Teaching content: experimental textbook for the fourth grade of compulsory education curriculum standard (Volume II) published by People's Education Press, page 117-18, example1,example 2.

Teaching objectives:

1. Through exploration, we found two kinds of rules of planting trees in different situations, one is planting trees at both ends, and the other is not planting trees at both ends.

2. Make students experience and understand the problem-solving strategies and methods of "simplifying the complex".

3. Let students feel the extensive application of mathematics in daily life, try to solve simple problems in real life with mathematical methods, and cultivate students' application consciousness and ability to solve practical problems.

First, the introduction of conversation, clear topics

Just after Mother's Day, we are about to usher in a happy festival-"Children's Day", which is also a festival for children all over the world. In fact, there are many meaningful days in a year. What else do you know? Can you say a few? (biology)

Do you know when March 12 is? (Arbor Day) Have you ever participated in tree planting activities? Planting trees can not only beautify the environment and purify the air, but also have many math problems. Today, in this class, we will study the problem of planting trees together. (Title on the blackboard: Planting Trees)

Second, guide the inquiry and discover the law of "planting at both ends"

1. Create a situation and ask questions.

① Courseware shows pictures.

Introduction: This is a new highway in our county. There is a green belt in the middle of the highway. Now we are going to plant a row of trees in the green belt. How to grow them?

Display title: The total length of this highway is 1000 meters, and a tree should be planted every 5 meters (both ends should be planted). How many seedlings does a * * * need?

2 Understand the meaning of the question.

A. read the questions by name. What information did you learn from the question?

B.do you understand what "both ends" mean?

Say its name, and then demonstrate it in kind: point out where the two ends of this stick are.

Note: If this stick is regarded as this green belt, it should be planted at both ends of the green belt.

(3) Calculate how many seedlings a * * * needs?

4 feedback the answer.

Method 1: 1000÷5=200 trees.

Method 2: 1000÷5=200 (tree) 200 +2=202 (tree).

Method 3: 1000÷5=200 (tree) 200+1=20 1 (tree)

Teacher: Now there are three answers, and each answer has many supporters. Which answer is correct? Can you draw a picture to simulate the actual species? If you plant a tree on the map to 1000 meters and count it, can you know whose answer is correct?

2. Simply verify and find the law.

(1) Painting is actually a kind of painting.

Courseware demonstration: We use this line segment to represent this green belt. "Two species", we start from this end of the green belt, first plant a tree on the head, then plant a tree every 5 meters, then plant a tree every 5 meters, and then plant a tree every 5 meters, and so on.

Teacher: Look, how many meters have you planted? It took so long to plant 45 meters. How many meters does it take to plant a tree? (1000m) Should we plant one tree at a time until 1000m? ! Students, what do you think? I'm too tired, too troublesome and too time-wasting.

Teacher: The teacher feels the same way. It's really too much trouble to plant a tree at 1000 meters. For such a complicated problem, there is actually a better research method in mathematics. Do you want to know? This method is not an ordinary method. Listen up, everyone. This method is: when encountering more complicated problems, think simple first, and start with simple problems to study. For example, 1000 meters is too long. We can plant one on the short circuit first and see four ants, argon and pepper, hitting the palace directly.

(2) draw a picture, simple verification, find the law.

A. Plant15m first, or plant a tree every 5m, and draw a picture to see how many trees are planted? Compare and see who can draw quickly and plant well. (blackboard writing: 3 sections and 4 trees)

B: As above, plant another 25 meters. How many segments did you plant this time? (blackboard writing: 5 sections and 6 trees)

C. Choose a certain distance at will and plant another tree. See how many sections you divided and how many trees you planted this time? What did you find out from it?

(blackboard writing: 2 sections and 3 trees; 8 trees in 7 lots; 10 section 1 1 tree. )

D. what did you find?

Summary: It's amazing that you found a very important rule on the problem of planting trees, that is:

(blackboard writing: plant both ends: tree = number of segments+1)

③ Use the law to solve problems.

A. Courseware demonstration: the previous example

Q: Can this law be applied to solve the previous problems? Which answer is correct?

1000÷5=200 What does 200 mean here?

200+1=20 1 why+1?

Teacher: Is this secret recipe good?

Through a simple example, the law is found and applied to solve this complex problem. Do you know what to do when you meet a "two-headed" tree?

B. Solving practical problems

During the sports meeting, insert colored flags on one side of the straight track, one side every 10 meter (both ends should be inserted). This runway is 100 meter long. A * * *, how many colorful flags should be planted? (Students do it independently. )

Q: Is this problem solved by planting trees?

Teacher: It seems that applying the law of planting trees can not only solve the problem of planting trees, but also solve many similar phenomena in life.

Summary: Just now we solved a practical problem by applying the discovered law. We already know that "two-planting" requires the number of tree segments+1; If no trees are planted at both ends, what is the relationship between the number of trees and the number of segments?

Third, cooperative exploration, the law of "not planting at both ends"

1. Guess the law of "no planting at both ends".

The result of the guess is that there is no species at both ends: tree = number of segments-1.

Teacher: Is the student's guess correct? Let's draw a picture first, and plant a picture with simple examples in the way we learned before.

Requirements: each person draws a road independently to see; Then communicate in groups of four. What rules did your group find?

2. Independent exploration, cooperation and exchange.

3. Show the research results of the group, find out the rules and verify the previous guesses.

Summary: The students are very good. By giving a simple example, they found the law of "no planting at both ends": tree = number of segments-1. If you wanted a tree and planted neither, would you do it?

4. Do it.

① Plant trees on one side of a 2000-meter-long road, and plant a tree every 10 meter (not at both ends). How many seedlings does a * * * need? (Students finish independently)

Teacher: Attention, class. What's wrong with this question?

Courseware flashing: changing "one side" into "two sides"

Q: What do you mean by "planting trees on both sides"? How many rows of trees do you actually want to plant? Can you do it? Do it quickly.

Summary: Today, we learned two situations of planting trees. Two species were found: tree = number of segments+1; Don't plant both: tree = number of segments-1. In the future, students must pay attention to distinguish between "planting at both ends" and "not planting at both ends"

Fourth, return to life and apply it in practice.

1. A piece of wood is 8 meters long and is sawed every 2 meters. How many times does a * * * have to be sawed? (Students do it independently. )

8÷2=4 (subsection)

4- 1 = 3 (times)

Q: Why-1? This is equivalent to the situation in the tree planting problem studied today?

2. Similar math problems around us.

Look, how many students are there in this column? (4) If the distance between every two students is 1 m, what is the distance from the student of 1 to the last student? What if there are 10 students in this column? 100 where are the students?

There are four students in this column. If the distance between every two adjacent classmates is 2 meters, what is the distance between the first classmate and the last classmate?

3. Plant trees on one side of a road, and plant 4 1 tree every 6 meters. 1 What is the distance from the tree to the last tree?

Verb (abbreviation of verb) class summary

What did you gain from today's study?

Teacher: Through today's study, we not only discovered the law of planting two trees and not planting two trees, but also learned a method to study problems, that is, to think simple before encountering complex problems. There is still a lot of learning about planting trees. Interested students can consult relevant materials and continue their research after class.

Lecture on "Planting Trees"

"Planting Trees" is the content of "Mathematics Wide Angle" in the second volume of the fourth grade experimental textbook of the new curriculum standard of People's Education Press. As we all know, the thinking method of mathematics is the soul of mathematics. The purpose of arranging "planting trees" in this book is to infiltrate students with the idea of starting with simple and complex problems. To this end, this lesson has set three teaching objectives:

1. Through exploration, we found two kinds of rules of planting trees in different situations, one is planting trees at both ends, and the other is not planting trees at both ends.

2. Students experience and understand the problem-solving strategies and methods of "simplifying the complex".

3. Let students feel the extensive application of mathematics in daily life, try to solve simple problems in real life with mathematical methods, and cultivate students' application consciousness and ability to solve practical problems.

The teaching of this course is divided into four parts:

First, the introduction of conversation, clear topics

Second, guide the inquiry and discover the law of "planting at both ends"

1. Create a situation and ask questions.

By creating a realistic problem situation of planting trees in the green belt in the middle of the highway, this paper puts forward the question of how many saplings * * * needs. Students have three different answers in the process of solving. Which answer is right? Guide students to test the actual situation by drawing. Through the simulation, students experienced that it was too troublesome to plant a tree at 1000m, so the teacher introduced the method of studying complex problems: think simple when encountering complex problems, and start with simple problems. (Note: In order to make students have a deeper understanding of simplifying complex problems, the original title of the textbook is to plant trees on the side of the path of 100 meters, and we changed it from 100 meters to 1000 meters. )

2. Simply verify and find the law.

In the process of drawing with a simple example, two small levels are arranged:

Draw according to the teacher's requirements.

② Students draw at will.

By drawing pictures according to the teacher's requirements, students have a certain perceptual understanding of the relationship between trees and segments. Then let the students draw a picture and plant one at will, which enriches the students' perceptual materials and lays the foundation for students to discover and summarize the laws smoothly.

3. Use the law to solve problems.

① Apply the law to verify which answer in the above example is correct.

② Apply the law to solve the problem of how many flags to plant.

On the one hand, it consolidates the newly discovered law, on the other hand, it makes students realize that the law of planting trees can not only solve the problem of planting trees, but also solve many similar problems in life.

Third, cooperate to explore the law of "not planting at both ends"

1. Guess the law of "no planting at both ends".

Guess is a good way to cultivate students' reasoning ability. Students discovered the law of "planting at both ends". At this time, the teacher asked, if you don't plant at both ends, what will happen to the number and number of trees? With the previous learning foundation, students' thinking is very active and their desire to express themselves is also very strong. Therefore, it is necessary for students to guess at this time. Through verification, it is proved that most students' guesses are correct, so the recognition of students' research results will give students a sense of accomplishment, thus enhancing their confidence in learning mathematics.

2. Operate independently and explore the law.

With the previous learning foundation, let students explore independently before cooperation and exchange, verify the previous conjecture through simple examples, and find the law of not planting at both ends. In this process, students have a deeper understanding of the mathematical thought of starting with simple problems.

Fourth, return to life and apply it in practice.

Three problems are designed: sawing wood, calculating the distance between the first classmate and the last classmate, and further consolidating the problem of calculating the distance. By solving problems in life, students can feel that mathematics knowledge comes from life and is used in life, and mathematics is around us. Let students deeply feel the application value of mathematics and stimulate their interest in learning mathematics.

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