say
course
rice straw
Division of the same base power.
Professional mathematics education
Instructor Lu Xiaoya
Class name number [1* * * * *] 8
May 25(th), 2008
I. Introduction to the topic
Selected from the first lesson of the first section of chapter 13 of the eighth grade mathematics in junior high school of East China Normal University Press.
Second, teaching material analysis
1, the position and function of this section in the textbook
The idempotent is one of the main contents of middle school mathematics and plays an important role in junior high school teaching. The main content of the division of power with the same radix is to introduce the origin and operational application of the division of power with the same radix. By learning the division with the same base number, we can consolidate the knowledge of multiplication with the same base number and the same base number, and it is also the basis for learning algebraic expressions and fractional division in the future. In addition, it is of great significance to cultivate students' innovative consciousness and their ability to observe, abstract, summarize, analogize, analyze and solve problems.
2. Target analysis
According to the requirements of the syllabus, the position, function and characteristics of the teaching materials in this section, and considering the cognitive level of senior two students, I have established the teaching objectives of this section from the following three aspects:
(1) knowledge goal: master the division algorithm of the same base power; Clever use of division with the same base is accurate.
(2) Ability goal: to cultivate students' abstract generalization ability by summarizing division operations; Train students' comprehensive problem-solving ability and calculation ability through examples and exercises.
(3) Emotional goal: Through students' active exploration, cooperative learning and mutual communication, they can feel the joy of exploration and success, thus enhancing their self-confidence; Understand the rigor of mathematics, develop a scientific attitude of seeking truth from facts and form rational thinking; Cultivate students' observation ability, make students have a strong interest in power learning, and let students actively integrate into learning.
3. Key points and difficulties
In order to achieve the above three goals, I have determined the key points and difficulties of this lesson as follows:
Emphasis: the division rules of the same base power and its application.
Difficulty: the origin of the same base power distribution rule.
Third, the analysis of teaching methods
According to the learning theory of constructivism, learning is a process in which learners actively construct new knowledge. Students pay attention to discovery, discover laws through analogy, solve problems, and develop inquiry ability and creativity. This course mainly adopts heuristic, analogy and discovery teaching methods.
Fourthly, the analysis of learning methods.
According to the concept of new curriculum standards, students are the main body of learning, and teachers are only the helpers and guides of learning. This course mainly enables students to learn by observing, analyzing, comparing, exploring and communicating, so as to acquire valuable theories and knowledge, flexibly use old knowledge to learn new knowledge, generate positive emotional experience, and then creatively solve problems, so that students can experience from "learning" to "learning".
Teaching process of verbs (abbreviation of verb)
According to the characteristics of teaching content, I divide this lesson into the following links:
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1, create a situation and review the introduction.
Situation 1: Ask students to recall, raise their hands to answer the rule of power with the same base, and encourage students to actively raise their hands to answer (and evaluate). At this time, write the rule of power with the same base: power with the same base, the base is unchanged, and the index is in phase.
m n m +n a？ A =a plus. That is (m and n are positive integers).
Situation 2: Calculate three questions. ① 10? × 10? = ,②25×2? 3A4A5 Design Intention: Review the old knowledge learned before, and let each student take the initiative to participate in learning mathematics in order to get into his role.
2. Ask questions and introduce new knowledge.
① 10? = 105，②25=28，③a 5=a 9。
Design intention: Compared with the first three questions, it reduces the difficulty of the questions, thus alleviating students' fear of doing the questions, narrowing the distance between teachers and students, and creating a relaxed and happy atmosphere for the next study and inquiry.
① 10? = 105，②25×28，③ a 5=a 9。
?
105÷ 10? = 10? = 105-3,28÷25= 2? =28-5，a 9÷a 5= a 4=a 9-5。
Question 1: What are the characteristics and similarities of these formulas?
Design intention: On the basis of students' existing knowledge, using Ausubel's "advance organizer" theory, let students discuss and find out the characteristics of these formulas themselves, and the teacher will guide them to get the division rule of the same base power. The purpose is to cultivate students' ability of observation and analysis.
Question 2: Can we draw any rules from these formulas?
Design intention: To guide students to explore, we found from the above calculation (same base powers's division rule: same base powers divides, the base remains the same, and the exponent decreases).
Namely:
Design intention: Let students discuss and summarize the connections and differences between the two laws, with the aim of deepening students' understanding of the laws and cultivating students' analogical and inductive abilities.
In order to deepen students' understanding and application of the law and consolidate new knowledge, let's enter the analysis of examples.
3, example analysis, familiar with new knowledge
Example 1 calculation
3①x 8÷x？ ，②(a+b) 10 \u( a+b)6，③\u y？ □y？ . (y 3)
Example 2: 81÷÷÷9 ÷í3 = 729. Find the value of X.
-3- 2x 2x
Design intention: The mastery of knowledge needs to go from shallow to deep, from easy to difficult. The three examples I designed increased in difficulty in turn. According to the principle of from the shallow to the deep, students learn to choose formulas first, and then go further to the deformation and application of formulas to consolidate their knowledge. In particular, the third question emphasizes the premise of applying rules: cardinality must be the same.
In order to deepen students' understanding and memory of the law, form the idea of "applying what they have learned" and arouse students' thinking, let them enter the stage of feedback practice and further consolidate their memory.
4, knowledge feedback, improve reflection
Practice 1 (1) oral answer
(a b ) ÷(b )(-)(-9)a ÷ a，② ① + a +，③ 3 ÷，
292082n+22n(-3)()⊙()(a b)⊙(a b)，6④，⑤ 33(-3) 2
(2) Calculation
8 2 18 ① 9 - 3 ÷ x ÷ x =，？ 27 ÷()=，②x 9333834
③. (1)? a ÷a =
Y 2x -y x a =3a a =2 Exercise 2: If you know, then =; 824 10
x -y =
Design Intention: According to Comenius' teaching consolidation principle, in order to cultivate students' ability to solve problems independently, after the example is explained, some students can perform on the blackboard, and the rest can complete exercises in the draft book to grasp the students' learning situation, so as to make appropriate supplementary reminders for the explanation content. At the same time, it can stimulate students' curiosity and strong thirst for knowledge, and gain good emotional experience while gaining experience and strategies.
5, summary and homework
This class is coming to an end. Let the students review the content of this lesson:
First, students summarize the content of this section, and then teachers supplement it.
1, the division rule of the same radix power;
2. Operating steps.
According to the new curriculum standard concept: everyone learns necessary mathematics; Everyone learns valuable mathematics; Different people get different development in mathematics. I divide my homework into compulsory questions and multiple-choice questions:
1, read textbooks and review what you have learned;
2. textbook p 23 5, 6, 7;
3. Choose question 8;
Preview the next section.
Sixth, blackboard design
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The design of blackboard writing directly affects the effect of this class, so it plays an important role. In order to make the whole blackboard writing focused and clear-cut, I divided it into four editions: the first edition is a new lesson explanation, the second and third editions are examples and exercises, and the fourth edition is a supplementary edition for reviewing old knowledge and asking situational questions, so that students can see at a glance.
My lecture is over, thank you!
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