster, which stimulates students' interest in computing< Third, strengthen the cultivation of oral calculation ability
the "Primary School Mathematics Syllabus" points out: "to cultivate students' calculation ability, we should pay attention to basic oral calculation training. Oral calculation is not only the basis of written calculation, estimation and simple calculation, but also an important part of calculation ability." If the ability of oral calculation is strong, the speed of written calculation will be fast, and the accuracy of calculation will be improved. From the first grade, we should pay attention to the practice of addition and subtraction. If we can skillfully calculate the addition and subtraction within 20, it will be of great help to the calculation of multiplication and division. For example, when students learn the unit of "three digits multiplied by two digits", some students make mistakes when they encounter this problem: 389 × 28, the first step is 389 × 8 was originally equal to 3112, but some got 3002, 3222... The problem is that 7 + 4 is not right< Fourth, cultivate good habit of calculation.
French scholar Bacon said: "habit is the master of life, people should strive to pursue good habit." So, to some extent, good habits can determine our destiny. Good calculation habits directly affect students' calculation ability. Often some students can correctly understand and master the calculation rules, but they still make mistakes. The main reason is that they don't form a good habit of calculation< In the first grade, I purposely put out a few questions on the blackboard for students to in the book. The students are required to proofread the copied topics carefully, ranging from numbers and symbols, so as to make sure they are good
2. Develop the habit of examining questions
I ask students to see clearly every data and operation symbol in the questions, determine the operation order, and choose a reasonable operation method< (2) develop the habit of checking calculation
I let the students learn the checking method of addition, subtraction, multiplication and division, and make strict requirements on checking calculation as an important part of the calculation process, and advocate using estimation to check the correctness of the answers
in a word, it's not a matter of a day to improve the fourth grade students' computing ability. We should take it as a long-term work. As long as teachers and students make unremitting efforts together for a long time, the students' computing ability will reach a new level.
3. It's not like that. The life of the graphics card is determined according to the usage. For example, if you play ordinary games, such as crossing the line of Fire Hero League, and the chassis of the same brand has the same heat dissipation, the life of the two graphics cards is almost the same. If you like to play some large games, the 1650 may always be in a full load state, while the 1660 can easily do it 0 will die in front of 1660.
of course, if you are talking about the elimination of performance, the better. You can use it for a long time, and the elimination will be slower
of course, if you are talking about the elimination of performance, the better. You can use it for a long time, and the elimination will be slower
4. Any behavior similar to those listed in the regulations on the prohibition of pyramid selling has not been approved by the Ministry of Commerce. All these behaviors are suspected of violating Article 224 of the criminal law: in the name of business activities such as promoting commodities and providing services, the organization and leaders require the participants to obtain the qualification of joining by paying fees or purchasing commodities and services, and form a hierarchy according to a certain order, directly or indirectly taking the number of development personnel as the basis of remuneration or rebate, to lure the participants Whoever coerces participants to continue developing pyramid selling activities in which others participate, swindles money or property, or disturbs economic and social order shall be sentenced to fixed-term imprisonment of not more than five years or criminal detention and shall also be fined; If the circumstances are serious, the offender shall be sentenced to fixed-term imprisonment of not less than five years and be punished for any act similar to those listed in the regulations on the prohibition of pyramid schemes without the approval of the Ministry of Commerce. All these behaviors are suspected of violating Article 224 of the criminal law: in the name of business activities such as promoting commodities and providing services, the organization and leaders require the participants to obtain the qualification of joining by paying fees or purchasing commodities and services, and form a hierarchy according to a certain order, directly or indirectly taking the number of development personnel as the basis of remuneration or rebate, to lure the participants Whoever coerces participants to continue developing pyramid selling activities in which others participate, swindles money or property, or disturbs economic and social order shall be sentenced to fixed-term imprisonment of not more than five years or criminal detention and shall also be fined; If the circumstances are serious, he shall be sentenced to fixed-term imprisonment of not less than five years and be punished
5. The ratio increasing method and the equal difference increasing method are two methods to calculate the rent in the leasing business. According to its basic formula, we can dece and calculate that if the rent is calculated and paid according to the equal proportion increasing method, the actual rent rate will drop, or even drop by a large margin, resulting in the loss of the interests of the lessor; If the rent is calculated according to the equal difference increasing method, the actual rent rate is always equal to the nominal rent rate, and the calculation is simple. Therefore, the equal difference incremental method is more fair, reasonable and practical than the equal ratio incremental method
with the continuous deepening of China's middle school teaching reform, the Shanghai primary and secondary school mathematics curriculum standard (Trial draft) proposes to vigorously promote the digital mathematics activity (Dima) based on modern information technology, and establish the digital mathematics activity system based on computers and calculators (including scientific calculators Function calculator and graphic calculator) as the support, has intelligent software and rich courseware, connection information network Dima platform. Using this platform, we can improve the processing and presentation of mathematics content, and let students learn independently in the information technology environment, and carry out experiments, exploration and research
today, when we vigorously promote the universal application of information technology in the teaching process and promote the integration of information technology and subject curriculum, our school is also implementing the curriculum reform, and the graphic calculator is also applied to the classroom of mathematics expansion course. For this reason, we designed a teaching case of "using graphic calculator to study several methods of expressing arithmetic and proportional sequence"< Teaching background:
in the chapter of sequence, when explaining the concepts of arithmetic sequence and arithmetic sequence, the content is relatively simple and easy for students to master. It is the basis of learning sequence, which is helpful to cultivate students' observation ability and inction ability. The contents of the equal ratio sequence and the equal difference sequence are completely parallel, including the definition, the nature, the formula of the general term, the equal ratio (difference) median of two numbers, etc
after more than half a year of using graphic calculators, senior one students have a preliminary understanding of using graphic calculators to analyze, construct and explore mathematical problems. They felt that the use of graphic calculator not only changed their way of learning mathematics, but also increased their interest in learning mathematics. They like this "do math" way of learning very much
Graphic Calculator has many functions to use sequence, such as the use of general formula and recursive formula of sequence, sequence image and image tracking function, expression function of sequence operation table, iteration function of sequence, programming function of sequence, etc. All these have played a great role in learning the basic knowledge of sequence, correctly understanding sequence, making students experience the cognitive process of formula, understand the mathematical thinking method, and improve the ability of problem-solving in the effective attempt to guess, reasonable inction, simplified operation and verification operation< The design concept of the lesson is the core of the whole series knowledge learning. Conjecture, inction, recursion, analogy and other mathematical ideas are fully reflected in the learning of these two basic knowledge, which can be described as "although a sparrow is small, it has all five internal organs". However, it is difficult to fully and correctly show these in the traditional sequence teaching. This will lead to students' one-sided understanding of what they have learned, which will have a negative impact on the follow-up study of sequence. The graphic calculator has many functions to use the sequence, such as the use of the general formula and recursive formula, the image and image tracking function, the expression function of the operation table, the iteration function and the programming function of the sequence. All these have played a great role in learning the basic knowledge of sequence, correctly understanding sequence, making students experience the cognitive process of formula, understand the mathematical thinking method, and improve the ability of problem-solving in the effective attempt to guess, reasonable inction, simplified operation and verification operation. Therefore, we envisage that students can have a clear understanding of the two conventional series by studying and expressing the series with graphic calculator. At the same time, we also want to cultivate students' initiative and inquiry spirit and improve their mathematics learning ability through this learning process<
Design and Implementation:
the teaching content of the new textbook pays more attention to the integration of function thought and computer technology. From the beginning of this chapter, the textbook puts the number sequence in the context of function and gives the definition: the number sequence is a function with a positive integer set (or its finite subset) as the domain of definition. When the independent variable values in the order from small to large, the corresponding function value is the term of the number sequence. Sequence is a kind of discrete function. In the allocation of exercises, teaching materials are often compared with function teaching. The general term formula, recurrence formula and image of arithmetic sequence and proportional sequence are the main contents of our research in this lesson. We imagine that with the help of graphic calculator, we can make students have a vivid, comprehensive and correct understanding of sequence knowledge by doing mathematics, so as to improve students' mathematical thinking ability and cultivate students' correct mathematical view, Really improve students' interest in mathematics learning
case 1 (1) find the 11th term of the arithmetic sequence - 121, - 110, - 99, - 88,...
2) write the general term formula and recurrence formula of the sequence
for this problem, in fact, according to its basic law, you can calculate the result. But using graphic calculator can make us think about the solution of the problem from many angles, which is concive to students' comprehensive and correct understanding of the characteristics of arithmetic sequence, so as to simplify the calculation
method 1: use the numerical iteration function (as shown in Figure 1):
①
method 2: use the array function of the graphic calculator (as shown in Figure 2):
②
method 3: use the recursive function of the calculator
Figure 3: Use & iquest on the premise of setting the function function function; Key, which is the same as Figure 1< Method 4: guess the recurrence formula and the general term formula of the sequence, check whether the recurrence formula and the general term formula of the sequence are correct through the sequence related function of the calculator, and calculate the 11th term of the sequence:
Figure 4 guesses the recurrence formula of the sequence according to the characteristics of the sequence, Using the function of figure calculator, using Y & # 39; Draw a table
④
Fig. Then, we also use y & # 39; Draw a table< Note: while solving this problem, we can also verify that "the general term formula of arithmetic sequence is a special first-order function" through graphic calculator
as shown in Figure 7, we can get that the image of sequence is a discrete point on a straight line, from which we can see that sequence is a special function< Method 5: because the number sequence is a special function, we use the function of graphic calculator to think about the problem.
figure 8 is under the cognitive condition of "the number sequence is a special function", we use the function of calculator to get the function y = - 121 + 11 (x-1), and use the connection between the function and the number sequence an = - 121 + (n-1) to think about the related problems of the number sequence< Method 6: make full use of the function fitting function of the graphic calculator to get the general term formula of the sequence through the combination of number and shape
Figure 9: use the linear regression function of the graphic calculator to list the table of the sequence first, and then connect the general term formula of the arithmetic sequence with the first-order function according to the data in the table, By using the fitting function of graphic calculator, the function relation is obtained, and the general term formula of sequence is obtained< Method 7: use the programming function of graphic calculator to solve the problem of sequence (as shown in Figure 10)
10
comments: Method 1 and method 2 use the iterative function of calculator, but method 2 shows the corresponding relationship between the serial number and the value of the item in the sequence, from which we initially realize that the sequence is a special function
the fourth method is to guess the recurrence formula and general term formula of the sequence, under the support of the sequence function of the calculator, from the operation table of the sequence or the tracking of the image of the sequence to verify whether your guess is correct, and get the answer to the problem to be solved. This kind of learning method is helpful to cultivate students' ability of analysis, conjecture, demonstration and inction. This is what we lack in our regular learning, and the use of graphic calculator has built us such a learning method platform
method 6 and method 7 are both under the condition that the number sequence is a special function. Supported by the function function of the calculator, we find a way to solve the problem by guessing or fitting the analytic formula of the function, which is helpful for students to learn the knowledge of the number sequence and understand the characteristics of the number sequence, Method 8 adopts the programming function of graphic calculator, which can't be achieved in general mathematics teaching. It reveals the essence of arithmetic sequence from another perspective< (3) is 209 the item in the sequence, and if so, what is it< Method 1, array method 2, table method 3, image method 4, equation solving method the purpose of setting this question is: on the basis of the first question, using the functions of operation, tracking and equation solving of graphic calculator to cultivate students' reverse thinking and improve their mathematical thinking ability
it should be pointed out that the sequence we discussed above is tolerance D & gt; 0, for beginners, they often have certain thinking set, such as: "tolerance D & gt; In order to avoid similar problems, we especially remind students to pay attention to the differences between the following two types of sequence
(1) constant sequence (2) arithmetic sequence with negative tolerance
- 2, - 2,... 3, 1, - 1, - 3, ...
students should have a correct understanding of the dialectical relationship between general and special<
case 2: make up a topic of equal ratio series, and study the related properties of equal ratio series
find out typical problems from students' many problems, and study them together with teachers and students, including the examples in the book
(in real life, such as loan to buy a house, population growth and the change of housing area - pay attention to the hot issues around the people, Pay attention to guide students to apply their knowledge to related subjects, life and proction practice, so that students can develop their thinking ability while acquiring and applying knowledge, so that students can use existing knowledge to communicate, and abstract practical problems into mathematical problems and establish mathematical models.)
such as "a foot of the hammer, half of the day, never exhausted", and asked to say its mathematical model, find out its general formula
(both new and old textbooks and textbooks are being compiled, etc.)
with the continuous deepening of China's middle school teaching reform, the Shanghai primary and secondary school mathematics curriculum standard (Trial draft) proposes to vigorously promote the digital mathematics activity (Dima) based on modern information technology, and establish the digital mathematics activity system based on computers and calculators (including scientific calculators Function calculator and graphic calculator) as the support, has intelligent software and rich courseware, connection information network Dima platform. Using this platform, we can improve the processing and presentation of mathematics content, and let students learn independently in the information technology environment, and carry out experiments, exploration and research
today, when we vigorously promote the universal application of information technology in the teaching process and promote the integration of information technology and subject curriculum, our school is also implementing the curriculum reform, and the graphic calculator is also applied to the classroom of mathematics expansion course. For this reason, we designed a teaching case of "using graphic calculator to study several methods of expressing arithmetic and proportional sequence"< Teaching background:
in the chapter of sequence, when explaining the concepts of arithmetic sequence and arithmetic sequence, the content is relatively simple and easy for students to master. It is the basis of learning sequence, which is helpful to cultivate students' observation ability and inction ability. The contents of the equal ratio sequence and the equal difference sequence are completely parallel, including the definition, the nature, the formula of the general term, the equal ratio (difference) median of two numbers, etc
after more than half a year of using graphic calculators, senior one students have a preliminary understanding of using graphic calculators to analyze, construct and explore mathematical problems. They felt that the use of graphic calculator not only changed their way of learning mathematics, but also increased their interest in learning mathematics. They like this "do math" way of learning very much
Graphic Calculator has many functions to use sequence, such as the use of general formula and recursive formula of sequence, sequence image and image tracking function, expression function of sequence operation table, iteration function of sequence, programming function of sequence, etc. All these have played a great role in learning the basic knowledge of sequence, correctly understanding sequence, making students experience the cognitive process of formula, understand the mathematical thinking method, and improve the ability of problem-solving in the effective attempt to guess, reasonable inction, simplified operation and verification operation< The design concept of the lesson is the core of the whole series knowledge learning. Conjecture, inction, recursion, analogy and other mathematical ideas are fully reflected in the learning of these two basic knowledge, which can be described as "although a sparrow is small, it has all five internal organs". However, it is difficult to fully and correctly show these in the traditional sequence teaching. This will lead to students' one-sided understanding of what they have learned, which will have a negative impact on the follow-up study of sequence. The graphic calculator has many functions to use the sequence, such as the use of the general formula and recursive formula, the image and image tracking function, the expression function of the operation table, the iteration function and the programming function of the sequence. All these have played a great role in learning the basic knowledge of sequence, correctly understanding sequence, making students experience the cognitive process of formula, understand the mathematical thinking method, and improve the ability of problem-solving in the effective attempt to guess, reasonable inction, simplified operation and verification operation. Therefore, we envisage that students can have a clear understanding of the two conventional series by studying and expressing the series with graphic calculator. At the same time, we also want to cultivate students' initiative and inquiry spirit and improve their mathematics learning ability through this learning process<
Design and Implementation:
the teaching content of the new textbook pays more attention to the integration of function thought and computer technology. From the beginning of this chapter, the textbook puts the number sequence in the context of function and gives the definition: the number sequence is a function with a positive integer set (or its finite subset) as the domain of definition. When the independent variable values in the order from small to large, the corresponding function value is the term of the number sequence. Sequence is a kind of discrete function. In the allocation of exercises, teaching materials are often compared with function teaching. The general term formula, recurrence formula and image of arithmetic sequence and proportional sequence are the main contents of our research in this lesson. We imagine that with the help of graphic calculator, we can make students have a vivid, comprehensive and correct understanding of sequence knowledge by doing mathematics, so as to improve students' mathematical thinking ability and cultivate students' correct mathematical view, Really improve students' interest in mathematics learning
case 1 (1) find the 11th term of the arithmetic sequence - 121, - 110, - 99, - 88,...
2) write the general term formula and recurrence formula of the sequence
for this problem, in fact, according to its basic law, you can calculate the result. But using graphic calculator can make us think about the solution of the problem from many angles, which is concive to students' comprehensive and correct understanding of the characteristics of arithmetic sequence, so as to simplify the calculation
method 1: use the numerical iteration function (as shown in Figure 1):
①
method 2: use the array function of the graphic calculator (as shown in Figure 2):
②
method 3: use the recursive function of the calculator
Figure 3: Use & iquest on the premise of setting the function function function; Key, which is the same as Figure 1< Method 4: guess the recurrence formula and the general term formula of the sequence, check whether the recurrence formula and the general term formula of the sequence are correct through the sequence related function of the calculator, and calculate the 11th term of the sequence:
Figure 4 guesses the recurrence formula of the sequence according to the characteristics of the sequence, Using the function of figure calculator, using Y & # 39; Draw a table
④
Fig. Then, we also use y & # 39; Draw a table< Note: while solving this problem, we can also verify that "the general term formula of arithmetic sequence is a special first-order function" through graphic calculator
as shown in Figure 7, we can get that the image of sequence is a discrete point on a straight line, from which we can see that sequence is a special function< Method 5: because the number sequence is a special function, we use the function of graphic calculator to think about the problem.
figure 8 is under the cognitive condition of "the number sequence is a special function", we use the function of calculator to get the function y = - 121 + 11 (x-1), and use the connection between the function and the number sequence an = - 121 + (n-1) to think about the related problems of the number sequence< Method 6: make full use of the function fitting function of the graphic calculator to get the general term formula of the sequence through the combination of number and shape
Figure 9: use the linear regression function of the graphic calculator to list the table of the sequence first, and then connect the general term formula of the arithmetic sequence with the first-order function according to the data in the table, By using the fitting function of graphic calculator, the function relation is obtained, and the general term formula of sequence is obtained< Method 7: use the programming function of graphic calculator to solve the problem of sequence (as shown in Figure 10)
10
comments: Method 1 and method 2 use the iterative function of calculator, but method 2 shows the corresponding relationship between the serial number and the value of the item in the sequence, from which we initially realize that the sequence is a special function
the fourth method is to guess the recurrence formula and general term formula of the sequence, under the support of the sequence function of the calculator, from the operation table of the sequence or the tracking of the image of the sequence to verify whether your guess is correct, and get the answer to the problem to be solved. This kind of learning method is helpful to cultivate students' ability of analysis, conjecture, demonstration and inction. This is what we lack in our regular learning, and the use of graphic calculator has built us such a learning method platform
method 6 and method 7 are both under the condition that the number sequence is a special function. Supported by the function function of the calculator, we find a way to solve the problem by guessing or fitting the analytic formula of the function, which is helpful for students to learn the knowledge of the number sequence and understand the characteristics of the number sequence, Method 8 adopts the programming function of graphic calculator, which can't be achieved in general mathematics teaching. It reveals the essence of arithmetic sequence from another perspective< (3) is 209 the item in the sequence, and if so, what is it< Method 1, array method 2, table method 3, image method 4, equation solving method the purpose of setting this question is: on the basis of the first question, using the functions of operation, tracking and equation solving of graphic calculator to cultivate students' reverse thinking and improve their mathematical thinking ability
it should be pointed out that the sequence we discussed above is tolerance D & gt; 0, for beginners, they often have certain thinking set, such as: "tolerance D & gt; In order to avoid similar problems, we especially remind students to pay attention to the differences between the following two types of sequence
(1) constant sequence (2) arithmetic sequence with negative tolerance
- 2, - 2,... 3, 1, - 1, - 3, ...
students should have a correct understanding of the dialectical relationship between general and special<
case 2: make up a topic of equal ratio series, and study the related properties of equal ratio series
find out typical problems from students' many problems, and study them together with teachers and students, including the examples in the book
(in real life, such as loan to buy a house, population growth and the change of housing area - pay attention to the hot issues around the people, Pay attention to guide students to apply their knowledge to related subjects, life and proction practice, so that students can develop their thinking ability while acquiring and applying knowledge, so that students can use existing knowledge to communicate, and abstract practical problems into mathematical problems and establish mathematical models.)
such as "a foot of the hammer, half of the day, never exhausted", and asked to say its mathematical model, find out its general formula
(both new and old textbooks and textbooks are being compiled, etc.)
6. At present, calculators are not allowed to be used in college entrance examination in all parts of the country except Shanghai. In the high school entrance examination, the use of different places, there are also reciprocating situation. Those who disapprove of using calculators should pay attention to the cultivation of students' mental calculation ability and regard mental calculation as an important calculation ability. This is relative to simple operations< In addition, besides the ability of spatial thinking, logical ability and problem-solving ability, the ability of calculation is also the focus of the test.
7. Brief introction: RRC hopes to build a distributed supercomputing network for personal terminals through blockchain technology, promote the computing power trading market of personal terminals, and form a computing power ecosystem. Build a distributed computing network with independent public chain and a global computing power trading platform
legal representative: Hu Jiawei
time of establishment: August 29, 2017
registered capital: RMB 15833330000
Instrial and commercial registration number: 310114003348254
enterprise type: limited liability company (joint venture of foreign-invested enterprise and domestic capital)
address: room j3224, building 2, No. 4268, Zhennan Road, Jiading District, Shanghai
legal representative: Hu Jiawei
time of establishment: August 29, 2017
registered capital: RMB 15833330000
Instrial and commercial registration number: 310114003348254
enterprise type: limited liability company (joint venture of foreign-invested enterprise and domestic capital)
address: room j3224, building 2, No. 4268, Zhennan Road, Jiading District, Shanghai
8.
the upcoming Shanghai auto show is the first large-scale international auto show of this year, and it is in the key node after the epidemic. It is basically certain that major auto companies will show their muscles, and electrification is the general trend, which will naturally be the highlight of this auto show. According to the information disclosed, overseas auto companies and independent brands all have heavy models, The above-mentioned models are only a part of them. In the future, I will continue to follow up the Shanghai auto show. You are welcome to continue to pay attention to them
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