The seventh grade junior high school mathematics "Algebraic addition and subtraction" teaching plan daquan one.
Teaching objectives:
1. Understand the concept of similar items and know similar items in specific situations.
2. Understand the close relationship between mathematics and human life.
Teaching emphasis: understand the concept of similar items.
Teaching difficulties: finding similar terms in polynomials according to the concept of similar terms.
Teaching process:
First, review the introduction.
1. Create problem situations
(1)5 people +8 people =; ?
(2)5 sheep +8 sheep =; ?
(3)5 people +8 sheep =. ?
2. Observe the following monomials and classify what you think belongs to 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, and different classification methods are projected and displayed after the teacher visits.
Let the students observe the formulas that fall into one category and think about their commonalities.
Ask the students to say their classification standards, and affirm each student's classification according to different standards.
Second, teach new lessons.
1. Definition of similar projects:
We often group things with the same characteristics. 8x2y and -x2y can be grouped together, 2xy2 and-can be grouped together, -mn2, 7mn2 and 0.4mn2 can be grouped together, 5a and 9a can be grouped together, and 0 and -x2y can also be grouped together. 8x2y and -x2y are just different in coefficients, both of which contain the letters X and Y and the index of X. Similarly, 2xy2 and-are just different in coefficients, both of which contain the letters X and Y, the index of X is 1 and the index of Y is 2.
In this way, projects with the same letters and the same index are called similar projects. In addition, all constant terms are similar. For example, the aforementioned 0 and 0 are similar projects.
2. Example:
Example 1 Judge whether the following statement is correct, put "√" in brackets for the correct statement and "×" for the wrong statement.
(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 items. ()
(5)23 and 32 are similar projects. ()
Example 2 points out the similar terms in the following polynomials:
( 1)3x-2y+ 1+3y-2x-5；
(2)3x2y-2xy2+xy2-yx2。
What is the value of example 3k, when 3xky and -x2y are similar terms?
If (s+t) and (s-t) are regarded as a whole, point out the similar terms in the following formula.
( 1)(s+t)-(s-t)-(s+t)+(s-t)；
(2)2(s-t)+3(s-t)2-5(s-t)-8(s-t)2+s-t
3. Classroom exercise: Please write a similar project of 2ab2c3. How much can you write? Is it your own similar item?
Third, the class summary
1. To understand the concept of similar terms, we will look for similar terms in polynomials, write similar terms of a monomial, and judge whether several monomials are 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 the foundation for merging similar terms in the next lesson.
Fourth, class assignments.
If the sum of 2amb2m+3n and a2n-3b8 is still a monomial, then the values of m and n are. ?
Merge similar projects in category 2.
Teaching purpose:
1. Understand the concept of merging similar items and master the rules of merging similar items.
2. Infiltrate the thinking method of classification analogy.
Teaching emphasis: correctly merge similar items.
Teaching difficulties: find out similar items and merge them correctly.
Teaching process:
First, review the introduction.
In order to do a good job in class activities, Li Minghe Zhang Qiang bought some soft-faced pens and soft-faced pens as prizes. They bought 15 soft-faced pens and 20 pens first. After budgeting, I found that so many prizes were not enough, and then I bought six soft-faced pens and five pens. Q:
1. How many soft copybooks and pens did they buy twice?
2. If the unit price of soft text is X yuan per copy and the unit price of fountain pen is Y yuan per copy, how much did they spend on this activity?
Second, teach new lessons.
1. Merge definitions of similar projects:
(Students discuss Question 2) Algebraic expressions can be listed in the chronological order of purchase, or by the types of purchased items. Then, similar items are combined by using the exchange law and association law of addition, and the whole polynomial is simplified, and the results are all (2 1x+25y) elements.
From this, it can be concluded that merging similar terms in polynomials into one term is called union similar term.
2. Example:
Example 1 Find the similar terms in the polynomial 3x2y-4xy2-3+5x2y+2xy2+5, and merge the similar terms.
According to the above example of merging similar items, let students discuss and summarize the rules of merging similar items:
The coefficients of similar items are added together, and the results are taken as coefficients, and the letters and letter indexes remain unchanged.
Example 2 Is it correct to combine the following questions with similar projects? If not, please correct it.
( 1)2 x2+3 x2 = 5 x4； (2)3x+2y = 5xy；
(3)7 x2-3 x2 = 4； (4)9a2b-9ba2=0。
Example 3 Combines similar terms in the following polynomials:
( 1)2a2b-3a2b+0.5 a2b；
(2)a3-a2 b+ ab2+a2 B- ab2+B3；
(3)5(x+y)3-2(x-y)4-2(x+y)3+(y-x)4。
Marking similar items with different tags will reduce operational errors. Of course, it can be omitted after proficiency. In question (3), (x+y) and (x-y) should be regarded as a whole, with special attention to (x-y)2n=(y-x)2n, where n is a positive integer. )
Example 4 Find the value of the polynomial 3x2+4x-2x2-x+x2-3x- 1, where x=-3.
Try to substitute x=-3 directly into the polynomial of Example 4, can you find its value? Compared with the above scheme, which scheme is simpler?
By comparing these two methods, students realize that it is easier to combine similar terms before finding their values when finding the values of polynomials.
3. Classroom exercises: P65 textbook exercises 1, 2, 3.
Third, the class summary
1. Keep in mind the rules and merge similar items skillfully and correctly to prevent errors like 2x2+3x2=5x4.
2. Draw the rule of merging similar items by analogy from practical problems, and apply this rule to correctly merge similar items.
Fourth, class assignments.
Textbook P69 Exercise 2.2 1 Question.
The brackets are removed from the third category.
Teaching objectives:
1. can explore the parenthesis rule by using the algorithm, and simplify the algebraic expression by using the parenthesis rule.
2. Through the operation of rational numbers with brackets, find the law of symbol change after removing brackets, and summarize the law of removing brackets, so as to cultivate students' ability of observation, analysis and induction.
Teaching emphasis: accurate application of brackets to simplify algebraic expressions.
Teaching difficulty: there is a "-"in front of brackets. Remove the brackets, and all the items in brackets should be changed, which is easy to make mistakes.
The seventh grade junior high school mathematics "Algebraic addition and subtraction" teaching plan Daquan II
Knowledge and skills:
1. Understanding algebraic addition and subtraction in real situations is actually to combine similar items and consciously cultivate their organizational thinking ability and language expression ability.
2. Understand the definition and merging rules of similar items, and use this rule to add and subtract algebraic expressions.
3. You should know that when finding the value of a polynomial, it is generally to combine similar items first, and then substitute them into numerical values for calculation.
Process and method:
Through the observation, thinking, analogy, exploration, communication and reflection of specific situations, students' innovative consciousness and classified thinking are cultivated, so that students can master the methods of studying problems and learn to learn.
Emotions, attitudes and values;
Through students' autonomous learning, we explore the definition and rules of the merger of similar items, cultivate students' autonomous learning ability and inquiry spirit, and improve their interest in learning. Feel the formal beauty and simplicity of mathematics, feel that learning mathematics is the enjoyment of beauty, and love and enjoy learning mathematics.
Teaching focus:
Cleverly merge similar terms and simplify algebra.
Teaching difficulties;
How to judge similar items and merge them correctly?
Teaching tools: multimedia or small blackboard,
Teaching process:
? First, create a scene.
Problem: Dig a round hole on both walls of A and B to install window grilles, and paint the rest. Please calculate the sum of the painting areas of (1)A and B according to the dimensions in the drawing. (2) How much is the painting area of A larger than that of B?
(Handling: ① Students think for a moment; ② Ask student representatives to exchange answers; The teacher summarizes the students' answers.
Blackboard writing:
(1)(2ab-πr2)+(ab-πr2) or (2ab+ab)-(πr2+πr2)
(2) (2ab-πr2)-(ab-πr2)
(Ask the students at this time: What are these three formulas? On the basis of students' answers, the topic is drawn-this lesson is learning: 2.3 Addition and subtraction of algebraic expressions.
Second, explore new knowledge.
The teacher asked himself: How to calculate (1) and (2)?
Then answer: This lesson will learn 2.2. 1 merging similar items (at this time, the blackboard title is-1. Merge similar projects).
1, the concept of similar terms
Observe the characteristics of the polynomial (2ab+ab)-(πr2+πr2): 2ab and ab.
Students exchange and discuss.
Teacher-student summary: (This is a similar item that we will introduce today. At this time the blackboard is 1. The concept of similar terms)
Items with the same letters and the same index are called similar items.
Several constant terms are similar.
Key points: ① The letters contained are the same; ② The indexes of the same letters are the same.
③ The coefficients can be different; ④ The alphabetical order can be different.
Together, the abbreviation is "two similarities and two differences"
For example: 2a and -a4 B4 a2, and -2a2b (note "two similarities and two differences")
4 Tips: There are similar phenomena in life; Please make a list.
Step 2 find friends
Send a small card to each group of five students (polynomial terms have been written), and the teacher keeps one. When the teacher shows his cards, please invite his good friend (a good friend of the same kind) to the podium and explain why he thinks he is a good friend.
Step 3 have a discussion
Textbook 7 1 Page Exercise 1 (explain why)
The seventh grade junior high school mathematics "Algebraic addition and subtraction" teaching plan Daquan III
design concept
Establish a teacher-student relationship of equality, cooperation and mutual respect, and create a learning atmosphere of teacher-student interaction and mutual learning. Pay attention to students' learning process and individual differences, so that different people can play different roles in mathematics learning, and help students understand and learn mathematics with courseware. Through observation, analysis, hands-on, brainstorming and other activities, let students learn while doing, so as to achieve "I want to learn".
course content
This lesson is the third section of the second chapter of the experimental textbook for compulsory education in Shanghai Science Edition, "Addition and subtraction of 2.3 algebraic expressions-1. Merge similar projects "(page 765,438+0 ~ 73).
Analysis of learning situation
The seventh-grade students are active in thinking, eager for knowledge, strong in self-awareness, and full of curiosity about observation, conjecture and exploratory questions. Therefore, students should set interesting and challenging contents in the selection and presentation of teaching materials and the arrangement of learning activities, so that students can feel that mathematics comes from life and returns to real life, which will inevitably produce strong learning interest and enthusiasm for exploration.
Students feel the close connection between mathematics and life mainly through the analysis of life scenes in teaching. By analyzing, discussing and communicating with each other on several issues, we can improve students' ability to use textbook knowledge through analogy and transfer, so as to understand the law of inducing and merging similar items, and consolidate and be familiar with the skills of merging similar items in practice. Finally, through review and reflection, talk about feelings and gains, and sublimate what you have learned into rational knowledge.
Textbook analysis
Combining similar items is an inquiry activity class. Based on students' existing life experience, we explore and study the definition of similar items and how to combine similar items, introduce letters to represent numbers, and then introduce algebraic expressions to evaluate algebraic expressions. Merging similar terms is the key knowledge in this chapter, and the application of its rules is the basis for learning to solve equations, algebraic operations and inequalities in the future. Therefore, learning this knowledge well is the main link to learn the following knowledge well. At the same time, the number operation is constantly used in the process of merging similar items, which is based on the operation law of numbers, so that students can realize that understanding things is a process from special to general and from general to special, thus cultivating students' preliminary dialectical materialism thought.
Teaching objectives:
1. Basic knowledge objective:
(1) Understand the definition of similar items in specific situations and identify similar items.
(2) Explore the law of merging similar items in specific situations, and be familiar with the operation of merging similar items.
(3) Know that when calculating the value of a polynomial, similar items are generally merged first, and then substituted into numerical values for calculation.
2. Ability training objectives:
(1) Through mathematical activities such as observation, thinking, analogy, inquiry, communication and reflection in specific situations, students' innovative consciousness and classified thinking are cultivated, so that students can master the methods of studying problems and learn to learn.
(2) Close to students' life through specific situations, so that students can dig and solve mathematical problems in their lives, make mathematics alive and make life mathematical. Will use the knowledge of merging similar items to solve some practical problems.
(3) To cultivate students' generalization ability, expression ability and logical thinking ability by combing knowledge.
3. Innovative quality objectives:
(1) By extending the addition and subtraction of numbers to the combination of similar items, students are trained to think from special to general.
(2) Guide students to discover mathematical problems from daily life, and cultivate students' awareness and ability of discovery; Mathematical activities such as exploration and communication cultivate students' team spirit and consciousness of active participation and diligent thinking.
4. Personality quality objectives:
(1) Cultivate students' innovative qualities of being brave in exploration, good at discovery and independent.
(2) Through the combination of similar items, students can obviously feel the formal beauty and concise beauty of mathematics, and realize that learning mathematics is a beautiful enjoyment, and they love and enjoy learning mathematics.
Teaching focus:
Cleverly merge similar terms and simplify algebra.
Teaching difficulties;
How to judge similar items and merge them correctly?
Teaching tools: multimedia or small blackboard,
Teaching process:
? First, create a scene.
Problem: Dig a round hole on both walls of A and B to install window grilles, and paint the rest. Please calculate the sum of the painting areas of (1)A and B according to the dimensions in the drawing. (2) How much is the painting area of A larger than that of B?
(Handling: ① Students think for a moment; ② Ask student representatives to exchange answers; The teacher summarizes the students' answers.
Blackboard writing:
(1)(2ab-πr2)+(ab-πr2) or (2ab+ab)-(πr2+πr2)
(2) (2ab-πr2)-(ab-πr2)
(Ask the students at this time: What are these three formulas? On the basis of students' answers, the topic is drawn-this lesson is learning: 2.3 Addition and subtraction of algebraic expressions.
Second, explore new knowledge.
The teacher asked himself: How to calculate (1) and (2)?
Then answer: This lesson will learn 2.3. 1 merging similar items (at this time, the blackboard title is-1. Merge similar projects).
1, the concept of similar terms
Observe the characteristics of the polynomial (2ab+ab)-(πr2+πr2): 2ab and ab.
Students exchange and discuss.
Teacher-student summary: (This is a similar item that we will introduce today. At this time the blackboard is 1. The concept of similar terms)
Items with the same letters and the same index are called similar items.
Several constant terms are similar.
Key points: ① The letters contained are the same; ② The indexes of the same letters are the same.
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