The seventh grade first volume mathematics "Algebraic Addition and Subtraction" teaching plan selection Fan Wenyi
Teaching objectives and requirements:
1. Understand the concept of similar items and know similar items in specific situations.
2. Through group discussion and cooperative learning. Experience the process of concept formation and cultivate students' ability to explore knowledge independently and cooperate and communicate.
3. Understand the close relationship between mathematics and human life.
Teaching emphases and difficulties:
Key point: understand the concept of similar items.
Difficulty: According to the concept of similar term, find the similar term in polynomial.
Teaching methods:
Teaching at different levels, combining teaching with practice.
Teaching process:
First, review the introduction:
1, creating problem situations
(1) 5 people +8 people =
⑵5 sheep +8 sheep =
(3) 5 people +8 sheep =
Mathematics teaching should be closely linked with students' real life and study, which is the task entrusted by the new curriculum standards. Students try to classify by category, color and other methods. On the one hand, they can provide students with opportunities to participate actively and adjust their attention and thinking activities to a positive state; On the other hand, it can cultivate the flexibility of students' thinking and embody the classified thinking method. )
2. Observe the following monomials and classify the formulas that you think are the same type.
8x2y，-mn2，5a，-x2y，7mn2，，9a，-0，0.4mn2，，2xy2 .
After the students discuss in groups, they are classified according to different standards. After the teacher visits, they show different classification methods through projection.
Let the students observe the formulas that fall into one category and think about their commonalities.
Ask the students to say their own classification standards, and affirm each student's classification according to different standards.
(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. Definition of similar projects:
We often group things with the same characteristics. 8x2y and -x2y can be combined, 2xy2 and-can be combined, -mn2, 7mn2 and 0.4mn2 can be combined, 5a and 9a can be combined, and 0 and can also be combined. The only difference between 8x2y and -x2y is the coefficient. They all contain letters X and Y. The exponent of X is 2, and the exponent of Y is 1. Similarly, 2xy2 and-only have different coefficients, and both contain the letters X and Y. The exponent of X is 1 and the exponent of Y is 2.
In this way, items with the same letters and equal indices of the same letters are called similar items. In addition, all constant terms are similar. For example, as mentioned earlier, 0 and 0 are similar projects.
Through the description of the characteristics, the items with the same letters and indexes are selected as the research objects, which are called similar items. (blackboard title: similar items. )
In order to make students understand the concept of similar items, teachers can ask what conditions similar items must meet and let students summarize. )
The concept of similar terms and all the constant terms summarized by students on the blackboard are similar terms.
2. Example:
Example 1: Judge whether the following statement is correct and tick "?" Correct in brackets. , wrong number "?" .
(1)3x and 3mx are similar projects. () (2)2ab and -5ab are similar projects. ( )
(3)3x2y and -yx2 are similar items. () (4) 5B2 and -2b2c are similar projects. ( )
(5)23 and 32 are similar projects. ( )
(This set of judgment questions can make students clearly understand the concept of similar items, in which the first question (3) meets the conditions of similar items, as long as the multiplication exchange law is used; Question (5) Both are constant terms and belong to the same category. Some students may simply look at different indexes and mistakenly think that they are not in the same category. )
Example 2: Game:
Rule: After a student says a single item, assign a classmate to answer its two similar items. [Source: Xue | Ke | Net Z|X|X|K]
Ask students to make their questions as different as possible.
Please introduce the experience of writing a single similar item to the students who answered correctly, so as to reveal the essential characteristics of similar items and thoroughly understand the concept of similar items.
Students' self-made questions are a kind of creative thinking activity, which can change the stylized practice of teachers asking questions blindly. Students who make self-made questions designate a classmate to answer them, which can make the classroom atmosphere active and students understand the knowledge thoroughly. This form is suitable for the age characteristics of junior high school students. After some attempts, students can get similar items by changing the coefficient of a single item, which actually captures the two "sameness" in the concept of similar items, thus profoundly revealing the connotation of the concept. )
Example 3: Point out similar terms in the following polynomials:
( 1)3x-2y+ 1+3y-2x-5； (2)3x2y-2xy2+xy2-yx2 .
Solution: (1)3x and -2x are similar terms, -2y and 3y are similar terms, and 1 and -5 are similar terms.
(2)3x2y and -yx2 are similar terms, and -2xy2 and xy2 are similar terms.
Example 4: When 3xky and -x2y are similar terms, what is the value of k?
Solution: In order to make 3xky and -x2y similar terms, the degree of x in these two terms must be equal, that is, k=2. So when k=2, 3xky and -x2y are similar terms.
Example 5: If (s+t) and (s-t) are regarded as a whole respectively, point out the similar terms in the following formula.
( 1)(s+t)-(s-t)-(s+t)+(s-t)；
2(s-t)+3(s-t)2-5(s-t)-8(s-t)2+s-t .
Solution: Omit.
(Organize students to answer the above three examples orally. For example, 3, similar items in polynomials can be underlined by teachers, and written answers can be typed by projectors to prepare for the merger of similar items. Example 4 Let the students make it clear that the index of the same letter in the same category is the same. Example 5 (s-t) and (s+t) must be regarded as a whole respectively. )
Through variant training, the meaning of "similar items" can be further clarified, and in the process of independent exploration and cooperative communication, basic mathematical knowledge and skills can be truly understood and mastered, and the recognition ability can be improved. )
6. Five-minute test:
1. Please write a similar project of 2ab2c3. How much can you write? Is it your own similar item?
Students answer in the textbook first, and then answer. If there are mistakes, please ask other students to correct them in time. )
Third, the class summary: [
(1) Understand the concept of similar terms, find similar terms in polynomials, write single similar terms, and judge similar terms.
② This course is applied to mathematical thinking methods such as classified thinking and holistic thinking.
③ The purpose of learning similar terms is to simplify polynomials and lay a foundation for merging similar terms in the next lesson.
Classroom summary is not only a list of knowledge points, but also a systematization of knowledge, which should be promoted to the summary and application of mathematical thinking methods. Using the classroom summary method of students' complementary and teachers' timely guidance can train students' ability of induction and expression and improve their enthusiasm and initiative in learning. )
Fourth, class assignments:
If the sum of 2amb2m+3n and a2n-3b8 is still a monomial, the values of m and n are _ _ _ _ _ respectively.
Blackboard design:
Postscript of teaching:
Based on students' cognitive development level, starting from students' existing life experience, some objects are classified through group discussion, which leads to the concept of similar items. Through learning activities such as practice, games, cooperation and communication, students can know similar items more clearly. In the teaching activities of the whole class, students' subjectivity is fully reflected, students are provided with opportunities to fully participate in mathematics activities, and they are helped to truly understand and master the basic knowledge and skills of mathematics in the process of independent exploration and cooperative communication, so as to cultivate students' practical ability, verbal ability, psychological ability and cooperative communication ability.
The seventh grade first volume mathematics "Algebraic addition and subtraction" teaching plan selection Fan Wener
Teaching objectives
Knowledge and ability: master the rules of bracket removal, use the rules and remove brackets correctly as required.
Process and method: Experience the operation of analogy with rational numbers with brackets, explore and find the law of symbol change when brackets are removed, summarize the law of removing brackets, and cultivate students' ability of observation, analysis and induction.
Emotion, attitude and values: through participating in inquiry activities, students are trained to actively explore, cooperate and communicate, have a rigorous learning attitude and realize the importance of cooperation and communication.
Emphasis and difficulty in teaching
Key points: removing the rules of brackets and applying the rules accurately will simplify the algebraic expression.
Difficulty: There is a "-"in front of the bracket. After removing the bracket, everything in the bracket changes sign.
teaching process
First, review the old knowledge.
1. Simplify
-(+5) +(+5) -(-7) +(-7)
Remove brackets
① -(3- 7) ② +(3- 7)
Second, explore new knowledge.
Think about it: according to the law of distribution, can you remove the brackets from the following formula?
①+(- a+c) ② - (- a+c)
③ +(a-b+c) ④ -(a-b+c)
Observe these two sets of formulas and see what changes have been made to the symbols of the items in brackets before and after the brackets are removed.
Support removal rules:
Parentheses are preceded by a+sign. Remove the brackets and the preceding+sign.
Nothing in brackets will change its sign;
There is a "-"before the brackets. Remove the brackets and the preceding "-".
Everything in brackets changes sign.
Phrases:
Remove the brackets and look at the symbols; It is the "+"number, and it is the same number; It's the "-"number, change all the numbers.
Third, consolidate the exercises:
(1) Remove the bracket:
a+(b-c)= _______ a- (b-c)= _____
a+(- b+c)= _______ a- (- b+c)= _____
(2) judging right or wrong
a-(b+c)=a-b+c()
a-(b-c)=a-b-c()
2b+(-3a+ 1)=2b-3a- 1()
3a-(3b-c)=3a-3b+c()
Example learning: remove the brackets from the following formula.
+3(a - b+c) - 3(a - b+c)
Five, the classroom test:
Not wearing a seat belt:
①9(x-z)②-3(-b+c)③4(-a+b-c)④-7(-x-y+z)
Sixth, the class summary
Precautions when removing the bracket:
(1), when removing brackets, you should first judge whether the brackets are preceded by "+"or "-".
(2) After the brackets are removed, the symbols in the brackets are either completely changed or completely unchanged.
(3) When the "-"is in front of the brackets, after the brackets are removed, the symbols of the items in the brackets should be changed, not only the symbols of the first item or the first few items.
Seven, homework:
Required questions: Exercise 2.2, Question 2 and Question 3 on page 70 of the textbook.
Multiple choice questions: Exercise 2.2, question 4, page 70 of the textbook.
Selected teaching plans of the first volume of mathematics "Algebraic Addition and Subtraction" in the seventh grade: Fan Wensan
Teaching purpose:
Knowledge and skills objectives:
Algebraic expressions can be added and subtracted, which can explain arithmetic and cultivate the ability of organizational thinking and language expression.
Process and method:
By exploring the problem of regularity, we can further understand the significance of symbolic representation.
Through the study of algebraic addition and subtraction, we can deeply understand the application of algebra in real life and lay a good foundation for studying equations (groups), inequalities and functions in the future. At the same time, let us realize that mathematics knowledge comes from the needs of actual production and life, on the contrary, it serves all aspects of real life.
Teaching emphases and difficulties:
Emphasis: addition and subtraction of algebraic expressions.
Difficulty: exploring the conjecture of the law.
Teaching time:
Teaching process:
First, create realistic situations and introduce new courses.
It takes 5 pieces to place the 1 th hut, 2 pieces to place the second hut and 3 pieces to place the third hut.
Keep swinging like this.
(1) A chess piece is needed to place the10th such small room.
(2) How much does it cost to put the nth such small room? How did you get it? Can you solve this problem in different ways? Group discussion.
Ii. teach new courses according to the actual situation.
Example description:
Exercise: 1, Calculation:
( 1)( 1 1x 3-2 x2)+2(x3-x2)(2)(3 a2+2a-6)-3(a2- 1)
(3)x-( 1-2x+x2)+(- 1-x2)(4)(8x y-3 x2)-5xy-2(3xy-2 x2)
2. Known as: A=x3-x2- 1, B=x2-2, calculated as: (1)B-A (2)A-3B.
Three. Do this.
P 1 1 classroom exercises
Ⅳ. Class summary
We should be good at finding laws in graphic changes and mastering the addition and subtraction of algebraic expressions.
ⅴ. Homework after class
P 12 exercise 1.3: 1 (2), (3), (6), 2.
Blackboard design:
Addition and subtraction of algebraic expressions in the second quarter (2)
First, the geometric figures found in the tour.
Second, the common geometry in life
Teaching postscript
The seventh grade first volume mathematics "Algebraic addition and subtraction" teaching plan selection Fan Siwen
(A) the status of teaching materials
The second chapter of the first volume of Mathematics for Grade Seven published by People's Education Publishing House is a link between the past and the future, which is not only the generalization and abstraction of rational numbers, but also the basis of algebraic operations such as multiplication and division of algebraic expressions, and also the basis of learning equations, inequalities and functions.
(B) unit teaching objectives
(1) Understand and master the concepts of monomial, polynomial and algebraic expressions, and find out the differences and connections between them.
(2) Understand the concept of similar items, master the method of merging similar items, and master the changing law of symbols when removing brackets, so as to merge similar items and remove brackets correctly. On the basis of accurate judgment and correct combination of similar items, add and subtract algebraic expressions.
(3) To understand the letters in algebraic expressions, the addition and subtraction operations of algebraic expressions are based on the operation of numbers; Understanding the basis of merging similar items and removing brackets is the distribution law; Understanding the operation rules and properties of numbers is still valid in the addition and subtraction of algebraic expressions.
(4) Be able to analyze the quantitative relations in practical problems and enumerate algebraic expressions. Experience the progress from arithmetic to algebra after using letters to represent numbers.
(5) Infiltrating the dialectical view that mathematical knowledge comes from life and serves life; Through the transition from addition and subtraction of numbers to addition and subtraction of algebraic expressions, students are trained to think from special to general; Understanding the addition and subtraction of algebraic expressions is essentially to remove brackets and merge similar items. The result is always simpler than the original, which embodies the beauty of simplicity in mathematics.
(C) Difficulties in unit teaching
(1) key: understand the related concepts of monomial and polynomial; Skillfully merge similar items and remove brackets.
(2) Difficulties: accurately merge similar items and accurately handle the symbols when brackets are removed.
(D) the concept and strategy of unit teaching
(1) Pay attention to the connection with primary school-related content.
(2) Strengthen the connection with reality.
(3) Learn "formula" by analogy with "number", strengthen the internal connection of knowledge and attach importance to the infiltration of mathematical thinking methods.
(4) Grasp the important and difficult points and strengthen the practice.
(E) Analysis of students' learning errors:
(1) ignores the definition of the monomial and mistook it for a monomial.
(2) Ignore the definition of single coefficient and mistake it for 4.
(3) Ignoring the definition of the degree of monomial and mistaking 3a for 0.
(4) Ignoring the definition of polynomial and mistaking it for monomial.
(5) Ignoring the definition of polynomial, the number of errors is 7.
(6) Ignoring the definition of polynomial term and mistaking polynomial term for.
(7) When rearranging the terms of the polynomial, ignore the symbols in front of it.
(8) Ignore the definition of similar items and mistake 2x3y4 and -y4x3 as not similar items.
(9) When merging similar projects, the indexes of letters are added up by mistake.
(10) Symbol processing after removing brackets.
(1 1) When two algebraic expressions are subtracted, the brackets are ignored.
(6) Teaching suggestions:
(1) What is the key to understanding algebra and learning to merge similar items?
Algebraic addition and subtraction is actually merging similar items. The concept of similar items and the method of merging similar items are the focus of this chapter. Similar items and their merging are based on monomials. Therefore, the concept or meaning of monomial is the key to complete the merger.
(2) What are the relations and differences between monomials and polynomials?
In textbooks, we should talk about monomials first, then polynomials, and then summarize them into monomials and polynomials, which are collectively called algebraic expressions. The coefficient of monomial is limited to digital coefficient (digital factor in monomial), which should be carefully understood and must not be extended, while polynomial has no coefficient; For the degree, the degree of monomial refers to the sum of the exponents of all letters, while the degree of polynomial is the degree of the highest degree term (monomial) in polynomial. It should be noted that the coefficient of a single item, including the symbol in front of it, should not be taken as a letter. The coefficient of a single item X is 1, and so is a single number (zero degree single item) or a letter. Every term of a polynomial should be preceded by a symbol; Single fraction and polynomial fraction cannot contain letters.
(3) Learning the method of merging similar items;
First, the similar items are marked separately, and then merged according to the similar item merging rules. The merged polynomials are arranged in descending or ascending order according to a certain letter. When the coefficients of similar terms in polynomials are opposite, they will be 0 after merging;
(4) What are the "two similarities" that should be paid attention to when merging similar items?
Merging similar items is the basis of algebraic expression addition and subtraction, and a deep understanding of the concept of similar items is also the key to mastering the merging of similar items. Through the introduction of an inquiry question (three fill-in-the-blank questions) in the textbook, the "two similarity" criteria for judging similar items are obtained: the items containing the same letters and the same index of the same letters are called similar items. Several constant items are also similar items, and there are at least two similar items. A single item is not called a similar item.
(5) Other precautions:
In the algebraic expression (1), only one term is a monomial, otherwise it is a polynomial. Algebraic expressions with letters in the denominator are not algebraic expressions, nor are they monomials or polynomials.
② The number of monomials is the sum of the indices of all letters; The degree of polynomial is the degree of the highest term in polynomial.
(3) The coefficient of the monomial contains the symbol before it, and the coefficient of each term in the polynomial also contains the symbol before it.
④ When deleting brackets, pay special attention to the situation that there is a "-"in front of brackets.
(seven) schedule:
1 category single item
Polynomials of the second kind
Addition and subtraction of algebraic expressions of the third kind (1)- merging similar terms.
Lesson 4 Addition and subtraction of algebraic expressions (2)- deletion of brackets.
Lesson 5 Addition and subtraction of algebraic expressions (3)- General steps.
Lesson 6 Addition and subtraction of algebraic expressions (4)- Simplified evaluation.
Math activities in the seventh class
Lesson 8 Review
The seventh grade first volume mathematics "Algebraic addition and subtraction" teaching plan selection Fan Wuwen
First, three-dimensional target.
(1) Knowledge and skills.
Can use the algorithm to explore the parenthesis rule, and use the parenthesis rule to simplify algebraic expressions.
(2) Process and method.
By analogizing the operation of rational numbers with brackets, the law of symbol change after removing brackets is found, and the law of removing brackets is summarized, thus cultivating students' ability of observation, analysis and induction.
(3) Emotional attitudes and values.
Cultivate students' awareness of active exploration, cooperation and communication and rigorous learning attitude.
Second, the importance, difficulty and focus of teaching.
1. key point: remove the bracket rule and apply it accurately to simplify algebraic expressions.
2. Difficulties: What is before brackets? Remove the brackets, the symbols in brackets are easy to make mistakes.
3, the key: accurately understand the law of brackets.
Third, the preparation of teaching AIDS.
Projector.
Fourth, the teaching process, classroom introduction.
Polynomials can be simplified by combining similar terms. In practical problems, the listed formulas often contain parentheses. How to simplify them?
5. Newly awarded.
Now let's look at the question (3) in the introduction of this chapter:
From Golmud to Lhasa, if it takes t hours for the train to pass through the frozen soil section, it takes (t-0.5) hours to pass through the unfrozen soil section, so the distance between the frozen soil section and the unfrozen soil section is100 km, so the total length of the railway section is 100 t+.
The difference between frozen area and unfrozen area is 100t? 120(t-0.5) km ②
The above formulas ① and ② have brackets. How should we simplify them?
Using the distribution law, you can delete brackets and merge similar items, and get:
100t+ 120(t-0.5)= 100t+ 120t+ 120(-0.5)= 220t-60