Power of rational numbers 1 Analysis of teaching content of teaching plan;
"Power of rational number" is the content of the fifth section of the first chapter of the seventh grade of People's Education Press, and it is a basic operation of rational number. Judging from the arrangement structure of teaching materials, this section is ***3 class hours, and this section is the first class. It is learned after students have learned the addition, subtraction, multiplication and division of rational numbers and Divison. It is the extension and continuation of rational number multiplication, and it is also the mixed operation and science of rational numbers in the follow-up study. Through this lesson, students can discover laws, cultivate inductive ability and feel the mathematical thought of classification.
Analysis of teaching objectives:
(1), knowing the concepts of power, base, exponent and power, can perform power operation of rational numbers;
(2) After deducing the concept of rational number power, cultivate students' ability of observation, comparison, analysis and generalization, and further feel the mathematical thinking method of classification.
(3) Students try to acquire new knowledge through knowledge transfer, and enhance their awareness of mathematics application by discovering problems, studying problems and exploring laws.
Analysis of teaching difficulties;
1. Analysis of learning situation: From the knowledge base, students have learned to find the area of a square and the volume of a cube in primary school, have the knowledge level of finding the square sum cube of a positive number, and just learned the multiplication of rational numbers, which can help students understand the definition and representation of power well and realize the positive transfer of knowledge. However, it is difficult for students to master the symbolic law of rational number power, and it is easy to confuse this calculation, which is the difficulty of this lesson.
2. Emphasis and difficulty in teaching
Teaching emphasis: understand the definition of power and carry out the power operation of rational numbers;
Teaching Difficulties: Formation and Application of Symbolic Rules for Rational Number Multiplication
Pedagogical analysis;
Teaching methods: heuristic teaching, multimedia-assisted teaching;
Learning methods: observation, comparison, induction and cooperative inquiry.
Teaching process design:
1, create situational questions
The area of a square with a side length of 3 (1) is ___3×3, which can be written as _ _ and read as _ _ _ _ _ _ _.
(2) The volume of a cube with a side length of 3 is _ _ 3× 3× 3, which can be written as _ _ and read as _ _ _ _ _ _ _ _.
By creating problem situations, we can arouse old knowledge and pave the way for learning new knowledge.
2, independent exploration, forming new knowledge.
What are the characteristics of observing the following types?
( 1)2×2×2×2=
(2)(-3)×(-3)×(-3)=
Through analogy, exploration and induction of the definition and expression of power, students are guided to realize knowledge transfer and cultivate their ability of induction and generalization. Obviously, power is a special form of multiplication, which embodies the mathematical thought of reduction.
3. Apply new knowledge to consolidate concepts.
Exercise 1 2 consolidates the definition of power and matters needing attention in power expression, and cultivates students' good study habits. Examples further strengthen the multiplication operation.
4. Explore and discover the law.
Through problem group training, exploring laws, cooperation and communication, the symbolic rules of power operation are obtained, and the role of students as learning subjects is fully exerted, reflecting the mathematical thought of classification.
5. Apply new knowledge to consolidate training.
Further consolidate students' ability to use symbolic rules and power knowledge to solve problems.
6. Expand the extension of thinking knowledge
Use stories to improve students' interest in learning mathematics, cultivate students' ability to solve problems by applying mathematics, and stimulate students' enthusiasm for exploration.
7. Class summary, induction and reflection
Exercise students' good habit of summarizing in time and inductive ability.
Teaching evaluation analysis;
Evaluate students' participation in the inquiry process and cooperation and communication with classmates, so as to enhance students' initiative in learning;
(1) Pay attention to students' intellectual participation.
(2) Students participate in the classroom.
2. Evaluate students at different levels through layered exercises to meet the development of students' knowledge and skills at different levels.
Lecture Notes of Power of Rational Numbers 2 The content of the lesson I am talking about today is the content of the first lesson of Power of Rational Numbers, the first volume of seventh grade mathematics published by People's Education Publishing House. The new curriculum standard puts forward the concept of "let students experience the process of abstracting practical problems into mathematical models and explaining and applying them, so that students can make progress and development in thinking ability, emotional attitude and values while understanding mathematics". In my design, I strive to make "independent exploration, hands-on practice, cooperation and communication" the main way for students to learn. Next, I will elaborate the design of this class from the following four aspects.
I. teaching material analysis
1, the position and function of teaching materials:
The power of rational number is a basic operation of rational number. Judging from the structure of the textbook arrangement, * * * needs four class hours, and this class is the first class hour, based on students' learning of addition, subtraction, multiplication and division and Divison. It is not only the promotion and continuation of rational number multiplication, but also the basis for continuing to learn rational number mixed operation, scientific notation and prescription science, which plays a role in connecting the past with the future and paving the way.
2. Teaching objectives:
According to the requirements of the new curriculum standards and the cognitive level of grade seven students, I set the teaching objectives of this lesson as follows:
(1), knowledge and skills:
Let students understand and master the concepts and meanings of power, power, base and exponent of rational numbers; Can correctly perform rational number multiplication.
2, process and method:
Let students get a preliminary experience of rational power in vivid scenes; Cultivate students' ability of observation, analysis, induction and generalization; Go through the deduction process from multiplication to power, and feel the mathematical thought of transformation from it.
(3), emotion, attitude and values:
Let students summarize the symbolic law of rational number power through observation and reasoning, so as to enhance students' self-confidence in learning mathematics well; Let students experience the process of knowledge expansion, cultivate students' ability of inquiry and operation, and realize the importance of cooperation and communication with others.
3. Teaching emphases and difficulties:
The meaning and operation of the power of rational number is the teaching focus of this course, and the understanding of the concepts of power, exponent and base in the power of rational number and their relations is the teaching difficulty of this course.
Second, the teaching law
1, learning situation analysis:
In terms of knowledge mastery, because students have just learned addition, subtraction, multiplication and division of rational numbers and Divison, their understanding of many concepts and laws is not necessarily profound, which may easily lead to knowledge forgetting and confusion. Therefore, in the study of this class, we should talk about it comprehensively and systematically.
In terms of knowledge barriers, students may be confused about the understanding of related concepts in the power of rational numbers and the derivation and application of their symbolic laws. Therefore, in the teaching of this class, we should make a simple and clear analysis.
As far as the characteristics of students are concerned, the seventh grade students are eager to learn and curious. Therefore, we should grasp this characteristic of students in teaching. On the one hand, we should use intuitive and vivid images to arouse students' interest and keep their attention in class. On the other hand, we should create conditions and opportunities for students to express their opinions and give full play to their initiative in learning.
2. Teaching strategies:
According to the teaching objectives, teaching materials and the comprehension and thinking characteristics of seventh grade students. I will take multimedia as the teaching platform, and adopt heuristic teaching method and teacher-student interaction teaching mode. Through well-designed questions and activities, we constantly create exciting thinking points, so that students can operate by themselves and explore conclusions in the learning process. Teaching students to observe more, work hard, make bold guesses and be willing to delve into the discussion-based learning method will enable students to gain full experience and development in the process of thinking, working hard and speaking, thus mobilizing their initiative and enthusiasm for learning.
Third, the teaching process
1. Set up games and introduce new lessons:
First, let all students play two origami games with the help of multimedia and cardboard prepared before class.
The first game is to fold the rectangular cardboard with an area of 1 in half along the middle, so that the two sides overlap completely. Ask the students to think: What is the area of a rectangle after being folded five times? Get the formula: xxxx
The second game is for students to fold the rectangular pieces of paper in half and then cut them along the crease, and then fold and cut all the pieces of paper together. Do this five times, how many pieces of cardboard are there? The formula is: 2× 2× 2× 2× 2;
Finally, guide students to think about the characteristics of these two formulas and introduce new lessons.
In this link, students can intuitively understand the characteristics of electric power operation through hands-on operation, which plays a navigation role in subsequent study.
2, cooperation and exchange, explore new knowledge:
Ask the students to discuss the characteristics of the following formulas in groups: ① xxxx, ② 2× 2× 2× 2, ③(-3)×(-3)×(-3)×(-3), ④(-0.3)×(-0.3)×(-0.3).
Then let the students think about the relationship between square area and side length a, and the relationship between cube volume and side length a, and draw the following conclusions: A A = A, a a a = a. Then let the students compare the notation and reading of the above four formulas, and finally guide the students to guess: the result of A is
The purpose of the link design of N A is to allow students to analogize the representation of power through the representation of square area and cubic volume from the game results, and to summarize related concepts. It not only embodies the process of students' thinking, but also permeates the transformation thought.
3, migration training, summing up the law:
In this session, I first ask students to put the formulas ① (-4 )×-4 (-4) and ② (-2) ×-2. Then the example 1 is evaluated, and the positive and negative laws of the power of negative numbers are summarized in combination with the solution results of the example 1. Then inspire students to think about changing the cardinality of each question in the example 1 to a positive number or 0. What will happen? On the basis of students' practice and discussion, the symbolic law of rational number power is summarized. That is, the odd power of a negative number is negative and the even power of a negative number is positive. Any power of a positive number is a positive number, and any power of a positive integer is 0. Finally, combined with Example 2, students are required to master the usage of the calculator and use the calculator to complete the exercises in the textbook to further understand the symbolic law of the power of rational numbers.
The design intention of this link is for students to practice by changing the conditions of example 1 and then draw a conclusion. It is conducive to stimulating students' interest in learning, exposing them to the wonders of mathematics and improving their enthusiasm and initiative.
4. Apply new knowledge and try to practice:
In this session, I mainly designed two groups of exercises. The first group of exercises aims at using the sign law, and by calculating (-2), -2 and -2, students can further master the application method of the sign law of rational number power, and make it compare with (-2) and \
The second group of exercises is designed for practical and comprehensive application of this ability, and there are two exercises in total. I hope that with the help of the first question, students can learn to use the power knowledge they have learned to solve practical problems and promote them to establish an idea of learning and using mathematics. The second question is the comprehensive application of power and rational number comparison, which can help students improve their mathematical analysis ability and comprehensive problem-solving ability.
5. Summarize and form a system:
First of all, encourage students to sum up the harvest and experience of this class freely; Then help students build their own knowledge system; Then arrange the extracurricular homework in this class; Finally, talk about the blackboard design of this lesson.
Fourth, the design description
The teaching design of this course is to determine the appropriate starting point and goal according to the requirements of the new curriculum standard and students' cognitive basis. Content arrangement is a process from the introduction of concepts to the discovery and application of the law of rational number power sign, which gradually displays knowledge and makes students' thinking gradually expand and deepen. In teaching, multimedia and learning tools are used to assist teaching, and pictures and animations are displayed, so that students can realize that mathematics is everywhere and used all the time, and find and ask questions from the perspective of mathematics. For example, from the simple origami game, we can get different types of electricity problems, and we can use the mathematical knowledge and methods we have learned to explore, study and solve these problems. It embodies the teaching concept of the new curriculum standard.