Teaching plan design of adding and subtracting algebraic expressions in junior high school mathematics
[learning objectives]
1, know the similar items, and understand the rules for merging similar items, so that similar items can be merged.
2, you can use the activity rate to bracket.
[Test site induction]
Test site 1: Merge similar items Test site 2: Rule of removing brackets Test site 3: Addition and subtraction of algebraic expressions.
[Exam Center Example]
Example 1. Combine similar terms in the following polynomials.
( 1)4x2y-8xy 2+7-4x2y+ 10x y2-4； (2)a2-2ab+b2+a2+2ab+b2。
Example 2. Remove brackets and merge similar items.
( 1)-3(2s-5)+6s(2)3x-[5x-3(x-4)]
(3)6a2-4ab-4(2a2+ ab) (4)
Example 3. (1) It is known that the sum of a polynomial and a2-2a+ 1 is a2 +a- 1. Find this polynomial.
(2) Given A=2x2+y2+2z, and B=x2-y2 +z, find 2 (a-b)+b.
[classroom testing]
1. As shown in the figure, connect similar items in two boxes with line segments:
2. When m = _ _ _ _ _ _ _ -x3b2m and x3b are similar items.
3. If 5akb and -4a2b are similar terms, 5akb+(-4a2b) = _ _ _.
4, the following statement is correct ()
A. Items with the same letters are similar. B. Only items with different coefficients are similar.
C.- 1 and 0. 1 are similar projects. D.-x2y and xy2 are similar projects.
Combine similar terms in the following polynomials.
( 1)4x2y-8xy 2+7-4x2y+ 10x y2-4； (2)a2-2ab+b2+a2+2ab+b2。
2 Simplify first, then evaluate.
(1) (5a2-3b2)+(a2-B2)-(5a2-2b2) where a=- 1 and b= 1.
(2) 9a3-[-6a2+2 (-a3-a2)] where a=-2.
3. and
The value.
[Extracurricular exercises]
1. The following merged similar projects are correct ()
a . 8a-3a = 5b . 7 a2+2 a3 = 9 a2 c . 3a B2-2a2b = ab2d . 3a2b-2ba 2 = a2b
2.ab minus equals ()
A.； b；
C.； D.
3. When sum, two values of algebraic expression ()
A. Equality; B. reciprocity;
C. reciprocal; D. neither equal nor antagonistic
4. In the following questions, the correct bracket is ().
Design of teaching plan for addition and subtraction of mathematical algebraic expressions in junior one.
Teaching objectives
Knowledge and skills: understand the concept of similar items and distinguish them correctly.
Process method: master the rules of merging similar items and be able to merge simple similar items.
Emotional attitude: cultivate students' inquiry ability and abstract generalization ability of problems by analogy. The principle of combining similar projects with teaching priorities. Teaching difficulties: the understanding of the concept of similar items and the application of the merger rules of similar items. Multimedia teaching methods for teaching preparation: interactive communication, group discussion, teaching process, creating situations, introducing new courses → cooperative communication, interpretation and exploration → application, migration, consolidation and improvement → summary, reflection, expansion, sublimation, interaction between teaching and learning, design intention 1. Create situations and introduce new lessons.
Question 1 When we visited the zoo, we found the tiger in one cage and the deer in another cage. Why not put the tiger and the deer in the same cage? Why do you put all kinds of items on different counters in the supermarket? What common sense does all this mean?
Question 2: On the Qinghai-Tibet Railway, there is a long frozen soil section between Golmud and Lhasa. When the train speed can reach 100 km/h in frozen soil area and 120 m/h in non-frozen soil area, please answer the following questions according to these data:
From Xining to Lhasa, it takes twice as long for the train to pass through the unfrozen area as it does through the frozen area. If it takes several hours to cross a frozen area, can you express the total length of this railway with the included formula?
Student activity: Analyze the quantitative relationship between known quantity and unknown quantity.
Students express their opinions. Guide students to realize that "classification" exists in life.
In specific situations, algebraic expressions are used to express the quantitative relationship in the questions, and practical questions are used to attract students' attention. Second, the interpretation of cooperation and exchange
Students think and answer: 100 +252t.
Question 3: Can the formula 100 +252 be simplified? What is the basis?
Explore 1
(1) Using the algorithm of rational numbers to calculate:
(2) Complete the following operations according to the method in (1), and explain the reasons.
Survey 2
( 1) ( )
(2) ( )
(3) ( )
Student activities: on the basis of independent completion, group cooperation and exchange.
The teacher asks questions and thinks: 1. What are the monomials of the above three polynomials?
2. What are the characteristics of the monomial in each polynomial? Can you calculate?
By observing the characteristics of terms in polynomials, the concepts of similar terms and merged similar terms are obtained.
Similar items: items with the same letters and the same index.
Merge similar items: merge similar items in polynomials into one item.
1, have fun: find friends of the same kind.
Methods: 1. At present, there are 16 cards written on the blackboard.
2. Students find cards that are considered to be similar items with digital serial numbers;
Ask other students to be references to see if you have found the wrong friend.
Student activities: cooperate and communicate, find out the answers and clarify the process.
Teachers' activities: teachers tour to guide students, and ask students to answer and confirm after the lecture.
Question 4
Try: Try to merge polynomials into similar items:
What terms does this polynomial contain?
What is the coefficient of each item?
Which projects can be merged into one project? Why?
Analogize the operation of rational numbers and explore the law of merging similar items.
Rule: The coefficient of the obtained item is the sum of the coefficients of the same category before the merger, and the letter part remains unchanged.
Note: (1) The premise of merger is similar items.
(2) Merging refers to the addition of coefficients, and the letters and their indexes remain unchanged.
(3) The basis of merging similar items is additive commutative law, associative law and distributive law.
Teacher-student activities: under the guidance of teachers, teachers and students cooperate to draw a conclusion, which is the same as induction and summary.
3. Exercise: Is the following calculation correct? If not, please correct it.
Teacher-student activities: teachers show questions, students cooperate and communicate, and individual students are invited to answer. Ask question 3, and let the students use this question to solve the inquiry.
Complete the exploration independently (1) and discuss in groups (2).
Through the discussion of inquiry 1 and inquiry 2, the concept of similar items is introduced.
It is not difficult for students to accept the definition of similar items, but it is very difficult to judge correctly. It is necessary to repeatedly emphasize the criteria for judging similar items through practice, so that students can gradually improve their accuracy and proficiency through screening and comparison.
Ask question 4, and let students get the concept and law of the merger of similar items by solving problems. Third, apply migration to consolidate and improve.
Example 1 combines the following categories of similar projects:
( 1) ;
(2) ;
(3) .
Solution (1)
(2)
(3)
Example 2 (1) Find the value of polynomial 2x2-5x+x2+4x-3x2-2, where;
(2) Find the value of the polynomial, where b=2 and c=-3. Solution: (1)
(2)
Example 3 (1) On the first day, the water level of the reservoir dropped continuously for one hour, with an average drop of 2cm per hour. On the second day, it rose continuously for one hour, with an average increase of 0.5m per hour. What is the overall change of water level in these two days?
Design of teaching plan for addition and subtraction of mathematical algebraic expressions in junior one.
Knowledge and skills can explore the law of bracket removal by using the algorithm, compare the process and method of algebraic expression simplification and rational number operation with brackets by using the law of bracket removal, find the law of symbol change when bracket removal, and summarize the law of bracket removal, thus cultivating students' observation, analysis and induction ability. Emotional attitudes and
Values allow students to experience the key points of analogical thinking teaching in inquiry activities and remove the teaching difficulties of bracket law. When there is a "-"before the bracket, the teaching process of symbol change after removing the bracket is designed. Attention [Activity 1]
[Activity 2]
Teach a new lesson
We know that to simplify the formula with brackets, we must first remove the brackets. Can you use the law of multiplication and distribution to calculate the following question/
( 1)20(a+b)= -20(a+b)=
Comparing the above two formulas, can we find the law of symbol change after removing brackets?
Support removal rules:
If the factor outside the brackets is positive, the symbols of the items in the original brackets are the same as the original symbols after the brackets are removed;
If the factor outside the bracket is negative, the symbol of the item in the original bracket is opposite to the symbol after the bracket is removed;
Note: When removing brackets, we should consider the symbols of each item in brackets, so that they all change or remain unchanged; In addition, after removing the brackets, there are still several items in the brackets.
Students try to answer the questions in the introduction.
Design of the fourth teaching plan for the addition and subtraction of algebraic expressions in junior high school mathematics
First, review and check each other (completed by a two-person team)
1. What is a similar item? How to merge similar projects?
2, using the law of multiplicative distribution calculation:
a(b-c)= 1
3(x- 1)= 1
- 1×(x- 1)= 0
-(x- 1)
How to remove the brackets by multiplication and division? What changes have been made to the symbols of the items in brackets before and after the brackets are removed?
Second, ask questions and guide reading.
Read the textbook P66——68 and complete the following questions:
How to simplify eq oac(○, 1) and eq oac(○, 2) in textbooks? The process between the eight flowers is completed.
eq oac(○， 1) 100t+ 120(t-0.5)
= 100t+ 120t+ 120á
=
eq oac(○，2) 100t- 120(t-0.5)
= 100t- 120t- 120×()
=
Retell the rule of removing brackets in the textbook.
In particular, +(x-3) and -(x-3) can be considered as multiplying (x-3) and.
Read Examples 4 and 5.
The factor before the second bracket in Example 4 (2) is, what should be paid attention to when calculating?
In textbook example 5, what do Formula 2(50+a) and Formula 2(50-a) mean respectively? Why do you put brackets? Can't you add it?
Third, self-test
Determine whether the following equation is correct.
( 1)2(3x+y)= 6x+y()(2)6(x-2)= 6x- 12()
(3)-7(x+3)=-7x+2 1()(4)8(a+ 1)= 8a+ 1()
(5)-(a- 10)=-a- 10()(6)-a+b =-(b+a)()
(7)2-3x=-(3x-2)
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