Teaching objectives of slightly complex equation mathematics teaching plan 1
1。 By learning and mastering the methods and steps of solving problems with series equations, slightly complicated equations can be solved. 2。 Experience the advantages of solving problems with sequence equations, and choose appropriate methods according to the characteristics of the problems. 3。 Use situational teaching to integrate problem-solving into a story situation. Through the study of this class, we can stimulate students' interest in learning, enhance students' awareness of application value and carry out humanistic education.
Emphasis and difficulty in teaching
Mastering the methods and steps of solving equations will solve slightly complicated equations. Experience the advantages of solving problems with sequence equations, and choose appropriate methods according to the characteristics of the problems.
teaching process
Preparation questions: (courseware demonstration)
1。 Use formulas containing letters to represent the following quantities.
(1) is five times larger than x.
② less than 2 times of x.
(3) Sum of 2× 34
(4) The difference between 5 times of x and 9.
Tell me about your thinking of solving equations?
2. Solve the following equations.
3x= 147 y—34=7 1
3. According to the following statement, talk about the equation relationship and write the equation.
Tucki is x years old this year, and his teacher is 35 years old, which is 1 year younger than Tucki.
First, the situation arouses interest and introduces new courses.
Show me football.
1, physical interest: Q: Please raise your hand if you like playing football (evaluation), and raise your hand if you know something about the composition of this football (exchange evaluation). The perfect composition of Little Football has aroused great interest of mathematicians, architects and aestheticians, and they all found the value of their own research. Today we will use a mathematician's eyes to discover the mathematical secrets hidden in this football composition, shall we? Please observe the theme map and find the information you need. solve problems
The black leather on football is pentagonal and the white leather is hexagonal.
There are 12 pieces of black leather * *, and 4 pieces of white leather are less than 2 times of black leather. * * * How many pieces of white skin are there? How to do an arithmetic calculation?
12×2—4
=24—4
=20 (block)
A: * * * There are 20 pieces of white leather.
2. Cooperative exploration
(1) Please observe the theme map and find the information you need.
Example 1: There are 20 pieces of white leather on the football, which is 4 pieces less than the double black leather. How many pieces of black leather are there?
(2) Reporting and communication: What information do you know? The black leather on football is pentagonal and the white leather is hexagonal. There are 20 pieces of white leather, 4 pieces of which are twice less than those of black leather. How many pieces of black leather are there? "
Check the problem and find useful information to solve it.
Reveal the theme: today we learn to solve this kind of problem with equations.
Teacher's blackboard writing: a slightly complicated equation
Analyze and find out the equal relationship between quantities. What is the relationship between white skin and black skin?
Students discuss in groups,
Report the results.
The possible equivalence relations are:
Number of pieces of black leather 2-4 = number of pieces of white leather.
Number of black leather blocks 2- Number of white leather blocks =4
Number of black leather blocks 2= Number of white leather blocks +4
(3) Discuss at the same table how to write the meaning of X clearly.
(4) How to list the equations.
(5) Exchange report, asking students to say the equivalent relationship represented by the listed equations according to the meaning of the questions. Allow students to list different equations.
Write the student equation on the blackboard and choose 2x-4 = 20 to discuss its solution.
Courseware demonstration: the solution of 2 ⅹ-20 = 4.
Students discuss solutions in groups and report to the exchange teacher on the blackboard;
Variant exercise:
The black leather on football is pentagonal and the white leather is hexagonal. The white leather is 20 yuan, twice as much as the black leather.
Four dollars more. * * * How many pieces of black leather clothes are there?
(6) Guide students to summarize.
Steps to solve problems with column equations:
(1) Find out the meaning of the problem, find out the unknown, and express it with X.
(2) Analyze and find out the equal relationship between quantity and column equation.
③ Solve the equation.
Test and write the answers.
Second, apply what you have learned and expand your practice.
Students, using the skills we have just learned, we will venture into the kingdom of mathematics. Do you have confidence?
1, my sister is 20 years old, just four years older than my brother. How old is my brother this year?
2. Only the equation has no answer.
Require independent completion, deskmate inspection, communication and display.
3. Solve the following equations, and comment on the whole class independently.
The Forbidden City in Beijing covers an area of 720,000 square meters, which is 65,438+600,000 square meters less than Tiananmen Square. Is the area of Tiananmen Square all square meters?
Complete independently and comment collectively.
5.* * * Tennis balls 1428, every five tennis balls are packed in a bucket, and there are three left after loading. How many barrels are there in a * *? Complete independently and comment collectively. Tell me why.
Three. abstract
What do you gain and regret from this lesson?
Teacher: We should look at things in life from a mathematical perspective, pay attention to mathematical problems in life, be good at thinking and learning, and learn mathematics well.
Blackboard writing:
A slightly complicated equation
Number of black leather blocks 2-4 = Number of white leather blocks 2x-4 = 20.
Number of black leather blocks 2- number of white leather blocks = 4 2x-20 = 4
Number of blocks of black leather 2= number of blocks of white leather +4 2x=20+4.
Teaching objectives of mathematics teaching plan 2 for slightly complex equations
Knowledge and skills:
Through the analysis of quantitative relationship, the general steps and methods of solving practical problems by using column equations are mastered.
Process and method:
Equations in the form of ax+b=c or AX-B = C can be listed and solved correctly.
Emotional attitudes and values:
Feel the connection between mathematics and real life, and cultivate students' awareness of mathematics application and good study habits.
Emphasis and difficulty in teaching
Teaching focus:
Master the solution of more complex equations.
Teaching difficulties:
Correctly analyze the quantitative relationship in the topic.
teaching tool
Multimedia equipment
teaching process
Teaching process design
1 introduction
(1) knowledge review:
Solve the following equation:
3x= 147 y—34=7 1
(2) Examples of imports
Question: Do students like to play ball in extracurricular activities? What ball games have you participated in? The following pictures are related to the slightly complicated equations we are going to learn today. (Show theme map courseware)
2 Reveal the topic
Writing on the blackboard-a slightly complicated equation
3 New knowledge exploration
1, Teacher: Let's see, what did they say?
There are 12 pieces of black leather * *, and 4 pieces of white leather are less than 2 times of black leather. * * * How many pieces of white skin are there?
What information did you get from it?
Health: From their conversation, I learned that the black leather on football is a regular pentagon and the white leather is a hexagon.
Teacher: Because there is such an interesting combination in football, many mathematicians are fascinated by it. Let's have a look. What is the secret relationship between the number of black skins and the number of white skins in football?
Teacher: So which color is more?
Health: It's relatively white.
Teacher: Students should study if they are so careful, because only careful observation can lead to a thorough understanding. Can the students help three children solve this problem?
Students say the teacher writes on the blackboard:
Solution: 12× 2-4
=24—4
=20 (block)
2. The students are great. Next, let's take a look at the following example. Ask a classmate to read it.
The black leather on football is pentagonal and the white leather is hexagonal. There are 20 pieces of white leather, 4 pieces of which are twice less than those of black leather. * * * How many pieces of black leather clothes are there? (Courseware demonstration)
Please think about it. What is the equivalence relation in this problem?
4. Name it. (Courseware demonstration)
Question: According to the equivalence relation and the information in the topic, can you determine which quantities are known and which are unknown? Please select a quantity relation to solve the problem.
5. Can equations be solved according to these relationships? Please make your own equations to solve, and then communicate with each other in groups to discuss whether the equations are correct and how to solve them.
6. Call the students to answer, and the teacher writes the problem-solving process on the blackboard.
Solution: Let * * have x pieces of black skin.
Number of blocks of black leather × 2-4 = number of blocks of white leather.
2x-4 = 20 (2x as a whole)
2x+4—4 = 20+4
2x = 24
X = 12
Teacher: Here, let's take 2X as a whole. According to the principle of balance, the left and right sides of the equation subtract 4 at the same time, which becomes 2X= 16. Then according to the principle of balance, divide the left and right sides of the equation by 2 at the same time, and finally get X=8. What should we pay attention to here? (If there is an X, don't write the company name. ) Let's answer together. Here, I have finished this problem, OK? Why?
Health: It's endless. We need to check whether X = 12 is the solution of the equation.
Students say the teacher writes on the blackboard:
Test: Left = 2× 12-4.
=20 is one step more than the previous equation.
= Right
So X = 12 is the solution of the equation.
7. What other equations can be listed in this question? Who wants to play in the front? And tell the students. (This can be based on the principle of balance and the relationship between parts. )
8. This classmate did really well, and the teacher is really happy for you.
9. We should not only learn knowledge, but also learn to summarize methods. Next, let the students sum up one or more equations at the same table to solve the problem.
Students review and summarize the general steps of solving equations.
Read the questions and raise your awareness.
When students answer and report independently, focus on their ideas.
Under what conditions do students report quantitative relations?
Teacher: Students, the equation we studied today is a little more complicated than before, and it is not difficult for us alone. Let's sum up the solutions of this kind of equation, shall we?
Teachers and students have concluded that the solution of the equation AX-B = C (A ≠ 0) should also be based on the properties of the equation, and the specific steps are as follows:
Solution: ax-b = c
ax—b+b=c+b
ax=c+b
ax÷a=(c+b)÷a
x=(c+b)÷a
Teacher: Let's summarize the basic steps of solving a slightly complicated equation.
Basic steps of solving slightly complicated equations. (Courseware demonstration)
(1) Explain the meaning of the problem and write the solution.
(2) Find the equivalence and list the equations.
(3) Solving the equation requires testing.
Teacher: On the earth where we live, there are both land and sea. How much do the students know about her? Let's take a look!
The teacher's courseware illustrates with examples.
Example: The surface area of the earth is 5. 65.438 billion square kilometers, of which the ocean area is about 2% of the land area. Four times, what are the areas of land and sea on the earth?
Teacher: What is the equivalent teacher of this problem?
Health: land area+ocean area = earth area.
The teacher leads the unknown.
Health: If the land area is X billion square kilometers, the ocean area is 2. 4 billion square kilometers.
The students tried to solve the equation.
x+ 2.4x=5. 1
(1+2.4)x=5. 1 (What algorithm is used? )
3.4x=5. 1
x= 1.5
So the ocean area is 2. 4× 1.5=3.6 (hundred million square kilometers).
Teacher: If the ocean area is X billion square kilometers, how should we formulate the equation?
Health: If the ocean area is X billion square kilometers, then the land area is x÷2. 400 million square kilometers.
x+ x÷2.4=5. 1
2.4x+x=5. 1×2.4 (basic properties of the equation)
3.4x= 12.24
X=3.6
So the land area is 3.6÷2.4= 1.5 (1 100 million square kilometers).
Teacher: Which equation do you think is more convenient to solve?
Students discuss and report diseases and explain the reasons.
Teacher: Students, let's look at the following question again:
Example: Mom goes to the supermarket to buy fruit, 2 pears per kilogram. 8 yuan, my mother bought 2 Jin of apples and 2 Jin of pears, and spent 10. 4 yuan. How much are apples per kilogram?
Teacher: Please read carefully and find out the equivalence in the topic.
Read the questions and find out the equivalence.
Total price of apples+total price of pears = total money or total money-total price of apples = total price of pears or unit price of two fruits ×2= total money.
Teacher: Choose your favorite equivalence relation and list the equations according to this relation. Just try it.
Health: column solution.
(1) Total price of apples+total price of pears = total amount of money.
If apples cost X yuan per kilogram, then according to the meaning of the question, there are
2x+2×2.8= 10.4
2x+5.6= 10.4
2x= 10.4—5.6
2x=4.8
x=2.4
(2 total amount of money-total price of apples = total price of pears.
If apples cost X yuan per kilogram, then according to the meaning of the question, there are
10.4—2x=2×2.8
10.4—2x+2x=2×2.8+2x
2x+5.6= 10.4
2x= 10.4—5.6
2x=4.8
x=2.4
(3) The unit price of two fruits ×2= the total amount of money.
If apples cost X yuan per kilogram, then according to the meaning of the question, there are
(2.8+ x)×2= 10.4
(2.8+ x)×2÷2= 10.4÷2
2.8+ x=5.2
x=5.2—2.8
x=2.4
Teacher: Although the quantitative relationship of this problem is complicated, it is not difficult for us. Students still found the equivalence relation of this problem, and listed and solved the equation according to the equivalence relation.
4 Consolidation and promotion
(A), only the equation has no answer.
(1) The library has 180 books on literature and art, 20 books on science and technology more than twice as many, and X books on science and technology.
2x+20= 180 or180-20x = 20 or ...
(2) There are 400 hens, 40 cocks less than 2 times and X cocks in the chicken farm.
2x-40 = 400 or 2x-40 = 400 = 40 or ...
(3) The school feeding group raised 25 rabbits this year, 8 fewer than the number raised three times last year. Last year, X rabbits were raised.
3x-8 = 25 or 3x-8 = 25 = 8 or ...
(4) The circumference of an isosceles triangle is 86 cm and the base is 38 cm. Its waist is x centimeters.
2x+38=86 or 86— 2x = 38 or ...
(2) Use a formula containing letters to express the following quantitative relationship.
3.7 is more than B (B+3.7)
The sum of 18 A (18A)
The quotient of x divided by 20 (X÷20)
A minus C equals 7. 1 multiple difference. (7. 1(A-C))
Quantity 1 1.2 is more than 5 times of x (5X+ 1 1.2).
(3) List the equations according to the meaning of the questions.
(1) The Forbidden City covers an area of 720,000 square kilometers, less than Tiananmen Square160,000 square kilometers. What is the area of Tiananmen Square? (If the area of Tiananmen Square is x square meters, then 2x- 16 = 72)
(2)*** tennis balls 1428, every five tennis balls are packed in a tube, and there are three left after the packing. How much does a * * * contain (suppose a * * contains X barrels, 5X+3= 1428).
Summary after class
What have you gained from learning this lesson? What problem can I help you solve?
(1) Explain the meaning of the problem and write the solution.
(2) Find the equivalence and list the equations.
(3) Solving the equation requires testing.
Write on the blackboard.
A slightly complicated equation
Solution: Set ***X pieces of black leather.
2X—20=4
2X=4+20 (written by students)
2X=24
x = 24 \2
X= 12
A: * * * There are 12 pieces of black leather.
To sum up, the solution of the equation AX-B = C (A ≠ 0) depends on the properties of the equation, and the specific steps are as follows:
Solution: ax-b = c
ax—b+b=c+b
ax=c+b
ax÷a=(c+b)÷a
x=(c+b)÷a
Steps to solve the equation:
(1) Explain the meaning of the problem and write the solution.
(2) Find the equivalence and list the equations.
(3) Solving the equation requires testing.
The key and difficult point in the teaching of Mathematics Teaching Plan 3 for Slightly Complex Equations is to master the solution of more complex equations and correctly analyze the quantitative relationship in the questions. The purpose of teaching is to further master the method of solving equations. On the basis of learning to solve relatively easy application problems with equations, this section teaches to solve slightly complicated two-step calculation application problems. If we use arithmetic to solve problems, it is difficult to think backwards, and students are prone to make the mistake of dividing first and then subtracting. Solving problems with equations is smoother, which shows the superiority of solving application problems with column equations.
First, start with what students like to see and hear, and reduce the difficulty of the question.
The key to solve this kind of application problem is to find the equal relationship between the quantities in the problem. In order to help students find out the equivalence relation of problems. I started with students' favorite football, which led to math problems, stimulated students' interest in learning math, established students' good feelings of loving sports, and made a lot of preparations for learning new knowledge.
Second, let students think and answer, and choose the best plan.
Let students be small teachers, find out the relationship between quantity and quantity from problems, find out the ideas to solve problems, and show and explain their own thinking process and results. This can not only increase students' learning confidence, but also cultivate their ability to analyze problems and expand their thinking space. Then, I boldly let go and let the students solve Example 2 in the way they have learned. Finally, the teacher asked the students to put all kinds of schemes on the blackboard, let the students analyze which scheme is reasonable, and then choose the best scheme. This not only highlights the best way to solve problems, but also strengthens the superiority and key of understanding equations and promotes the development of students' logical thinking.
Third, teaching students learning methods is more important than teaching knowledge.
The key to practical problem teaching is to clarify thinking, teach methods, enlighten thinking and improve problem-solving ability. In the teaching of this class, teachers dare to let go, let students observe pictures, understand picture information, organize students to discuss and communicate in groups, then draw line segments in exercise books, and then guide students to analyze the relationship between quantity and quantity according to line segments, discuss communication and solve problems, so that students can become masters of learning and participate in the whole process of teaching. Therefore, in the teaching of application problems, teachers should guide students to learn how to analyze the problem-solving methods of application problems. In short, teaching students learning methods is more important than teaching knowledge, so that students can truly become the main body of learning. Teachers are the organizers and guides of the teaching process.