Teaching content:
Compulsory Education Curriculum Standard Experimental Textbook for Grade Four, Volume II, Tree Planting, Page 1 17, Example 1, Example 2.
Brief analysis of teaching materials;
Unit 8 "Mathematics Wide Angle" mainly permeates some ideas and methods about planting trees. Through some common practical problems in real life, students can find some laws, extract their mathematical models, and then use the found laws to solve some simple practical problems in life.
The thinking method to solve the problem of planting trees is a mathematical thinking method widely used in real life. The problem of planting trees usually refers to planting trees along a certain route. The total length of this route is divided into several sections (intervals) by trees. Due to different routes and different tree planting requirements, the relationship between the number of road sections (intervals) divided by routes and the number of trees planted is also different. Example 1 is to discuss the problem of planting trees on one route, and trees should be planted at both ends. Let the students first find the relationship between the number of trees and the number of intervals by drawing lines, and then solve the practical problems with the rules found. Example 2 discusses the case where no trees are planted at both ends. Through examples in life, let students know the thinking method of solving the problem of planting trees and the application of this method in solving practical problems. At the same time, cultivate their ability to explore laws and find effective methods to solve practical problems, and initially cultivate their ability to extract mathematical models.
Target preset:
1. Knowledge and skills: Through exploration, we found the law of planting trees at both ends and not planting trees at both ends, and used this law to solve problems in real life.
2. Process and method: Through trying to explore, experiment, intuitive demonstration, observation, analysis and discussion, experience and understand the problem-solving strategy of "simplifying complex problems".
3. Emotion, attitude and values: Feel the extensive application of mathematics in daily life, try to solve simple problems in real life with mathematical methods, cultivate application awareness and ability to solve practical problems, and infiltrate patriotic education.
Emphasis and difficulty in teaching: discover the relationship between the number of trees planted and the number of intervals, and use the discovered rules to solve practical problems.
teaching process
First, pre-class activities:
1, every student has a pair of dexterous little hands, which not only can write, draw and work, but also contains interesting mathematical knowledge. Do you want to know? Please raise your right hand, and ask each student to raise his right hand high, straighten and close his five fingers.
Teacher: Now, please open your five hands and count. How much space is there after opening? (4)
Teacher: In mathematics, we call this space "interval". Just now we stretched out our five fingers and there were four spaces, that is, four intervals.
2. For example, "intervals" in life can be seen everywhere. For example, planting trees along the road, there is a distance between every two trees, so we call this distance interval, stairs, sawing wood and so on.
You can clearly see that there are four gaps between five fingers. Then, how many gaps (four) are there between five small trees when the fingers are replaced by small trees? How about six o'clock? How about seven trees?
Today, we are going to learn the interesting problem of planting trees.
In pre-class activities, create situations from students' lives and use problem situations. "Every student has a pair of dexterous hands, which can not only write, draw and work, but also contain interesting mathematical knowledge. Do you want to know? " Fully arouse students' enthusiasm and introduce new courses.
Second, reveal the learning objectives: (media presentation)
What problems should we solve through this lesson?
1. According to relevant conditions, how many seedlings are needed or the distance between two trees can be calculated.
2. Be able to use the problem of planting trees to flexibly solve similar practical problems in life.
Third, explore new knowledge:
1. Create a situation and ask questions.
① Courseware shows pictures.
Introduction: This is a new highway in our town. 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?
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 different answers in the process of solving. Which answer is right? Guide students to test the actual situation by drawing. Through the simulation, students experience that it is too troublesome to plant a tree at 1000 meters, so they introduce 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.
(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?
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 have a look. Do you want to try this method?
(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.
B: As above, plant another 25 meters. How many segments did you plant this time?
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?
D. what did you find?
Summary: It's amazing that you have found a very important rule in the problem of planting trees, that is: (blackboard writing: plant at 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?
1, 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.
2, in the application of law to solve practical 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.
3. 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 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.
A. For A.2000-meter-long road, plant a tree every 10 meter (not both ends). How many seedlings does a * * * need? (Students finish independently)
B. Teacher: Attention, students. What is this problem?
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"
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, it is proposed that if the two ends are not planted, what will be the law of the number of trees and the number of segments? 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, change and integration:
1. Do: 1 18 pages. Students do it independently. (When reviewing, talk about your own ideas, and focus on asking students to find out the interval number first, that is, 36 trees have 35 intervals. )
2. Question 2 on page122. Complete independently, communicate at the same table, and perform for life.
Verb (abbreviation for verb) test feedback: courseware demonstration (completed independently)
1. On one side of a 400-meter-long road, spaced from beginning to end.