Algebraic expression, math teaching plan for junior one.

Teaching objectives and requirements of algebraic expression (1);

1. Understand the concepts of monomial and monomial coefficient and degree.

2. Will accurately and quickly determine the single coefficient and times.

3. Initially cultivate students' thinking ability and application consciousness such as observation, analysis, abstraction and generalization.

4. Through group discussion and cooperative learning. Experience the process of concept formation and cultivate students' ability to explore knowledge independently and cooperate and communicate.

Teaching emphases and difficulties:

Key points: master the concepts of single item and single item's coefficient and frequency, and determine a single item's coefficient and frequency accurately and quickly.

Difficulties: the establishment of the concept of monomial.

Teaching methods:

Teaching at different levels, combining teaching with practice.

Teaching process:

First, review the introduction:

1, column algebra

(1) If the side length of a square is a, the area of the square is ().

(2) If the length of one side of a triangle is a and the height of this side is h, the area of this triangle is ().

(3) If X represents the length of a square, the volume of the square is ()

(4) If m represents a rational number, its inverse is ()

(5) Xiaoming saves X yuan from his monthly pocket money and donates it to Project Hope. Xiaoming donates () yuan every year.

Mathematics teaching should be closely linked with students' real life, which is the task entrusted by the new curriculum standards. Let students list algebraic expressions, not only to review the previous knowledge, but also to pave the way for the latter monomial, and at the same time let students receive better ideological and moral education. )

2. Ask the students to say the meaning of the listed algebraic expressions.

3. Ask students to observe which operations are included in the listed algebraic expressions and what are the characteristics of * * * identity operations.

After group discussion, the group recommended the staff to answer, and the teacher gave appropriate guidance.

(Fully allowing students to observe, discover and describe themselves, and carry out autonomous learning and cooperative communication can greatly stimulate students' enthusiasm and initiative in learning, satisfy students' desire for expression and inquiry, make students learn easily and happily, and fully reflect the openness of classroom teaching. )

Second, teach new lessons:

1. Single item:

Through the description of characteristics, students are guided to generalize the concept of monomial, thus introducing the topic: monomial, and summarizing the concept of monomial on the blackboard, that is, the algebraic expression composed of the product of numbers and letters is called monomial. Then the teacher added that a single number or letter is also a monomial, such as a, 5.

2. Exercise: Determine which of the following algebraic expressions is a monomial?

( 1)ABC； (2)B2； (3)-5ab 2； (4)y； (5)-xy2； (6)-5。

(Strengthen students' intuitive understanding of different forms of monomials, and at the same time use the teaching of changing the coefficients and times of monomials into monomials in practice)

3. Single coefficient and times:

Directly guide students to further observe the structure of monomial, and summarize that monomial consists of two parts: number factor and letter factor. Take four single items a2h, 2πr, abc and -m as examples, and ask students to tell what their numerical factors are, so as to introduce the concept of single item coefficient and write it on the blackboard. Then ask the students to say what the letter factor of the above monomial is and what the letter index is, so as to introduce the concept of monomial times and write it on the blackboard.

Concept:

Single factor: the numerical factor in a single item.

The number of times of a monomial: the sum of the indices of all the letters in the monomial.

4. Example:

Example 1: Determine whether the following algebraic expressions are monomials. If not, please explain the reasons; If yes, please indicate its coefficient and frequency.

①x+ 1； ② ; ③πR2； ④-ab .

Answer: ① No, because the addition operation appears in the original algebraic expression;

② No, because the original algebraic expression is the quotient of 1 and x;

③ Yes, its coefficient is π and its degree is 2;

④ Yes, its coefficient is-1 and its degree is 3.

Example 2: Is the judgment of the following question correct?

① The coefficient of-7xy2 is 7; ②-x2y3 and x3 have no coefficients; ③ The number of-Ab3c2 is 0+3+2;

④ The coefficient of-A3 is-1; ⑤-32x2y3 times is 7; ⑥ The coefficient of π r2h is.

Through counterexample exercises and examples, the following points should be emphasized:

① π π is a constant;

② When the coefficient of a single item is 1 or-1, "1" is usually omitted, such as x2, -a2b, etc.

③ The number of monomials is only related to the letter index.

5. Game:

Rules: one group of students say a monomial, and then specify the coefficient and the number of times for another group of students to answer him; Then exchange and see who answers quickly and accurately in the two groups.

(Students' self-writing questions is a creative thinking activity, which can change the form of teachers' blind writing questions. Students who write their own questions can designate a classmate to answer them, which can enliven the classroom atmosphere, activate students' thinking, let students thoroughly understand knowledge and cultivate students' sense of competition. )

6. Classroom exercise: textbook P56: 1, 2.

Third, the class summary:

(1) Single item and single item coefficient and times.

(2) According to the feedback from the teaching process, summarize the problems.

③ By judging the coefficient and frequency of a single item, students' ability to understand and apply new knowledge is cultivated, and the teaching purpose of this course is achieved.

Fourth, homework:

Textbook P59: 1, 2.

2. 1 algebraic expression of the second kind.

course content

Related concepts of 1, polynomial and algebraic expression.

2, correctly distinguish between monomial and polynomial.

Teaching objectives

1, knowledge and skills

(1) Students understand the concept of polynomials.

(2) Enable students to accurately determine the degree and number of terms of polynomials.

(3) Can correctly distinguish between monomials and polynomials.

2. Process and method

Cultivate students' divergent thinking by distinguishing monomial and polynomial.

3. Emotions, attitudes and values

In this kind of teaching, students are infiltrated with the dialectical thought that mathematics knowledge comes from life and serves life.

Emphasis and difficulty in teaching

1. Key points: the concept of polynomial and the relationship and difference between individual terms.

2. Difficulties and emphases: the determination of polynomial degree, the symbols of each term in polynomial, the relationship and difference between polynomial and single term.

teaching process

First, create situations and introduce new lessons.

Teacher: Last class, we learned the related concepts of monomials. Students look at the following questions.

1. Which of the following algebraic expressions is a monomial? This is a monomial. Please indicate its coefficient and degree.

, , ,2, , ,

2. If the radius of a circle is, the area of the semicircle is _ _ _ _ _ _ _ _, and the total length of the semicircle is _ _ _ _ _ _ _ _.

Student activity: Answer the above two questions and try to see who thinks comprehensively and answers accurately. The teacher praised and encouraged their accuracy and speed.

The teaching method is that students can review some knowledge points about monomials through 1 questions, and then naturally lead out the content of this section through the circumference of a half circle in the two questions.

Teacher: In the above two questions, is the algebraic expression representing the area of a semicircle a monomial? Why? What about the perimeter formula of a semi-circle?

Student activities: Discuss with classmates, and then choose representatives to answer.

Teacher: Who can read the formula in 1 (The teacher writes the corresponding blackboard writing)

Student activities: group discussion,,, According to the structural characteristics of these algebraic expressions, the group chooses representatives to explain. If it is not complete, other students can add it.

Second, explore new knowledge.

Teacher: Formulas like the above are called polynomials. We will learn polynomials in this class. The above formulas are all polynomials.

Student activities: Discuss and summarize what polynomials are. Students can complement each other.

The teacher summed it up and wrote it on the blackboard.

Polynomial: The sum of several monomials is called polynomial.

Teacher: Emphasize the symbolic problems of each item to attract students' attention.

Exercise: The following algebraic expressions,,,,, are polynomials:

___________________________________________________________.

Student activities: Students answer the above questions first, then each student writes two polynomials in the exercise book, and the deskmates exchange scores with each other, and then discuss them if there are any questions.

This teaching method discusses the concept of inductive polynomial by observing the characteristics of formulas, which embodies students' subjective role and participation consciousness. The concept of polynomial is the focus of this teaching. In order to let students really understand the concept, let each student write two polynomials, which can feedback the problems existing in students' knowledge in time so as to correct them in time.

Teacher: Question, are polynomials,,, and each obtained by adding several monomials? Who does each monomial refer to? How many monomials are there? Guide the students to answer, and the teacher will give affirmation, negation and correction according to the students' answers.

Teacher: In Chinese, it is obtained by adding two monomials, which are called binomials. Of the two monomials, the degree is 1, the degree is 1, and the highest degree is once, so we say that the polynomial has one degree, and the whole formula is called a binomial.

Student activities: discuss how to call,,, at the same table, and then let the students answer.

Teacher: Summarize and write it on the blackboard appropriately:

Student activities: Through the above example, students discuss the terms and degrees of polynomials, and then choose the representative to answer.

According to the students' answers, the teacher concluded:

In polynomial, each term called polynomial monomial is the sum of several monomials, and each term contains its symbol. If this term is not the degree of the highest degree term in polynomial, it is called polynomial degree, that is, the highest degree term is called polynomial degree, and the term without letters is called constant term.

The teaching method shows that through students' perception of the above polynomials, students have a certain understanding of the special properties of polynomials, and teachers can gradually guide them to sum up some conclusions themselves, thus training students' oral expression ability and inductive ability.

Teacher: Question: How many terms are there in polynomial? What is the term of polynomial, the number of monomials and the index of each letter?

Student activities: discussion (students should be able to answer accurately)

The teacher summarized: the index of each letter, found that the polynomial arrangement is arranged according to the ascending power of the letter B, and pointed out that the polynomial expression must be arranged according to the ascending power or descending power of the letter.

Can also be expressed as, anything else?

Student activities: discuss and show the results of each group in groups.

Third, apply new knowledge to solve problems.

1, fill in the form:

2. Fill in the blanks:

(1) is _ _ _ _ times; It is a _ _ _ _ _ term; The constant term of is _ _ _ _ _ _.

(2) It is a _ _ _ _ _ _ _, the highest degree is _ _ _ _ _, the coefficient of the highest term is _ _ _ _ _ _, and the constant term is _ _ _ _ _ _ _.

3. Arrange the following polynomials according to the ascending power and descending power of letters.

Student activities: answer the question 1 first, and the students at the same table will give a positive or negative answer, and give the positive basis, and then give the correct answer if it is negative; After observing the questions, students should finish them in exercise books or projection films, and some films will be projected. Teachers and students will analyze and discuss together and give affirmation or correction to the answers.

Explanation of teaching method: in this group of exercises, the topic of 1 is to perceive that a polynomial is the sum of monomials and the terms of polynomials are monomials in the form of filling in a table; Make students further understand the relationship between polynomials and monomials, and avoid the disadvantages of memorizing concepts and not being accurately applied to solving problems. 2 Questions Comprehensive training is conducted on the basis of understanding the concept and completing the 1 question, so that students can gradually learn to use mathematical language.

Induction: monomials and polynomials are collectively called algebraic expressions.

Note: The teacher summed up polynomials and monomials and wrote them on the blackboard, and then put forward that they should be collectively called algebraic expressions and written on the blackboard, so that the learned knowledge can be incorporated into the knowledge system.

Fourth, application expansion.

1, the following algebraic expression: 0,,,, where the monomial is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Student activities: after the observation, students answer, supplement and correct each other, reminding students not to miss it.

Teaching methods show that the essence of mathematics lies in application. Through the training of the above questions, students can clearly understand the differences and connections between monomials and polynomials, and their relationship with algebraic expressions.

2. The sum of the monomial,, and _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

3. It is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

4. It is a _ _ _ _ _ _ _ _, the highest term is _ _ _ _ _, the coefficient of the highest term is _ _ _ _ _ _ _ _, and the constant term is _ _ _ _ _ _ _.

5. The sum of the squares of the sum of 2 times is _ _ _ _ _ _ _ _ _, which is _ _ _ _ _ (fill in a single item or polynomial).

Student activities: each student completes the exercise book independently, then the group exchanges and supplements each other, and finally the group selects representatives to speak.

Teacher: Yes or no, it is emphasized that the coefficient of the highest term in the three questions is a number, not a letter, because it can only represent the value of pi, and a letter can take different values.

The teaching method shows that this group is a set of training questions arranged after mastering the basic knowledge of this lesson, in order to make students know more about the number and number of polynomials, especially to have a clear understanding of this number.

6. Self-editing exercises:

Each student writes six algebraic expressions, both monomials and polynomials, and then gives them to the classmates at the same table to complete the following tasks: ① Find out the monomials and polynomials first, and ② Write the coefficients and times of the monomials, but how many times have the polynomials been written and what is the highest number? What is a constant term, and then discuss with each other whether the other's solution is correct.

Self-made topic training in teaching guidance can enliven the classroom atmosphere and enhance students' sense of participation; Second, it can cultivate students' divergent thinking and reverse thinking ability.

Teacher: Through the above exercises, students have a clear understanding of the concept of algebra. Now, according to the teacher's request, make up a quartic trinomial to see who can make it fast and accurate, and then make up a polynomial with no more than three times.

Student activities: Students write on the blackboard while answering the teacher, and then discuss whether they meet the requirements.

The teaching method shows that through the above training, students can further consolidate the concepts of polynomial terms and degrees, and also cultivate the ability of reverse thinking.

Verb (abbreviation of verb) abstract

Students' induction and teachers' comments

Related concepts of "polynomial"; When mastering the concept of polynomial, we should pay attention to its term number and degree. We have also learned the monomial before, so we should pay attention to its coefficient and degree when mastering the monomial.

Homework design for the second class

1. True or false

(1)-5 is not a polynomial ()

(2) It is a quadratic binomial ()

(3) It is a quadratic trinomial ()

(4) It is a trinomial ()

The highest coefficient of (5) is 3 ()

fill (up) a vacancy

(1) Fill the above algebraic expressions in the corresponding brackets.

, , ,0, , ,

; ;

(2) If the algebraic expression is about the cubic binomial principle,

3. Fill in the following algebraic expressions in the corresponding circles:

2m，xy3+ 1，2ab+6，ax2+bx+c，a，

Monomial polynomial

4. How many terms are there in the following polynomial? What is the coefficient and frequency of each item?

( 1) (2)

5. Polynomial is a quadratic term, the highest term is, and the constant term is, in descending order of the letter Y, as follows.

6, the following operations, the error is ().

A.B.

C.D.

7. It is the second term, and the coefficient of the highest term is. The polynomial 2x2-3x+ 1 is a secondary term.

8. The polynomial 1-x3+x2 is ()

A. quadratic trinomial B. cubic trinomial C. cubic binomial D. quintic trinomial

9. The highest degree term of the polynomial x3-2x2y-xy2- 1 is ().

A.x3 B.2x2y C.-xy2 D.x3，-2x2y，-xy2

10 and 52x2-x are ()

A. First binomial B. Quadratic binomial

C. quartic binomial

In 1 1 and the polynomial 3xy2-2x2y+x3y3, the exponent of x is descending, and the exponent of y is descending _ _ _ _ _ _ _.

12, when A = and B =, is a cubic binomial about x and y.

13, if x+y=3, then 4-2x-2y =.

14, a polynomial about the letters x and y, except for the constant term, the degree of other terms is 3. How many terms does this polynomial have at most? Can you write a polynomial that meets the requirements?

The first volume of the seventh grade of People's Education Press "Algebraic Form"

Summary class (1)

One: Teaching objectives

Knowledge and skills objectives:

(1), understand the concepts of monomial, polynomial, monomial degree, polynomial degree, algebraic expression and similar items;

(2) Master the method of merging similar items and the changing law of symbols when brackets are removed;

(3) Understand the number of letters in algebraic expressions and the distribution law of bases that combine similar terms and remove brackets;

(4) Being able to analyze the quantitative relations in practical problems and list algebraic expressions;

Process and method objectives:

(1) Develop a sense of symbol in the process of expressing quantitative relations with letters;

Emotional attitudes and values goals

In algebraic calculation, we should be careful when we understand things.

Second, teaching focus: the concept of similar terms, the number of monomials and polynomials.

Third, teaching difficulties: merging similar items, removing and adding brackets, and looking for quantitative relations;

Fourth, the class type: summary class

V. Schedule: One class.

Sixth, teaching methods: lecture style

Seven, the teaching process:

Review the concepts of monomial, polynomial, degree of monomial, degree of polynomial and similar terms.

(1) monomial: the formula expressed by the product of numbers and letters is called monomial, and the numerical factor of monomial is called monomial coefficient; The sum of the exponents of all the letters in the monomial is called the number of times of the monomial. In particular, a single number or letter is also a monomial.

(2) Polynomial: The sum of several monomials is called polynomial. In polynomials, each monomial is called a polynomial term, and the term without letters is called a constant term; In polynomial, the degree of the highest degree term is called the degree of polynomial;

(3) Similar items: monomials with the same letters and the same index of the same letters are called similar items. The rule of merging similar items is coefficient addition, and the result is taken as the merged coefficient, and the index of letters remains unchanged.

Summarize the rules for deleting brackets and adding brackets:

Rules for removing brackets: brackets are preceded by a "+"sign. Remove the brackets and the "+"sign in front, and nothing in brackets will change the symbol; Parentheses are preceded by a "-". Remove the brackets and the "-"sign. Everything in brackets should be changed in sign, "+"should be changed to "-",and "-"should be changed to "+".

Parenthesis rule:

The "+"sign in front of brackets indicates that all the coefficients in brackets remain unchanged, and the "-"sign in front of brackets indicates that all the coefficients in brackets have changed.

Example: Point out the highest term, constant term and how many terms there are in the polynomial 3 -5a -2 -5.

Analysis: This question examines the concept of polynomials, and each polynomial must contain symbols.

Solution: The highest term is: 3 Constant term: -5 This polynomial is quartic.

Example: simplify first, then solve.

2 -3 +4 x-(x+3 -2) where x=- 1.

Analysis: Ask students to write the steps without brackets, then merge similar items and finally get the value.

Solution: bracket removal: 2 -3 +4 x- x-3 +2.

Merge similar items: 2 +2 -3 -3 +4 x- x=4 -6 +3 x.

Value: -4 -6 -3=- 13

Example: Two shopping malls, A and B, deal in the same commodity with the same purchase price and price tag. In order to promote the 30% price increase of the goods in Mall A, they are offering a 10% discount (i.e. price reduction 10%) and Mall B is offering a 10% discount (i.e. price reduction 10%). Which mall is profitable?

Assuming the price is A, the final selling price of Mall A is: A (1+30%) (1-kloc-0/0%) =1.17a.

The final selling price of Mall B is: A (1-10%) (1+30%) =1.17a.

So the profit is the same.

Algebraic expression, mathematics teaching plan for grade one in junior high school;

Understand the rules of polynomial multiplication, and use the rules to carry out simple polynomial multiplication.

Learning focus:

Polynomial multiplication rule and its application.

Learning difficulties:

Understand the algorithm and its exploration process.

First, pre-class training:

( 1)-3a2b+2 B2+3a2b- 14 B2 =，(2)-=；

(3)3a2b2 ab3 =，(4)=；

(5)- = ,(6) = 。

Second, exploration exercises:

(1) As shown in figure 1, a large rectangle has the area of four small rectangles.

Expressed as:;

(2) The length and width of a big rectangle should be.

Calculating its area is what it contains.

The operation is.

From the above questions, we can find that: () () =

Polynomial Multiplication Polynomial Rule: A polynomial is multiplied by a polynomial, and the terms of another polynomial are taken first, and then the product is taken.

3. Solve problems with rules.

Four. Consolidation exercise:

3. Calculation: ①,

4. Calculation:

5. Improve outward bound training:

5. If you find the value of m, n 。

6. Find the values of m and n when the known result does not contain terms and terms.

7. Calculate (a+b+c)(c+d+e). What did you find?

Evening training of intransitive verbs:

(7) 2a2(-a)4 + 2a45a2 (8)

3.( 1) Observation value: 4×6=24

14× 16=224