How to Design Tree Planting Teaching Part I: 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. Let students experience and understand? Simplify complex problems? Strategies and methods to solve problems.
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 will have a happy holiday soon? Six? Children's day? This 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. In this class today, shall we study it together? Planting trees? . (Title on the blackboard: Planting Trees)
Second, guide the exploration and discovery? Two-headed? The law of
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? Two ends? What do you 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 (tree)
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-headed? Starting from this end of the green belt, we plant a tree on our head first, then another tree every 5 meters, another 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 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. (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 sections; 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? What does 5=200.200 mean here?
200+1=20 1 why+1?
Teacher: This? Secret recipe? OK or not?
Through a simple example, the law is found and applied to solve this complex problem. Later, meet again? Two-headed? Begging for a tree, do you know what to do?
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, two heads are planted? Find the number of tree segments+1; What if? Don't plant both. What does a tree have to do with the number of segments?
Third, cooperative exploration, not the rule of planting at both ends.
1. Guess? Don't plant the law 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. Through a simple example, they found it again? Don't plant it at both ends: tree = number of segments-1. What if? Don't plant a tree at both ends, ok?
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: Yes? Side? Change to? Both sides?
Q:? Planting trees on both sides? What do you mean? 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 at both ends: tree = number of segments? 1。 Students must pay attention to the distinction when doing problems in the future, right? Two-headed? Or? Don't plant it 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 after class to continue their research.
? Planting trees? Submit a teaching plan
? Planting trees? Is it the second volume of the fourth grade experimental textbook of the new curriculum standard of People's Education Press? Mathematical wide angle? The content of. As we all know, the thinking method of mathematics is the soul of mathematics. The arrangement of this book? Planting trees? The purpose of this paper is to instill in students the idea of starting with simplicity for 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. Student experience and experience? Simplify complex problems? Strategies and methods to solve problems.
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 exploration and discovery? Two-headed? The law of
1. Create a situation and ask questions.
By creating the realistic problem situation of planting trees in the middle green belt of highway, this paper puts forward? * * * How many seedlings do you need? . 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 one side of a path of 1000 meters, and we changed it from 1000 meters to1000 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, cooperative exploration? Don't plant the law at both ends
1. Guess? Don't plant the law at both ends.
Guess is a good way to cultivate students' reasoning ability. The students found out? Two-headed? At this time, the teacher asked, if the two ends are not planted, what is 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, 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.
How to Design the Teaching of Tree Planting Ⅱ: Teaching Design
Teaching theme
Tree planting problem (example 1)
I. teaching material analysis
? Planting trees? It is a teaching content in the wide angle of mathematics in the first volume of the fifth grade of People's Education Press. 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 the tree on average. 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. In real life, there are many similar problems, such as installing street lamps on both sides of the expressway, arranging flowers in flower beds, and arranging squares in queues. , all hide the relationship between total and interval, so we call this kind of problem planting trees. Are you planting trees? Planting trees? The route can be a line segment or a closed curve, such as a square, a rectangle or a circle. Even regarding the planting of a line segment, there may be different situations, such as planting at both ends, planting at one end only, or planting at both ends.
Example 1 is about planting trees on a line segment and planting them at both ends. According to the intention of the textbook, let students go through the process of mathematical exploration such as guessing, experiment, reasoning, etc., solve complex problems from simple situations, let students choose their favorite methods to explore the relationship between planting trees and spacing, inspire students to discover the law through phenomena, and make students understand the thinking method of solving tree planting problems and the application of this method in solving practical problems.
Second, student analysis
Because of students' first contact? Planting trees? Students will be very interested in this part of the learning content, and their enthusiasm for learning will be relatively high, but according to previous teaching experience, this part of the content is not easy for students to understand and master. Students have mastered the relevant knowledge about line segments, and also have certain life experience, analytical thinking ability and calculation ability. Therefore, in order to make students better understand the teaching content of this unit, we should properly integrate teaching materials, make full use of students' original knowledge and life experience, and organize students to carry out various teaching activities.
Third, the teaching objectives
Knowledge and skills objectives:
1, using students' familiar life situations and hands-on activities, let them discover the relationship between the interval number and the number of trees planted;
2. Through group cooperation and communication, on the basis of understanding the law between the number of intervals and the number of trees, solve the simple problem of planting trees.
Process objectives:
1, let students experience the process of perceiving and understanding knowledge, and cultivate students' ability to discover laws from practical problems and solve problems by using them;
2. Infiltrate the idea of combining numbers and shapes to cultivate students' consciousness of solving problems with graphics;
3. Cultivate students' sense of cooperation and develop good communication habits.
Emotional goals:
1. Stimulate the emotion of loving mathematics through practical activities;
2. Feel that there is mathematics everywhere in daily life and experience the joy of learning success.
Fourth, the teaching environment
? Simple multimedia teaching environment, interactive multimedia teaching environment, network multimedia teaching environment, mobile learning, etc.
Five, information technology application ideas (highlight three aspects: which technologies are used? How to use these technologies in which teaching links? What is the expected effect of using these technologies? ) 200 words
In the teaching process of Tree Planting, PPT is mainly used to present the teaching content through words, pictures and animations, so as to better highlight the teaching focus of this lesson and break through difficulties, such as inquiry? How many intervals? And then what? Trees? When discussing the relationship between the two, the teacher showed the process with animation and demonstrated the relationship between the number of trees planted and the number of intervals with line diagrams, so as to better understand and discriminate the relationship between the two, fully stimulate students' interest in learning and successfully complete the effect of learning objectives.
Teaching process design of intransitive verbs (additional lines can be added)
Teaching link
(such as: introduction, teaching, review, training, experiment, discussion, inquiry, evaluation and construction)
Teachers' activities
Student activities
Information technology support (resources, methods, means, etc. )
Create situations and introduce new lessons.
The courseware shows the hand chart, so that students can clearly define the concept of interval, and then transform the hand chart into a straight line planting problem. Introduce the new lesson, show the pictures of intervals in life, and let the students understand the interval problem.
Students observe the hand figure and find that there are four intervals between the five fingers, three intervals between the four fingers and two intervals between the three fingers, and preliminarily find out the relationship between intervals and hand index.
The courseware shows the hand diagram and highlights the interval. In life? Interval? Pictures to better understand the interval problem.
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Show examples and ask questions.
The courseware gives an example of 1 Let the students read the meaning of the questions clearly, observe and analyze the mathematical information and questions, and then highlight the key words in the questions with courseware for students to understand.
Students analyze and understand according to the mathematical information provided by the teacher, and determine the research goal: the relationship between the number of intervals and the number of trees.
Courseware shows examples, focusing on animation to demonstrate understanding? Plant both sides at the same time? Meaning of.
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Teachers and students sum up and find out the rules.
The students' inquiry results are displayed by physical projection.
The teacher showed the students' findings and vividly revealed them in the form of animation? How many intervals? And then what? Trees? The relationship between. Solve the problem according to the law.
According to their own operation, students tell their own pendulum and discovery law. Solution example 1.
Physical projection shows the results of students' activities and multimedia shows the laws.
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Consolidate new knowledge
Multimedia shows all kinds of life? Planting trees? And demonstrate the solution process with animation.
Students apply and solve problems according to the obtained rules.
Courseware demonstrates the process of solving problems.
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Teacher-student summary and promotion
We learned to plant trees in this class. What have you learned? What else is there to plant trees? Can you guess the relationship between trees and intervals?
The students answered.
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Seven, teaching characteristics (such as adjustment for personalized teaching, support for autonomous learning, design for students' ability training, innovation of teaching and learning methods, etc.). ) About 200 words.
This teaching design is mainly aimed at how to combine information technology to solve it. Planting trees? Medium? How many intervals? With what? How many trees are there? The relationship between them, so as to solve the problems related to tree planting in life. This lesson draws rules from the introduction of knowledge to the exploration of new knowledge. Every link of applying knowledge is designed with corresponding information technology support, or focuses on the teacher's talk or the students' discussion and exchange. Teachers and students have formed a good interaction, among which multimedia technology has played a very good role, reminding key points, enlightening difficulties, allowing students to think, discuss, show and consolidate problems better, and giving both teaching and learning opportunities for reflection. Design problems, through animation display, make students have an intuitive impression and better inspire them to think, which not only concentrates their attention, but also does not limit their divergent thinking, which is conducive to the cultivation of learning ability.
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How to design tree planting teaching Part III: Teaching objectives;
Knowledge and skills objectives:
1, using students' familiar life situations and hands-on activities, let them discover the relationship between the interval number and the number of trees planted;
2. Through group cooperation and communication, on the basis of understanding the law between the number of intervals and the number of trees, solve the simple problem of planting trees.
Process objectives:
1, let students experience the process of perceiving and understanding knowledge, and cultivate students' ability to discover laws from practical problems and solve problems by using them;
2. Infiltrate the idea of combining numbers and shapes to cultivate students' consciousness of solving problems with graphics;
3. Cultivate students' sense of cooperation and develop good communication habits.
Emotional goals:
1. Stimulate the emotion of loving mathematics through practical activities;
2. Feel that there is mathematics everywhere in daily life and experience the joy of learning success.
Teaching focus:
Do you understand? Planting trees (two kinds)? The characteristics of applying laws to solve problems.
Teaching difficulties:
Do you understand? Spacing number+1= number of trees, number of trees-1= spacing number.
Teaching process:
First, design scenarios and introduce topics
1, teaching? Interval? Meaning of
Teacher: Every student has a pair of dexterous hands. He can not only write, draw and work, but also hide interesting mathematical knowledge on him. Do you want to know him? Please raise your right hand. (fingers straight, together, open)
Teacher: How many gaps are there in the open five fingers? (4) Let's put this in math? Gap? Call? Interval? . We found four gaps between five fingers. What about the four fingers? How about three?
2. Give an example of life? Interval?
Teacher: In life? Interval? Can be seen everywhere. Can you give some examples? (between two trees, between two classmates, the bell? )
3. Understand the interval number and introduce the topic.
When planting trees on a road, the equal number of segments between every two trees is called interval number (courseware demonstration), and the length of each interval is called interval. Studying the relationship between interval number and tree number, we collectively call it the problem of planting trees. In this lesson, we will learn about planting trees. (blackboard writing topic)
Second, explore new knowledge and laws.
1, show the recruitment notice
There is a 20-meter-long path next to the playground. The school plans to plant trees on one side of the path, and it is required to plant a tree every 5 meters. Specially invited several campus designers to design a tree planting plan and selected the best one.
2. Show examples and understand the meaning of the question:
Teacher: (Courseware shows examples. )
Teacher: Who can understand it? What mathematical information does this question tell us? What's the problem? Which words do you think are the most important in this question?
(Courseware explains key words to deepen students' understanding)
Teacher: What do you think is the key to how many trees are required to be planted? (Interval number) So what is the relationship between interval number and tree number? Let's take a look at it.
3. Show cooperation requirements.
(1) The teacher explained the requirements of group cooperation.
(2) A group of four people started cooperative learning and designed a tree planting scheme with school tools. (Yes.
Expressed in different forms)
(3) Teachers patrol and guide students to cooperate in groups.
(4) Group work display and group evaluation. Teachers timely comment on students' design plans and encourage students in time.
(5) Guide students to sum up that there are three kinds of tree planting in real life: the first is planting at both ends, the second is planting at one end, and the third is not planting at both ends.
4. Explore the relationship between the number of trees and the number of intervals within the group:
(1) Count: Count the number of trees and intervals.
(2) Comparison: Compare the laws between the number of trees and the number of intervals.
When planted at both ends, the number of plants is more than the number of intervals 1 (number of plants = number of intervals+1).
When planting only one end, the number of plants planted is the same as the number of intervals (number of plants = number of intervals).
When both ends are not planted, the number of plants is less than the number of intervals 1 (number of plants = number of intervals-1).
Third, class summary, feedback exercises
1, the total length of bus lines is 12km, and the distance between two adjacent stops is 1km. How many stations are there?
The big clock in the square struck five times at five o'clock, and it struck in eight seconds. 12 knock 12 how long does it take?