Teaching plan of Secondary Roots 1 1. Content and content analysis
1, content
The concept of quadratic radical.
2. Content analysis
This lesson is based on students' learning the concepts of square root, arithmetic square root and cube root, knowing that the root sign is used to represent the square root and cube root of numbers, and that the root and power are reciprocal operations, learning the concept of quadratic square root. It is not only a comprehensive application of the previous knowledge, but also a foundation for learning the properties and four operations of quadratic roots later.
The textbook first sets three practical problems, and the results of these problems can be expressed in the form of quadratic roots, which all represent the arithmetic square roots of some positive numbers, thus leading to the definition of quadratic roots. Then, through the example of 1, the range of the number of letters in the quadratic root is discussed, so as to deepen students' understanding of the definition of quadratic root.
The teaching emphasis of this lesson is: understanding the concept of quadratic radical;
Second, the goal and goal analysis
1, teaching objectives
(1) Understanding and learning quadratic roots is a realistic need.
(2) Understand the concept of quadratic radical.
2. Analysis of teaching objectives
(1) Students can express the relationship between quantity and quantity in practical problems with quadratic roots, and realize the necessity of learning quadratic roots.
(2) Students can understand the concept of square root according to the meaning of arithmetic square root, know the reason why square root must be non-negative, and know that square root itself is a non-negative number, and they will find the range of letters in square root.
Third, the diagnosis and analysis of teaching problems
For the definition of quadratic root, students should focus on understanding "double nonnegative", that is, the number of roots ≥0 is nonnegative, and the arithmetic square root ≥0 is nonnegative. In teaching, we should pay attention to guiding students to recall the meaning and characteristics of square roots learned in the chapter of real numbers, help students understand this requirement, let students draw the conditions for the establishment of quadratic roots, and make a meaningful judgment on quadratic roots by using the conditions that the number of square roots is non-negative.
The teaching difficulty of this lesson is to understand the double nonnegativity of quadratic radical.
Fourth, the teaching process design
1. Create situations and ask questions.
Question 1 Can you fill in the blanks with the formula with the root sign?
(1) The side length of a square with an area of 3 is _ _ _ _ _ _, and the side length of a square with an area of S is _ _ _ _ _ _ _.
(2) A rectangular fence, twice as long as its width, with an area of 130? , its width is _ _ _ _.
(3) The time t (unit: s) when an object falls freely from a height to the ground and the height h (unit:) when it begins to fall satisfy the relationship h =5t? If t is expressed by an expression containing h, then t = _ _ _ _.
Teacher-student activities: Students independently complete the above questions, and the results are expressed as arithmetic square roots, and teachers give appropriate guidance and evaluation.
This design is intended to make students feel the close connection between quadratic roots and real life in the process of filling in the blanks, and realize the necessity of learning quadratic roots.
Question 2. What is the meaning of the formula obtained above? What do they have in common?
Teacher-student activities: Teachers guide students to say various meanings and summarize their * * * similarities: they all represent a non-negative arithmetic square root (including non-negative numbers expressed by letters or expressions).
This design intention paves the way for popularizing the concept of quadratic radical.
2, abstract generalization, forming a concept
Question 3: Can the arithmetic square root of a non-negative number be expressed by a formula?
Teacher-student activities: Students discuss in groups and communicate with the whole class. The teacher gave the definition of quadratic radical: generally speaking, we call the formulas with the shapes of (a≥0) quadratic radical and ""quadratic radical sign as quadratic radical.
The design intention is to let students experience the process from special to general and cultivate their generalization ability.
Follow-up: Why should we emphasize "a≥0" in the concept of quadratic radical?
Teacher-student activities: Teachers guide students to discuss the reasons why the square root of quadratic form must be non-negative.
This design aims to further deepen students' understanding that the square root of quadratic form must be non-negative.
3. Distinguish concepts and consolidate them through application.
Example 1 What kind of real numbers are meaningful in the range of real numbers?
Teacher-student activities: guide students to think from the concept and consolidate students' understanding of the right and wrong of the square root of the quadratic root.
When it is a real number, does it make sense in the range of real numbers? And then what?
Teacher-student activities: Let students think independently before asking questions.
The design intention is to deepen students' understanding of quadratic square root nonnegativity.
Question 4: Can we use 0 to compare sizes?
Teacher-student activities: through the discussion of two situations, compare the size of 0, guide students to draw the conclusion of ≥0, and strengthen students' understanding of the right and wrong of square root itself.
The design intention is to improve students' migration ability and application consciousness through the design of this activity; Cultivate students' ability of classified discussion and induction.
4. Comprehensive application, consolidation and improvement.
Complete the exercises on page three of the textbook.
Exercise 2 When x is a real number, the following are meaningful.
( 1) ; (2) ; (3) ; (4) 。
The design intention distinguishes the concept of quadratic root and determines the meaningful conditions of quadratic root.
Design intention design has a certain comprehensive topic, which examines students' flexible application ability, broadens students' horizons and trains students' thinking.
5. Summary and reflection
Teachers and students review the main contents of this lesson together and ask students to answer the following questions.
(1) What new expressions did you learn in this class?
(2) What are the conditions for quadratic roots to be meaningful? What is the range of the square root?
(3) What is the relationship between quadratic square root and arithmetic square root?
Teacher-student activities: teacher guidance, student summary.
Design intention: Students * * * sum up each other, learn from each other's strong points, highlight the learning focus of this lesson again, and master the problem-solving methods.
6。 Task:
Textbook exercise 16. 1 question 1, 3, 5, 7, 10.
Five, the target detection design
1, in the following categories, it must be quadratic ().
A. B. C. D.
The design intention is to investigate the understanding of the concept of quadratic root, paying special attention to whether the root sign is negative or not.
2, when the square root is meaningless.
The design intention is to investigate the meaningless condition of quadratic root, that is, the number of prescriptions is less than 0, so we should pay attention to the examination of the questions.
3. If the quadratic radical has a minimum value, its minimum value is.
Design Intention This topic mainly investigates the flexible application of quadratic non-negative square root.
4. For Xiaohong, according to the number of roots is non-negative, the range of values obtained is ≥0. Xiaohui thinks that we should also consider the case that the denominator is not 0. Do you think Xiaohui's idea is right? Try to find out the range of ...
The design intention is to check whether the square root of quadratic formula is non-negative, and the denominator of a formula cannot be 0, so it needs to be considered comprehensively when solving problems.
"The second radical" teaching plan 2 teaching material analysis:
The content of this section comes from the first lesson of the third section of Chapter 2 1 in the first volume of ninth grade mathematics. In this section, on the basis of learning the simplest multiplication and division methods of quadratic roots, we will learn the addition and subtraction algorithm of quadratic roots to further improve the simplification of quadratic roots. This section mainly talks about the addition and subtraction of quadratic roots. The textbook leads to the addition and subtraction of quadratic roots from a practical problem, which makes students feel it necessary to study the addition and subtraction of quadratic roots to solve practical problems. By exploring the quadratic radical addition and subtraction operation and using it to solve some practical problems, we can improve our consciousness and ability to solve practical problems with mathematics. In addition, the study in this section paves the way for students to skillfully add and subtract quadratic roots and the mixed operations of addition, subtraction, multiplication and division.
Student analysis:
The content of this lesson is the continuation and innovation of knowledge. Students actively participate in discussion, communication and construction, and independently explore, operate and cooperate. The whole class has solid knowledge and strong innovation ability. Most students can achieve teaching objectives through self-study and group discussion, while a few students have difficulties in learning, poor foundation and poor self-study ability. Therefore, we should provide appreciative evaluation teaching strategies, give individual care, psychological hints and appropriate spiritual incentives to overcome inferiority complex.
Design concept:
Effective classroom teaching in the new curriculum clearly advocates that students are the masters of learning. On the basis of self-learning texts, students practice, explore and cooperate independently, and advocate new learning concepts, thus completing the second part of radical addition and subtraction knowledge research. Teachers have changed from the past knowledge imparting to the designers and organizers of students' independent, inquiry and cooperative learning activities, and they have zero-distance contact with students and explore together. In the teaching process, teachers set up open, practical and challenging problem situations, so that students can cultivate their ability of analysis, induction and summary in trying, exploring, thinking, communicating and cooperating, and change "I want to learn" into "I want to learn". Through open-ended propositions, teachers try to find solutions to problems from different angles, develop good study habits, master learning strategies, and cultivate students to boldly elaborate and explain according to demonstration and guidance in activities. So as to create a good atmosphere of acceptance, support and inclusive learning.
Teaching objectives Knowledge and skills objectives:
Can simplify quadratic roots, understand the concept of similar quadratic roots, and can add and subtract simple quadratic roots; Solve practical problems in life through addition and subtraction.
Process and method objectives:
Experience the process of quadratic radical addition and subtraction by analogy with algebraic expression addition and subtraction; Students experience the process of introducing practical problems into mathematical problems and develop abstract generalization ability.
Emotional attitudes and values:
Through the exploration of quadratic radical addition and subtraction, we can stimulate students' enthusiasm for exploration and let them fully participate in the process of mathematics learning, so as to experience the fun of success.
Key points and difficulties: key points:
Merging similar quadratic roots with the same open number will perform simple quadratic root addition and subtraction operations.
Difficulties:
Practical application of quadratic radical addition and subtraction.
Key questions:
Understand the concept of similar quadratic roots, merge similar quadratic roots, and add and subtract quadratic roots.
Teaching methods:.
1. Guided discovery method: under the guidance of teachers, students are encouraged to actively participate, and the research mode of "problem-exploration-discovery" is adopted in combination with practical problems, so that students can explore independently, learn cooperatively, draw conclusions and master the rules.
2. Analogy: introducing quadratic radical addition and subtraction from practical problems; Analogy merging similar items merging similar quadratic roots.
3. Attempt training method: Through students' attempts, teachers give guidance on individual problems to achieve good educational results.
"Secondary Rooting" Teaching Plan Part III Teaching Objectives
Curriculum standards require that students should learn to learn and learn to study independently, so as to lay a solid foundation for students' lifelong learning. According to the requirements of syllabus and new curriculum standards, according to the content of teaching materials and the characteristics of students, I have determined the teaching objectives of this class.
1, understand the concept of quadratic radical
2. Understand the basic properties of quadratic roots, experience the process of observing, comparing and summarizing the basic properties of quadratic roots, and cultivate students' ability of induction and generalization.
3. By exploring the concept and nature of quadratic root, improve the ability of mathematical inquiry and inductive expression.
4. Students experience observation, comparison, summary, application and other mathematical activities, feel that mathematical activities are full of exploration and creativity, experience the fun of discovery, and improve their awareness of application.
Teaching Emphasis: Concept and Basic Properties of Quadratic Radical
Teaching difficulty: flexible application of basic properties of quadratic roots
Teaching methods and learning methods
The essence of teaching activities is a kind of cooperation and communication. Students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning. This lesson mainly adopts the methods of autonomous learning, cooperative inquiry and guiding improvement. According to the age characteristics of students and the existing knowledge base, this course focuses on strengthening the vertical connection between knowledge, expanding the space for students to explore and reflecting the cognitive process from concrete to abstract. In order to lay a solid foundation for the following study, for example, in the chapter of "pointed trigonometric function", many practical problems will be encountered, and the quadratic root will be transformed into the simplest quadratic root in the process of solving practical problems. Let students form the habit of learning mathematics from the perspective of connection and development.
teaching process
Activity 1: according to the students' existing knowledge, explore the concept of quadratic radical.
(1) Explore the concept of secondary roots. Starting with four practical problems (three geometric problems and one physical problem), set up problem situations to make students feel that learning secondary roots comes from life and serves life. Thinking: Fill in the blanks with the formula with the root sign to see what the results are. (1) Make a triangular ruler with two right angles of 7cm and 4cm respectively, and the length of its hypotenuse should be cm.
(2) The side length of a square with an area of S is
(3) The construction area is 6. 28m2 circular fountain with a radius of m(∏ take 3. 14)
(4) The time t (unit: s) for an object to freely fall from a height to the ground and the height h (unit: m) at the beginning of falling satisfy the relationship h=5t2. If the formula containing H is used to represent T, then t= Students find that the filled results all represent the arithmetic square root of a number, and the teacher guides students to use a formula to represent these formulas with the same characteristics. The students say "A". At this time, the teacher inspired the students to recall the nature of the square root they had learned and asked them to sum up the condition "A". On this basis, the concept of quadratic radical is summarized.
Example Analysis Example 1: What is a quadratic root? Exercise: What is the value of x? The following are meaningful. Through the training of four small questions, let students experience the preliminary application of the concept of quadratic root. Deepen the understanding of the definition of quadratic root, pay attention to the connection between old and new knowledge, solve problems with the idea of transformation, and summarize the law of solving problems: transform the range of unknown values into a series of inequalities or inequality groups with root number greater than or equal to 0 and denominator not equal to 0 to solve problems.
Activity 2: Explore the properties of square root 1 Explore the relationship between (a) and 0. Students discuss and explore that: (a) is non-negative, and then sum up the first property of quadratic root: double non-negative. Cultivate students' ability of classified discussion and generalization. Example 2:, and then the variant:,
Activity 3: Explore the Properties of Quadratic Radical 2 Explore () 2=a(a) Study the second properties of Quadratic Radical from specific positive numbers and zeros in textbooks. First of all, let students feel this conclusion through inquiry activities. Then, starting from the meaning of arithmetic square root, combining with concrete examples to analyze this conclusion, guiding students from concrete to abstract, drawing general conclusions, and discovering the relationship between square root operation and square operation, cultivating students' thinking mode from special to general. The first two questions are dictated by the teacher on the blackboard, and the last two questions are analyzed by the students on the blackboard. (2)(4) The essence is multiplication of products and multiplication of fractions. On the other hand, (a) paves the way for the simplest quadratic root (simple denominator is rational number). Example 4: Factorization in Real Number Range
Activity 4: Explore the properties of quadratic roots. Inquiry Show the fourth page of the textbook on the basis of Activity 3: Guide students to compare the differences between Activity 3 and Activity 4. The topic of activity 3 is to square non-negative numbers first, and then square them; The title of activity 4 is just the opposite, that is, square first, then square. Thirdly, from the special to the general, let the students summarize another property of the quadratic radical. Cultivate students' ability and consciousness of observation and comparison. At this time, guide the students to talk about the similarities and differences of the sum of () 2=a(a ()): ① There are sum of squares and square operations; ② The operation results are all non-negative; ③ Only when A is used, () 2= difference: ① From form and operation order: () 2. Front, rear; ② Value range from a: () 2. (A is an arbitrary number) ③ From the operation result.
The fourth part of the teaching plan of "Secondary Roots" I. On the position and function of teaching materials
1, content:
Addition and subtraction of quadratic root, using the mathematical idea of quadratic root simplification to solve the application problem, multiplying and dividing the monomial with quadratic root; Multiplication and division of polynomials and monomials; Multiplication and division of polynomials; Application of multiplication formula.
2. The position and function of this section in the textbook:
Quadratic roots continue to learn after learning the contents of Chapter 17 "Inverse Proportional Positive Function" and Chapter 18 "Pythagorean Theorem and Its Application" in the second volume of Grade 8, which is also the basis for learning other mathematical knowledge in the future.
Second, talk about teaching objectives, key points and difficulties:
1, teaching objectives:
(1) knowledge and skills:
1. Multiplication and division of quadratic root formula and application of quadratic root polynomial multiplication formula.
2. Review the operation knowledge of algebraic expressions and apply this knowledge to multiplication, division and multiplication of quadratic root formulas.
Understand and master the addition and subtraction method of quadratic root.
3. Solve application problems by quadratic root sum simplification.
4. Through review, the quadratic root is changed into the simplest quadratic root with the same number of roots, and the application problem after merging is solved.
(2) Mathematical thinking:
First, ask questions, analyze problems, and penetrate the understanding of the addition and subtraction method of quadratic roots in the analysis of problems. Then summarize the experience to guide the calculation and simplification of radicals.
(3) Problem solving: Ask questions first, let students discuss and analyze the problems, and teachers and students sum up the concepts together. Then the connotation of the concept is analyzed, and several important conclusions are drawn, and these important conclusions are used to calculate and simplify the quadratic root.
(3) Emotion, attitude and values: Cultivate students through the study of this unit: use the rigorous scientific spirit of accurate calculation and simplification, and cultivate students' ability to observe, analyze and find problems by exploring the important conclusions of quadratic roots and the laws of multiplication and division of quadratic roots.
2. Emphasis and difficulty in teaching: turning quadratic root into the simplest root. Rules for multiplication, division and multiplication of quadratic roots;
Third, how to highlight key points and break through difficulties:
The key to the difficulty: it is not only the focus of this lesson, but also the difficulty and focus of this lesson to judge whether it is the simplest quadratic root and explain the solution of the application problem clearly. Transfer from algebraic expression operation knowledge to quadratic root operation
In order to break through the difficulties, I pay attention to:
1, subtly cultivate students' reasoning ability from concrete to general, highlight key points and break through difficulties.
2. Cultivate students' ability to make accurate calculations by using the provisions of quadratic roots and important conclusions, and cultivate students' meticulous scientific spirit.
Analysis of learning situation: Quadratic root is the basis of learning the contents of Chapter 17 "Inverse Proportional Positive Function" and Chapter 18 "Pythagorean Theorem and Its Application" in the second volume of Grade 8, and it is also the basis of learning other mathematical knowledge in the future.
Fifth, talk about teaching strategies and learning methods.
(A) Analysis of teaching methods
According to the curriculum standards, students can take the initiative to try when facing practical problems, and use the knowledge and methods they have learned from the perspective of mathematics to seek strategies to solve problems. The teaching methods are group discussion, cooperative inquiry and problem teaching. Try to let the students ask questions, think about the answers, write the process and summarize by themselves. Let the step-by-step questions fill the classroom teaching and inspire students' thinking at all times. This teaching method conforms to the following educational laws:
1, following the principle of from shallow to deep, from special to general and then to special, embodies the law of unity of mastering knowledge and developing intelligence.
2. Creating problem situations, teachers constantly inspire and guide students to think, from easy to difficult, simplifying the complex, reflecting the law of combining the leading role of teachers with the main role of students.
(B) Analysis of learning methods
Make students learn to observe life, pay attention to practical problems in life, and learn to explore knowledge by themselves; Cultivate students' habit of observation and thinking, and encourage students to apply what they have learned to their lives. Learn to discover, discover and summarize, and gradually master the ability to actively acquire knowledge.
(3) Teaching methods
Using multimedia teaching, students can be better taught the research method of "quadratic root addition and subtraction" through visual demonstration, and at the same time, the teaching content can be displayed through multimedia auxiliary means, which can expand the classroom capacity and improve the teaching efficiency.
Sixth, the design of the teaching process:
This lesson is divided into five parts:
(A), review the introduction of new lessons:
Using the introduction of "similar secondary roots", students' curiosity and thirst for knowledge are stimulated, and scenarios are created, thus leading to new topics. It not only achieved the purpose of review, but also led to new lessons.
(2) Explore new knowledge:
Through the activities of 1 quotations and two examples, students can learn to abstract the basic properties of central symmetry from practical problems and solve practical problems by adding and subtracting quadratic roots. It not only cultivates students' observation ability, but also cultivates students' rational painting ability.
(3) Consolidation exercises:
In this link, after-school exercises and selected extracurricular exercises are used to consolidate the addition and subtraction of quadratic roots and achieve the purpose of highlighting key points.
(4), summary reflection:
In this class, I ask students to talk about their gains and experiences. Make students have a comprehensive review and reflection on this class, grasp the main idea and focus of this class, that is, fully mobilize the enthusiasm of students, so as to cultivate students' ability of induction and language expression.
(5), homework:
Expansion and sublimation: this part is divided into compulsory questions: questions in teaching materials. Choose to do the problem: (think about the problem) from the workbook. We must do all the students' questions well, consolidate the key points and train up to the standard. The choice of questions makes different students have different development. This not only achieves the goal of facing all students, but also achieves the goal of teaching students in accordance with their aptitude.
"Secondary Root" Teaching Plan 5 I. Talking about Teaching Materials
This lesson is selected from the first section of the second part of chapter 2 1 in the first volume of ninth grade mathematics of People's Education Press. "Quadratic Radical" is an important content of the curriculum standard "Number and Algebra". In this chapter, the real number (13.1square root; 13. Cubic root; 13.3 real number), the concept, properties and operation of quadratic roots are further studied. The content of this chapter is closely related to the real number, algebraic formula, Pythagorean theorem and so on, and also lays an important foundation for the acute angle trigonometric function, quadratic equation of one variable and quadratic function to be learned in the future.
Second, talk about learning.
Students have learned the square root (arithmetic square root) and other related knowledge, and have a certain knowledge base and cognitive ability. The knowledge learning in this class and beyond needs students' rigorous thinking, classified discussion and analogical mathematical thinking. If students can't understand and correctly recognize here, it will have a great impact on the subsequent study, so students are required to actively explore and think, train and consolidate in time, overcome learning difficulties, and truly "learn".
Third, talk about teaching objectives.
According to the requirements of the syllabus and the content analysis of the textbook structure, combined with the actual level of ninth-grade students and taking into account the psychological characteristics of students' existing cognitive structure, the following teaching objectives can be determined in this lesson:
1, knowledge and skills: master the concept of quadratic root, the value range of quadratic root and the value range of square root.
2. Process and method: the ability to deal with problems according to conditions and the ability to discuss problems by classification.
3. Emotional attitude and values: rigorous scientific spirit.
Fourth, talk about the key points and difficulties in teaching.
Teaching emphasis: the range of square root number of quadratic form
Teaching difficulty: the range of square root
Verb (abbreviation for verb) Speaking and teaching methods
The essence of teaching activities is a kind of cooperation and communication. Students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning. According to the age characteristics of students and the existing knowledge base, this course focuses on strengthening the vertical connection between knowledge, expanding the space for students to explore and embodying the cognitive process from concrete to abstract. In order to lay a solid foundation for the following study, for example, in the chapter of "pointed trigonometric function", many practical problems will be encountered, and in the process of solving practical problems, problems such as the constraints of quadratic roots will be encountered. In this class, we should strengthen the practice appropriately, so that students can form the habit of learning mathematics from the perspective of connection and development.
Six, said the learning method
The new curriculum standard points out that students are the main body of learning. In order to make students become real masters, teachers should guide students to think independently, explore cooperatively and sum up together in the process of mathematics teaching, thus reflecting students' dominant position in learning. This course mainly adopts the methods of autonomous learning, cooperative inquiry, guidance and promotion, heuristic, teaching and practice. First, ask questions, let students discuss and analyze problems, and teachers and students jointly summarize the concepts; Then the connotation of the concept is analyzed, and several important conclusions are drawn, and these important conclusions are used to calculate and simplify the quadratic root. Through the study of this lesson, we can inspire students' divergent thinking, train students' ability to observe, analyze and find problems, and cultivate students' dialectical materialistic views.
"Secondary Roots" Teaching Plan 6 I. Talking about Teaching Materials
First of all, talk about my understanding of the textbook. This lesson is selected from the first volume of the eighth grade of People's Education Press, and mainly explores the calculation method of quadratic radical addition and subtraction. Before, students had the experience of simplifying quadratic roots when learning the properties of quadratic roots and multiplication and division, which laid a good foundation for the study of this course. The study of this lesson lays the foundation for the subsequent study of the mixed operation of quadratic roots.
Second, talk about learning.
Let's talk about students. At this stage, students have the ability to find and solve problems, and their logical thinking and calculation ability have also been greatly improved. Therefore, in the teaching process, teachers should carry out targeted teaching according to the characteristics of students, so as to facilitate the effective development of course content.
Third, talk about teaching objectives.
Based on the above analysis, I have formulated the following three-dimensional teaching objectives:
Knowledge and skills
Master the calculation method of quadratic radical addition and subtraction and use it to solve simple problems.
(2) Process and method
By exploring the calculation process of quadratic radical addition and subtraction, I can further feel the idea from special to general and improve my calculation ability.
(3) Emotion, attitude and values
Feel that mathematics is closely related to life and enhance your interest in learning mathematics.
Fourth, talk about the difficulties in teaching.
In the process of realizing the teaching goal, the teaching emphasis is the calculation method of quadratic radical addition and subtraction, and the teaching difficulty is the exploration of the calculation method of quadratic radical addition and subtraction.
V. preaching the law
Modern teaching theory holds that in the teaching process, students are the main body of learning and teachers are the organizers, guides and collaborators of learning. According to this teaching concept, I will adopt teaching methods such as teaching, practice and group cooperation and inquiry in this class.
Sixth, talk about the teaching process.
The following focuses on the teaching process I designed.
(A) the introduction of new courses
At this time, I will ask students to try to summarize the calculation method of quadratic radical addition and subtraction. With students' existing ability, they can tell the key content. On this basis, let me standardize: generally speaking, when adding and subtracting secondary roots, you can first change the secondary roots into the simplest secondary roots, and then merge the secondary roots with the same number.
The above activities enable students to personally experience the formation process of knowledge, which is easier to understand and accept, and at the same time improve their ability to analyze, solve and transfer by analogy.
(3) Classroom exercises
For this lesson, exploring calculation methods is one of the goals, and consolidating exercises is equally important. I will choose example 1 and example 2 in the textbook as classroom exercises.
The (1) sub-item of example 1 is the subtraction of two concrete quadratic roots, which is relatively simple, so the calculation method of addition and subtraction of quadratic roots is directly examined; (2) The quadratic root of the event contains letters, which is general and tests abstract thinking to some extent.
In Example 2, (1) item is more difficult, not only the quadratic root is relatively complex, but also the addition and subtraction mixed operation; In the second sub-question, parentheses appear on the basis of addition and subtraction, and parentheses cannot be combined, so they are removed one more step.
This practice not only further improves the calculation method of quadratic root addition and subtraction, but also makes students realize the consistency between quadratic root addition and subtraction and algebraic expression addition and subtraction in the process, thus establishing the connection between old and new knowledge and perfecting the knowledge system.
(4) Summarize the homework
Finally, I will let the students summarize the harvest of this class independently, and get teaching feedback while exercising their ability to summarize and express.
On the one hand, the homework is to complete the exercises after class and consolidate the addition and subtraction of quadratic roots again; On the other hand, the concept, properties and algorithm of quadratic root are summarized, thus forming systematic cognition.