Before this, the students in this class have already had experience in exploring the law of rational number addition, and most of them can explore problems under the guidance of teachers. Because students have understood the process of adding with the number axis and are not familiar with the change of water level, they use the number axis instead of the process of multiplication.
Second, preparation before class
According to the homogeneity between groups and heterogeneity within groups, students are divided into 10 groups, which is convenient for cooperative learning and competitive learning within groups and forms a good learning atmosphere.
Third, the teaching objectives
1, knowledge and skills target
Master the multiplication rule of rational numbers, and use the multiplication rule to multiply rational numbers correctly.
2, ability and process objectives
By exploring and summarizing the process of rational number multiplication rules, students' ability of observation, induction, guess and verification is cultivated.
3. Emotional and attitudinal goals
Let students explore the law by themselves and get the joy of success.
Four, the focus and difficulty of teaching
Key points: Use rational number multiplication rule to calculate correctly.
Difficulties: the exploration process and understanding of rational number multiplication law and symbolic law.
Teaching process of verbs (abbreviation of verb)
1. Create problem situations to stimulate students' desire for knowledge and introduce new lessons.
Teacher: Due to the long-term drought, the reservoir releases water to fight drought. We have put 2 meters of water every day for 3 days, and now the water depth is 20 meters. How many meters deep was the reservoir before releasing water for drought relief?
Student: 26 meters.
Teacher: Can you write formulas?
Student:
Teacher: This involves the multiplication algorithm of rational numbers, which is exactly what we need to discuss today (the topic of teacher's blackboard writing).
2. Group exploration and induction of laws
(1) The teacher shows the following questions and the students explore them in groups.
Taking the origin as the starting point, the eastern direction is defined as the positive direction and the western direction as the negative direction.
a.23
2 means moving 2 meters to the east, and 3 means moving 3 times to the original direction.
Result: Moving rice.
23=
b.-23
-2 is regarded as moving 2 meters to the west, and 3 is regarded as moving 3 times to the original direction.
Result: Moving rice.
-23=
c.2(-3)
2 means to move 2 meters to the east, and (-3) means to move in the opposite direction for 3 times.
Result: Moving rice.
2(-3)=
d.(-2)(-3)
-2 is regarded as moving 2 meters to the west, and -3 is regarded as moving in the opposite direction for 3 times.
Result: Moving rice.
(-2)(-3)=
E. If the multiplicand is zero or the multiplier is zero, the result is that people are still in the same place.
(2) Students' inductive rules
A. Symbols: We only look at symbols in the above four formulas. What are the rules?
(+) (+) = Same sign
(-) (+) = different symbol.
(+) (-) = Different symbol.
(-) (-) = same number
B. the absolute value of the product is equal to.
C. when any number is multiplied by zero, the product is still.
(3) Teachers and students use words to describe the multiplication rules of rational numbers.
3, the use of law calculation, consolidate the law.
(1) According to the textbook P75, Case 1, the teacher asked the students to explain the reasons for each step.
(2) Guide students to observe the relationship between the two factors (3) and (4) in the analysis example 1, and get that the two rational numbers are reciprocal, and the product is.
(3) Students do exercise P76 1( 1)(3), and the teacher comments.
(4) Teachers guide students to do Example 2 of P75, so that students can tell the rules of each step and make them more familiar with the rules. At the same time, let the students summarize the symbolic rules of multi-factor multiplication. Multiply multiple factors, the sign of the product is determined by, and when there is a negative factor, the product is; When there are negative factors, the product is; As long as one factor is zero, the product is.
4. Discuss and compare to make students' knowledge systematic.
Rational number multiplication rational number addition
The same symbol must take the same symbol.
Multiply by absolute value
(-2)(-3)=6 Add the absolute values.
(-2)+(-3)=-5
The sign of the opposite sign is negative, and the sign of the addend with large absolute value is taken.
Multiply by absolute value
(-2)3=-6(-2)+3= 1
Absolute value minus a larger absolute value.
Any number and zero of any number.
5, layered operation, consolidate and improve.
Six, teaching reflection:
The introduction of situation in this class makes students quickly enter the role and devote themselves to exploring the law of rational number multiplication, thus improving the teaching efficiency of this class. In the teaching implementation of this course, students are guided to explore and summarize from beginning to end, which truly embodies the teaching concept of taking students as the main body. This course pays special attention to process teaching, which is conducive to cultivating students' analytical and inductive ability. The teaching effect is satisfactory. If it is in the application of rules, it is possible to make up some oral arithmetic questions to train symbol rules, and it will be better to deal with example 2 next class.
Comments: In this class, Mr. Zhang first created a problem scene close to social life and drought resistance, thus introducing a new lesson and exploring the multiplication law of rational numbers by using the number axis that students are familiar with, which fully embodies the concept that courses originate from life, serve life, and students' learning is self-constructed on the original knowledge. Teaching should face students' life world and social practice, and teaching activities must respect students' existing knowledge and experience, which is the basis of learning.
Exploring the law of rational number multiplication is the focus of this lesson, and it is also an exploratory and challenging problem. Therefore, Mr. Zhang spent a lot of time in this teaching process, carefully designed the problem training list, and divided the students into study groups for cooperative learning according to the principle of homogeneity between groups and heterogeneity within groups, so that students could experience the process of exploring laws, gain profound emotional experience, construct knowledge, obtain solutions to problems, and cultivate students' exploration spirit and innovation ability.
In order to make students incorporate new knowledge into the original cognitive structure, which is convenient for them to remember and extract, in the last part of the teaching, Mr. Zhang organized students to compare the multiplication of rational numbers with the addition of rational numbers, and made the knowledge systematic and organized through discussion and comparison, and constantly optimized their cognitive structure. Students' self-construction of knowledge is the basic viewpoint of constructivist learning view. When new knowledge is acquired, it must be organized in a certain way in order to find a home and settle down for it.
Students are a living person and a developing person, and the development among students is extremely unbalanced. In order to respect students' differences, Mr. Zhang takes students' individual development as the foundation, makes use of students' individual personalities and adopts heterogeneous grouping in teaching, so that students with different personalities can exchange roles and achieve the goal of complementary personalities. By using the method of hierarchical homework, different people have made different progress in mathematics learning, and everyone's understanding has been improved, which is the core concept of new curriculum development-the concrete embodiment of developing each student.
In this class, we also see that in the two teaching links of introducing new curriculum and exploring laws, Mr. Zhang's design is completely different from the teaching materials, which fully reflects that teachers use teaching materials instead of teaching, which is also the teaching concept advocated by the new curriculum. Teaching textbooks is the performance of traditional teachers, and teaching with textbooks is the attitude that modern teachers should have. We teachers should proceed from the reality of students, teach students in accordance with their aptitude, creatively use textbooks, make bold choices, further process and recreate the contents of textbooks, design vivid and colorful classrooms, fully and effectively activate textbook knowledge, and form textbook knowledge with teachers' personality. We should not only have the ability to explain problems clearly and concisely, but also guide students to explore and learn independently.