The meaning of the first equation
Teaching content: Example 1 and Example 2 on page 1 of the textbook, and try to complete the exercises and exercises 1, 1~2.
Teaching objectives require:
Understand the meaning of equation, and preliminarily understand the relationship and difference between equation and equation. Understanding equation is a special equation.
Teaching focus:
Understand and master the meaning of the equation.
Teaching difficulties:
The order equation represents the quantitative relationship.
Teaching process:
I. Teaching examples 1
1. Give the balance diagram of the example 1 for students to observe.
Question: What is the picture? What can we know from the picture? Think of what?
2. Guide:
(1) Let the students who are not familiar with the balance know the balance and understand its function.
(2) If students can list equations on their own initiative and tell them that the formula "50+50= 100" is an equation, ask them to talk about the significance of this equation; If students can't list equations, they can ask, "Will you use equations to represent the mass relationship between objects on both sides of the balance?"
Second, teaching examples 2
1. Draw the balance diagram of Example 2, and guide students to express the mass relationship of objects on both sides of the balance with formulas respectively.
2. Guidance: Tell students that the "X" in these formulas is unknown; Look at these formulas and tell which ones are equations. What are the characteristics of these equations?
3. Discussion and communication: Some of the written equations are equations and some are not, and all the written equations contain unknowns. On this basis, the concept of equation is revealed.
Third, practice.
1, which of the following equations is an equation? What is the equation?
2. Rewrite the unknowns represented graphically in each formula into letters.
Fourth, consolidate practice.
1. Finish the exercise 1, question 1.
First, carefully observe the formulas in the question, and talk about which equations are and which ones are within the group, and then communicate with the whole class. Tell the students that the unknowns in the equation can be represented by letters such as X and Y, so as to prevent students from mistaking the equation for an equation containing the unknown X. ..
2. Complete question 2 of exercise 1
Verb (abbreviation of verb) abstract
What did we learn today? What have you gained? What should students pay attention to? Is there a problem?
Sixth, homework
Complete supplementary exercises
Blackboard design:
Meaning of equation
X+50= 100
X+X= 100
An equation whose unknown number is X+50= 150 and 2X=200 is called an equation.
Properties of the second equation and its solution (1)
Teaching content:
Try examples 3 and 4 on pages 2-4 of the textbook and complete questions 3-5 of exercise 1 and exercise 1.
Teaching objectives require:
1. Make students understand that in a specific situation, adding or subtracting the same number on both sides of the equation at the same time will still result in an equation, and will use the properties of the equation to solve a simple equation.
2. In the process of observation, analysis, abstraction, generalization and communication, students can accumulate experience in mathematical activities, cultivate independent thinking, and actively cooperate and communicate with others.
Teaching focus:
Understand that "both sides of an equation add or subtract the same number at the same time, and the result is still an equation"
Teaching difficulties:
Will use the properties of this equation to solve simple equations.
Teaching process:
I. Teaching Examples 3
1. Talk: We already know the equation and the equation. Today, we will continue to learn about equations and equations. Please look at the balance sheet here. Can you write an equation according to the picture?
Q: It's balanced now. If a weight of 10g is added to one side of the balance, what will happen to the balance?
Talk: Now that the balance is back in equilibrium, can you write an equation according to the above equation to express the relationship between the mass of objects on both sides of the balance?
2. Show the second set of balance diagrams and tell how the mass of the objects on both sides of the balance changes. Can you list two equations separately?
3. Show the third and fourth balance diagrams and ask: Can you tell us how the mass of the objects on both sides of the two balance diagrams changes respectively?
Talk about: How to use equations to express the relationship between objects on both sides of the balance before and after the change?
Revelation: How did these two equations change? What are the common features of their changes?
4. Q: Just now, we drew two conclusions by observing the balance chart. Can you combine them in one sentence?
5. Do the exercise of 1.
Second, teaching examples 4
1. Draw the equilibrium diagram of Example 4. Can you list the equations according to the equal mass relationship between the objects on both sides of the balance?
2. Description: To find the unknown value in the equation, you must write "solution" first, and pay attention to the equal sign.
Complete the attempt
Finish the exercise
Question: when solving the equation here, what can I do to make the equation only have X on the left?
Third, consolidate the practice.
1. Do the third question of 1.
2. Question 4 of doing exercise 1
3. Do exercises 1, question 5
Fourth, the class summarizes.
Question: What did we learn in this class today? What have you gained? Are there any questions you don't understand?
Verb (short for verb) homework
Complete the supplementary exercises.
Blackboard design:
Properties of equality and solution equation
The Properties of Equality Solve the Equation
50=5050+ 10=50+ 10 solution: X+ 10 = 50.
x+a = 50+a50+a-a = 50+a-aX- 10 = 50- 10
X=40
Test: Substitute x=40 into the original equation to see if the left and right sides are equal. 40+ 10=50, and x=40 is correct.
Properties of the third equation and its solution (2)
Teaching content:
Textbooks P4 ~ P5, Cases 5 ~ 6, P5 "Try" and "Practice" P6 ~ P7, Exercise 1, Questions 6 ~ 8.
Teaching objectives require:
1. Make students further understand and master the essence of the equation, that is, multiply or divide the same number on both sides of the equation at the same time, and the result is still an equation.
2. Use the corresponding properties to make students master the equation of one-step calculation.
Teaching focus:
Make students further understand and master the essence of the equation, that is, multiply or divide the same number on both sides of the equation at the same time, and the result is still an equation.
Teaching difficulties:
Using the corresponding properties, students can master the equation of one-step calculation.
Teaching process:
First, review the essence of the equation.
1. In the last lesson, we studied the properties of the equation. Who remembers?
2. Add and subtract the same number on both sides of an equation at the same time, and the result is still an equation. Let's guess, if we multiply or divide the same number on both sides of an equation at the same time (except 0 when dividing), will the result be an equation?
3. Feel free to guess and give your reasons.
Then, let's test our guess by studying.
Second, teaching examples 5
1. Guide students to carefully observe Figure 5 of P4 case and fill in the blanks with pictures.
2. Collective inspection
What do you find from these figures and formulas?
X=202x=20×2
3x3x÷3=60÷3
Next, please write an equation in the exercise book at will. Please multiply both sides of this equation by the same number at the same time to calculate the observation, or is it an equation? Then both sides of this equation are divided by the same number at the same time. Is it still an equation? Can you divide by 0 at the same time?
5. What did you find through the activity just now?
6. Guide students to summarize the properties of the equation (about multiplication and division). Multiply or divide 0 lines?
7. Attribute 2 of the equation:
When both sides of an equation are multiplied or divided by the same number that is not equal to 0, the result is still an equation.
8.P5 "Try it"
(1) Read the title by name
(2) What did you fill in?
Three. Teaching example 6
1. Show P5 case 6 teaching wall chart.
Read the questions by name, and ask the students to observe the pictures in Example 6 carefully.
2. How to calculate the area of a rectangle?
3. How to list the equations according to the meaning of the questions? what do you think? Blackboard writing: 40X=960
4. When calculating, how much should the two sides of the equation be divided? Why?
5. After calculating X=24, how to determine whether this number is correct? Please take an oral test. Finally, complete Example 6.
6. Summary: In the process of calculating Example 6, we divided both sides of the equation by 40 at the same time. Why? Why is the equation still valid when both sides of the equation are divided by 40 at the same time?
7. Exercise 7.P5.
Solving equation: X÷0.2=0.8
Teachers patrol to help students with difficulties.
After practice, ask the students by name: How do you solve the equation? Why can you do this?
Fourth, consolidate practice.
1. Only X is left in each equation below. How many times should both sides of the equation be multiplied or divided at the same time?
0.6x=7.2 Both sides of the equation should be simultaneous.
The two sides of the equation x÷ 1.5=0.6 should be simultaneous.
2. Simplify the following categories
8X÷850+X-40
X÷9×9X- 1.4+ 1
3.P6 Question 7
The teacher instructed the students to do equations.
4.p7 Question 8: Write the test process of solving the equation with "".
x+0.7 = 140.9 x = 2.4576+x = 9 1
x÷9 = 90x-54 = 182. 1x = 0.84
Verb (abbreviation of verb) course summary
What did you get from this lesson? What knowledge have you learned? What is the key when solving the equation? What should I pay attention to?
Sixth, homework
Complete the supplementary exercises.
Blackboard design:
Properties of Equation and Solution of Equation
X=202x=20×240X=960
3x3x÷3=60÷3 Solution: 40X÷40=960÷40
X=24
Both sides of the equation are multiplied or divided by the same number that is not equal to 0 at the same time. Test: If x=40 is substituted into the original equation, the result is still the equation. Left =40×24=960, right =960.
X=40 is the solution of the original equation.