Teaching background:
Matching method is a very important thinking method in junior high school mathematics, which has an important role and status. It frequently appears in the senior high school entrance examination, which is a necessary mathematical ability for junior high school students. It is widely used in solving quadratic equations, quadratic functions, factorization, solving special equations, problems related to maximum or minimum, algebraic evaluation and so on.
Teaching objectives:
1, understand the definition of matching method;
2. Understand and master the application of matching methods;
Teaching methods:
Video teaching and example explanation
Teaching process:
First of all, review the old and learn the new.
What is a matching method?
Matching method refers to obtaining the complete square form by matching and rounding, and then using the non-negative property of the complete square term to increase the topic conditions.
Second, learn new knowledge.
Four aspects of application of display matching method;
(a), a quadratic equation matching solution.
Example 1: Solve equation 3x2+8x-3=0 by matching method.
Steps:
1. Transform 1: transform the quadratic coefficient into1;
2. Shift the term: shift the constant term to the right of the equation;
3. Formula: the square of half of the absolute value of the first coefficient is added to both sides of the equation;
4. Deformation: the left side of the equation decomposes the factor, and the right side merges the same kind;
5. Square root: According to the meaning of square root, both sides of the equation are squares;
6. Solution: Solve the linear equation of one variable;
7. Definite solution: Write the solution of the original equation.
Focus on steps one and three.
(2) Finding the maximum value of quadratic function by matching method.
Example 2: Given that X is a real number, find the maximum value of Y =x2-6x+ 10.
Analysis: when the formula is vertex-shaped, the maximum value of the function can be obtained.
(3) Find the maximum value of algebraic expression by collocation method.
Example 3: Prove that the value of algebraic expression 2x2-3x+ 10 is always greater than zero, no matter what the real number is.
Analysis: Put this quadratic trinomial into it, and you can judge what its maximum value is.
Then ask: Can you find the maximum value of this algebraic expression?
(4) Solving special equations by matching method.
Example 4: The equation x2-10x+y2-8y+41= 0 is known. Find the value of x+y.
Analysis: First solve the equation to get the values of x and y, and divide 4 1 by 25+ 16. If the formula on the left side of the equation is made into two completely flat ways, it can be transformed into a formula with the sum of the squares of two numbers being 0, so that the values of x and y can be obtained respectively.
Third, the aftertaste is endless.
1, the application of matching method
1. Solving the quadratic equation with one variable by matching method.
Second, find the maximum value of quadratic function by collocation method
Third, find the maximum value of algebraic expression by collocation method
Fourthly, the matching method is used to solve special equations.
2. Thinking: Among the four applications of the above matching method, which are "matching" and which are "gathering"?
The key to the first, second and third aspects lies in matching, and the key to the fourth aspect lies in matching.
Fourth, homework design: see advanced exercises.
Teaching summary of verb (abbreviation of verb);
Matching method occupies a very important position in junior high school mathematics, is an important means of identity deformation, is a common skill to study equality relations and discuss inequality relations, and is a powerful tool to mine hidden conditions in topics. Students must learn it well.