Seventh grade mathematics open class
Knowledge and skill objectives
1 Make students understand the concept of linear equation with one variable and use the deformation of the equation to solve the linear equation with one variable flexibly; Let students use the rules of moving items and brackets correctly.
Program objective
1. Experience the difference between removing brackets and moving items;
2. Through the process of solving the equation, the general steps of solving the equation are obtained.
teaching process
First, create a situation
The last two classes discussed the solutions of some equations, so what are those equations? Let's look at the following equations first: What are the characteristics of the equations in each row? (mainly from the number and number of unknowns contained in the equation) .4+x = 7; 3x+5 = 7-2x； ; x+y = 10； x+y+z = 6； x2-2x–3 = 0； x3- 1 = 0。
Second, explore and compare, what is the difference between the equation in the first line (that is, the first three equations) and other equations? As can be seen from the students' answers, the characteristics of the previous equation are: (1) contains only one unknown; (2) The number of unknowns is once. "Yuan" refers to the number of unknowns, and "degree" refers to the highest number of terms containing unknowns in an equation. What is the above equation according to this naming method? (Student answers)
There is only one unknown, and the formulas containing the unknown are all algebraic expressions, and the number of the unknown is 1. Such an equation is called a linear equation with one variable.
The characteristics of the second line equation are: there is more than one unknown in each equation; The characteristic of the third line equation is that the number of unknowns in each equation is greater than 1. According to the definition of linear equations, the last four equations are not linear equations. Note that the equations of numbers refer to the whole equation, that is, both sides of the equation are algebraic expressions. This is not a linear equation.
The equations we discussed in the last two classes are all linear equations with one variable, and some steps to understand linear equations with one variable are obtained. Next, we will continue to discuss the solution of one-dimensional linear equation and brackets in the equation. Solve equation 2 (x-2)-3 (4x-1) = 9 (1-x). There are parentheses in the analytical equation.
Solution 2x-4- 12x+3 = 9-9x, ...............................................................................................................................................
= 10, when using the distribution method to delete brackets, don't omit the items in brackets; (3) -x = 10, which is not the solution of the equation. We must change the coefficient to 1 and get x =-10, which is the result. As can be seen from the above' Solving Equation', the steps to solve the linear equation with brackets are: (1) removing the brackets; (2) moving items; (3) merging similar projects; (4) The coefficient is 1.
Iii. Practical application example 1 Solving equation: 3(x-2)+ 1 = x-(2x- 1).
There are parentheses in the analytical equation. First, remove the brackets and transform them into the characteristics of the equation mentioned in the last lesson, and then solve the equation. Remove the bracket.
3x-6 + 1 = x-2x + 1，
Combine similar terms
3x-5 =-x + 1，
Interchange of terms
3x+x = 1+5, the combined similar term 4x = 6, and the coefficient is x = 1.5. Example 2 If there are multiple brackets in the equation analysis equation, remove the brackets first, then remove the brackets, and finally remove the braces. Remove brackets and merge similar items to remove brackets and merge similar items to remove brackets-12x-3 =
The term-12x = 8, and the coefficient is 1. Note 1. This problem combines similar terms and brackets that have been removed many times, and the steps can be flexibly selected according to the characteristics of the equation when solving the problem. 2. You can also remove all the brackets and combine similar terms to solve the problem.
What is the value of equation example 3 y? The value of 2(3y+4) is 3 greater than that of 5(2y -7). Analyze such a problem, make the equation 2(3y+4)-5(2y -7)= 3, and then find X. Solve 2(3y+4)-5(2y -7)= 3, remove the brackets 6y+8-65438+-4y+43 = 3, and merge the similar items.
Fourth, the step of removing brackets from solving the linear equation with one variable by AC feedback (1); (2) Move (3) Merge the same kind
Item; (4) The coefficient is 1. Note that (1) bracket deletion is based on bracket deletion rules and distribution rules. Pay special attention to the symbols outside brackets when opening brackets, and don't omit the items inside brackets! (2) After the brackets are removed, if the polynomials on both sides of the equation have similar terms, the similar terms can be merged first and then moved to simplify the problem solving process.
Verb (abbreviation for verb) detects feedback 1. Is the solution of the following equation correct? If not, how to correct it? Solve the equation: 2 (x+3)-5 (1-x) = 3 (x-1) Solve 2)5(x+2)= 2(5x-5x = 3x-3, 2x-5x-3x =-3+5-3.
- 1); (3)2(x-2)-(4x- 1)= 3( 1-x)； (4)4x-3(20-x)= 6x-7(9-x)； (5)3(2y+ 1)= 2( 1+y)+3(y+3)。 3. Solve the column equation: (1) When x takes any value, algebraic expressions 3(2-x) and 2(3+x). (2) When x takes what value, the algebraic expressions 3(2-x) and 2(3+x) have opposite values? 4. Know the solution of the equation and find the value of m 。
Seven-grade mathematics knowledge points
Binary linear equations
8. 1 binary linear equations
An equation contains two unknowns (X and Y) whose exponents are 1. Equations like this are called binary linear equations.
Two binary linear equations are combined to form a system of linear equations with two unknowns.
The values of two unknowns that make the values on both sides of the binary linear equation equal are called the solutions of the binary linear equation.
The common * * * solution of two equations of binary linear equations is called the solution of binary linear equations.
8.2 elimination
The idea of solving the unknowns one by one from more to less is called elimination thought.