Teaching design of solving equations by People's Education Press Part I Teaching content:
Textbook P67 ~ 68 Case 1, Cases 2 and 3 and Exercise 15, Question 1, 2 and 7.
Teaching objectives:
Knowledge and skills: let students understand it initially? The solution of the equation? With what? Solve the equation? What do you mean by harmony? The solution of the equation? And then what? Solve the equation? The connection and difference between them.
Process and Method: Using the properties of equations to solve simple equations.
Emotion, attitude and values: pay attention to the abstract generalization process from concrete to general, and cultivate students' algebraic thoughts.
Teaching focus:
Do you understand? The solution of the equation? And then what? Solve the equation? The connection and difference between them.
Teaching difficulties:
Know the shape of a? X =b equation principle, master the correct solution equation format and test method.
Teaching methods:
Create a situation; Observe, guess and verify.
Teaching preparation:
Multimedia.
teaching process
First, situational introduction
Dialogue: Students, shall we play a guessing game? Show a box and ask the students to guess how many balls there are. Students will think that it can be any number. )
Teachers continue to supplement the conditions through multimedia, and show the situational diagram of the example 1 on page 67 of the textbook.
Q: What information do you learn from the pictures?
Look at the picture and answer: There are nine balls in the box and three balls outside.
And expressed by the equation: x +3=9 (the teacher writes on the blackboard)
Second, the new interactive award.
1. Let the students recall the properties of the equation first, and then think about using the properties of the equation to find the value of x.
Students think, communicate and try to talk about their own ideas.
2. The teacher helps students understand through the scale.
Show the first balance chart on page 67 of the textbook, and let the students observe and say it.
The cuboid box represents the unknown x balls, and each small cube represents a ball. Then the balance has x +3 balls on the left and 9 balls on the right, and the balance is balanced, that is, the formula: x +3=9.
Observation: Take off three balls on the left. What can I do to keep balance?
(Take off three balls on the right, too. )
Follow-up: How to express it by formula? Student exchange report: x +3-3=9-3.
x =6
Question: Why should we subtract 3 from both sides? What do you want?
According to the nature of the equation: the two sides of the equation subtract the same number, and the left and right sides are still equal. )
Is your idea right? Show the third balance chart to prove that the students' ideas are correct.
3. Teacher's summary: Just now we calculated that x =6, which is the unknown value that makes the left and right sides of the equation equal, is called the solution of the equation. In other words, x =6 is the solution of the equation x +3=9. The process of solving equations is called solving equations. (blackboard writing: solving equations)
4. Guidance: Who can tell me the difference between the solution of the equation and the solution of the equation? Students may initially know that the value of x is the solution of the equation by reading the textbook independently; The process of solving is to solve the equation.
Teachers guide students to sum up: the solution of the equation? Are you online? Solution? It means that the value of the unknown quantity that can make the left and right sides of the equation equal is a numerical value; And then what? Solve the equation? Are you online? Solution? Refers to the process of finding the solution of the equation, which is a calculation process.
5. Checking calculation: Is x =6 the correct answer? How do we test it?
Guide students to think independently and communicate in groups.
To sum up the students' answers, you can substitute the value of x =6 into the left side of the equation and calculate it to see if it is equal to the right side of the equation.
Namely: the left side of the equation =x +3.
=6+3
=9
= Right side of the equation
Let the students try to check and pay attention to guiding writing.
6. Show the situational diagram of Example 2 on page 68 of the textbook.
Ask the students to observe the picture and understand the meaning of the picture, and express it with the equation: 3x = 18.
Guide students: try to solve this problem through the experience of solving equations just now.
Students try to solve problems independently, and teachers patrol and guide them.
Report the problem-solving process: divide both sides of the equation by 3 at the same time, and the solution is x =6.
According to the students' answers, the blackboard is 3x = 18.
3x？ 3= 18? three
x =6
Question: What is your answer based on?
Introduction summary: According to the nature of the equation: both sides of the equation are multiplied or divided by a number that is not O at the same time, and the left and right sides are still equal.
Ask the students to try to check whether the calculation result is correct.
7. Show example 3 on page 68 of the textbook and ask the students to try to answer.
Because the question is? a-x？ Type B, some students may have difficulty in doing the problem and don't know how to do it. Some students may add both sides of the equal sign at the same time? x？ But x is on the right side of the equal sign and will not continue to do it.
Teachers can guide students to think. According to the properties of the equation, as long as both sides of the equation add and subtract equal numbers or expressions at the same time, and the left and right sides are still equal, then we can add at the same time? x？ .
Through calculation, let the students find that only? 20? What about the right? 9+x？ .
Continue to guide students to think: 20 and 9+x are equal, you can swap places and continue to solve problems. Students continue to complete the questions and reports. According to the report committee:
20-x =9。 Let the students try the test independently: the left side of the equation = 20-x.
20-x +x =9+x =20- 1 1
20=9+x =9
9+x =20 = the right side of the equation
9+x -9=20-9
x =ll
8. Discussion: What should we pay attention to when solving equations? Before the report, let the students speak for themselves.
Summary: Solve the equation according to the properties, and write first when solving the equation? Solution? The equals sign should be aligned and the result should be tested.
Third, consolidate and expand.
1. After reading page 67 of the textbook? Do it. Questions 1 and 2.
2. After reading page 68 of the textbook? Do it. Questions 1 and 2. Students work out their own solutions and revise them collectively.
Fourth, class summary. Teacher: What did you learn in this class? What did you get?
Leading summary: 1. When solving the equation, solve it according to the properties of the equation. 2. The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation. 3. The process of solving equations is called solving equations.
Homework: problems 15, 1, 2, 7 on page 70 ~ 7 of the textbook.
Blackboard design:
Solve the equation (1)
Example 1: Example 2: Example 3:
X -3=9 equation left =x +3 3x = 18 20-x =9.
x +3-3=9-3 =6+3 3x？ 3= 18? 3 20- x + x =9+x
x =6 =9 x=6 20=9+x
= Right side of Equation 9 +x =20
So x =6 is the solution of equation 9+x -9=20-9.
x =ll
The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation. The process of solving equations is called solving equations.
Teaching reflection:
In the teaching of this lesson, I start from the following aspects:
First, feel the balance phenomenon of the balance and understand the change of the equation.
In learning, I use multimedia to demonstrate the nature of the balance equation of the balance, so that students can understand the nature intuitively. The condition of balance is that both sides increase or decrease the same weight at the same time to maintain balance. However, when applied to equations, students' sensory activities are an effective way to acquire real knowledge. Through the above activities, students can successfully draw a conclusion that the balance is still balanced when the same mass is added to both sides of the balance.
Second, the essence of equality, a preliminary understanding of its wonderful use.
In class, students are not familiar with solving equations with the properties of equations. In their initial experience, they prefer to use the relationship between addition and subtraction parts to solve equations. Therefore, special attention should be paid to guiding students to realize the benefits of solving equations with the properties of equations, thus forming the habit of solving equations with the properties of equations.