(a) Numbers and algebra

Quantity and calculation:

1.0000 plus or minus (2)

Originally, it was ranked in the fourth volume as "addition and subtraction within ten thousand years (1)".

2. Division with remainder

Originally in the fourth volume, it is now in the fifth volume because the whole division has moved back.

3. Multiply multiple numbers by one number

The basic content is basically the same as the compulsory education textbook.

4. Preliminary understanding of scores

Originally arranged in the seventh volume, it is now advanced to the fifth volume, because the overall requirements of numbers and calculations have been reduced.

Quantity and measurement:

1. Measurement (mm, decimeter, kilometer, ton)

2. Hours, minutes and seconds

The contents of hours, minutes and seconds in the original four volumes are now distributed in volumes one, two and five respectively. This volume mainly recognizes the unit "second" and emphasizes students' experience for a period of time.

(b) space and graphics

Quadrilateral, mainly teaching the understanding of parallelogram and the calculation of the perimeter of long and square.

(3) Statistics and probability

possibility

According to the requirements of curriculum standards, new contents are added to let students experience the certainty and possibility of events and the possibility of different results.

(D) Mathematical thinking methods

Mathematical wide angle (arrangement, combination)

In the second grade, the first book has been infiltrated. Here, more emphasis is placed on letting students find simple permutation and combination numbers through charts.

Second, the specific introduction of each unit

Unit 1 Measurement

I. Teaching content

1. Length units: millimeters, decimeters and kilometers.

2. Mass unit: ton

Second, the teaching objectives

1. Make students know the length units of millimeters, decimeters and kilometers and the mass units of tons, and establish the length concepts of 1mm, 65438+ decimeters, 1km and the quality concepts of1t.

2. Let students learn the conversion between unit names.

3. Let students experience the process of measurement, develop measurement skills and cultivate estimation consciousness and ability.

Third, the arrangement characteristics

1. Draw length units with the help of students' life experience to help students establish the concepts of length and quality.

(1) "Millimeter" comes from the activity of measuring the length, width and thickness of textbooks.

(2) By observing the scale of the ruler, the concept of the length of 1mm is established, and with the help of the thickness of 1mm coins, the students are helped to consolidate the shape of 1mm, and students are asked to talk about which items in life are generally measured in millimeters.

(3) Draw decimeter by measuring the length of the desk, and establish the concept of 1 decimeter by observing the ruler.

(4) Draw the length of "1 decimeter" with gestures.

(5) Use the road signs on the expressway to lead out "kilometers".

(6) Draw out "ton" with the fairy tale situation of bridge weight limitation, and help to establish the quality concept of 1 ton with the help of students' weight and animals' weight. Ask students to talk about which objects in life are measured in tons.

(7) Arrange "Mathematics in Life" separately.

2. Pay attention to the cultivation of estimation consciousness and ability.

P2' s measurement activity and P5' s question 3 are both estimation before measurement, so that students can constantly adjust their estimation strategies by comparing the estimation results with the accurate results.

Fourth, specific arrangements.

(A) understanding of millimeters and decimeters

1. Example 1 (understood as millimeters)

(1) Students first estimate the length, width and thickness of the textbook. When estimating, students take the "centimeter" they have learned as the unit.

(2) In actual measurement, the length of the textbook is still a whole centimeter, and the width cannot be expressed by a whole centimeter. Students describe it in two ways: 8 cells are larger than 14 cm and 2 cells are smaller than 15 cm. At this time, students still don't know the concept of "millimeter", only talking about more or less cells. When measuring the thickness of math books, it is less than 1 cm, which also makes students have the desire to continue exploring.

(3) At this point, the elf asked such a question, "What if the measured length is not the whole centimeter?" Naturally, it leads to the necessity of producing "millimeter".

(4) By asking students to count several squares with the length of 1 cm on the scale, the relationship between the concept of "millimeter" (helping students to establish the appearance of millimeter by observing the scale) and "1 cm = 10 mm" is directly given.

(5) Consolidation of the "mm" representation: thickness of 1 min. In teaching, students can give more examples, such as the thickness of savings card, IP card and IC card. )

(6) Application of "mm": The lead cores in mechanical pencil are 0.7mm and 0.5mm, with precipitation. Encourage students to tell more examples.

2. Example 2 (Decimeter Understanding)

(1) It is more convenient for two students to measure the length of desks in different ways, and it is more convenient to take 10 cm as the unit, which highlights the necessity of "dividing meters".

(2) Directly express by scale, and explain how long the decimeter of 1 is (establish the expression of length) and the relationship between decimeter and centimeter.

(3) The relationship between meters and decimeters is not given in the textbook, but students are allowed to think for themselves.

(4) Ask students to indicate the length of 1 decimeter by hand, and consolidate the concept of 1 decimeter.

3. Exercise 1

(1) Measurement (estimation, actual measurement): Question 1 ~ 3.

(2) Consolidate the concept of length by using real life: Question 5.

(3) Unit conversion and calculation: Questions 4 and 6.

(4) Actual investigation: Question 7.

(B) the understanding of kilometers

1. Example 3 (km knowledge)

(1) From the actual situation of road signs, explain the existence of mathematics in real life, let students feel the necessity of knowing "kilometers", and let students understand the specific meaning of road signs through their language description.

(2) With the help of the school playground, a familiar theme for students, help students to establish the concept of 1 km, and give the relationship between km and meters. (Teaching can be adapted to local conditions to help students establish the appearance of 1 km. For example, the distance from a to b is about 1 km. )

2. Example 4 and "Do it" (further experience the length of 1 km with the sense of the body)

You can experience the length of 1 km by feeling the distance, the length of time, the number of walking steps and the degree of physical fatigue.

3. Example 5 (Unit Conversion)

4. Exercise 2

(1) Consolidate the concept of length: problems 1 and 2.

(2) Unit conversion and calculation: questions 3 and 5 (the fifth question reflects the diversity of algorithms).

(3) Choose different modes of travel according to different distances to solve practical problems: Question 4.

(3) understanding of tons

1. Example 6 (Understanding of Ton, Relationship between Ton and Kilogram)

(1) leads to the theme through fairy tale situations. In the process of solving "can we cross the bridge at the same time", the concept of "ton" and the relationship between ton and kilogram are naturally introduced.

(2) After students have mastered the relationship between tons and kilograms, let them go back and solve the problems raised in the theme map.

(3) Establish a quality concept of 1 ton based on students' life experience. In addition to the examples in the textbook, you can also talk about other examples, such as a car with a deadweight of 3 tons, a ship with a tonnage of 10,000 tons, and so on. Students can also think about how much 1 ton rice there is (25 kg per bag), and let them establish the quality concept of 1 ton with the help of familiar objects.

2. Example 7 (Unit Conversion)

"hands-on"

Question 1, the application of tons in life.

Problem 2, solving practical problems with calculation and unit conversion.

4. Exercise 3

Question 1, consolidating the concept of quality.

Question 2, unit conversion, calculation.

Question 3: Diversification of solution strategies.

Question 4: Make a practical investigation and carry out environmental education.

Mathematics in life

Let students understand the application of "kilometer", "kilogram" and "ton" in real life.

Do you know that Cao Chong's story, which is familiar to everyone, makes students realize the idea of equivalent replacement.

Suggestions on teaching verbs (abbreviation of verb)

Help students to establish the concepts of length and quality in various ways.

Students should not only learn the conversion of units and apply it to practical problems, but also establish the concepts of length and quality. Some larger units (kilometers, tons), because it is difficult for students to feel in a measured way, mainly combine life examples to help students understand.

Unit 2 Addition and subtraction within ten thousand years (2)

I. Teaching content

It is mainly the calculation of adding and subtracting three digits and adding and subtracting three digits.

In the past, this part was arranged in Volume IV within 10,000, plus or minus (I) * * *.

Compared with the 91 textbook, there are the following changes:

1. The problem of finding one more number and one less number was originally arranged in this unit. Now this part has appeared in three volumes.

2. Originally, it was arranged in the order of discontinuous carry-continuous carry and discontinuous abdication-continuous abdication. Now, discontinuous carry and discontinuous abdication are basically not taught, and the pace of reform is even greater.

3. The original calculation of addition and subtraction is arranged in addition and subtraction respectively, and the calculation method is simple (addition can only be calculated by exchanging addends, and subtraction can only be calculated by adding and subtracting differences). Now the calculation and arrangement of addition and subtraction are combined, which highlights the reciprocal relationship of addition and subtraction, and the calculation strategies are more diversified.

According to the requirements of the curriculum standard, the addition and subtraction within 10,000 is limited to the addition and subtraction within three digits. Calculators can calculate more digits.

For arithmetic, we no longer use intuitive charts or dynamic vertical calculation process to help students understand.

Second, the teaching objectives

1. Let the students calculate the addition and subtraction of three digits correctly.

2. Enable students to estimate according to the situation and improve their estimation consciousness and ability.

3. Understand the significance of checking calculation, check addition and subtraction, and initially form the habit of checking.

Third, the arrangement characteristics

1. Teaching calculation combined with solving practical problems.

(1) Supplement: Calculate the species number of some wild animals in China.

(2) Subtraction: Yunnan tourism.

(3) Calculation of addition and subtraction: shopping.

2. Strengthen the estimation.

Addition and subtraction are estimated first and then calculated accurately.

3. Reflect the learning style of cooperation and communication.

(1) When calculating 500- 185, the algorithm is diversified.

(2) Add and subtract to check the diversity of strategies.

(3) The law induction of addition and subtraction no longer gives ready-made conclusions, but allows students to discuss.

4. Let students use the ability of transfer analogy to calculate.

* Three-digit addition and subtraction, three-digit addition without carry and subtraction without abdication do not appear separately.

* Three digits plus three digits, and the sum is four digits. There is no single example, only in practice.

* Subtract three digits from three digits, and there is 0 in the minuend. Let the students use the previous calculation method to complete it by themselves.

Fourth, specific arrangements.

(1) Add

1. Theme map

(1) Based on the statistics of the world known species, China endemic species, endangered and threatened species of four animals, on the one hand, it provides information for the following calculation problems, on the other hand, it educates students on the environment.

(2) After students learn the latter calculation method, they can go back and ask students to choose the information in this statistical table, and then ask some questions to make full use of the theme map.

2. Example 1 (continuous carry addition of two digits plus two digits, and the sum exceeds 100)

(1) Ask questions from the topic map and learn the calculation method in the process of solving problems.

(2) Students have mastered the ideas and skills of notes, and can add them by pen. Here is mainly to let students learn continuous carry addition by using transfer analogy, which lays the foundation for the following three-digit plus three-digit continuous carry addition.

(3) No longer use intuition to help students understand arithmetic.

3. Example 2 (three-digit plus three-digit continuous carry addition)

The theme of (1) is still extracted from the theme map.

(2) Estimate first and then calculate accurately, so that students can cultivate the habit and ability to judge the rationality of the results in their daily study.

(3) The continuous carry addition principle in Example 2 is extended to three digits plus three digits (which digit adds up to ten, it goes to the previous digit, which is also the embodiment of cultivating students' ability to transfer analogy.

4.P 18 "Do it"

The last question is that the sum of three consecutive carryovers exceeds 1000, and students are required to use migration analogy to calculate.

5. Exercise 5

There are various forms of calculation, from the digits of addend, there are three digits plus two digits, and there are also three digits plus three digits. Judging from the number of carry times, there are those who don't carry, those who carry once, and those who carry two or three times in a row. Formally, there are simple calculations, calculations combined with practical problems, and corrections.

Question 9 shows great openness. If you only consider the route without considering the distance, you can adopt various methods and then choose the nearest route according to the distance. To make the whole route shortest, it is necessary to have the shortest local route for each section. Among them, there is only one route from home to the post office and from the post office to the bookstore. Of the two roads from the bookstore to the supermarket, the way back to the post office and then to the supermarket is shorter, and the way home from the supermarket without going through school is the shortest. When comparing the distance between the two routes, students can adopt estimation strategies according to actual needs. If you want to compare the size of 75+329 and 440, you can use 80+330 to estimate. If you want to compare the size of 4 10+ 125 and 5 10, you only need to think of 4 10+65438+.

(2) subtraction

1. Example 1 (generally three digits minus three consecutive abdications minus)

(1) With the help of the tourism situation in Yunnan, on the one hand, it provides good materials for naturally asking mathematical questions from real life, on the other hand, it also provides students with certain opportunities to learn geographical knowledge. For example, the landmark tourist attraction in Kunming is Shilin, Dali is the Three Pagodas, and Lijiang is the Yulong Snow Mountain. Teachers can also introduce this knowledge to students in teaching.

(2) The three illustrations reflect different levels. The first picture shows the relative positions of the three cities and the distances from Kunming to Dali and from Kunming to Lijiang. The second picture is the specific situation of the story, which is the simplest travel problem that does not involve time and speed. It gives the starting point, ending point, current position, relative distance and other elements, and naturally asks questions. The third diagram is a line segment diagram, which is a way to mathematize practical problems. From this map, we can clearly see various situations (such as the direction of walking, the distance from Kunming to Dali and Lijiang, what we are looking for, and so on). )

(3) It is also estimated first and then calculated accurately. The textbook only gives an estimation strategy. In practical teaching, students can also choose appropriate estimation strategies according to their actual situation, such as 520- 150.

(4) The detailed process teaching material of written calculation is not given, but students are allowed to use the knowledge of abdication subtraction they have learned before and learn through group discussion to give full play to the students' main role.

(5) Like addition, there is no intuitive operation and dynamic abdication process diagram in textbooks to help understand arithmetic.

2.P23 "Do it"

All kinds of questions can be asked, addition and subtraction can be done.

3. Example 2 (Successive abdication in which one tenth of the minuend is 0 minus)

(1) Change the data based on the example 1.

(2) Only the vertical type is listed in the textbook, and the specific calculation is done by the students themselves. The arrangement intention is the same as before, that is, let students use their existing knowledge to solve calculation problems by themselves.

4. Example 3 (The minuend is a continuous decrease of an integer)

The focus of teaching here is not the calculation method of continuous abdication subtraction, because students have mastered the skills of continuous abdication subtraction with 0 in the middle of the minuend, so I won't focus on it here. The key point is to embody the idea of algorithm diversification. Three different algorithms are provided in the textbook to encourage students to come up with more algorithms.

5. Exercise 6

The topics of continuous subtraction, addition and subtraction have been compiled, such as questions 2 and 3.

Question 6: When solving practical problems, we should consider the different possible situations of the relative positions of the three points. According to whether Xiao Ming's family and Xiao Hong's family are on the same side or different sides of the school, the formulas of subtraction and addition can be listed respectively.

(3) addition and subtraction operations

1. Theme map

Children and their mothers can go shopping together. By calculating the total price of two items, the contents of 1 and Example 2 are calculated.

Putting the calculation of addition and subtraction behind addition and subtraction at the same time is conducive to strengthening the understanding of the reciprocal relationship of addition and subtraction, and the calculation methods can be more diverse.

2. Example 1 (check addition)

The emphasis is on the diversity of verification methods (three types: exchanging addend positions, one addend minus one equals the other addend).

Implicit Mathematics Knowledge: the Relationship between additive commutative law and Addition and Subtraction.

3. Example 2 (Checking Calculation of Subtraction)

The same example, 1, highlights the diversity of verification methods (two kinds: the subtraction of the minuend equals the minuend, and the addition and subtraction of the difference equals the minuend).

4. Exercise 7

Question 8: Encourage students to ask questions. For example, students can ask what the total price of two commodities is and how much one commodity is more expensive than the other. Pay attention to openness when solving problems. For example, when solving the problems raised by elves, the first problem can be solved by estimation, and then the second problem can be solved by accurate calculation.

(4) sorting out and reviewing

1.0000 Review of addition and subtraction by pen.

Let the students solve it by themselves through discussion.

2. Review of solving problems by calculation.

Encourage students to ask their own questions and then solve them, reflecting openness.

Suggestions on teaching verbs (abbreviation of verb)

1. Let students learn to calculate in the process of solving practical problems.

When teaching, we should start from practical problems and let students have the desire to solve calculation problems. When teaching, you can use the theme in the textbook, or you can design your own situation according to the local actual situation.

2. Let students explore and complete the calculation task by themselves.

Students should use what they have learned, the ability of transfer and analogy, and solve their own calculation problems through cooperation, exchange and discussion among classmates.

However, it should also be noted that students can help them understand arithmetic through intuition if they have difficulty in mastering it. Although the operations of continuous carry addition and continuous abdication subtraction are not difficult to understand, students are still prone to make mistakes in their studies, so we should ensure a certain training time and quantity in teaching.

Unit 3 quadrilateral

I. Teaching content

1. Understanding of Quadrilateral and Parallelogram

2. The concept of perimeter, the perimeter calculation of rectangle and square.

3. Length estimation

Second, the teaching objectives

1. Make students understand the characteristics of quadrilateral, have a preliminary understanding of parallelogram, and express parallelogram in different ways.

2. Let students understand the concept of perimeter and calculate the perimeter of rectangle and square.

3. Cultivate students' concept of length by estimating the length and circumference.

Third, the arrangement characteristics

1. Introduce the concept of geometry from daily life so that students can learn geometry knowledge in familiar situations.

Understanding quadrangles and parallelograms by using campus situations. Know and calculate the perimeter with familiar things (leaves, textbooks, small national flags, clock faces).

2. Use activities to consolidate the understanding of geometric concepts.

Various activities are designed in the textbook: coloring, classifying, drawing a parallelogram, circling a parallelogram on a nail board, drawing a parallelogram on a square paper, cutting out a parallelogram with a rectangular paper, assembling a jigsaw puzzle with a jigsaw puzzle, and actually measuring the circumference of an object. This is also determined by the intuitive operability of geometric knowledge.

3. The concept of perimeter emphasizes the introduction from a general perspective and reflects the formation process of knowledge.

Starting with arbitrary figures (including irregular figures), make students realize that perimeter is a general concept, and avoid the mindset that only regular figures such as rectangle, square and circle can find perimeter. In addition, through the exploration of finding the perimeter of general figures, students can experience the knowledge formation process of finding the length and the perimeter of a square.

Fourth, specific arrangements.

(A) the understanding of quadrilateral and parallelogram

1. Theme map

Provides a campus scene. There are many geometric figures in the drawing, including many quadrangles. For example, there are parallelograms on the sliding door of the school gate, rectangles, squares, parallelograms and diamonds on the sidewalk, a rectangular basketball court and backboard, a rectangular frame on the backboard, many rectangles on the badminton court, rectangles and trapezoid on the football door, parallelograms on the stairs of the teaching building in the distance, and rectangular windows. When teaching, students should be fully observed. Some nouns, such as parallelogram, trapezoid and diamond, have never been learned, but if students have this knowledge, teachers should give them affirmation. By observing the theme map, we can see that there are various quadrangles in life.

2. Example 1 (known quadrilateral)

Ask the students to color the figure they think is a quadrilateral, and let them find out the characteristics of a quadrilateral through discussion: there are four straight sides and four corners. Now that students have the basic knowledge of long and square, they can use the characteristics of sides and corners of long and square to summarize the characteristics of quadrilateral. This is also a manifestation of reasonable reasoning (induction).

Some students may think that the second figure in the third row is also a quadrilateral at first. After understanding these two characteristics of quadrilateral, we can judge correctly.

Through this example, let students have a perceptual understanding of various special quadrangles and even general quadrangles that appear in primary schools, and they will understand them one by one in future study.

3. Example 2 (Classification of Quadrilateral)

(1) The purpose of example 1 is to distinguish quadrangles from other figures, and example 2 is to classify inside quadrangles.

(2) Three classification results are given in the textbook:

A. Rectangles and squares belong to one category, while others belong to the same category. Highlight the characteristics of the four corners of a rectangle and a square. )

B rectangle, square, parallelogram and diamond are one kind, and trapezoid is one kind. (Highlight the characteristics that the two groups of opposite sides of all parallelograms are parallel and equal respectively. )