First, the overall introduction of this textbook
This textbook is compiled on the basis of the basic concept and specific content objectives of the Mathematics Curriculum Standard for Full-time Compulsory Education (Experimental Draft), which embodies the knowledge and thought of compiling the Mathematics, a classroom standard textbook for compulsory education in the new century. This textbook strives to embody the basic characteristics of the whole set of textbooks, attach importance to students' life experience, and closely link mathematics with reality; Presenting learning content with students' mathematical activities as the main line; Create vivid and interesting situations, and guide students to experience the process of abstract mathematical model, explanation and application in the process of solving practical problems, so as to gain understanding and experience of mathematical knowledge; Pay attention to developing students' sense of number, spatial concept and statistical concept; Avoid stylized narration and rigid practice of "arithmetic". Below I will talk about some of our teaching suggestions for the specific content of each unit:
Second, the main content of this textbook
Numbers and algebra
1. Unit 1 "Know a bigger number". Students will go through the process of collecting information from daily life.
Looking at the process of large numbers,
Feel the necessity of learning large numbers and understand the practical significance of large numbers; Know the counting units within 100 million, understand the relationship between each unit, and read and write correctly; Can compare the scale of hundreds of millions; Master the method of expressing large numbers in tens of thousands and hundreds of millions; Know the divisor, find the divisor of a number and estimate the large number.
2. Unit 3 "Multiplication". Students will master the calculation method of multiplication of two or three digits.
And can correctly calculate, will use the knowledge to solve some practical problems; Understand the practical significance of large numbers and be able to estimate them; Mastering the use of calculator, I will use calculator to explore some mathematical laws and know the operation rules of addition and multiplication.
Unit 5 Division. Students will master the calculation method that divisor is the division of two digits.
Method, and can be executed.
Correct calculation; Understand the relationship between distance, time and speed in actual situations and solve simple problems in life; Experience the process of exploring the invariable law of quotient, master the exploration method initially, and be able to solve simple practical problems by using the discovered law; Understand the necessity of using parentheses in calculation, and correctly calculate the three-step integer elementary arithmetic with parentheses.
Unit 7 "Negative Numbers in Life". Students will understand the significance of negative numbers in daily life and use negative numbers to represent some phenomena in daily life.
Space and graphics
1. Unit 2 "Lines and Angles". Students will be able to recognize line segments, rays and straight lines, and will use letters to represent them. Know the parallel lines and vertical lines on the plane and draw them with a triangular ruler; Know that two points determine a straight line, and the line segment between them is the shortest; Know boxers and rounded corners; Will use a protractor to measure the degree of the specified angle and draw the angle of the specified degree.
2. Unit 4 "Graphic Transformation". Students will experience the process of transforming a simple figure into a beautiful figure, and can rotate the simple figure 90 degrees on a square paper; Able to operate graphic transformation on grid paper and tell the translation or rotation process in graphic transformation.
Unit 6 "Direction and Location". Students will be able to use several pairs to represent the position of an object under certain circumstances; In certain cases, the position of an object is represented by direction and distance.
Statistics and probability
Unit 8 Statistics students will understand the necessity of using 1 grid to represent multiple units in statistical charts, and further understand the characteristics of bar statistical charts. Knowing the characteristics of broken-line statistical chart, we can draw some data in life into broken-line statistical chart, and we can predict the trend of things from broken-line statistical chart.
Comprehensive application
The two comprehensive application activities of "Walking into Nature" and "Data Tell Me" encourage students to initially establish confidence in using mathematics to solve problems, accumulate experience in solving simple practical problems, feel the interconnection of mathematical knowledge, and gradually understand the role of mathematics in practice.
Completion and review
The textbooks are arranged to be sorted out and reviewed twice. Sorting and reviewing has changed the mode of simply doing problems, focused on cultivating students' awareness of self-reflection and promoted students to form their own knowledge structure. Each sorting and review is divided into three parts: sorting out what you have learned, putting forward mathematical questions and trying to answer them, and some exercises.
The purpose of "What have you learned" column is to encourage students to review and reflect on what they have learned, and simply sort out the main contents of what they have learned by using lists or other forms.
"Put forward relevant mathematical problems according to what you have learned and try to solve them", aiming at cultivating students' ability to put forward and solve problems; Deepen the understanding of the learned knowledge in the process of solving problems; Review your own experience and progress in the learning process.
Third, the difficulties of each unit and teaching suggestions
Unit 1 Know a bigger number
(a) unit difficulties:
In a specific situation, knowing, reading and writing numbers within 100 million and knowing the decimal counting method will represent large numbers in units of 10 thousand and 100 million. Understand the function of divisor in real life and ask for a divisor of a number according to actual needs.
(2) Teaching suggestions:
Suggestion 1: Provide materials for students to experience the intuitive and vivid activity of "counting a number" and understand the meaning of large numbers.
For example, when counting to carry, the teacher should ask questions to let the students know when to carry, and then let the students count together. For example, if the students count to 90,000, the teacher can ask 1 10,000. Deepen students' understanding of the relationship between counting units and intuitively feel the size of counting units. In addition, ask the students to dial a number on the counter, count and deepen.
Impression of "full ten into one"
Suggestion 2: Go through the process of collecting and processing data and draw a reading and writing method for large numbers.
(1)P6 large numbers should be read and written in combination with numerical sequence tables to enhance students' intuitive feelings. When teaching, let students experience reading and writing with large numbers under the guidance of teachers, instead of memorizing several "reading methods" and "writing methods". On the basis of students' full understanding, students can be guided to summarize the methods of reading and writing in their own language.
(2) Note: It is relatively difficult to read and write "Numbers with zeros in the middle and at the end". We should focus on guiding students to experience methods in the practice of reading and writing numbers, and arrange some comparative exercises at the same time.
Recommendation 3: Use knowledge transfer to learn new knowledge.
Example1:p9Students are no strangers to numerical comparison. When teaching, let students review the old knowledge first, such as comparing: 45000, 8000, 45600, the size of these three numbers. On this basis, let the students review the method of comparing the number size within 10 thousand, and then let the students move to the number size comparison within 100 million. Using the transfer of knowledge to learn not only cultivates students' subjective initiative in learning, but also trains their mathematical thinking.
Example 2: When rewriting data, let the students understand that rewriting data is a change in the form of data representation, and the size has not changed. And explain to the students why they should write the counting unit after rewriting: for example, 9600000 equals 9.6 million. The number to the left of the equal sign is based on "one". Generally, the counting unit does not write "one", while the number to the right of the equal sign is "ten thousand". If you don't write, it will become based on "one", which is so different.
Recommendation 4: Recognize the difference between exact number and divisor according to the situation, and master the method of calculating divisor.
(1) Students can see for themselves why these approximate figures are formed. Then give an example to talk about the approximate figures in life. Understand the difference between exact number and divisor, and master the method of finding divisor (mainly rounding method).
(2) In teaching, it is necessary to distinguish the rewriting of divisor and number, strengthen training in this respect, and add some words with the same meaning as seeking divisor: accurate to …… and reserved to …… and so on.
The second unit line and angle
(1) Key points of unit teaching:
1. Differences and connections between straight lines, rays and line segments.
2. I will measure the angle with a protractor and draw an angle of a specified degree.
(2) Teaching suggestions:
Suggestion 1: Make clear the differences and connections between straight lines, rays and line segments.
It is known that a line segment is a part of a ray and a ray is a part of a straight line, but only the length of a line segment and a line segment can be compared. Because rays and straight lines are unmeasurable, line segments cannot be compared with rays or straight lines.
Suggestion 2: How to deal with some details about reading and drawing corners.
(1) When drawing a special angle with a triangle, the angle is not sharp, so pay attention to the method guidance. When you spell the corner with a triangle, you should leave traces of drawing the corner.
(2) When students read the angle, the inner and outer circles are not divided, and the reading is the complement. It can be determined by combining whether the angle reading is obtuse or acute.
Recommendation 3: Expand knowledge through concrete perception.
(1) This line segment is the shortest among countless connecting lines between two points.
(2) The line segment leading from a point outside the line is the shortest.
(3) The vertical line segments between parallel lines are equal everywhere.
Teaching suggestion of "going into nature";
Comprehensive practice, especially the teaching content of "going into nature", can best reflect the concept of "mathematics comes from life and serves life" in the syllabus. Therefore, when teaching this section, teachers should let go, let students try to describe, let students explore methods and show their views. If possible, children should be allowed to enter real life. Teachers with immature conditions should also try to create corresponding scenes (such as talking, wall charts or slides ...) to stimulate students' interest in learning and let children feel the importance of life to mathematics.
After reviewing the knowledge of each section, we should sum up the knowledge points so that students can form a knowledge system:
1. Read and write large numbers.
2. Students should be shown the definition, drawing and application of parallel lines and vertical lines in life.
Related lines in life.
3. Angle measurement and drawing
The third unit multiplication
(A) teaching focus:
1. It is correct to explore and master the calculation method of two-digit and three-digit multiplication in combination with specific conditions.
Accurate calculation,
Multiplication can be used to solve some practical problems.
2. Summarize some settlement methods and use them flexibly.
3. Know and use calculators, and use calculators to explore some mathematical laws.
4. Explore and discover the laws of multiplication and addition.
(2) Teaching suggestions:
Suggestion 1: In situational activities, master the vertical calculation method of multiplication through algorithm diversification.
(1) P23 After the "satellite running time" shows the situation, the students list the formulas independently.
After that, ask the students to estimate one.
Estimate and recalculate, and encourage students to use more methods.
(2) In the vertical calculation of "two digits multiplied by three digits", it should be noted that there is a zero at the end.
Vertical specialty
Intensive training in writing and vertical calculation, middle 0.
(3) The processing of application problems should be combined with the meaning of multiplication. Strengthen the quantitative relationship:
Number of copies × number of copies =
total
Suggestion 2: Guide students to summarize the estimation methods.
(1) The method of inducing students to estimate is a key point in this unit, and multiplication can be used in teaching.
Meaning guides students to estimate the whole by parts, from small to large, from less to more.
P36 The data of the second question is basically around 200. With 200 as the standard, we can know 10 days.
Turnover. Students can also communicate with each other and discuss "how to estimate?" "According to what?"
The third problem of P38 is the application of estimation methods to guide students to judge with different estimation methods.
P38 Question 4: Pay attention to guiding students to obtain mathematical information from charts, and teach students to calculate time vertically according to the actual situation.
P37 is a comprehensive exercise, including several mathematical models such as distance, speed and time.
And the relationship between them, but also involves the estimation method, which can gradually appear problems in teaching and reduce the difficulty of estimation. We should pay full attention to it and guide students to clarify the quantitative relationship.
Recommendation 3: Go through the process of exploring the law.
(1) exploration and discovery (1) requires students to use calculators to explore laws, guide students to discover and express laws on the basis of exploration, and cultivate students' good study habits of quiet observation and comparison.
(2) The teaching of algorithm should be combined with the cultivation of simple calculation consciousness, and students should deal with 25 before teaching.
×2, 25×4, 25×8, 125×8 were all memorized. Secondly, the teaching of arithmetic should start with the meaning of multiplication, strengthen the memory of letter model and solve problems with model.
Note: multiplication and division are both important and difficult. It is suggested that students must go through the exploration process of discovering problems, putting forward assumptions, verifying with examples, and summarizing laws in order to understand the logic in actual situations and speak it out in the application process.
Organize and review (1)
Teaching suggestions:
1. At the beginning of teaching, arrange some time for students to read math books from the first unit, review and sort out what they have learned, and write a clue in the draft book.
2. By listening to students' reports, teachers write knowledge clues on the blackboard in an orderly way, helping students sort out knowledge clues, which is more conducive to students' mastery of knowledge, thus forming a knowledge network and integrating knowledge into students' knowledge system.
3. Teachers should also focus on reviewing common problems in combination with students' classroom performance and homework in previous teaching.
Unit 4 Graphic Transformation
(A) teaching focus: the elements of translation and rotation
(2) Teaching suggestions:
Suggestion 1: Experience the process of graphic transformation in hands-on operation.
(1) The windmill rotation diagram on page 54 of the textbook, experience the characteristics of graphic transformation, teacher.
Induce while demonstrating
Three elements of rotation: center point, direction and degree.
(2) In the transformation of graphics, different operation methods are advocated. Students can prepare some primary school furniture for practical operation before class, and then try it on grid paper to improve their perceptual knowledge.
Suggestion 2: Pay attention to the level of handling exercises.
For example, on page 55 of the textbook, it is said that the topic 1 is to solve the problem of rotating center and let students know.
No matter how many degrees you rotate, the center point will not change its position. The first two sub-topics of the second question focus on solving the direction problem, and the third sub-topic focuses on solving the degree problem. Several exercises have clear levels, so it is best not to change them easily.
Suggestion 3: Encourage students to design and make beautiful patterns.
After this unit, you can organize a tabloid exhibition of pattern design to consolidate students' knowledge of translation and rotation, improve their interest in learning and develop the concept of space.
Unit 5 Division
(A) the focus of teaching
1. Can correctly calculate the division of three digits divided by two digits.
2. Understand and master the relationship between distance, time and speed.
3. Simple calculation by using the law of quotient invariance.
(2) Teaching suggestions:
Suggestion 1: Summarize the calculation methods in the specific exploration process.
Example 1: P59 "buying stationery" is the basis for dividing the last two digits by three digits. In the teaching here, we advocate the diversification of algorithms, pay attention to vertical calculation, pay attention to the positioning of quotient and carry out intensive training.
Example 2: P6 1 Exercise 1 Question "How much can you fill in the brackets?" This kind of problem is the basis for students to try their business and needs long-term training.
The teaching of P62 Distance, Time and Speed is inseparable from the significance of multiplication, so we must keep the model in mind.
Recommendation 2: Improve the estimation ability in specific situations.
(1) In this module, the estimated requirements are basically arranged before each operation for adding.
Strengthen the cultivation of students' estimation ability. At the same time, it is helpful to improve students' ability to use estimation methods to test.
(2) P73 "National Stadium" teaching is also the cultivation and transmission of estimation consciousness.
Be familiar with "surroundings"
Things to "depict" a larger number, develop students' sense of number, and let learning live in activities.
The feeling in the process.
(3) Note: There are many ways to "try business", but teachers should focus on one.
Intensive training, and
And stick to it for a long time.
Recommendation 3: Find the law in the calculation process.
(1) "Quotient Invariant Law" discovers laws by inferring the relationship between data. Supplementary teaching: the situation in which the quotient remains unchanged but the remainder changes.
(2) The teaching of "brackets" should strengthen the training of operation sequence, and make comments, guidance and communication in time according to the students' learning situation.
Unit 6 Direction and Position
(1) teaching emphases and difficulties:
1. In certain cases, the position can be determined by the number pairs on the grid paper.
2. Understand the role of direction and distance in determining the position through specific situations.
Use, and according to
Direction and distance determine the position of an object.
3. You can describe a simple road map.
(2) Teaching suggestions:
1. It is necessary to understand the role of "number pair" in determining the position according to the specific situation. The representation method of "number pair" is generally to represent the horizontal direction first and then the vertical direction.
2. Make it clear that the direction and position are relative, and the four directions of southeast and northwest rotate clockwise.
3. When dealing with exercises, you can ask students to mark the direction first, draw an arrow, and then find the specific position accordingly.
Unit 7 Negative Numbers in Life
(1). Teaching emphases and difficulties:
1. Understand the meaning and representation of negative numbers in daily life, and use negative numbers to represent some days.
In daily life
problem
2. Know that 0 is neither positive nor negative.
(2) Teaching suggestions:
1. Make clear the expression and meaning of negative numbers according to the actual life.
2. Let the students understand that the closer a negative number is to 0, the bigger the number is, and the closer a positive number is to 0, the smaller the number is. It can help students understand through specific quantities such as temperature or axis.
3. About practical design.
(1) The practice of the difference between two numbers. For example, -7 and -2, -7 has 7 squares from 0 and -2 has 2 squares from 0, so -7.
(2) A person went 7 meters east from "3" and then 4 meters west. Where is this person now? Further consolidate the knowledge and practical application of negative numbers.
Sorting and reviewing (2)
Suggestion 1:
Through recalling, discussing and communicating, let the students summarize and sort out the four knowledge units of graphic transformation, division, direction and position, and negative numbers in life, so as to make them systematic and orderly and deepen students' understanding of what they have learned.
Recommendation 2:
When dealing with the first question, let the students think independently, talk about the number of positive and negative numbers in the table in groups, and then organize students to communicate with each other in class. The third question (1) is a small one. First, guide the students to know about which point the figure rotated by 90 degrees rotates, and then let the students draw the rotated figure independently. (2) Let the students know that before drawing, we must first determine a certain point or a certain line segment in the original figure as a reference, then determine the translation of other points or line segments, and finally let the students draw the translated figure.
Unit 8 Unified Planning
(A) teaching focus:
1. goes through the process of data collection, collation, description and analysis.
2. Through examples, further understand the bar chart (1 grid represents multiple units) and line chart.
3. Ask and answer simple questions according to the data in the statistical chart, and communicate with your peers.
This idea.
(2) Teaching suggestions:
Suggestion 1: Make full preparations before school starts.
(1) In order to let every student experience the process of data collection, we should try our best to arrange the practical activities of "planting garlic seedlings" and guide the students' activities. Such as: grouping arrangement, how to plant garlic seedlings, how to measure the height of garlic seedlings, how to record measurement data (rounded to the whole centimeter), and record some activities and feelings.
(2) Before class, talk about the data collection process and discuss the data collection methods. In the comparison of garlic seedling height of each person in 15 day group, the method of data description is discussed. For example, students will find that it is more intuitive to fill in the statistical table than to describe it in language, and they will also find that the statistical chart can more intuitively show the garlic seedling height of the group students on 15. Let students find the value of statistical chart in comparative communication.
Recommendation 2: Creating contradictions: Introducing grids to represent the necessity of making statistical charts by multiple units.
When drawing a statistical chart, based on students' existing cognitive basis (a grid represents a unit), let students draw a statistical chart first. In the process, they find that the grid is not enough. Then lead the students to discuss how to solve the problem of insufficient painting. This paper introduces the teaching of making a unit statistical chart. How many cells does a grid fit into? Let the students choose according to the characteristics of statistical data. Specifically, look at the maximum number and minimum number of this set of data. There are several grids on the horizontal axis and the vertical axis, so as to determine the unit represented by a grid.
Suggestion 3: In practice, pay attention to guiding students to analyze statistical charts and encourage students to get as much information as possible from charts.
Recommendation 4: Understand the similarities and differences between bar charts and line charts through statistics of data and comparison of statistical charts.
Recommendation 5: Guidance for drawing statistical charts. Focus on guiding the way to find something. See clearly what the horizontal and vertical axes represent before tracing points, then see clearly how many units a grid represents, and then draw a statistical chart.
Teaching suggestion of "data tells me";
Recommendation 1: Go through the process of collecting data. For example, you can search online, look up information in the library, extract information from newspapers and magazines or conduct field surveys.
Suggestion 2: Students can use what they have learned to solve math problems. Therefore, we must review the knowledge of large numbers, multiplication and division, statistics and so on before class. In the process of solving problems, teachers should play a leading role and students should not be allowed to solve problems independently.
Suggestion 3: Pay attention to the analysis of the information told by the data, and carry out moral education on environmental protection and water saving for students. And feel the changes in life and the development of science and technology through data.