How to write the teaching content of the teaching design of tree planting: the standard version of the teaching curriculum for the fourth grade elementary school mathematics book P 117-118 pages: Example1,Example 2 and? Do it.
Teaching objectives:
1. Experience the process of abstracting the actual problem into a tree planting problem model, and master the relationship between tree planting and interval number.
2. We will use the mode of planting trees to solve some related practical problems, and cultivate students' application awareness and ability to solve practical problems.
3. Feeling establishing mathematical model is one of the important methods to solve practical problems.
Teaching emphases and difficulties:
Understanding the relationship between tree planting and interval number will apply tree planting model to solve some related practical problems.
Teaching process:
First, create situations and ask questions.
1, create a situation
Students, this September 1, the campus transformation of Feng Fan Primary School in Shizhen will be successful, and rural primary school students will also have a good learning and living environment. Are you happy for them? Next, we need to green and beautify the new campus. I want you to help the general manager of our school. (Courseware II shows the recruitment notice)
2. Teacher: Although everyone is so interested, the design scheme involves the problem of planting trees, so we must make clear the concept and relationship of related quantities of planting trees. (Courseware 3 shows the relevant content)
Teacher: If you want to design a reasonable plan, you must learn to calculate the problem of planting trees.
Write on the blackboard: plant trees
3. Show me the problem.
(Courseware 4 shows the problem): The school is going to plant trees along the road, with a total length of 100 meters, and plant a tree every 5 meters (both ends should be planted). How many seedlings does a * * * need?
Teacher: Today, let's solve the problem of planting trees in mathematics. Would you like to?
Second, solve the problem and find the law.
1, for information.
Look at the question and say what information you have got.
Presupposition: Understand the meaning of the question from the following points.
(1) What is it? When planting trees
(2) Can you explain it? Two-headed? Really? (blackboard writing: plant both ends)
Follow-up: use? Planting on both sides? Does it mean the same thing?
(3) What do you mean by every 5 meters?
Health: Between two trees? Distance? ;
Teacher: The distance between two trees can also be regarded as an interval.
2. Guess.
Teacher: If a line segment is used to represent one side of the road, how many seedlings does a * * * need? (20 or 2 1)
What do you all think? It all sounds reasonable. Which answer is right? Can you draw a picture in a more intuitive way to verify your answer?
3. simplify the complex.
(1) Simplify the complex.
Teacher: I have a simple question here, please ask the students in the adjacent seats to cooperate and discuss it, and finish it by drawing line drawings? Plant trees along the road 10 meter (both ends should be planted), and how many trees should be planted every 5 meters. Teacher's Note: Pay attention to the number of intervals and trees (the topic of the first part of Courseware 5)
Students try, teachers patrol and guide. Collect information.
(2) Students report their studies and the teacher summarizes them (most students have done well). Please read it. Is that so? (Courseware 5 shows intuitive views one by one)
Teacher: How many meters is the interval length? How many intervals are there? How many trees have you planted? There are only two intervals, why can we plant three trees? (Courseware 5 shows intervals and trees one by one)
Teacher: Starting from this simple example, do you find any relationship between the number of intervals and the number of trees? (Answer by name)
(3) Example verification.
Teacher: An example can't explain the law of planting trees. We need other examples. Now let's finish another problem by ourselves? Plant trees on one side of a 20-meter-long path (both ends should be planted), plant a tree every 4 meters, and how many trees should be planted (courseware 6 gives the topic)
Students study independently. (The teacher visits to guide and collect information. )
(4) After the students report the inquiry results, the teachers show the courseware 6 one by one. Is that so?
(5) Let's draw a line segment on the paper and draw 10 points on it (including two endpoints) to see how many intervals there are.
(6) By drawing, we found out the interval number and the number of trees. Now please observe the table quietly. What did you find? (Discussion and communication among students) (Show courseware 7)
Health: full length? Interval length = interval number+1= number of trees (show courseware 8)
The teacher asked: That is to say, how many trees need to be planted? What do you need first? (Number of intervals)
(7) Game: You ask me and I answer.
In other words, if there are 50 sections on a road, how many trees are there? 100 interval? What about the 400 interval? 1000 interval?
Conversely, if there are 36 trees on a road, how many intervals are there? What about 85 trees? 100 tree?
Summary: It seems that this rule exists generally on the problem of planting trees at both ends.
4. Apply the law to solve the original problem. (Courseware 9 takes 1 as an example)
Teacher: Can you solve this problem now? Please try to list the formulas. Let the students act out and say how to solve the problem. )
The teacher asked: What do you want first? What do you want? Why add 1?
5, combing method.
Teacher: Let's recall that just now we met the problem of planting two trees. How did we finally solve it successfully?
Health:
Teacher's summary: What should I do if I encounter problems that cannot be solved directly, such as drawing directly at 100 meters? You can give a guess first, and to judge whether this guess is right or not, you can simplify it, verify it with simple examples, find the law from simple examples, and then apply the found law to solve the original problem. This is a very important learning method, and we will often use it in the future!
Third, contact life and build a model.
Students, there are not only problems in planting trees, but also many problems in life. Who can give some examples of this?
Students speak freely. If the students can't say it, the teacher explained: It's hard to think of such examples in life, but the teacher came up with several:
1. Hands up. We have five fingers and there is a gap between them. Please observe how many fingers and gaps there are. What is the relationship between them? Four fingers, how many intervals are there? Where are the three fingers? Where are the two fingers?
2, small game:
Choose any two students at the next table (referring to Xiaoshu) to stand up and hold hands (at intervals).
Q: How many small trees are there and how many intervals are there?
The teacher held hands and asked: Now there are (2 sections, 3 small trees).
One more student, and now I will continue to talk (today's strong seedlings will grow into pillars of the country in the future)
3. Students are free to talk about life examples.
4. Summary after feedback: Through the example just now, we know that the problem of planting trees is common in our lives. The number of fingers, the number of floors, the number of people in the team, the lamps and desks in the classroom, the street lamps and flower pots on the roadside are equivalent to the number of trees we mentioned above, while the spacing between fingers, the number of ladders and the distance between people are equivalent to the number of intervals. So the relationship between the number of trees planted at both ends can be used? Number of trees = number of intervals+1? This relationship is manifested in.
Fourth, apply the model to solve practical problems.
(Courseware 10 shows problem-solving exercises one by one)
Students do it independently and teachers patrol.
One report at a time.
Verb (abbreviation of verb) expansion exercise
Students cooperate, discuss and communicate (courseware 1 1 show topics)
Note: the connection and difference between this question and the topic just learned (whether it is planted at both ends? )
Student report, teacher summary
Six, the class summary (courseware 12)
Teacher: What did you learn through this class?
How to write the instructional design of tree planting I. Teaching objectives:
1. Knowledge and skill goal: Through hands-on practice and cooperative inquiry, students can experience the process from real problems to mathematical modeling in the process of doing mathematics, and understand and master the relationship between the number of trees and the number of intervals.
2. Process and Methods Objective: To cultivate students' hands-on operation, cooperative communication and flexible ability to solve different problems through students' independent experiments, exploration, communication and discovery of laws.
3. Emotion and attitude goal: Let students experience the joy of learning success and the importance of understanding the inductive law for subsequent learning in the process of exploring, modeling and using the model, cultivate students' awareness of exploring the inductive law and experience the thinking method of solving the problem of planting trees.
Second, the teaching focus: understand the relationship between planting trees and spacing.
Teaching difficulties: we can flexibly apply the model of tree planting problem to solve some related practical problems.
Preparation of teaching AIDS: multimedia courseware and unfinished forms.
Fourth, the teaching process:
Preparation before class: (multimedia screening of Newton and Apple's story)
Teacher: What did the story of the scientist tell you? Diligent in observation, good at thinking and bold in guessing? )
Dialogue introduction: It is better to say than to do. Let's see who observes the most carefully, thinks the most actively, and finds the rules from ordinary things in this class. Are you ready?
(a), ask questions, lead to thinking, explore the law.
1, thinking caused by hands.
Teacher: Hold out your left hand, open your fingers and look at it mathematically. What did you find?
Teacher: Everyone has a pair of sharp eyes on mathematics and finds that there is also mathematics between fingers and space. In fact, those common phenomena in life can be found by careful observation and thinking. In this lesson, we will deeply study the mathematical problems such as fingers and spacing.
2, overall perception, determine the research direction.
Show courseware: plant trees along the path of 15 meters, and plant one tree every 5 meters. There may be several situations.
Show the students' guesses: (planting at both ends, ***4 trees) (planting at one end only, 3 trees) (planting at both ends only, 2 trees)
Understand:? Interval? 、? How many intervals? 、? How many trees are there? .
(B), group cooperation, explore the law
1, ask questions.
Courseware: Plant trees on one side of Dading Road in mengzhou city, with a total length of 1000m. Plant a tree (both ends) every 10m. How many seedlings do you need?
Students' guesses may have different results:1000; 100 1; 1002)
2. Independent investigation.
What is the relationship between the number of trees and the number of intervals? Let the students guess boldly and verify with the chart.
The courseware shows: plant a tree every 10 meter, plant a tree every 10 meter, and draw until 1000 meter! Students think it's ok to draw one tree at a time, but it's too much trouble and a waste of time.
Guide students: Is there a simpler way to study the relationship between the number of trees and the number of intervals?
Let students think and communicate, and try to start with simplicity and use? Decimal large numbers? Research methods, infiltration? Simplify the complex? The mathematical thought of.
3. discover the law.
Students began to draw pictures, fill in forms, compare and analyze, and then show their research results, and found that small data was planted at both ends. The number of trees is more than the interval 1? Law.
Teacher:? The number of trees is more than the interval 1? The law is studied by students with small data. If the data increases, does this rule still hold?
Courseware dynamic demonstration: one interval corresponds to one tree, and so on, 1000 intervals will have 1000 trees. Have you finished planting?
Teacher: If this road becomes very long and infinitely long, is it still such a rule to plant two crops at the same time? Let the students realize that no matter how big the number is, use? One-to-one correspondence and finally one more tree to achieve the effect of planting at both ends. This link, imperceptibly? Limit? The idea.
4. Summarize.
Induction? Simplify the complex? Strategies for solving problems. Let the students realize that the research problem can start with simplicity, turn the difficult into the easy, and simplify the complex. Only in this way can the problem be effectively solved. Infiltrate abstract mathematicization into teaching so that students can learn? Moisturize things silently? Experience the value of mathematical thinking method and improve the quality of thinking.
5. Summarize the law.
Teacher: Can you express this law in a formula?
Number of intervals on the blackboard+1= number of trees-1= number of intervals.
6, contact life
There are many phenomena similar to planting trees in our life. Did you find them?
Let students experience the extensive application of tree planting in life through examples. At the same time, let students clearly understand the life phenomena such as street lamp arrangement and queuing. Planting trees? Have the same mathematical structure, and also give a complete modeling of this mathematical idea.
(3), click on life
① Judgment: On the Lantern Festival, 200 red lanterns were hung from beginning to end on the side of Zhonghua Street. If a Chinese knot is hung between every two lanterns, it needs 20 1 Chinese knot ().
② (Find the interval length) The total length of the bus line is 9 kilometers, with a total of 10 stops from the starting station to the terminal station. What is the distance between two adjacent stations?
(3) (Ask for the number of trees) The teacher climbed the ancient pagoda. Each floor has 1 1 steps. He took 55 steps from the first floor. What floor is Teacher Long on?
(4) Ring the bell on the tower, every 4 seconds from the first ring to the fifth ring. How many seconds is the interval?
(4) expand and extend.
(Courseware shows world-famous math problems)
Teacher: There is one in the history of mathematics? Twenty trees? For centuries, the problem of planting trees has always attracted the interest of scientists. This is:? 20 trees, if there are 4 trees in each row, how can I plant more trees?
As early as16th century, ancient Greece and other countries completed the arrangement of sixteen rows. (display 1)
/kloc-In the 8th century, American mathematician Sam completed an eighteen-line atlas. (as shown in figure 2)
In the 20th century, math lovers drew 20 lines of maps, setting a new record and keeping it to this day. (as shown in figure 3)
(Conclusion) In the 2 1 century, there are 20 trees with 4 trees in each row. Can there be any new progress? The math world is waiting! I look forward to students' bold exploration and positive thinking, and I believe you will certainly have greater gains!
Reflecting on the whole teaching process, I think this course has achieved the following points:
First, create an easy-to-understand prototype of life and let mathematics approach life.
Creating a learning situation that is closely related to students' living environment and knowledge background and is of interest to students is conducive to students' active participation in mathematics activities. In pre-class activities, I choose students' small hands as materials to introduce the study of tree planting. Students can clearly see that there is a 1 difference between the number of fingers and the number of spaces in the activities of finger closing and opening. Then make a quick question-and-answer game, so that students can intuitively understand and summarize the relationship between intervals and points, pave the way for later study and arouse students' interest in learning.
Second, pay attention to students' independent exploration and experience the joy of inquiry.
Experience is the process that students transfer from old knowledge to implicit new knowledge. In teaching, I create situations, provide many opportunities for students to experience, create a democratic, relaxed and harmonious learning atmosphere for students, and give them sufficient time and space. If life experience is the basis of learning and cooperation and communication between students is the driving force of learning, then helping students understand with graphics is a crutch for students to construct knowledge. With this crutch, students can walk more steadily and better. Therefore, in the teaching process, I pay attention to the infiltration of the consciousness of combining numbers with shapes. After the introduction of the life scene diagram, show the diagram, guide the students to observe the statistical images and fill in the form to find out the relationship between trees and spaces when planting trees at both ends! When students have a clear understanding of the physical diagram, the teacher abstracts the graphic image into a line diagram, so that students can still find the relationship between trees and intervals after leaving the physical diagram. In the computer demonstration, students intuitively realized the relevant quantities in the problem of planting trees. After observation and thinking, students further verified the relationship between trees and intervals. This shows the whole process of analyzing, thinking and solving problems, so that students can experience this process and learn some methods and strategies to solve problems.
Third, the use of student resources to strengthen student-student cooperation
There are differences between students' cognitive starting point and the logical starting point of knowledge structure. The difference between students is learning resources, which should be fully displayed and reasonably used on the platform of group communication.
Fourthly, pay attention to the expansion and application of the tree planting problem model.
The model of tree planting problem is an amplification of similar events in the real world, which originates from reality and is higher than life. Therefore, it has a wide range of application values in reality. In order to make students understand the significance of this modeling and strengthen the practice of model application function, the practice in this lesson has the following two levels:
(1) Directly apply the model to solve simple practical problems. In class, students are arranged to complete the practice of finding the number of trees with known total length and spacing, and finding the total length with known total length and spacing, so that students can directly apply the model to solve simple practical problems from both positive and negative aspects. Cultivate students' bidirectional reversible thinking ability.
(2) It is extended to some problems similar to the problem of planting trees, so that students can further understand that many different events in real life, such as the arrangement of flower pots on campus and the events at bus stops, all contain the same quantitative relationship as the problem of planting trees, and all of them can be solved by the model of planting trees, and realize the significance of mathematical modeling.
How to write down the teaching objectives in the teaching design of tree planting;
1. Experience the process of abstracting the actual problem into a tree planting problem model, and master the relationship between tree planting and interval number.
2. We will use the mode of planting trees to solve some related practical problems, and cultivate students' application awareness and ability to solve practical problems.
3. Feeling establishing mathematical model is one of the important methods to solve practical problems.
Teaching focus:
Understanding the relationship between tree planting and interval number will apply tree planting model to solve some related practical problems.
Teaching difficulties:
Applying tree planting problem model to solve related practical problems flexibly.
Teaching preparation:
CAI courseware and some paper trees
Teaching process:
First, create a prototype.
1. Teacher: Students, mathematics is everywhere around us. Please reach out and open your fingers. Have you seen math? See what?
Evaluate at any time according to the students' answers. If the students only say? Hands? Or? Fingers? Point it out? This is not math? And say? Want to look at the problem from a mathematical point of view? ; What does the student say? Five fingers? The teacher asserted that he had a gift for mathematics. )
Teacher: What else did you see?
Teacher: The teacher also saw a number. Do you want to know? That's it? 4? . Who knows, this? 4? What do you mean? (4? Empty? In mathematical language, the space here is the space between fingers, that is, there are four fingers between five fingers? Interval? ) blackboard writing: interval
Teacher: What is the relationship between hand index and interval number? Who can tell me? (The hand index is more than the interval number 1, or the interval number is less than the hand index 1)
Teacher: Can you express the quantitative relationship between hand index and interval number? (We can express it by quantitative relation: hand index = interval number+1)
Blackboard writing: hand index = interval number+1
2. Teacher: Have we met? Interval? Knowing that hand index = interval number+1, in fact, problems like this can be seen everywhere in our lives. Mathematically, it also has a name, which is planting trees. Title on the blackboard: planting trees. In today's class, we will learn to plant trees together. Are you interested?
Second, build a model.
1. Hands-on operation and inquiry 1:
(1) Teacher: Speaking of planting trees, Teacher Liu really wants to ask you a favor. The road construction in front of our school has been completed. In order to beautify the campus, the school is going to plant some trees on the way into the school gate. How to plant them well? Should we plant randomly or equidistantly? How many saplings do you need to prepare? What must we know to find out this problem? How long is this road and how many trees are there? ) the child is very thoughtful. The school has collected this information clearly. Let's have a look.
Question 1: Chuanyi Primary School should plant trees on the side of the road outside the school gate. This road is150m long, and trees should be planted every 5m (both ends). How many seedlings does a * * * need?
(2) Examination: Who will examine the questions? What information did you learn from the question? What do you mean?
(blackboard writing: plant both ends)
(3) How many seedlings do you need to calculate a * * *?
(4) feedback the answer.
Method 1: 150? 5=30 (tree)
Method 2: 150? 5=30 (tree) 30 +2=32 (tree)
Method 3: 150? 5=30 (tree) 30+1=3 1 (tree)
Teacher: Now there are three answers, and each answer has many supporters. Which answer is correct? This needs verification. We can draw pictures to simulate the actual situation. We use this line to represent the path because? Two-headed? First plant 1 tree on the left, draw a tree, plant every 5 meters 1 tree, plant every 5 meters 1 tree, plant every 5 meters 1 tree. Plant again every 5 meters 1 tree.
Teacher: How many meters have we planted? (30 meters) It takes so long to plant 30 meters, and plant a * * to 150 meters. If you want to plant one tree at a time, how will you feel? (too much trouble)
Teacher: Yes, the teacher's hands are sore. In fact, there is a better research method in mathematics that can simplify complex problems like this. Use simple examples to study their laws, and then use the discovered laws to solve the original problems. Do you want to try this?
(5) Draw and write to find the law.
Teacher: We changed 150m to 20m. Read the questions together:
The students planted trees on one side of the 20-meter-long path, and planted a tree (both ends) every 5 meters.
How many seedlings do you want?
Treatment method: ① Please use drawing method to simulate planting calculation. When the teacher visited, he reminded: Count the children who drew. Did you draw 20 meters?
Think about it, how many 5 meters are there in 20 meters?
Please talk to each other in groups of four: How many trees have a * * * planted? How to calculate it?
Requirements: the group leader should carefully organize and speak one by one in turn. Other students should pay attention and add comments in a low voice so that all four people in the group can hear them.
Who will tell us how to calculate? 20? 5+ 1=5 (tree), how is the diagram drawn? (Pumping performance)
④20? What does 5 mean? (there are four 5 meters in 20 miles), and this 4 is equivalent to? Finger problem? What is the quantity? (Number of intervals)
⑤ Why add 1?
⑥ The teacher explained (refer to the picture) to change it with red chalk: every 5 meters 1 tree, there are 4 5 meters in 20 meters, and 4 trees are planted (one for demonstration). Because both ends have to be planted, the last one has been planted, and the leftmost one has to be planted, so adding 1 tree means adding the leftmost one.