1. Junior high school mathematics courseware
First, the teaching purpose
1. Through the analysis of many practical problems, students can realize the function of linear equations as mathematical models of practical problems.
2. Let students build a linear equation to solve some simple application problems.
3. Will judge whether a number is the solution of an equation.
Second, the key points and difficulties
1. Important: We will make a linear equation to solve some simple application problems.
2. Difficulties: Understand the meaning of the question and the "reciprocal relationship".
Third, the teaching process
(a) review of issues
A notebook 1.2 yuan. Xiaohong is 6 Qian Qi, so how many notebooks can she buy at most?
Solution: Suppose Xiaohong can buy a notebook, then according to the meaning of the question, it is 1.2x=6.
Because 1.2×5=6, Xiaohong can buy five notebooks.
(2) Newly awarded
Question 1: There are 328 teachers and students in the first grade of junior high school in a school, who go out for a spring outing by car. There are already two school buses that can seat 64 people. How many 44-seat buses do you need to rent? Let the students think, then answer, and then the teacher comments. )
Arithmetic: (328-64)÷44=264÷44=6 (vehicle).
Equation: Suppose you need to rent X buses, you can get.
44x+64=328( 1)
Solve this equation and you will get the desired result.
Q: Can you solve this equation? Try it?
Question 2: In extracurricular activities, Teacher Zhang found that most of her classmates were 13 years old, so she asked her classmates, "I am 45 years old this year. How many years later, your age will be one third of mine? "
Through analysis, the equation is listed: 13+x=(45+x).
Q: Can you solve this equation? Can you be inspired by Xiao Min's solution?
Let x=3 to generate equation (2), left = 13+3= 16, right =(45+3)=×48= 16,
Because left = right, x=3 is the solution of this equation.
This method of getting the solution of the equation through experiments is also a basic mathematical thinking method. You can also test whether a number is the solution of an equation.
Q: If "one third" in Example 2 is changed to "one half", what is the answer? Just try it. What problems have you found?
Similarly, it is difficult to get the solution of the equation by testing, because the value of x here is very large. In addition, the solutions of some equations are not necessarily integers, so where should we start? What if I can't find the manpower for the test?
Fourth, consolidate practice.
Textbook exercise
Verb (abbreviation of verb) abstract
In this lesson, we mainly learned how to set equations to solve practical problems and solve some practical problems. Talk about your study experience.
2. Junior high school mathematics courseware
First, the 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.
Second, teaching suggestions
(A) the focus and difficulty of teaching
Key points: Understand and apply the formula through concrete examples.
Difficulties: Find the relationship between quantity and abstract it into concrete formulas from practical problems, and pay attention to the inductive thinking method reflected from it.
(2) 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.
(C) 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.
Three. 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.
3. Junior high school mathematics courseware
First, the teaching objectives
(A) knowledge teaching points
1. Enable students to use formulas to solve simple practical problems.
2. Make students understand the relationship between formulas and algebraic expressions.
(2) Key points of ability training
1. Ability to solve practical problems with mathematical formulas.
2. The ability to derive new formulas from known formulas.
(C) moral education penetration point
Mathematics comes from production practice, which in turn serves production practice.
(D) the starting point of aesthetic education
Mathematical formulas use concise mathematical forms to clarify the laws of nature, solve practical problems, form colorful mathematical methods, and let students feel the beauty of simplicity of mathematical formulas.
Second, the guidance of learning methods
1. Mathematical method: guided discovery method, which breaks through the difficulties on the basis of reviewing the formulas learned by asking questions in primary schools.
2. Students' learning methods: observation → analysis → deduction → calculation.
Three. Key points, difficulties, doubts and solutions
1. Emphasis: A new graphic calculation formula is derived from the old formula.
2. Difficulties: The emphasis is the same.
3. Doubt: How to decompose the required graphics into the sum or difference of the already familiar graphics.
Fourth, the class schedule
One class.
Verb (abbreviation for verb) Prepare teaching AIDS and learning tools.
Projector, homemade film.
Sixth, the design of teacher-student interaction activities.
The instructor projects and displays the figure that deduces the trapezoidal area formula, the students think, and the teachers and students * * * solve the problem as an example1; Teachers inspire students to find the area of graphics, and teachers and students summarize the formula for finding the area of graphics.
4. Junior high school mathematics courseware
First, the 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.
Second, the key points and difficulties
(A) 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.
(2) 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 is permeated with 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, under the premise of giving concrete examples, teachers first create situations 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 can participate in the excavation of the ideas contained in it, make clear that the application of the formula is universal and realize the flexible application of the formula.
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.
Verb (abbreviation of verb) teaching goal
(A) the main points of knowledge teaching
1, so that students can use formulas to solve simple practical problems.
2. Make students understand the relationship between formulas and algebraic expressions.
(2) Key points of ability training
1, the ability to use mathematical formulas to solve practical problems.
2. The ability to derive new formulas from known formulas.
(C) moral education penetration point
Mathematics comes from production practice, which in turn serves production practice.
(D) the starting point of aesthetic education
Mathematical formulas use concise mathematical forms to clarify the laws of nature, solve practical problems, form colorful mathematical methods, and let students feel the beauty of simplicity of mathematical formulas.
Sixth, the teaching steps
(A) the creation of scenarios, review the import
Teacher: As you already know, an important feature of algebra is to use letters to represent numbers. There are many applications of letters to represent numbers, and formulas are one of them. We learned many formulas in primary school. Please recall which formulas we have learned. Teaching methods show that students can participate in classroom teaching from the beginning, and later they are unfamiliar with formula calculation.
After the students said several formulas, the teacher suggested that we learn how to use formulas to solve practical problems on the basis of primary school study in this class.
Blackboard writing: formula
Teacher: What area formulas have you learned in primary school?
Blackboard: S = ah
(Display projection 1). Explain the area formulas of triangle and trapezoid.
5. Junior high school mathematics courseware
First, the teaching objectives
Knowledge and skills
Knowing the concept of number axis, rational numbers can be accurately represented by points on the number axis.
(2) Process and method
Through observation and practical operation, we can understand the corresponding relationship between rational numbers and points on the number axis, and realize the idea of combining numbers with shapes.
(3) Emotion, attitude and values
In the process of combining numbers with shapes, we can experience the fun of mathematics learning.
Second, the difficulties in teaching
(A) the focus of teaching
The three elements of the number axis represent rational numbers with points on the number axis.
(B) Teaching difficulties
The thinking method of combining numbers and shapes.
Third, the teaching process
(A) the introduction of new courses
Ask a question: through the example of the meaning of numbers on a thermometer, it is concluded that there is also an axis in mathematics that can be used to represent numbers like a thermometer, which is the number axis we are studying today.
(2) Explore new knowledge
Student activities: group discussion, showing the relationship between poplars, willows and bus stop signs on the east-west road in the form of painting;
Question 1: In the above questions, "east" and "west", "left" and "right" all have opposite meanings. We know that positive and negative numbers can represent quantities with opposite meanings. Then, how to use numbers to represent the relative positions of these trees, telephone poles and bus stop signs?
Student activity: Ask questions after painting a picture.
Question 2: What does "0" stand for? What is the practical significance of the symbols of numbers? Answer the thermometer.
The teacher gave a definition: in mathematics, numbers can be represented by points on a straight line, which is called the number axis, and it meets the following conditions: take any point to represent the number 0, representing the origin; Usually, the right (or up) on a straight line is the positive direction, and the left (or down) from the origin is the negative direction; Select the appropriate length as the unit length.
Question 3: How to understand the three elements of the number axis?
Both teachers and students sum up that the "origin" is the "benchmark" of the number axis, which means 0 and is the dividing point between positive and negative numbers. The positive direction is artificially specified, and the appropriate unit length should be selected according to the actual problem.
(3) Classroom exercises
As shown in the figure, write the numbers represented by points A, B, C, D and E on the number axis.
(4) Summarize the homework
Question: What did you get today?
Guide the students to review: the three elements of the number axis, and use the number axis to represent the number.