As a mathematics educator, it is often necessary to prepare teaching plans, which are the main basis for implementing teaching and play a vital role. The following is the template of junior high school math teaching plan I compiled for you, I hope you like it!

Junior high school mathematics teaching plan template 1 1, teaching material content

_ _ Press, Mathematics, Experimental Textbook of Compulsory Education Curriculum Standards, Volume II, pages 2-4, Example 1, Example 2.

Second, the teaching objectives

1. Guide students to know negative numbers in familiar life situations and read and write positive numbers and negative numbers correctly; Know that 0 is neither positive nor negative.

2. Make students learn to express some practical problems in daily life with negative numbers and experience the connection between mathematics and life.

3. Carry out patriotic education for students in combination with negative history; Cultivate students' good mathematics emotion and attitude.

Third, the importance and difficulty of teaching

Understand the meaning of negative numbers.

Fourth, the teaching process

(1) Talking and communicating

Dialogue: Students, as soon as class begins, everyone will do a set of opposite actions. What is that? (Stand up and sit down. ) Today's math class begins with this topic. (On the blackboard: On the contrary. There are many natural and social phenomena around us that have the opposite situation. Look at the screen. The sun rises in the east and sets in the west every day; Someone got on and off at the bus stop; There are buying and selling in the bustling market; There are losers and winners in the fierce competition ... can you name some such phenomena?

(B) new teaching knowledge

1. quantities with opposite meanings

(1) Introduce an example

Dialogue: If you continue to "chat" along the topic just now, you will naturally enter mathematics. Let's look at a few examples (courseware demonstration).

(1) The sixth grade was transferred to six students last semester and six students this semester.

② Aunt Zhang made a profit 1500 yuan in February, and lost money in 200 yuan in March.

③ Compared with the standard weight, Xiaoming weighs 2.5 kg and Xiaohua is light 1.8 kg.

④ The water level of the reservoir rises by meters in summer and drops by meters in winter.

It is pointed out that when these opposing words are combined with specific quantities, they become a group of "quantities with opposite meanings". (Supplementary blackboard writing: quantity in the opposite sense. )

(2) Try

How can these quantities with opposite meanings be expressed mathematically?

Please choose an example and try to write a statement.

(3) Show communication

2. Know positive and negative numbers

(1) introduces positive and negative numbers.

Let's talk about it: Just now, some students wrote "+"in front of 6, which means 6 people are transferred, and adding "-"means 6 people are transferred (blackboard writing: +6-6), which is completely in line with mathematics.

Introduction: Numbers like "-6" are called negative numbers (blackboard writing: negative numbers); The number is: minus six.

"-"has a new meaning and function here, which is called "minus sign". +is a plus sign.

Like "+6" is a positive number, pronounced as: plus six. We can add "+"before 6 or omit it (blackboard writing: 6). In fact, many of the numbers we used to know were positive.

(2) Give it a try

Please use positive numbers and negative numbers to represent another set of quantities with opposite meanings.

After writing, communicate and check.

3. Connecting with practice and deepening understanding

(1) What do the numbers in the passbook mean? (Teaching example 2. )

(2) Combining with real life, a set of quantities with opposite meanings are given, which are expressed by positive numbers and negative numbers.

① Communicate at the same table.

② Class communication. Write it on the blackboard according to the students' speeches.

Can you finish writing such positive and negative numbers? (blackboard writing: ...)

Emphasize that these familiar integers, decimals and fractions are all positive numbers, also called positive integers, positive decimals and positive fractions; Put a negative sign in front of them, and they become negative integers, negative decimals and negative fractions, collectively called negative numbers.

practise

Read and fill in.

Display theme

Students, think about it. What new knowledge did you learn today? Who is your new friend? Can you decide a topic for today's math class?

Summarize what you have learned in this lesson according to the students' answers, and choose the topic on the blackboard: understanding negative numbers.

Junior high school mathematics teaching plan template 21. Teaching objectives:

1, understand the concept of binary linear equation and its solution;

2. Learn to find several solutions of a binary linear equation and test whether a pair of values is the solution of a binary linear equation;

3. Learn to use the linear expression of an unknown in a binary linear equation to represent another unknown;

4. In the process of solving problems, the analogy method is infiltrated into education.

Second, the teaching emphasis and difficulty:

Emphasis: the significance of binary linear equation and the concept of solution of binary linear equation.

Difficulties: The essence of transforming a binary linear equation into an algebraic expression about an unknown number to represent another unknown number is to solve an equation with a letter coefficient.

Third, teaching methods and teaching means:

Strengthen students' analogical thinking method by comparing with linear equation of one variable; Through "cooperative learning", let students understand that mathematics develops according to actual needs.

Fourth, the teaching process:

1, scene import:

News link: Old people over x70 can get living allowance.

Get the equation: 80a+ 150b=902880,

2. New teaching:

Guide students to observe whether equation 80a+ 150b=902880 is similar to linear equation.

The concept of binary linear equation is obtained: an equation with two unknowns and the term 1 degree is called binary linear equation.

Do it:

(1) List the equations according to the meaning of the question:

(1) Xiaoming went to visit his grandmother, bought 5 Jin of apples and 3 Jin of pears and went to 23 yuan. He asked for the unit price of apples and pears respectively, and set the unit price of apples as X yuan/kg and pears as Y yuan/kg.

(2) On the expressway, the car at 2 o'clock is 20 kilometers longer than the truck at 3 o'clock. If the speed of the car is a km/h and the speed of the truck is b km/h, the equation can be obtained:

(2) Exercise P80 in textbook 2. Decide which equations are binary linear equations.

Cooperative learning:

Full of love in the activity background —— Qiushi Middle School's "Caring for the Elderly" volunteer activity.

Question: The 36 volunteers who participated in the activity were divided into labor group and literature and art group, including 3 in labor group and 6 in literature and art group. The Communist Youth League Secretary plans to arrange 8 labor groups and 2 literature and art groups. Just considering the number of people, is this plan feasible? Why? Substitute x=8 and y=2 into the binary linear equation 3x+6y=36 to see if the left and right sides are equal. The concept that the two sides of the equation can be made equal and the solution of the binary linear equation can be obtained by students' test: a pair of unknown values that make the two sides of the binary linear equation equal is called a solution of the binary linear equation.

And put forward the writing method of paying attention to the solution of binary linear equation.

3. Cooperative learning:

Given the equation x+2y=8, male students give the value of Y (X is an integer whose absolute value is less than 10), and female students immediately give the corresponding value of X; Next, boys and girls communicate (compare which students react faster). Ask the fastest and most accurate student to talk about his calculation method, and ask: given the value of X, what is the coefficient of Y when calculating the value of Y, and what is the easiest way to calculate Y?

For example, it is known that the binary linear equation x+2y=8.

(1) x is expressed by an algebraic expression about y;

(2) y is expressed by an algebraic expression about x;

(3) Find the corresponding value of y when x = 2,0 and -3, and write three solutions of the equation x+2y=8.

When y is represented by a linear formula containing x, please play a game to let students know whether the calculation speed is fast or not. )

4. Classroom exercises:

(1) It is known that 5xm-2yn = 4 is a binary linear equation, then m+n =;

(2) In the binary linear equation 2x-y= 3, when x=2, the equation can be transformed into y =;

5. Can it be solved?

Xiaohong went to the post office and sent a registered letter to her grandfather who was far away in the countryside. She needs 3 yuan and 80 cents for postage. Xiaohong has several stamps with a ticket amount of 60 cents and 80 cents. How many stamps of these two denominations does she need? Tell me your plan.

6, class summary:

The meaning of (1) binary linear equation and the concept of its solution (pay attention to the writing format);

(2) Uncertainty and correlation of the solution of binary linear equation;

(3) The binary linear equation is transformed into an algebraic expression of an unknown to represent another unknown.

7. Task:

A little.

Formula method of junior high school mathematics teaching plan template 3

Understand the derivation process of root formula of quadratic equation in one variable, understand the concept of formula method, and skillfully apply formula method to solve quadratic equation in one variable.

This paper reviews the solving process of finite number quadratic equation with one variable by collocation method, introduces the derivation of the root formula of ax2+bx+c=0(a≠0), and applies the formula method to solving quadratic equation with one variable.

focus

Derivation of root formula and application of formula method.

difficulty

Derivation of root formula of quadratic equation with one variable.

First, review the introduction.

1, we have learned the "direct Kaiping method" for solving quadratic equations in one variable, for example, equations.

( 1)x2=4 (2)(x-2)2=7

Question 1 What is the (theoretical) basis of this solution?

Question 2: What are the limitations of this solution? (It is only valid for the special quadratic equation "the flat track is equal to non-negative" and cannot be applied to the general quadratic equation. )

2. What should I do in the face of this limitation? (Using collocation method, the general quadratic equation is formulated into a form that can be "directly squared". )

(Student activity) Solve equation 2x2+3=7x by matching method.

(Teacher's comment)

Summarize the steps of solving a quadratic equation with collocation method (students summarize and teachers comment).

(1) First, transform the known equation into a general form;

(2) The coefficient of quadratic term is1;

(3) The constant term moves to the right;

(4) Add the square of half the coefficient of the first term to both sides of the equation, so that the left side is matched in a completely flat way;

(5) The deformation form is (x+p)2=q, and if q≥0, the root of the equation is x =-p q；; If you ask

Second, explore new knowledge.

Solving equations by matching method;

( 1)ax2-7x+3 = 0(2)ax2+bx+3 = 0

If the general form of this unary quadratic equation is ax2+bx+c=0(a≠0), can you work out two of them with the steps of the matching method above? Please complete the following questions independently.

Question: Given ax2+bx+c=0(a≠0), try to find its two roots, x 1=-b+b2-4ac2a, x2=-b-b2-4ac2a (is there a solution to this equation? When will there be a solution? )

Analysis: Because we have made a lot of specific numbers, now we might as well take A, B and C as a specific number and continue to push according to the above steps.

Solution: Move the item to get: AX2+BX =-C.

Convert the quadratic term into 1 and get x2+bax=-ca.

Formula: x2+bax+(b2a)2=-ca+(b2a)2.

That is, (x+b2a)2=b2-4ac4a2.

∵4a 2 & gt； 0, when b2-4ac≥0, B2-4ac2 ≥ 0.

∴(x+b2a)2=(b2-4ac2a)2

Direct square, x+B2a = B2-4ac2a.

X =-b B2-4ac2a。

∴x 1=-b+b2-4ac2a,x2=-b-b2-4ac2a

As can be seen from the above, the root of the unary quadratic equation ax2+bx+c=0(a≠0) depends on the coefficients A, B and C of the equation, so:

(1) When solving a quadratic equation with one variable, we can first change the equation to the general form ax2+bx+c=0. When b2-4ac≥0, we can substitute A, B and C into the equation X =-B B2-4ac2a to get the root of the equation.

(2) This formula is called the root formula of quadratic equation in one variable.

(3) The method of solving a quadratic equation in one variable by finding the root formula is called formula method.

Understanding of formula

(4) According to the root formula, a quadratic equation with one variable has at most two real roots.

Example 1 Solve the following equation by formula method:

( 1)2 x2-x- 1 = 0(2)x2+ 1.5 =-3x

(3)x2-2x+ 12 = 0(4)4x 2-3x+2 = 0

Analysis: to solve a quadratic equation with one variable by a formula, we must first turn it into a general form and then substitute it into a formula.

Supplement: (5)(x-2)(3x-5)=0

Third, consolidate the practice.

Exercise 1. Textbook page 12 (1)(3)(5) or (2)(4)(6).

Fourth, class summary.

This lesson should master:

The concept of (1) formula for finding roots and its derivation process;

(2) The concept of formula method;

(3) Steps to solve a quadratic equation with one variable by formula: 1) Turn the given equation into a general form, pay attention to changing the sign of the term, and try to make A >；; 0; 2) Find out the coefficients A, B and C, and note that the coefficients of each item contain symbols; 3) b2-4ac is calculated, and if the result is negative, the equation has no solution; 4) If the result is non-negative, substitute it into the root formula and calculate the result.

(4) Understand the roots of quadratic equation in one variable.

Verb (abbreviation for verb) assignment

Textbook/kloc-page 0/7 Exercise 4

Factorization method

Master factorization method to solve quadratic equation with one variable.

By reviewing the collocation method and formula method for solving the quadratic equation of one variable, we know and explore a simpler method for solving the quadratic equation of one variable-factorization method, and apply factorization method to solve some specific problems.

focus

Solving quadratic equation with one variable by factorization.

difficulty

Through the comparison of various methods, let students understand how to solve a quadratic equation with one variable.

First, review the introduction.

(Student activities) Solve the following equations:

(1)2x2+x=0 (by matching method) (2)3x2+6x=0 (by formula method)

Teacher's comments: (1) After dividing both sides of the equation by 2, the coefficient before X should be 12, and half of 12 should be 14, so (14) 2 should be added and (14 subtracted).

Second, explore new knowledge.

(Student activity) Please answer the following questions orally.

(The teacher asked) (1) Are there constant terms in the above two equations?

(2) Are the terms on the left side of the equation the same factor?

(Students answer first, the teacher answers) The above two equations have no constant terms; The left side can be factorized.

Therefore, the above two equations can be written as:

( 1)x(2x+ 1)= 0(2)3x(x+2)= 0

Because the product of two factors should be equal to 0, at least one factor should be equal to 0, that is, (1)x=0 or 2x+ 1=0, so x 1=0, x2=- 12.

(2)3x=0 or x+2=0, so x 1=0 and x2=-2. (How do the above solutions achieve reduction? )

Therefore, we can find that the solution of the above two equations is not the square root reduction, but the factorization of the equation into the form that the product of two linear equations is equal to 0, and then the two linear equations are equal to 0 respectively, thus reducing the order. This solution is called factorization.

Example 1 Solving equation:

( 1) 10x-4.9 x2 = 0(2)x(x-2)+x-2 = 0(3)5x 2-2x- 14 = x2-2x+34(4)(x- 1)2 =(3-2x)2

Thinking: What are the conditions for solving a quadratic equation with one variable by factorization?

Solution: ellipsis (one side of the equation is 0, and the other side can be decomposed into the product of two linear factors. )

Exercise: Among the following solutions of quadratic equation with one variable, the correct one is ().

A.(x-3)(x-5)= 10×2,∴x-3= 10,x-5=2,∴x 1= 13,x2=7

B.(2-5x)+(5x-2)2=0,∴(5x-2)(5x-3)=0,∴x 1=25,x2=35

C.(x+2)2+4x=0,∴x 1=2,x2=-2

D.x2=x, divide both sides by x to get x= 1.

Third, consolidate the practice.

Exercise on page 14 of the textbook 1, 2.

Fourth, class summary.

This lesson should master:

(1) Use factorization, that is, extracting common factors, cross multiplication, etc. Solution of quadratic equation with one variable and its application.

(2) Factorization method should multiply one side of the equation by two linear factors, and the other side is 0, and then make each linear factor equal to 0.

Verb (abbreviation for verb) assignment

Exercise 6, 8, 10, 1 1 on page 17 of the textbook.

Junior high school mathematics teaching plan template 4 1. Teaching objectives:

1, cognitive goal:

1) Understand the concept of binary linear equations.

2) Understand the concept of solutions of binary linear equations.

3) I will try to find the solution of binary linear equations by listing.

2, ability goal:

1) permeates the idea of abstracting practical problems into mathematical models.

2) Cultivate students' exploration ability by trying to solve it.

3, emotional goals:

1) Cultivate students' careful study habits.

2) Promote emotional communication between teachers and students in positive teaching evaluation.

Two. Emphasis and difficulty in teaching

Emphasis: the concept of binary linear equations and its solution.

Difficulty: try to find the solution of equations by list method.

Three. teaching process

(A) create scenarios and introduce topics

1. There are 40 students in this class. Can you confirm the number of people? Why?

(1) If there are x boys, _ people in this class, how can it be expressed by an equation? (x+y=40)

(2) What equation is this? According to what?

2. Boys are better than two. Suppose there are x boys, _. How to express the equation? What are the values of x and y?

There are 2 boys and 40 boys in this class. There are x boys in this class. How to express the equation?

What does x mean in the two equations? Y in two similar equations represents?

In this way, the same unknown represents the same quantity, so we connect them with braces to form an equation group.

4. Point out the topic: Binary linear equations.

[Design intent: Take data from students and make them feel that there is mathematics everywhere in their lives]

(2) Explore new knowledge and practice consolidation.

1, the concept of binary linear equations

(1) Please read the textbook, understand the concept of binary linear equations and find out the key words.

Let the students read the books and draw their attention to the teaching materials. Find the key words and deepen their understanding of the concept. ]

(2) Exercise: Judge whether the following are binary linear equations:

x+y=3，x+y=200，

2x-3=7，3x+4y=3

y+z=5，x=y+ 10，

2y+ 1=5，4x-y2=2

Students make judgments and give reasons.

2. The concept of solution of binary linear equations.

(1) The student gives the answer to the example, and the teacher points out that this is the solution of the system of equations.

(2) Exercise: Fill in the order of the following groups in the appropriate position in the figure:

x = 1； x =-2； x =； -x=

y = 0； y = 2； y = 1； y=

The solution of equation x+y=0, the solution of equation 2x+3y=2, and the solution of equation x+y=0.

2x+3y=2

(3) The solution that satisfies both the first equation and the second equation is called the solution of the binary linear equations.

(4) Exercise: It is known that x=0 is the solution of the system of equations x-b=y, and the values of A and B are found.

y=0.55x+2a=2y

(3) Cooperation and exploration, and efforts to solve.

Now let's explore how to find the solution of the equation.

1, given two integers x, y, try to find the solution of the equation set 3x+y=8.

2x+3y= 10

Students explore in pairs. And let the students who have found the solution of the equations use physical projection to explain their own problem-solving ideas.

Refining method: list trial and error method.

Take an appropriate xy value from one equation and try to substitute it into another equation.

Return the classroom to students, let them explore and answer questions, and accumulate experience in mathematics activities while acquiring new knowledge. ]

It is understood that a store sells two kinds of "double happiness" table tennis with different asterisks. Among them, "Double Happiness" two-star table tennis has 6 in a box and Samsung table tennis has 3 in a box. A classmate bought 4 boxes, which happened to have 15 balls.

(1) Suppose the classmate "Double Happiness" bought X boxes of two-star table tennis, and Samsung bought Y boxes of table tennis. Please list the equations about x and y according to the conditions in the question. (2) Solving the equations with list trial algorithm.

Finish it independently by students, and analyze and explain it.

(D) class summary, homework

1. What knowledge and methods have you learned in this course? (Binary linear equations and solution concepts, list trial and error method)

2. Do you have any questions or ideas to communicate with you?

3. Exercise book.

Explain the design description:

1. There are two main lines in the design of this lesson. One is the knowledge line, from the concept of binary linear equations to the concept of binary linear equations to the list trial algorithm, which is interlocking and step by step; The second is the ability training line. Students learn the concept of binary linear equation and inductive solution by reading books, and then explore independently and try to solve problems by listing, step by step and gradually improve.

2. "Let students become the real subject of the classroom" is the theme of this course design. Students give data and get results. After actively trying to achieve mutual evaluation among students, let them explain. Give everything in the class to the students, and I believe they can further learn and improve their existing knowledge. The teacher is just on call, guiding the way.

3. In the course of designing this course, the teaching materials have also been modified appropriately. For example, considering several generations, students gradually lost interest in movies, so they switched to playing table tennis, which students are familiar with. On the other hand, fully tap the role of practice, lay a solid foundation for the implementation of knowledge and pave the way for students' further study in the future.

Junior high school mathematics teaching plan template 5 1, master the relationship between the roots and coefficients of a quadratic equation and apply it initially.

2. Cultivate students' ability of analysis, observation, induction and reasoning.

3. Understand the law of things from special to general, and then from general to special.

4. Cultivate students' enthusiasm for discovering laws and the spirit of daring to explore.

focus

The relationship between root and coefficient and its derivation

difficulty

Correctly understand the relationship between roots and coefficients. The relationship between roots and coefficients of a quadratic equation in one variable refers to the relationship between the sum of two roots and the product and coefficient of two roots.

First, review the introduction.

1, given that one root of equation x2-ax-3a=0 is 6, then find the value of a and the other root.

2. From the above questions, we can know that the coefficient of quadratic equation in one variable is closely related to the root. In fact, the formula for finding roots we have learned also reflects the relationship between roots and coefficients. This relationship is more complicated. Is there a more concise relationship?

3. According to the root formula, the two roots of the unary quadratic equation ax2+bx+c=0(a≠0) are x 1=-b+b2-4ac2a, and x2=-b-b2-4ac2a. Looking at the right side of the two equations, the denominator is the same, and the numerators are -b+b2-4ac and-.

Second, explore new knowledge.

Solve the following equations and fill in the table:

Equation x1x2x1+x2x1? x2

x2-2x=0

x2+3x-4=0

x2-5x+6=0

What conclusion can you draw by observing the above table?

(1) equation x2+px+q=0(p, q is constant, p2-4q≥0) What is the relationship between two x 1, x2 and the coefficients p, q?

(2) What is the relationship between the equation ax2+bx+c=0(a≠0) and the coefficients A, B and C? Can you prove your guess?

Solve the following equations and fill in the table:

Equation x1x2x1+x2x1? x2

2x2-7x-4=0

3x2+2x-5=0

5x2- 17x+6=0

Summary: the relationship between root and coefficient:

(1) equation x2+PX+Q = 0 The relationship between X (P, q is constant, p2-4q≥0)X2 and the coefficients p, q is: x 1+X2 =-P, x 1? X2=q (Note: The prerequisite of the relationship between root and coefficient is that the discriminant of root must be greater than or equal to zero. )

(2) For the equation in the form of ax2+bx+c=0(a≠0), we can first convert the quadratic term into 1, and then use the above conclusion.

That is, for the equation ax2+bx+c=0(a≠0).

∵a≠0,∴x2+bax+ca=0

∴x 1+x2=-ba,x 1？ x2=ca

(It can be proved by the formula for finding the root)

Example 1 Do not understand the equation, and write the sum and product of the following equations:

( 1)x2-3x- 1 = 0(2)2 x2+3x-5 = 0

(3) 13x2-2x=0 (4)2x2+6x=3

(5)x2- 1 = 0(6)x2-2x+ 1 = 0

Example 2 Do not solve the equation, and check whether the solution of the following equation is correct?

( 1)x2-22x+ 1 = 0(x 1 = 2+ 1，x2=2- 1)

(2)2x2-3x-8=0 (x 1=7+734，x2=5-734)

Example 3 It is known that the two roots of a quadratic equation are-1 and 2. Please write the equation that meets the requirements. How many ways do you have? )

Example 4 It is known that one root of the equation 2x2+kx-9=0 is -3, so find the value of the other root and k. ..

Variant 1: Given two opposites of equation x2-2kx-9=0, find k;

Variant 2: It is known that the two roots of equation 2x2-5x+k=0 are reciprocal to each other, and k is found.

Third, the class summary

1, the relationship between root and coefficient.

2. The premise of the relationship between root and coefficient is that (1) is a quadratic equation with one variable; (2) Discriminant is greater than or equal to zero.

Fourth, homework

1, don't understand the equation, write the sum and product of the following equation.

( 1)x2-5x-3 = 0(2)9x+2 = x2(3)6x 2-3x+2 = 0

(4)3x2+x+ 1=0

2. Given that one root of the equation x2-3x+m=0 is 1, find the value of the other root and m. ..

3. Given that one root of equation x2+bx+6=0 is -2, find the value of the other root and b.