1. Junior high school mathematics courseware
I. teaching material analysis
The content of this section is "Mathematics (May 4th Academic System), an experimental textbook for compulsory education courses" published by People's Education Publishing House (Tianjin Edition), the second volume of Grade 8, Chapter 10 Algebraic Addition and subtraction in the first quarter and Algebraic addition and subtraction in the second quarter.
Second, the design ideas
The content of this section is that students have mastered the extended learning of related concepts of algebraic expressions, which lays a foundation for the subsequent study of algebraic expression operation, factorization, quadratic equation of one variable and function knowledge. It is a formal transition from "number" to "formula" and has a very important position.
Grade eight students have strong numerical operation skills and a sense of "combination" (used to solve a linear equation), as well as preliminary observation, induction and exploration skills. Therefore, based on the teaching materials, with the aim of making every student develop, I use cooperative inquiry learning to carry out teaching activities, guide students by designing targeted and multi-style questions, and provide students with a full and harmonious inquiry space for students to learn. Learning activities not only cultivate students' awareness of simplification and improve their mathematical operation skills, but also make students deeply realize that mathematics is an important tool to solve practical problems and enhance their awareness of applying mathematics.
Third, the teaching objectives:
(1) Knowledge and skill objectives:
1, understand the meaning of similar items and distinguish them.
2. Master the method of merging similar items and be proficient in merging similar items.
3. Master the addition and subtraction of algebraic expressions and operate skillfully.
(2) Process and method objectives:
1. Cultivate students' ability of observation, induction and inquiry by exploring the definition and combination of similar items.
2. Through the combination of addition and subtraction exercises of similar terms and algebraic expressions, students' operation skills and accuracy are improved, students' awareness of simplification is cultivated, and their ability of abstract generalization is developed.
3. Develop students' thinking in images and cultivate students' sense of symbols by studying examples and exploring examples 1.
(3) Emotional value goal:
1. Cultivate students' awareness of cooperation and communication and the spirit of daring to explore unknown issues through communication, consultation and group inquiry.
2. Cultivate students' scientific and rigorous learning attitude through learning activities.
Four, the teaching emphasis and difficulty:
Combine similar terms
Five, the key to teaching:
The concept of similar goods
Six, teaching preparation:
Teacher:
1, select math problems and carefully set the problem situation.
2. Make two physical models of rectangular cartons with different sizes and unfold them.
3. Design multimedia teaching courseware. (It is necessary to highlight ① the characteristics of coefficient, letter and index in a single item ② the perspective view and development diagram of rectangular carton. )
Student:
1, review the concept of monomial, the four operations of rational numbers and the rule of removing brackets)
2. Make two cuboid carton models with different sizes in each group.
2. Junior high school mathematics courseware
First, the content characteristics
It is similar to the first expansion of number system in knowledge and method. It is also the basis of subsequent content learning.
Content orientation: understand the concepts of irrational number and real number, and understand the concept of (arithmetic) square root; Will use the root sign to represent the (arithmetic) square root of a number, will find the square root and cube root, will use rational numbers to estimate the approximate range of an irrational number, and will perform four simple operations on real numbers (the denominator is not required to be rational numbers).
Second, the design ideas
Overall design ideas:
The introduction of irrational number-the expression of irrational number-real number and related concepts (including real number operation), the application of real number runs through the whole content.
Learning object-real number concept and its operation; Learning process-introducing irrational numbers through puzzles, explaining how to express irrational numbers by solving specific problems, and then establishing the concept of real numbers; The algorithm of seeking truth by analogy and inductive exploration; Learning methods-operation, guessing, abstraction, verification, analogy, reasoning, etc.
Specific process:
Firstly, the concept of irrational number is given through puzzle activities and calculator exploration activities, and then the concepts of square root and cubic root and the operation of square root are introduced by solving specific problems. Finally, the textbook summarizes the concept and classification of real numbers, and introduces the related concepts, operation rules and operation properties of real numbers by analogy.
The first section: How numbers are not enough: Let students feel the actual background of irrational numbers and the necessity of introducing them through puzzles; With the help of calculator, it is explored that irrational numbers are infinite acyclic decimals, and the idea of infinite approximation is realized. Will judge whether a number is rational or irrational.
Section two and section three: square root and cube root: how to represent the side length of a square? What is its value? The concepts of arithmetic square root, square root, cube root and square root are introduced.
Section 4: How wide is the park? In real life and production, we often get the approximate value of irrational numbers through estimation. Therefore, this section introduces the estimation methods, including estimating the comparison size and checking the rationality of the calculation results, in order to develop students' sense of numbers.
Part 5: Find the square root and cube root with a calculator. Experience the activities of using calculators to explore mathematical laws and develop the ability of rational reasoning.
Section 6: Real numbers. The concept and classification of real numbers are summarized, and the related concepts, operation rules and operation properties of real numbers are introduced by analogy.
Third, some suggestions.
1. Pay attention to the process of concept formation, so that students can gradually understand the concepts they have learned in the process of concept formation; Pay attention to students' understanding of the meaning of irrational numbers and real numbers.
2. Encourage students to explore and communicate, and attach importance to students' ability of analysis, generalization and communication.
3. Pay attention to the use of analogy, so that students can understand the differences and connections between old and new knowledge.
4. Desalinate the concept of quadratic radical.
3. Junior high school mathematics courseware
I. Content and content analysis
1. Content
The concept of related elements in triangle, the classification of edges and the trilateral relationship of triangle.
2. Content analysis
Triangle is one of the most basic geometric figures and the basis for understanding other figures. In this chapter, we have learned the related concepts and properties of triangles well, laying a good foundation for further learning the related contents of polygons. This section mainly introduces the concept of triangles, classification by sides and the relationship between triangles, so that students can have a deeper understanding of the relevant knowledge of triangles.
The teaching focus of this lesson: related concepts in triangle and triangular trilateral relationship.
The teaching difficulty of this lesson: the trilateral relationship of triangle.
Second, the goal and goal analysis
1. Teaching objectives
(1) Understand the related concepts in the triangle and learn to express the corresponding elements in the triangle with symbolic language.
(2) Understand and flexibly use the triangular trilateral relationship.
2. Analysis of teaching objectives
(1) Understand the concept of triangle and its basic elements by combining specific figures.
(2) Symbols and letters are used to represent related elements in triangles, and triangles are classified by edges.
(3) Understand the property that the sum of two sides of a triangle is greater than the third side, and use this property to solve problems.
Third, the diagnosis and analysis of teaching problems
In the process of exploring the triangular relationship, let students experience activities such as observation, inquiry, reasoning and communication, and cultivate their harmonious reasoning ability and cooperative learning spirit.
Fourth, the teaching process design
1. Create situations and ask questions.
Question: Recall an example of a triangle in your life. Combined with your previous understanding of triangle, please give the definition of triangle.
Teacher-student activities: Let the students discuss in groups first, and then send representatives from each group to speak. According to the definition given by students, various graphic counterexamples are given, as shown below, to point out their incompleteness and deepen students' understanding of the concept of triangle.
The acquisition of the concept of design intention triangle requires students to go through the process of its description, thus cultivating students' language expression ability and deepening their understanding of the concept of triangle.
2. Abstract generalization, forming a concept
Dynamically demonstrate the animation of "head to tail" and summarize the definition of triangle.
Teacher-student activities:
Definition of triangle: A figure composed of three line segments that are not on the same straight line and are connected end to end is called a triangle.
The design intention is to let students experience the process from abstract to concrete, and to cultivate students' language expression ability.
Supplementary note: Students are required to learn the concepts and geometric expressions of triangles, vertices, edges and angles of triangles.
Teacher-student activities: Teachers combine specific graphics to guide students to analyze and let students learn the transition from written language to geometric language.
The design intention is to further deepen students' understanding of the related elements in the triangle and to be familiar with the application of geometric language in learning.
3. Concept discrimination and application integration
As shown in the figure, all triangles are identified without repetition and omission, and expressed in symbolic language.
(1) What are the triangles with AB as one side?
(2) What are the triangles with internal angles ∠D?
(3) What are the triangles whose vertices are E?
(4) Name three angles of δδBCD.
Teacher-student activities: guide students to think from the concept and deepen their understanding of the concepts of related elements in the triangle.
4. Broaden the extension and explore the classification.
We know that triangles can be divided into acute triangles, right triangles and obtuse triangles according to the size of three internal angles. If you want to classify triangles according to the size relationship of sides, how should you divide them? Talk among the students in the group and talk about your ideas.
Teacher-student activities: Through discussion, students use the method of classification by angle to classify triangles by edges, and then introduce the concepts of isosceles triangle and equilateral triangle to guide students to understand the relationship between isosceles triangle and equilateral triangle and strengthen their understanding of triangle classification by edges.
4. Junior high school mathematics courseware
First, the teaching purpose
1. Make students further understand the range of independent variables and the significance of function values.
2. Let the students draw a graph of a simple function.
Second, the focus and difficulty of teaching
Key points: 1. Understand and recognize the meaning of function images.
2. Cultivate students' ability to read pictures.
Difficulties: How to correctly select the corresponding values of independent variables and functions in the drawing three-step list.
Third, the teaching process
Review questions
What are the three representations of 1. function? Answer: Analytical method, tabular method and graphic method.
2. Combined with the image of function y=x, what is the image of the function?
3. Name the quadrant or coordinate axis where the following points are located:
New lesson
1. The method of drawing function images is the method of tracing points. The steps are as follows:
(1) list. Pay attention to the appropriate selection of independent variables and corresponding values of functions. What is "appropriate"? -This requires selecting several key points that represent the image features of this function. For example, if you draw an image with function y=3x, the key point is the origin (0,0). Just choose another point, such as m (3 3,9).
Generally speaking, we regard the corresponding values of independent variables and functions as the abscissa and ordinate of points respectively, so we should list the corresponding values of independent variables and functions.
(2) Point tracking. We take the ordered real number pairs given in the table as the coordinates of the points and trace the corresponding points in the rectangular coordinate system.
(3) Connect straight lines with smooth curves. According to the resolution function, such as y=3x, we connect (0,0) and (3,9) into a straight line.
Generally speaking, there are only a limited number of points in our list and description according to the resolution function. We only need to connect these finite points into curves (or straight lines) representing functions in a plane rectangular coordinate system.
2. Explain the three steps and examples of drawing function images. Draw an image of the function y=x+0.5.
summary
The focus of this lesson is to let students draw their own pictures according to the three steps of drawing function images by resolution function.
practise
(1) Select the teaching materials to practice (the previous section has already done: list and trace points, and this section requires contact)
② Supplementary question: Draw the image of function y = 5x-2.
homework
Choose a textbook to practice.
Fourth, teaching considerations
1. Pay attention to the idea of combining numbers with shapes. By studying the image of a function, we can have a more vivid and intuitive understanding of the change of one variable represented by the image with another variable. It is more helpful to understand the essential characteristics of the function by combining the analytical formula, list and image of the function.
2. Pay attention to fully arouse the enthusiasm of students to draw their own pictures.
People realize that the popularity of calculators and computers has replaced the function of manual drawing, so it is necessary to cultivate students' ability to read pictures in teaching.
5. Junior high school mathematics courseware
Teaching objectives
1. Understand the meaning of the formula, so that students can use the formula to solve simple practical problems;
2. Initially cultivate students' ability of observation, analysis and generalization;
3. Through the teaching of this course, students can initially understand that formulas come from practice and react to practice.
Teaching suggestion
First, the focus and difficulty of teaching
Key points: Understand and apply the formula through concrete examples.
Difficulties: Find the relationship between quantity from practical problems and abstract it into concrete formulas, and pay attention to the inductive thinking method embodied in it.
Second, analysis of key points and difficulties
People abstract many commonly used and basic quantitative relations from some practical problems, which are often written into formulas for application. For example, the area formulas of trapezoid and circle in this lesson. When applying these formulas, we must first understand the meaning of the letters in the formula and the quantitative relationship between these letters, and then we can use the formula to find the required unknowns from the known numbers. The concrete calculation is to find the value of algebraic expression. Some formulas can be deduced by operation; Some formulas can be summed up mathematically from some data (such as data tables) that reflect the quantitative relationship through experiments. Solving some problems with these abstract general formulas will bring us a lot of convenience in understanding and transforming the world.
Third, knowledge structure.
At the beginning of this section, some commonly used formulas are summarized, and then examples are given to illustrate the direct application of formulas, the derivation of formulas before application, and some practical problems are solved through observation and induction. The whole article runs through the dialectical thought from general to special, and then from special to general.
Four. Suggestions on teaching methods
1. For a given formula that can be directly applied, the teacher creates a situation under the premise of giving specific examples to guide students to clearly understand the meaning of each letter and number in the formula and the corresponding relationship between these numbers. On the basis of concrete examples, students participate in excavating the ideas contained therein, make clear that the application of formulas is universal, and realize the flexible application of formulas.
2. In the teaching process, students should realize that there is no ready-made formula to solve problems, which requires students to try to explore the relationship between quantity and quantity themselves, and derive new formulas on the basis of existing formulas through analysis and concrete operation.
3. When solving practical problems, students should observe which quantities are constant and which quantities are changing, make clear the corresponding change law between quantities, list formulas according to the laws, and then solve problems further according to the formulas. This cognitive process from special to general and then from general to special is helpful to improve students' ability to analyze and solve problems.