Junior high school mathematics first grade teaching plan "from formula to equation" model essay, the whole book.
Teaching and learning objectives
I. Knowledge and skills
1. By dealing with practical problems, it is an improvement for students to experience algebraic methods from arithmetic methods.
2. Learn how to find the equation relationship in the problem, list the equations, and understand the concept of the equations.
3. Cultivate students' ability to obtain information, analyze and deal with problems.
Second, the process and methods
Feel the connection between mathematics and life through practical problems.
Third, emotional attitudes and values
Cultivate students' optimistic life attitude of loving mathematics and life.
teaching method
Exploratory teaching method
Teachers prepare courseware for teaching.
teaching process
First, the introduction of new courses.
The teacher asked the question on page 79 of the textbook, and the following picture appeared at the same time:
Question 2: Can you calculate the distance from Wangjiazhuang to Cuihu by arithmetic?
Question 3: Can we use the knowledge of equations to solve this problem?
Students can be prompted to consider time, distance, speed and the order of the four places. )
When students list different formulas, they should be asked to explain the meaning of each formula.
Teachers can review and summarize according to students' answers:
Three basic physical quantities involved in the 1. problem and their relationships;
2. The speed of the car can be obtained from the known information;
3. Different formulas can be listed from the perspective of distance:
If the distance from Wangjiazhuang to Cuihu is X kilometers, then Wangjiazhuang is kilometers from Qingshan and Wangjiazhuang is kilometers from Xiushui.
Question 1: What does "the car is driving at a constant speed" mean?
Question 2: How to express the speed from Wangjiazhuang to Qingshan Road? Can you point out the speed of other sections?
Question 3: According to the equal speed, can you list the equations?
The teacher guides the students to set an unknown number and use letters containing the unknown number to indicate the related quantity.
The teacher guides the students to find the equation relationship and list the equations.
Teachers analyze students' answers, such as:
According to "the speed from Wangjiazhuang to Qingshan = the speed from Wangjiazhuang to Xiushui", the equation can be listed:
According to "the speed from Wangjiazhuang to Qingshan = the speed from Qingshan to Xiushui"
Countable equation:
The concept of equation is given, and the concepts of equation, left side of equation and right side of equation are introduced.
Equations with unknowns are called equations.
Two steps to solve practical problems by inductive equation;
Model essay on the teaching plan of "from formula to equation" in Mathematics II of Grade One in junior high school
Teaching objectives:
1. By dealing with practical problems, it is an improvement for students to experience algebraic methods from arithmetic methods.
2. Learn how to find the equation relationship in the problem, list the equations, and understand the concept of the equations.
3. Cultivate students' ability to obtain information, analyze and deal with problems.
The emphasis and difficulty of teaching: seeking equality from practical problems.
Teaching process:
First, situational import
Put forward the problem of textbook P78, and demonstrate the driving situation described by the topic with multimedia.
1. Understand the meaning of the question: the bus passes through B earlier than the truck 1 hour. From this sentence, what is the relationship between the distance and time traveled by buses and trucks?
2. Whether the distance between A and B can be calculated by formula requires that the actual meaning expressed by the listed formula can be explained.
Step 3 ask a question. If the letter X stands for the distance between A and B, what formula will you get according to the meaning of the question?
Second, learn new knowledge.
1. Guide students to reflect the meaning of the question in tabular form:
Distance (km) Speed (km/h) Time (h) Truck x 60 Bus x 70
2. Students review the concept of equations, discuss and list the equations, and tell the basis for listing the equations.
3. Discuss the significance of column equation, and compare the advantages of arithmetic method in solving column equation and calculation formula.
4. Reflection: In this question, besides the distance between A and B is an unknown quantity, are there any other quantities unknown? If there are other unknowns, can you express this unknown with letters (or unknown Y) and list different equations? Students discuss in groups.
5. List the known and unknown quantities in the question in the table:
Distance (km) Speed (km/h) Time (h) Truck 60 y Bus 70 y- 1
6. Discussion: ① List the equation about y; (2) Explain the practical significance of this equation (or list the basis of this equation); How to solve the problem: the distance between a and B.
7. Summarize the above methods of listing two equations with different unknowns X and Y: ① If the distance is unknown, list the equations according to the relationship between the driving time of two cars; ② If the driving time is unknown, the equation is listed according to the relationship between the driving distances of two vehicles.
8. Compare the characteristics of the two methods: Read the textbook P79.
9. Draw inferences from the other: calculate the formula, set the unknown equation, and solve the following problems:
(1) The sum of a number equals 8. Find this number;
(2) There are 32 girls in the class, more than boys, so ask for the number of boys;
(3) The park repurchased a number of landscape trees, among which osmanthus trees accounted for the total, camphor trees were more than osmanthus trees, and fir trees were more than the sum of the first two trees 12. How many trees are there in this batch?
Third, the preliminary application
1. example 1: textbook P79 example 1.
Example 2 (Supplement): List the equation about X according to the following conditions:
The sum of (1)x and 18 equals 54;
(2) Half of the difference between 27 and X is equal to 4 times of X. 。
After listing the equations, the teacher explained that "4x" is the product of 4 and x. When there are letters in the multiplier, the multiplication sign "x" is usually omitted, and the digital multiplier is written in front of the letter multiplier.
2. Practice (supplement)
(1) expression:
(1) Number 9 less than A; ② Sum of 2 times of x and 3;
③ Half of the difference between 5 and y; ④ The sum of 7 times of A and B 。
(2) List the equation about x according to the following conditions:
① The difference between12 and x is equal to 2 times of x;
The sum of one third of x and 5 is equal to 6.
Fourth, class summary.
1. What have we learned in this lesson?
2. What have you gained?
Verb (abbreviation for verb) class assignment
Xiaoqing's family earned one yuan in March and spent one third of their living expenses, leaving 2,400 yuan.
One-dimensional linear equation of the second kind
Teaching objectives:
1. Understand the concept of linear equation with one variable and its solution.
2. Master the method of testing whether a value is the solution of an equation.
3. Cultivate students' ability to find the equation relationship according to the problem and list the equations according to the equation relationship.
4. Experience the process of finding the solution of the equation by estimation, and cultivate students' realistic attitude.
Teaching emphasis: find the equation relationship and list the equations.
Teaching difficulties: For a complicated equation, finding the solution of the equation through estimation requires many attempts and certain estimation ability.
Teaching process:
First, situational import
Q: The sum of the ages of Xiaoyu and Xiao Si is 25 years old. Xiaoyu is twice as old as Xiao Si. He is eight years older. How old are Xiaoyu and Xiao Si?
If Xiaoyu's age is X, can you express Xiao Si's age in different ways? (25, 2, 8)
Since these two different formulas represent the same quantity, we can write it as: 25-x=2x-8, so we get an equation.
Second, try independently.
1. Try: Let students try to solve the example of textbook P79.
2. Communication:
On the basis of students' basic solutions, please quote the listed equations and explain the meaning of the left and right formulas of the equation equal sign.
3. On the basis of the students' answers, the teacher makes supplementary explanations, emphasizing that both sides of the (1) equation equal sign represent the same quantity; (2) The expressions on the left and right sides are different.
4. Discussion:
Question 1: In the question (1), can you express another quantity in two different ways and then list the equation?
Question 2: In question (3), can other unknowns be set as X?
Step 5 build a concept
The establishment of the concept of (1);
On the basis of students' observation of the above equations, the teacher came to the conclusion that each equation contains only one unknown, and the number of unknowns is 1. Such an equation is called a one-dimensional linear equation.
"One yuan": an unknown number; Once: The unknown index is once.
Judge whether the following equation is linear:
①23-x =-7； ②2a-b = 3；
The third edition of "from formula to equation" teaching plan model for junior one mathematics.
Teaching objectives 1. Understand the concepts of equation, linear equation, solution of equation, solution of equation, etc.
2. Mastering the properties of the equation can transform the equation.
3. Solve a simple one-dimensional linear equation by using the properties of the equation.
Teaching emphases and difficulties: 1. One-sided linear equation. 2. Use the definition of equation solution to find the value of undetermined letters. 3. The properties of the equation.
Difficulties: 1. Using the properties of equations to solve simple linear equations. 2. Column equation. Pay attention to the completion of after-class teaching □ Normal completion □ Early completion □ Incomplete students accept □ Complete acceptance □ Partial acceptance □ No acceptance of students' classroom performance □ Very positive □ Relatively positive □ Generally, the last homework is completed □ Complete □ Incomplete (completion quality: points /5 points) The last note arrangement □ Complete □ Incomplete (completion quality: points /5 points) Teaching reflection lesson plan design.
(The content includes knowledge points, typical examples, classroom exercises, assignments and design intentions) 1. Related concepts of equation.
1.
Equations with unknowns are called equations. For example, wait.
Understanding should pay attention to the following two points.
Equations must be equations and must contain unknowns. Equation is an equation that represents the known number and unknown number and their equal relationship, and the unknown number is not necessarily one, for example, sum is unknown.
The difference and connection with algebraic expression: algebraic expression is not an equation (there is no equal sign in algebraic expression), and the left and right sides of the equation are algebraic expressions.
2. The solution of the equation
The value of the unknown quantity that makes the left and right sides of the equal sign in the equation equal is called the solution of the equation.
If there is only one unknown in the equation, then the solution of the equation is also called the root of the equation. For example, the left side of the equation =, then it is the solution of the equation, or the root of the equation.
3. Solve the equation
Finding the value of the unknown quantity that makes the left and right sides of the equation equal is called solving the equation.
The difference between solving equations and solving equations;
(1) Solving an equation is a process of determining the solution of the equation and a homomorphic deformation process, in which the solution is a verb.
(2) The solution of the equation is the result, which is the numerical value of the unknown. It can make the values on the left and right sides of the equation equal, which is determined by the equal relationship between the unknown and the known number. The solution in the solution of the equation is a noun.
Example 1: Please indicate which of the following equations are equations.
Exercise: 1 In the following categories, it is an equation; This is the equation.
Example 2: Check the values of the unknowns in brackets in the following questions to determine whether it is the solution of the previous equation.
( 1)
(2)
(3)
Exercise: 2. Which of the following equations is the solution ()
A.B. C. D。
3. The solution of one-dimensional linear equation is ()
A.B. C. D。
Second, one-dimensional linear equation
There is only one unknown, the number of unknown is 1, and both sides of the equal sign are algebraic expressions. Such an equation is called a one-dimensional linear equation.
The simplest form, the standard form
For example, the equation is a linear equation with one variable.
To judge whether an equation is a linear equation, three conditions need to be met: ① it contains only one unknown; ② The number of unknowns is1; ③ Integral equation. Three points are essential.
Example 3: The following equation is linear, but it is ().
A.B. C. D。
Example 4: If it is a linear equation about, the value of is ().
A.1B. Any number C.2 D. 1 or 2.
Exercise: 4. If the equation is linear, evaluate.
Third, the nature of the equation.
Properties of 1. Equation 1
Add (or subtract) the same number (or formula) on both sides of the equation and the result is still the same. That is to say, if.
2. Properties of Equation 2
Multiply by the same number on both sides of the equation, or divide by the same number that is not 0, and the result is still equal. That is, if, then; If.
Example 5: Fill in the blanks with appropriate numbers or formulas, so that the result is still an equation, and point out which property of the equation it is based on and how it is deformed.
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