Teaching emphasis: the writing method of multiplying three digits by two digits.

Teaching difficulties: correctly understand the arithmetic of written calculation, and understand that when the number of the second factor is multiplied by the number of the first factor, the last digit of the product should be written in the tenth place.

Second, the breakthrough proposal

(a) Choose a situation that is easy to explain to students.

1. Learning situations with simple travel problems as the background.

The situation created by textbooks and selected learning materials is familiar to students and typical. For example, in the presentation of the example 1, a situation of knowing the speed, time and distance is created, and 12 hour is the discussion point, which makes it easier for students to think of dividing 12 hour into 10 hour and 2 hours to explain, which is different from using "ten digits" when the multiplier is two digits.

The teaching emphasis of Example 1 and Example 2 is to explore and master the algorithm and method of multiplying three digits by two digits, and transfer the general method of three-digit multiplication to multi-digit multiplication; The difficulty in teaching lies in understanding the written algorithm of multiplying three digits by two digits.

2. Pay attention to the combination of book knowledge and common sense of life.

Make students understand the common quantitative relationship, that is, the model describing the relationship between unit price, quantity and total price: unit price × quantity = total price. The model of the relationship among speed, time and distance: speed × time = distance. This part of knowledge contains rich teaching resources in students' life. In teaching, we should organically combine the examples in books with those in students' life, so that students can sum up the relationship between speed, time and distance from their familiar common sense of simple motion of objects and use this relationship to solve practical problems.

3. Give full play to students' enthusiasm and cultivate their interest in learning.

In teaching cases 4 and 5, students can exchange the unit price and transportation speed of the received goods before class, which not only enriches the learning resources, but also effectively mobilizes students' interest and enthusiasm in learning activities. It can not only expand students' cognitive space, but also improve students' interest in mathematics.

(B) Let students establish their own written cognitive structure of multiplication.

1. Let the students calculate independently according to the meaning of the question.

The content learned in this section is the expansion and popularization of the two-digit multiplication that students have mastered. Therefore, in teaching, we should pay close attention to students' existing knowledge, experience and cognitive development level, and provide students with a broad background from old knowledge to new knowledge. Let each student experience the calculation process of "145× 12".

Because students have mastered the written calculation of three digits multiplied by one digit and two digits multiplied by two digits, this part highlights independent exploration. After the estimation, it directly reveals the writing process of 145× 12, and puts forward "how to write the second part?" Let the students think independently: What does the multiplication result of "1" and "145" in the second factor mean? Where should the end of the product be aligned with the first part of the product? Finally, the specific steps of 145× 12 are summarized. In addition, estimation is integrated into the teaching of written calculation to help students form good calculation habits.

First, let students estimate the approximate range of 145× 12, and then try to calculate the result of 145× 12 in a vertical way. According to your own estimation, it is very helpful to calculate the error between the estimated value and the accurate value, which is helpful to improve the accuracy of students' estimation. Pay attention to the students who usually have a high calculation error rate when practicing, and see if the writing positions and calculation results of each part of their product are correct. When giving feedback, students can talk about the calculation process of "145× 12" in their own words. When it comes to the process, we should say the following: ① What is the first thing; 2 What is it? What is the writing position of the product? (3) what is the last. The process of students sorting out the calculation steps is the process of summarizing the general method of three-digit multiplication with two-digit calculation, so that students know how to operate and think in an orderly manner and how to solve a specific problem in an orderly manner. Students who have difficulty in trying to calculate independently can be instructed as follows: First review the calculation of "45× 12 =?" Or "145× 2 =?" , and then calculate "145× 12".

Teaching example 2 should guide students to recall the calculation and estimation of multiplying two digits by two digits or multiplying three digits by one digit, and think about what to calculate first, and then what is more convenient and reasonable after vertical column; In the process of using old knowledge to solve new problems, students can deepen their understanding of the meaning of multiplication, improve their calculation skills in writing and estimating multiplication, improve their ability to solve specific problems by multiplication, and form a good cognitive structure of writing multiplication.

2. Teachers should carefully design classroom teaching activities.

By introducing multiplication into the discussion of practical problems, students can feel its necessity and pay attention to the diversity of problem-solving strategies. First, let the students estimate the number according to the existing knowledge, and then let the students use the knowledge of multiplying two digits by two digits to try the problem of multiplying three digits by two digits and explore the written calculation method. In the calculation, students are specially asked to exchange their understanding of "why the number multiplied by the tenth place at the end of the product should be aligned with the tenth place of the factor", highlighting the operation of written multiplication.

In the calculation of Example 2, the discussion focuses on the simple writing and product of vertical type: ① How to deal with the counterpoint problem of "0" and "non-0" numbers when writing vertically? ② How to determine the number of zeros at the end of the product? When giving feedback to question (2), we will focus on the following questions: ① Simple and convenient vertical writing. ② When calculating "106×3", because the middle "0" is multiplied by 3 to get 0, can this process be omitted? How do you write the product in this position? Highlight the operation of written multiplication to help students establish a good cognitive structure.

3. Understand the simple calculation and writing of "160×30" and "106×30" in comparison.

The step-by-step learning factor is multiplied by the middle or end zero. This example is divided into two small problems. The first question (1) learns the multiplication of two zero-tailed factors:160× 30; Question (2) Learn the multiplication of one factor with zero in the middle and zero at the end of the other factor: 106×30. The problem (1) focuses on simple vertical writing and the determination of the number of zeros at the end of the product. The textbook guides students to make use of the old knowledge they have mastered in this field and the characteristics of 0 in multiplication operation, and independently adjust classes to derive a simple algorithm in which the two factors are all zeros at the end: multiply the numbers before 0, then see how many zeros are at the end of the two factors, and then add several zeros at the end of the product. The focus of question (2) is not only the simple vertical writing, but also the question of whether the 0 in the middle of one factor should be multiplied by another factor. Because these problems have been solved in the previous multiplication study, the textbooks are intentionally left blank, which provides sufficient space and opportunities for students to solve these problems independently.

(3) Pay attention to guiding students to explore the law in operation and make some induction and abstraction.

1. Create problem situations for each student to explore independently.

The situation created by Example 3 comes not from life, but from teaching itself. Therefore, we should put forward questions that can arouse students' positive thinking from the perspective of mathematics, so that every student can devote himself to the exploration of problems as much as possible. When teaching, you can also slightly change the right set of formulas in the textbook to get the following two sets of formulas:

6×2= 12 80×4=320

6×20= 120 40×4= 160

6×200= 1200 20×4=80

And asked: "Can you write two more formulas according to the characteristics of each group of formulas above?" Give it a try! "Let each student try to find the rules by himself in the process of writing formulas. In this process, both hands and brain are used together, which makes the exploration of the law implemented.

2. The enlightenment education of dialectical thinking

Exploring the changing law of product in multiplication operation is an important aspect of the content structure of integer four operations. In this example, two sets of multiplication expressions are used as the carrier to guide students to explore the change of the product when one factor and the other factor are constant, and to sum up the change law of the product. On the basis of students' expression in their own language, teachers should supplement or revise in time to make the generalization rule simple and smooth: one factor remains unchanged, another factor expands (or shrinks) several times, and the product also expands (or shrinks) by the same multiple. Through the exploration of this process, students can not only understand that when two numbers are multiplied, the product changes with the change of one factor (or two factors), but also realize that things are closely related and inspired by dialectical thinking.

3. Use multiplication to cultivate students' reasoning ability.

In particular, the ability of rational reasoning is an important task in this unit teaching. This unit not only arranges some contents to guide students to explore the law in the design of related exercises, such as 12 in Exercise 8 and 4 and 6 in Exercise 9. (Although some of the questions are marked with "*", they are generally not required, and they are good materials for developing students' reasoning ability), and we will take exploring the law of product change as an example for special research. In teaching, students should be encouraged and guided to participate in activities to explore the operating rules. By observing the characteristics of data and explaining the rationality of calculation, students can not only form reasonable and flexible calculation ability, but also cultivate their sense of numbers and reasoning ability.

4. Teaching the concept of "speed" and highlighting the connotation of "speed"

Teaching the concept of "speed" by intuitive description. What highlights the connotation of "speed" is the distance traveled per unit time. Compared with "unit price", it is more difficult to understand "speed", and the connotation of "speed" is the distance traveled per unit time. The textbook uses compound units to express the speed, such as the speed of the express train and the speed of Kobayashi walking, which are written as 150km/h and 60m/min respectively, in order to make students realize that it is simple and clear to express the movement speed with such symbols. Combined with solving simple travel problems, this paper discusses the relationship between speed, time and distance, constructs a mathematical model of "speed× time = distance", and applies this model to solve practical problems.

Examples 4 and 5 attach importance to guiding students to explore the quantitative relationship in operation and initially learn the mathematical methods of modeling. The focus of teaching is to understand and use the quantitative relationship between unit price, quantity and total price, and the quantitative relationship between speed, time and distance; Teaching difficulties: understand the concept of "speed and unit price" and master the method of expressing speed and unit price with conforming units.