One: the teaching content of number and algebra
The first grade is 1, and the number in life is between 10 and 100;
2. Compare the numbers in 10 and 100;
3. Addition and subtraction of numbers within10, 20 and 100;
4. Know the clock;
5. shopping;
Second grade, 1, number one and multiplication, understand the meaning of multiplication;
2. Learn multiplication formula;
3. Divide into one point and two points to understand the meaning of two points and the reciprocal relationship between two points and three points;
4. Hours, minutes and seconds;
5. Addition, subtraction, multiplication and division, addition, subtraction, multiplication and division, addition, subtraction, multiplication and division, and two-step parenthesis;
6. Cognition and learning of numbers within 10 thousand, addition and subtraction of numbers within 10 thousand;
Grade 3: within 1, 100, one digit is multiplied by two digits, and one digit is divided by two digits;
2. Understanding and learning of kilograms, grams and tons;
3. Double multiplication of two digits by one digit, three digits by one digit, and two digits by two digits;
4. The mixed operation of dividing two or three digits by one digit and the cultivation of estimation consciousness;
5. Study by year, month and day;
6. A preliminary understanding of the score;
Fourth grade 1, know the number within 100 million;
2. Three digits multiplied by two digits;
3, three digits divided by integer ten, three digits divided by two digits, this is the last learning content of integer operation in primary school;
4. Preliminary understanding of negative numbers;
5. Understanding decimals and learning decimal addition and subtraction, decimal multiplication and decimal division;
6. Understand the equation;
Grade 5: 1, multiples and factors;
2. Identification of scores;
3. Learning of fractional addition, subtraction, fractional multiplication and fractional division;
4. Fractional mixed operation;
5. Percent learning;
The application of 1 and percentage in the sixth grade;
2. Understanding of the ratio;
3. Positive and negative proportional learning;
Second, the number and algebra teaching specific objectives
In this part of the narrative, the whole textbook is divided into two parts, the first phase (1-3 grade) and the second phase (4-6 grade).
(A) the specific objectives of the first stage
1: Understanding of Numbers
(1) can recognize, read and write numbers within 10000, and use numbers to indicate the number of objects or the order and position of things.
(2) Understand the meaning of symbols, =, and be able to describe the number of players with symbols and words. Case: For the numbers 50, 98, 38, 10, 5 1, please describe the relationship between them in terms of bigger, smaller, much bigger and much smaller. And use ""to indicate their size relationship.
(3) Be able to name each number and identify the meaning of the number on each number.
(4) estimate the significance of large numbers in combination with real materials. Case1:1how thick is 200 sheets of paper? 1200 how many classes can students form? /kloc-how long is the 0/200 step? Case 2: Estimate the number of words in a newspaper page.
(5) Be able to understand the meaning of fractions in combination with specific situations, and be able to read and write decimals and simple fractions.
(6) be able to use numbers to express some things in daily life and communicate. Case: Please name some figures closely related to daily life and their functions.
2. Number of operations
(1) Combined with the specific situation, I realized the significance of the four operations. It is emphasized here that three fives can be written as 3×5 or 5×3 about multiplication.
(2) Proficient in oral calculation of addition and subtraction within 20 and multiplication and division within the table, and able to oral calculation of addition and subtraction within 100.
(3) can calculate the addition and subtraction of three digits, one digit multiplied by three digits, two digits multiplied by two digits, and three digits divided by one digit.
(4) Calculate the addition and subtraction of fractions with the same denominator (the denominator is less than 10) and the addition and subtraction of one decimal place.
(5) Be able to estimate according to the specific situation and explain the estimation process. Case: If each park ticket is 8 yuan, a school will organize 97 students to visit the park. Is 800 yuan enough?
(6) Experience the process of communicating their respective algorithms with others.
(7) Be able to flexibly use different methods to solve simple problems in life and judge the rationality of the results. Case: Each ship is limited to 4 people. /kloc-how many boats do 0/7 people need to rent? What do you think is an appropriate distribution?
3. Ordinary quantity
(1) In real situations, know elements, angles and points, and understand their relationships.
(2) be able to know clocks and watches and understand the 24-hour timing method; Combine your own life experience and experience the length of time. Case: Estimate the number of pulse beats per minute, reading, skipping and walking steps.
(3) Know the year, month and day and understand the relationship between them.
(4) Feel and understand grams, kilograms and tons in specific life situations, and make a simple conversion.
(5) Solve simple problems related to common usage in combination with real life.
Step 4 explore the law
Discover the simple laws implied in a given thing. Case: Fill in the appropriate figures in the following lines and explain the reasons: 1, 1, 2, 1, 1, 2,-,-;
(B) the specific objectives of the second phase
1: Understanding of Numbers
(1) In a specific situation, recognize, read and write numbers within 100 million, and know the decimal counting method. Large numbers will be expressed in units of 10,000 and 100 million.
(2) Further understand decimals and fractions, and understand percentages; Explore the relationship among decimals, fractions and percentages, and carry out conversion (not including converting circulating decimals into fractions).
(3) Will compare the size of decimals, fractions and percentages.
(4) If we understand the meaning of negative numbers in familiar life situations, we will use negative numbers to express some problems in daily life.
(5) Feel the meaning of large numbers and estimate them in combination with the real situation. Case: How long does it take for a normal person to have a heartbeat of 654.38+00,000? /kloc-How many years is 0/10,000 hours equivalent? /kloc-How thick is 0/10,000 sheets of paper?
(6) further understand the role of numbers in daily life, use numbers to represent things and communicate. Case 1: A school numbers each student, with boys 1 and girls 2 ending; 97 1332 1 means "1997 recruits 32 students from Class 3, Grade 1, Senior High School, all male." So what year did the students represented by 95320 12 enter school? What grade and class are there? What's the student number? Is it a boy or a girl?
(7) From the natural numbers from 1 to 100, all common multiples of a natural number within 10 can be found, and the characteristics of multiples of 2, 3 and 5 can be guided, and the common multiples and minimum common multiples of two natural numbers within 10 can be found.
(8) In the natural number of 1- 100, all the factors of a natural number can be found, and the common factor and the greatest common factor of two natural numbers can be found.
(9) Know integer, odd number, even number, prime number and composite number.
2. Digital operation
(1) You can multiply and divide a number within 100 by two numbers.
(2), will write three digits multiplied by two digits, three digits divided by two digits.
(3) Be able to understand the operation sequence in combination with physical objects and perform simple integer elementary arithmetic (mainly divided into two steps, no more than three).
(4) Explore and understand the algorithm, and be able to use the algorithm to perform some simple operations.
(5) Experience the reciprocal relationship of addition, subtraction, multiplication and division in the process of specific operation and solving simple practical problems.
(6) Simple decimal, decimal (excluding decimal) addition, subtraction, multiplication, Divison and mixed operation (mainly in two steps, no more than three steps) will be carried out separately.
(7) It can solve simple practical problems about decimals, fractions and percentages.
(8) In the process of solving specific problems, we can choose appropriate estimation methods and form the habit of estimation. Case 1: Aunt Li wants to buy two bags of rice (35.4 yuan each),1beef from 4.8 yuan, vegetables from 6.7 yuan,1fish from 2.8 yuan. Aunt Li brought 100. Is that enough? Case 2: What is the approximate result of 9.2× 7. 1? Is the result of 1/2-4/7 greater than 1?
(9) With the help of calculator, we can perform complex operations, solve simple practical problems and explore simple mathematical laws. Case: Given four different numbers arbitrarily, the maximum number and the minimum number are formed, and the maximum number is subtracted from the minimum number. Repeat the above process for the four numbers of the result. What will you find? (using a calculator)
3. Formulas and equations
(1) Numbers are represented by letters in certain cases.
(2) Equation will be used to express the equivalence relation in simple cases.
(3) Understand the properties of the equation and use it to solve simple equations.
4. Positive proportion and inverse proportion
(1) Understand what proportional distribution is in actual situation and solve simple problems.
(2) Through specific problems, the quantity is directly proportional and inversely proportional.
(3) Drawing on grid paper with coordinate system according to the given data in direct proportion, and estimating the value of another quantity according to the value of one quantity. Case: Ribbon per meter 4 yuan. Buy 2 meters, 3 meters, ... ribbons respectively?
Fill in:
Length (m) 0 1 234 567 ...
Price (RMB) 0 4
Draw the points corresponding to the length and price in the above table on the coordinate paper, and then connect them in turn to answer the following questions:
A.are these points on a straight line?
B: How much does it cost to buy a ribbon of 1.5m?
C the length of the ribbon Xiao just bought is three times that of Xiao Hong. How much time did he spend?
(4) Be able to find out examples of positive and negative proportions in life and communicate with them.
Explore the law
Explore the hidden laws or trends in a given thing. Case: At the get-together, Xiaoming strung balloons in the order of 3 red balloons, 2 yellow balloons and 1 green balloon to decorate the room. Do you know what color the 16 balloon is?
Third, the characteristics of the compilation of number and algebra textbooks
Compared with traditional textbooks, this textbook emphasizes that students can experience, feel and understand the meaning of numbers and operations through actual situations, understand the process of establishing numbers and their operation models, emphasize the development of students' sense of numbers and symbols, and pay attention to cultivating students' consciousness and ability to solve simple practical problems by using numbers and operations.
(A) the understanding of quantity
Number is the basic content of mathematics learning, which has important significance and function.
1. Pay attention to let students gradually understand the meaning of numbers from real situations and develop their sense of numbers. Whether it is integer, fraction, decimal or negative number, it is a summary of human life practice and is closely related to solving practical problems. Therefore, the textbook attaches great importance to the connection between numbers and the real world, trying to reveal the process of abstracting numbers from the real world and highlighting the model role of numbers.
2. Provide rich materials for students to understand the relationship between the relative sizes of numbers and get the feeling of large numbers. Comparing the size of numbers is an important part of learning numbers. Textbooks not only simply compare the size relationship between two abstract numbers, but also provide rich materials for students to master the relative size relationship of numbers in specific situations, which is an important aspect of developing students' sense of numbers.
3. Enable students to use numbers to express some things in daily life and communicate.
(2) Number of operations
The mathematics curriculum in our country has always regarded the operation of numbers as the main content of primary school mathematics, and attached importance to cultivating students' operation ability. Digital operation content should pay attention to the following aspects:
1. Experience the process of abstracting the operation from the actual situation and pay attention to the understanding of the operation. With regard to the design of digital operation content, the textbook first pays attention to letting students experience the process of abstracting the operation from the actual situation and paying attention to the understanding of the operation meaning; Establish the internal relationship between actual operation and mathematical operation, so that students can have an intuitive experience in actual operation, find the realistic background of digital operation, and promote students to understand the meaning and essence of operation, and can consciously use it to solve application problems.
2. Attach importance to estimation and be able to estimate the result of operation. Estimation can help students develop their understanding of logarithms and their operations, enhance their flexibility in using numbers and operations, promote their understanding of the rationality of conclusions, reduce errors in operations, and cultivate students' attitude of being responsible for operation results. Therefore, this textbook attaches importance to the cultivation of estimation ability.
3. Encourage diversification of business methods. In the process of trying to calculate, students will produce different calculation methods from their own experience and thinking. In teaching, teachers should encourage reasonable algorithms and cultivate students' self-confidence.
4. Master basic arithmetic and writing skills and avoid complicated operations. This textbook focuses on students' exploration of algorithms and mastery of basic skills. According to students' cognitive characteristics, it adopts colorful forms to ensure students' mastery of skills and stimulate students' interest in learning.
5. Use a calculator to solve practical problems and explore laws. Mathematics curriculum attaches great importance to the use of modern technical means to save students from a large number of complex and repetitive operations and put more experience into practical and exploratory mathematics activities.
6. Effectively solving practical problems is the primary goal for students to learn numbers and operations. Let's talk about the reform of application problems here.
First, simplify the arithmetic application problems that lack practical background and are too skillful, and add some practical problems that are in line with students' experience and have certain mathematical value and exploration.
Second, solving practical problems is a natural part of learning numbers and operations.
Thirdly, downplay the artificially compiled application problems, emphasize the real understanding of the practical and mathematical significance of the problems, and encourage students to find the implicit quantitative relationship in the problems and solve them according to the meaning of the learned mathematical knowledge.
Fourth, pay attention to the diversification of problem solving.
Fifth, the teaching materials focus on providing information and presenting problems in various forms.
Sixth, it is emphasized to test the solution of the problem, not only whether the solution is correct, but also whether the solution of the problem conforms to the reality.
(3) Common quantity
For the common learning of quantity, the textbook emphasizes understanding the practical significance of quantity with the help of students' life experience and understanding the practical significance of the unit of quantity from multiple angles; Can choose the appropriate unit of quantity according to the actual problem; Able to perform simple unit conversion; Combined with the reality of life, solve the practical problems related to common quantities.
(D) Explore the law
Establishing models, researching models and seeking laws are important contents of mathematics learning. This set of teaching materials has designed a large number of activities to explore laws, which are embodied in the following aspects:
First, emphasize the relationship between the number and quantity contained in the operation.
Second, provide opportunities to help students discover the changing laws of numbers, figures and other meaning from various angles and describe them in their own language.
Third, let students know some special relationships.
Fourth, pay attention to the role of symbolic representation and equation model in equation research.
Fourth, the number and algebra teaching suggestions
1. Pay attention to creating situations in teaching, guide students to get in touch with concrete and interesting things around them, and feel and understand the meaning of numbers through rich activities such as observation, operation and problem solving, so as to establish a sense of numbers. Correctly grasp the standards, do not raise the requirements for students, and do not artificially increase the difficulty.
For example, when teaching senior one students to understand the meaning of numbers, they can count the things on campus and describe how many windows, desks and classmates there are in the classroom, so as to realize that numbers have the meaning and function of representing the number of objects. To understand 0, we need to combine the reality and students' life experience to understand the different meanings of 0 in different situations.
When understanding decimals in grade three, start with the shopping that students are familiar with, and initially understand the meaning of decimals; In this kind of teaching, teachers must not raise the requirements for students to accurately describe the meaning of decimals, which will affect students' interest in learning mathematics. As long as students use decimals to express some things in daily life and communicate with each other, they should not artificially increase the difficulty of learning. Decimals are further studied in the fourth grade.
In the teaching of grade three, students are only allowed to understand the meaning of the score in combination with specific situations and intuitive operations, so that students can understand that the score must be average, and there is no need to force students to describe the exact meaning of the score. More in-depth and meticulous study is a new understanding of the first semester score of grade five.
2. In the teaching of number operation, we should attach importance to the cultivation of students' estimation ability, actively advocate the diversification of calculation methods, and let students understand the operation methods in exploration and comparison.
(1) Teachers should pay attention to the training of verbal calculation, which directly determines the students' written calculation ability. The textbook specially arranges a unit of oral multiplication and division in the fifth volume. This is the basis for students to master multiplication and division in tables, and it is also the basis for students to learn multi-digit multiplication and division. Teachers should attach importance to the study of this unit, encourage students to have reasonable oral calculation methods in teaching, and find relatively optimized oral calculation methods in communication and exploration.
(2) Pay attention to the cultivation of students' estimation ability. In our usual teaching, we don't pay enough attention to estimation, and even some teachers give up the content of estimation chapters or pass by. Some teachers ask students to calculate accurately before estimating, and then make appropriate modifications to make the final estimation result. This kind of teaching actually distorts the meaning of estimation, misinterprets the editor's intention and puts the cart before the horse. Therefore, we should first cultivate students' awareness of estimation in teaching, and let students realize the necessity and value of estimation by designing situations. Then, in practical training and specific calculation, let students estimate first and then calculate, and gradually cultivate students' estimation ability.
(3) Encourage the diversification of calculation methods. Because people have different life experiences, thinking habits and understanding abilities, there are different ways to solve problems. At this time, teachers should be patient and give students enough space and time to think independently and try to solve them. Reasonable and unique algorithms should be affirmed and encouraged. Teachers and students should choose the best calculation method instead of telling the general method directly.
(4) The teaching of the Four Arithmetic Method should really let students master the essence of its operation, so as to draw inferences from others and achieve mastery.
In the teaching of addition and subtraction, when students are exposed to addition and subtraction for the first time, that is, integer addition and subtraction, they must emphasize the alignment of the same number of digits, that is, they can add and subtract with the same counting unit. Only by understanding the essence of this operation, the natural decimal points will be aligned when adding and subtracting decimals, and only the same denominator can be directly calculated when adding and subtracting fractions, so it is not difficult for students to understand.
In the teaching of multiplication and division and integer multiplication and division, it is necessary to strengthen training so that students can understand the operation process and lay a solid foundation for the operation of decimal multiplication and division.
3. Teaching strategies of application problems.
Arithmetic application problem is an important content of traditional primary school mathematics curriculum, which aims to cultivate students' ability to solve practical problems by using mathematical operation content. The current textbook defines this part as an effective way to solve practical problems in daily life, so our teachers should grasp the following points when teaching this part:
(1), starting from the lower grades, train students to find mathematical information in the given situation diagram and put forward corresponding questions according to the existing mathematical information. For example, there are the following information in the picture: 6 ducks, 3 monkeys, 2 squirrels, 12 birds, 1 peacock and 8 chickens. You can propose a division based on this information. At this time, students will use the multiple knowledge they have learned to choose relevant information to ask questions; You can also train in reverse: What information do you need to know to solve a problem? How many people are there in grade two than in grade three? To solve this problem, students will definitely think, how many students are there in Grade Two? How many people are there in grade three? We teachers should not underestimate this kind of training. In fact, the students here have internalized the meaning of operation and taken a gratifying step, which is worth encouraging. This is actually laying the foundation for us to solve complex problems in the future.
(2) Connecting with the reality of life, let students understand that mathematics comes from life, and there is mathematics everywhere in life. The teaching of practical problems should start with students' familiar life, first of all, eliminate students' ideological fear of difficulties, and let them understand and feel mathematics from life. For example, how many tiles are needed to decorate the house at home and tile the living room, and how much can it cost? This kind of problem is very practical, and students are very enthusiastic about it. Let them cooperate, and use their rest time to go to the market to find some mathematical information needed to solve these two problems, such as the area of the living room, the size and unit price of each floor tile, so as to extract valuable information to solve the problems. In the process of solving problems, it can also cultivate students' cooperative ability and social ability.
(3) Traditional methods to solve application problems such as analysis and synthesis still need to be used. Analysis is to start with the problem and what conditions are needed to solve this problem; The comprehensive method is to start with the existing conditions and what results can be obtained from these two conditions. In fact, this part of the training has been carried out in our lower grades, and now it is further deepened. If one step can't be completed, students need to continue the analysis until the problem is solved.
Pay attention to the creation of situations, study mathematics with existing experience, and understand the characteristics of teaching materials. Only by grasping the characteristics of teaching materials, studying the curriculum standards seriously and sorting out the vertical and horizontal connections of each book's knowledge can we achieve remarkable results.