Eighth grade mathematics factorization teaching plan People's Education Edition teaching material analysis
? Factorization (extraction of common factors)? what's up East China Normal University Edition Grade 8 Mathematics (Volume I)? Chapter 13, section 5. Where is this class scheduled? Multiplication of algebraic expressions? Then the relationship between factorization and algebraic expression multiplication is clarified, which plays a role in linking and developing knowledge. Extracting common factor method is the basic method of factorization, and it also lays a solid foundation for learning other methods of factorization and solving quadratic equations with factorization.
Analysis of factorization teaching plan of eighth grade mathematics in People's Education Press
Because most of the students in our class come from rural immigrants, their foundation is weak and their interest in learning is not strong, so I introduce new courses through realistic situations to arouse students' enthusiasm for learning.
Three-dimensional target people's education edition of factorization teaching plan for eighth grade mathematics
According to the requirements of the syllabus, combined with the characteristics of this textbook and students' cognitive ability, the teaching objectives are determined as follows:
Knowledge and skills: 1. Understand the meaning of factorization and judge whether the deformation of a formula is factorization.
2. Cleverly use the method of extracting common factors to decompose factors.
Process and method: In the teaching process, the mathematical thought of experiencing analogy gradually forms the habit of independent thinking and active exploration.
Emotion, attitude and values: through realistic situations, let students realize the application value of mathematics and improve their environmental awareness of the living environment.
Important and difficult points in factorizing teaching plans in eighth grade mathematics.
Teaching emphasis: understand the significance of factorization and decompose factors by extracting common factors.
Teaching difficulties: reasonable grouping, using the method of extracting common factors to decompose factors.
Teaching methods and means of factorization teaching plan for eighth grade mathematics
Teaching methods: analogy and inquiry teaching method
Infiltrate the mathematical thought of analogy in the teaching process to form a new knowledge structure system; Set up inquiry teaching to let students experience the formation of knowledge, so as to achieve a profound understanding and flexible use of knowledge.
Learning method: independent, cooperative and inquiry learning method.
In teaching activities, we should not only improve students' ability to solve problems independently, but also cultivate the spirit of unity and cooperation, expand the depth and breadth of students' inquiry and reflect the requirements of quality education.
Analysis of the factors in the teaching process of eighth grade mathematics teaching plan
Teaching process, teaching content, student activity design intention
Create a situation
4? Import column substitution example
In recent years, the problem of land desertification in China is serious, and many cities have been attacked by sandstorms, but wild sand can't bury hope. Three teams of young volunteers declared war on the desert and organized a plant afforestation activity. Each team planted 37 rows of trees, including one row 102, two rows of 93, and three rows 105. How many saplings do you need to complete this tree planting activity?
Formula: 37? 102+37? 93+37? 105
Is there a simple algorithm?
=37? ( 102+93+ 105)
=37? 300= 1 1 100 (tree)
In this process, M replaces 37, A replaces 102, B replaces 93, and C replaces 105.
So there is: m? a+m？ b+m？ c= m (a+b+c)
Use algebraic expression multiplication to verify:
m (a+b+c)= m？ a+m？ b+m？ c
Ask questions through demonstrations.
Students' thinking pattern
Reverse multiplication and division, transfer to algebraic expression multiplication and verification. By introducing realistic situations, students' learning enthusiasm is mobilized and their awareness of environmental protection is improved.
Using factorization to replace letters with numbers, introducing factorization to make knowledge coherent, and using algebraic expression multiplication to verify the equation, paving the way for the connection between factorization and algebraic expression multiplication.
New lesson explanation
4? Questioning analogy and introducing new knowledge
Factorization: transforming a polynomial into the product of several algebraic expressions.
Object: polynomial result: product form of algebraic expression.
Students give examples: (Explain what factorization is)
Thinking: the relationship between algebraic multiplication and factorization: sum-difference product
1 Multiplication with Algebraic Expressions
factoring
2. Algebraic expression multiplication is used to test the correctness of factorization.
Practical thinking (discriminant factor decomposition)
Ma+mb+mc=m(a+b+c) Do you want to learn this factorization method?
This is the way to extract the common factor to understand the concept.
Students think and answer, and teachers give encouragement and evaluation.
Independent thinking and cooperative communication inspire students to cultivate their divergent thinking and innovative consciousness from the perspective of algebraic expression multiplication. At the same time, students can find the correct and wrong understanding of factorization according to examples, and teachers can guide and correct it in time. Let the students discover the relationship between algebraic expression multiplication and factorization through the mathematical thought of analogy.
Feedback learning quality in the form of exercises in connection thinking, practice while learning, and form mathematical activity experience without increasing memory burden.
New lesson explanation
1 1? Game exploration
Inductive summary
Common factor: Every term in the polynomial ma+mb+mc contains the same factor M, which we call common factor.
Find the common factor game: find the common factor of this polynomial according to the polynomial and the algebraic expression provided.
① 3a+3b ② 2 1x2y2+7x2y
a，b，3 2 1xy，7x2y，7x2y2
③ -x3y2+3xy2-xy ④ x(x-y)2-y(x-y)
xy，-xy，3xy x(x-y)，y(x-y)，(x-y)
Ways to find common factors:
(1) Take the greatest common divisor of the coefficients in the polynomial as the digital factor in the common factor.
(2) Take the letter (or polynomial) in each term that is the same as the letter (or polynomial) in the common factor, and take its lowest power.
Understand this concept
Prepare cards with algebraic expressions and polynomials. Students are divided into four groups. Each group chooses four students to play. Three of them hold algebraic expression cards of a set of questions. The fourth student finds out the common factors of polynomials in this group of problems according to the suggestions of the team members and explains the reasons.
Students discuss and summarize the methods. After introducing the concept of common factor, students' interest in learning new knowledge is stimulated through game activities, which makes the classroom atmosphere relaxed and active.
This setting breaks the traditional method of finding common reasons taught by teachers, and students passively accept memories. Instead, let students unite and cooperate in the game and explore methods independently, which is conducive to developing thinking ability and cultivating students' ability to summarize, express and communicate.
Example point
Analysis of methods for extracting common factors;
This paper puts forward the common factor, and decomposes the polynomial ma+mb+mc into the product of M and A+B+C. This factorization method is called the improved common factor method.
Example: Break down the following categories:
( 1)3a+3b(2)2 1x2y 2+7x2y
(3) ? x3y2+3xy2-xy
Typical mistakes that are prone to occur:
1, symbol 2, project number to understand the concept
Teachers and students work together to correct the mistakes that are easy to occur and write a standardized problem-solving format. There have been examples in the game. After putting forward the common factor, we can focus on the changes of each item, and it is easier for students to learn to extract the common factor accurately.
Example: (4)x(x-y)2-y(x-y)
(5)(x-y)3-(y-x)2
Note: n is an even number (x-y) n = (y-x) n.
N is an odd number (x-y) n =-(y-x) n.
Students actively think, discuss and answer. This example shows that the same algebraic expression can also be used as part of the common factor, paving the way for the future study of method of substitution.