Teaching objective: 1. Let students understand the significance of rational number addition in practical situations.
2. Experience the process of exploring the law of rational number addition, master the law of rational number addition, and perform the addition operation accurately. []
3. Appropriate infiltration of classified discussion ideas in teaching.
Key point: the addition rule of rational numbers
Key point: the law of addition of two numbers with different symbols
Teaching process:
Second, teach new lessons.
1, the law of adding two numbers with the same sign.
Question: When an object moves in the left-right direction, we specify that the left side is negative and the right side is positive. Move 5m to the right and 5m to the left as -5m. If an object moves 5m to the right first, then 3m to the right, what is the total result after two moves?
The student replied: After two moves, the object moved 8 meters from the starting point to the right. Write the formula as 5+3 = 8 (m)
Teacher: If an object moves 5m to the left first, then 3m to the left, what is the total result after two moves?
The student replied: After two moves, the object moved 8 meters from the starting point to the left. The formula is (-5)+(-3) =-8 (m).
Teachers and students have the same induction rule: add two numbers with the same symbol, take the same symbol as the addend, and add the absolute values.
2. The law of adding two numbers with different symbols.
Teacher: If an object moves 5 meters to the right and 3 meters to the left, how many meters does it move from the starting point in which direction after two moves?
The student replied: After two moves, the object moved 2m from the starting point to the right. Write the formula as 5+(-3) = 2 (m)
Teachers and students use this conclusion to guide students to summarize the law of adding numbers with different symbols: add the numbers with different symbols, take the symbol with the larger absolute value, and subtract the one with the smaller absolute value with the larger absolute value.
The sum of two opposite numbers is equal to zero.
Teacher: If an object moves 5m to the right and 5m to the left, what is the total result after two moves?
The student replied: After two movements, the object returned to its original point. That is, the object moves 0 m.
Both teachers and students think that the sum of two opposite numbers is zero.
Teacher: Can you explain this rule with the law of addition?
Student answer: It can be explained by the law of adding two numbers with different symbols.
Generally speaking, there is another number added to 0 to get this number.
Third, consolidate knowledge.
Textbook P 18, example 1, example 2, textbook P 1 18, exercise 1, 2 questions.
Fourth, summary.
The key to operation: first classify, then operate according to law;
Operation steps: first determine the symbol, and then calculate the absolute value.
Note: the number axis should be used to further verify the addition rule of rational numbers; To add two numbers with different signs, first determine the signs, and then add the absolute values.
Verb (abbreviation for verb) assigns homework.
Textbook P24 exercises 1.3 questions 1 and 7.
absolute value
First, the design of teaching objectives
[Knowledge and Skills Objectives]
1, with the help of the number axis, understand the concept of absolute value, you can find the absolute value of a number, and compare the sizes of two negative numbers with the absolute value.
2, through the application of absolute value to solve practical problems, understand the significance and role of absolute value.
[Process and method objectives]
Give full play to students' subjective participation, so that students can learn new knowledge easily and happily in the communication and exploration between teachers and students under the guidance and inspiration of teachers.
[Emotional attitudes and values]
Solve mathematical problems with the help of the number axis, and consciously form the idea of combining numbers with shapes, so that students can adopt the learning mode of independent exploration and cooperative communication.
Second, the interpretation of teaching materials
With the help of the number axis, the concept of absolute value is introduced. Through calculation, observation, communication and discovery of the nature and characteristics of absolute value, the size of two negative numbers is compared by using absolute value.
Let students understand the meaning of absolute value intuitively, and don't have multiple symbols and sums inside the absolute value symbol.
Letters to encourage students to observe, summarize and verify.
Design and Analysis of Teaching Process
First, situational introduction
[Courseware display to stimulate interest perception]
Distance relationship between museums and farms and schools and museum farms.
[Media show courseware to recognize some problems in life]
Regardless of the opposite meaning, only consider the specific value.
[Creating situations and importing examples] Show students the absolute values in interesting pictures with animation to stimulate students' interest.
The image of the object conforms to the students' psychology. Students are interested in speaking enthusiastically, and 95% can solve the problem smoothly.
Teacher-student interaction
[Ask questions and start discussion]
1, guide students to get the definition and representation of absolute value.
2. Give examples to each other at the same table.
[Show: Inspire students to communicate and understand the absolute value]
Summarize the concept of absolute value, and the teacher points out the expression method.
[Teacher-student interaction, exploring new knowledge]: Students initially perceive the absolute value according to the situation, and solve the absolute value of a number by understanding the concept of the number.
For example, between deskmates, the effect is good, which embodies the "independent-cooperative" learning.
Read the text and explore interactively.
Discuss after solving the absolute value of each number.
1. Think about the relationship between the absolute values of two mutually opposite numbers. Students give examples and observe, compare and summarize.
2. What is the relationship between the absolute value of a number and this number? Discuss and communicate in groups. The teacher guides the students to describe the conclusion in their own words. Teacher asks: Is the absolute value of a number negative? Students understand the inner meaning of absolute value through analysis.
Read the text: Summarize the algebraic meaning of absolute value from the absolute value of each number.
[Read the text: "Think about it"] Ask questions to arouse students' thinking.
[Read the text: "Discussion"]
Students analyze the relationship between the absolute values of various numbers and themselves, and explore the teacher's doubts.
[Interesting and wonderful answers, ideas and inspirations] Through students' thinking with examples, observe and compare the absolute values of two mutually opposite numbers, and then get their relationship.
Students sum up the algebraic meaning of absolute value from the classification of "special-general", and summarize the internal meaning of absolute value through induction, which embodies the students' subjectivity.
Actively mobilize students' thinking, so that students can gradually explain the problems clearly and concretely in consultation and discussion, and achieve a more comprehensive and correct understanding of what they have learned on the basis of enjoying the fruits of collective thinking.
Step 3 do this
[exciting exploration]
The teacher showed the customs clearance questions.
Students finally find a way to compare the sizes of two negative numbers through independent exploration, and the larger absolute value is smaller.
Two ways for teachers and students to sum up the size of two pages.
【 Explore the method of comparing two negative numbers with absolute values 】
Formal process of empirical concept
The introduction of old knowledge allows students to acquire new knowledge in a relaxed and pleasant environment, and gradually change from existing knowledge to new knowledge, which can not only stimulate students' interest, but also cultivate their exploration spirit, and at the same time decompose the difficulties in this section.
The introduction of old knowledge makes students interested, improves the teaching effect, breaks through the difficulties and is easy for students to accept.
Consolidation exercise
[Application of absolute value comparison of two negative numbers]
Situation: Compare the sizes of the following groups.
[Media demonstration, demonstration exercise]:
Compare negative numbers with absolute values.
[Turn into training and consolidate feedback]
Continue to consolidate the size of the negative absolute value.
Through the above exercises, students' ability to solve problems has been greatly improved and impressed.
Knowledge expansion
[Student's inquiry, teacher's guidance]
[Media Demo]
Flexible application of absolute value definition, algebraic meaning and intrinsic meaning.
[knowledge extension, goal sublimation]
Give full play to students' independent exploration ability and let them understand the knowledge points in depth and in detail.
Students can comment on each other and explore together, which not only develops the ability of autonomous learning, but also strengthens the spirit of cooperation.
Seven, teaching blackboard design
absolute value
The absolute value of the concept positive number is itself.
Algebraic Meaning of Absolute Value The absolute value of 0 is 0 and non-negative.
The absolute value of a negative number indicates that the method || is its inverse.
For example: |-2|=2 |+3|=3 The number with the smallest absolute value is 0.
Complete square formula (1)
First, the content introduction
Topic of this lesson: Through a series of inquiry activities, guide students to sum up two complete square formulas from the calculation results.
Key information:
1, based on the teaching materials and according to the mathematics curriculum standards, to guide students to experience and participate in the scientific inquiry process. First, what is the relationship between the two multiplied polynomials on the left side of the equal sign and the three terms on the right side of the equal sign? Students discover problems independently, make assumptions and guesses about possible answers, and draw correct conclusions through repeated tests. Students acquire knowledge, skills, methods, attitudes, especially innovative spirit and practical ability through activities such as collecting and processing information, expressing and communicating.
2. Draw conclusions with standard mathematical language, so that students can feel the rigor of science and inspire their learning attitudes and methods.
Second, the learner analysis:
1, the basic knowledge and skills that should be possessed before learning this course:
(1) Definition of similar projects.
② Rules for merging similar projects
③ Polynomial multiplication polynomial rule.
2. Learners' level of what they will learn:
Before learning the complete square formula, students have been able to sort out the correct form of the formula. The purpose of this lesson is to let students summarize the application methods of formulas from the relationship between the left and right forms of equal signs.
Three. Teaching/learning objectives and corresponding curriculum standards;
Teaching objectives:
1, by exploring the process of complete square formula, the sense of symbol and thrust ability are further developed.
2. A complete square formula can be derived, and simple calculation can be made by using the formula.
(b) Knowledge and skills: Understanding is reasonable through the process of abstracting symbols from specific situations.
Numbers, real numbers, algebraic expressions, defensive cities, inequalities, functions; Master the necessary calculation (including estimation) skills; Explore the quantitative relations and changing laws in specific problems, and describe them with algebraic expressions, guarding cities, inequalities, functions, etc.
(4) Problem solving: being able to find and put forward mathematical problems in combination with specific situations; Try to learn from different people.
Seek solutions to problems from different angles, and effectively solve problems, and try to evaluate the differences between different methods; Through the reflection on the process of solving problems, we can gain experience in solving problems.
(5) Emotion and attitude: Dare to face the difficulties in mathematics activities and have the ability to overcome them independently.
And have the confidence to learn math well. And respect and understand the opinions of others; Can benefit from communication.
Fourth, educational ideas and teaching methods:
1. Teachers are the organizers, promoters and collaborators of students' learning: students are the masters of learning, learning actively and individually under the guidance of teachers, experiencing with their own bodies and feeling with their own hearts.
Teaching is a process of communication, positive interaction and common development between teachers and students. When students get lost
Wait, the teacher does not tell the direction easily, but instructs him how to distinguish the direction; When a student is afraid of climbing, the teacher does not drag him away, but arouses his inner spiritual motivation and encourages him to keep climbing.
2. Adopt the mode of "problem scenario-inquiry communication-summary-intensive training"
Start teaching.
3. Teaching evaluation methods:
(1) Pay attention to students' initiative in observation, summary and training through classroom observation.
Dynamic participation and awareness of cooperation and exchange, timely encourage, strengthen, guide and correct.
(2) Give students more opportunities to relax naturally by judging and giving examples.
Revealing the thinking process and giving feedback on the mastery of knowledge and skills will help teachers diagnose the situation in time and investigate teaching.
(3) Through after-class interviews and homework analysis, timely check and fill gaps to ensure the expected results.
Teaching effect.
Verb (abbreviation of verb) Teaching media: multimedia. Teaching and activity process:
The teaching process is designed as follows:
< 1 >, ask questions.
[Introduction] Students, we have learned the rule of polynomial multiplication and the rule of merging similar items. By operating the following four small questions, can you sum up the relationship between the result and the two monomials in the polynomial?
(2m+3n)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _，(-2m-3n)2=____________，
(2m-3n)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _，(-2m+3n)2=____________ .
< 2 >, analyze the problem
1, [student answers] discuss in groups
(2m+3n)2= 4m2+ 12mn+9n2，(-2m-3n)2= 4m2+ 12mn+9n2，
(2m-3n)2= 4m2- 12mn+9n2，(-2m+3n)2= 4m2- 12mn+9n2 .
(1) The characteristics of the original formula.
(2) The item number characteristics of the results.
(3) The characteristics of trinomial coefficients (especially the characteristics of symbols).
(4) The relationship between three terms and two monomials in the original polynomial.
2. [Student answers] Summarize the language description of the complete square formula:
The square of the sum of two numbers is equal to the sum of their squares, plus twice their product;
The square of the difference between two numbers is equal to the sum of their squares minus twice their product.
3. [Student's solution] Mathematical expression of complete square formula:
(a+b)2 = a2+2ab+B2；
(a-b)2=a2-2ab+b2。
(3) Using formulas to solve problems
1, oral answer: (the form of rushing to answer, active classroom atmosphere, stimulate students' enthusiasm for learning)
(m+n)2 = _ _ _ _ _ _ _ _ _ _ _ _ _，(m-n)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _，
(-m+n)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _，(-m-n)2=______________，
(a+3)2=______________，(-c+5)2=______________，
(-7-a)2=______________，(0.5-a)2=______________。
2. Judges:
()① (a-2b)2= a2-2ab+b2
()② (2m+n)2= 2m2+4mn+n2
()③ (-n-3m)2= n2-6mn+9m2
()④ (5a+0.2b)2= 25a2+5ab+0.4b2
()⑤ (5a-0.2b)2= 5a2-5ab+0.04b2
()⑥ (-a-2b)2=(a+2b)2
()⑦ (2a-4b)2=(4a-2b)2
()⑧ (-5m+n)2=(-n+5m)2
3, small test knife
①(x+y)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _； ②(-y-x)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _；
③(2x+3)2 = _ _ _ _ _ _ _ _ _ _ _ _ _； ④(3a-2)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _；
⑤(2x+3y)2 = _ _ _ _ _ _ _ _ _ _ _ _； ⑥(4x-5y)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _；
⑦(0.5m+n)2 = _ _ _ _ _ _ _ _ _ _ _ _； ⑧ (a-0.6b)2 =_____________。
< 4 > student summary
What problems do you think should be paid attention to in the application of complete square formula?
(1) Formula * * * has three terms on the right.
(2) The sign of two square terms is always positive.
(3) The symbol of the middle item is determined by whether the two symbols on the left side of the equal sign are the same.
(4) The middle term is twice the product of the two terms on the left of the equal sign.
(5) Adventure Island:
( 1)(-3a+2b)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
(2)(-7-2m)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
(3)(-0.5m+2n)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
(4)(3/5a- 1/2b)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
(5)(Mn+3)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
(6)(a2 B- 0.2)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
(7)(2xy 2-3x2y)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
(8)(2n 3-3 m3)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
(6) Students' self-evaluation
[Summary] What have you gained and learned from this lesson?
In this lesson, we summed up the complete square formula by calculating and analyzing the results ourselves. In the process of knowledge exploration, students actively think, boldly explore, unite and cooperate and make progress together.
【 Homework 】 P34 Classroom exercise P36
Seven, after-school reflection
Although this lesson is not a difficult point in the textbook, it is the focus of the chapter on algebraic expressions. This is a simple operation in a special form of polynomial multiplication. Students need to be familiar with the use of two forms of formulas to improve the operation speed. In the teaching process, we should pay attention to let students summarize the characteristics of the equal sign on both sides of the formula, let students express the content of the formula in language, and let students explain the problems that are easy to appear in the process of using the formula and the details that pay special attention to. Then, through the in-depth practice step by step, the application of two forms of complete square formula is consolidated. It makes full reference for the practical application and improvement of the second category of complete square formula.