How to write a teaching design on tree planting issues

Introduction: In this lesson, we learned about tree planting problems, and can use tree planting problems to solve similar practical problems in life. When answering, we should focus on distinguishing the relationship between the number of trees planted and the number of intervals. Later, we will also There are some different situations, and I hope everyone can use their brains and handle them flexibly. How to write a teaching design for tree planting issues? I have shared some sample lesson plan design essays, hoping to give everyone a reference! How to write a teaching design for tree planting issues

Teaching content: P117, second volume of the fourth grade primary school mathematics version of the People's Education Curriculum Standard Edition -118 pages of Example 1, Example 2 and "Do it"

Teaching objectives:

1. Experience the process of abstracting practical problems into tree planting problem models, and master the process of planting trees relationship with the number of intervals.

2. Be able to apply the tree planting problem model to solve some related practical problems, and cultivate students' application awareness and ability to solve practical problems.

3. Understand that constructing mathematical models is one of the important methods to solve practical problems.

Teaching important and difficult points:

Understand the relationship between planting trees and the number of intervals, and be able to apply the tree planting problem model to solve some related practical problems.

Teaching process:

1. Create situations and ask questions.

1. Create a situation

My classmates, on September 1st this year, the campus renovation of Fengfan Primary School in Shizhen will be successful, and rural primary school students will also have good learning and Living environment, are you happy for them? Next, we need to green and beautify the new campus. I would like to ask you to help the director of general affairs of our school to provide advice. (Courseware 2 shows the recruitment notice)

2. Teacher: Although everyone is so interested, the design plan involves tree planting issues, so we must understand the concepts and relationships of the relevant quantities of tree planting issues. (Courseware 3 provides relevant content)

Teacher: If we want to design a reasonable plan, we must learn the relevant calculations for tree planting problems.

Blackboard topic: tree planting problem

3. Present questions.

(Question from Courseware 4): The school plans to plant trees on one side of the 100-meter-long path, with trees planted every 5 meters (planting at both ends). How many saplings are needed for one ***?

Teacher: Today we will solve the tree planting problem in mathematics, are you willing?

2. Solve problems and find patterns.

1. Understand the information.

Please read the question and tell me what information you have obtained?

Default: Understand the meaning of the question from the following points

⑴What is? Planting trees while ?

⑵ Can you explain? Planting at both ends? (Write on the blackboard: Planting at both ends)

Follow-up question: Does it mean the same as Planting at both ends?

⑶What does every 5 meters mean?

Student: It is the distance between two trees;

Teacher: The distance between two trees , we can also regard it as an interval.

2. Conjecture.

Teacher: If one side of this road is represented by a line segment, can you please calculate how many saplings are needed for one ***? (20 or 21 trees)

All of you What do you think? It all sounds reasonable. Which answer is correct? Can you draw a picture in a more intuitive way to verify your answer?

3. Make the complex simple.

　⑴ Simplify the complex

Teacher: I have a simple question here. Ask students in adjacent seats to discuss it together and complete it by drawing a line segment diagram? On the side of the path 10 meters away Plant trees (plant at both ends), one tree every 5 meters, how many trees should be planted? Teacher’s tip: pay attention to the number of intervals and trees (topic in the first part of courseware 5)

Students try it out, and the teacher patrols and guides . Gather information.

⑵ Students reported their learning status and the teacher summarized it (most students completed it very well), please see if this is the case? (Courseware 5 shows visual diagrams one by one)

Teacher: Interval How many meters is the length? How many intervals are there? How many trees are planted? There are only 2 intervals, why can 3 trees be planted? (Courseware 5 shows the intervals and trees one by one)

Teacher: From above Starting with a simple example, have you found any relationship between the number of intervals and the number of trees? (Answer by name)

(3) Verify with an example.

Teacher: One example cannot explain the law of tree planting. We need other examples. Now let's complete another problem independently? Plant trees on one side of a 20-meter-long path (planting at both ends). One tree should be planted every 4 meters. How many trees should be planted? (Problem shown in Courseware 6)

Students conduct independent research. (The teacher patrols and guides and collects information.)

(4) After the students report the research results, the teacher shows the courseware 6 one by one. Is this true for you?

(5) Everyone writes on the paper Draw a line segment and draw 10 points (including two endpoints) on it to see how many intervals there are?

(6) By drawing, we have found the number of intervals and the number of trees. Now please be quiet. Observe the table quietly, what do you find? (Discuss and exchange among classmates) (Show courseware 7)

Students: Full length? Interval length = number of intervals Number of intervals 1 = number of trees (show courseware 8)

The teacher asked: In other words, if you ask how many trees to plant per day, what is required first? (Number of intervals)

(7) Game: You ask and I answer

That is to say, if there are 50 intervals on a road, how many trees are there? What about 100 intervals? What about 400 intervals? What about 1000 intervals?

On the contrary, If there are 36 trees on a road, how many intervals are there? What about 85 trees? What about 100 trees?

Summary: It seems that this pattern is common in tree planting problems at both ends. of.

4. Apply the rules to solve the original problem. (Example 1 in Courseware 9)

Teacher: Can you solve this problem now? Please try to list the formulas. (Ask students to perform on the blackboard and explain their ideas for solving the problem)

The teacher asked: What do you ask for first? What do you ask for next? Why add 1?

5. Sorting method.

Teacher: Let us recall that we just encountered the tree planting problem at both ends. How did we finally successfully solve it?

Student:?

Teacher summary: When we encounter a problem that cannot be solved directly, such as 100 meters, which is difficult to draw directly, what should we do? We can first give a guess. To judge whether the guess is correct, we can reduce the complex to simple and use simple Verify by examples, and you can discover patterns from simple examples, and then apply the patterns found to solve the original problem. This is a very important learning method, and we will use it frequently in the future!

3. Connect with life and construct models.

Students, examples like this involving points and intervals are not only found in tree planting problems, but also in many problems in life. Can anyone give a few such examples?

Students can speak freely. If the student cannot speak, the teacher will explain: It is hard to think of examples like this in life, but the teacher can think of a few:

1. Show your hand, we have five fingers. , there are gaps between fingers. Please observe how many fingers and gaps there are. What is the relationship between them? How many gaps are there for 4 fingers? What about 3 fingers? What about 2 fingers?

2. Mini game:

Randomly select 2 students at the next table (like small trees) to stand up and hold hands (interval)

Question: How many small trees are there? How many intervals are there between trees?

The teacher joins in, holding hands, and asks: There are now? (2 intervals, 3 small trees)

Add another student, how many are there now? Continue to Let’s talk about it below (Today’s strong seedlings will surely grow into pillars of the country in the future)

3. Students can freely talk about examples in life.

4. Summary after feedback: Through the example just now, we know that the problem of tree planting commonly exists in our lives. The number of fingers, the number of floors, the number of people in the team, classroom lights and desks, street lights, flower pots, etc. are equivalent to the number of trees we mentioned above, and the spacing between fingers and the number of ladders , the distance between people, etc. are equivalent to the number of intervals. Therefore, the relationship between the numbers of tree planting problems such as planting at both ends can be expressed by the relationship: number of trees = number of intervals 1? .

IV. Apply the model to solve practical problems

(Courseware 10 shows problem-solving exercises one by one)

Students complete it independently, and the teacher inspects

Report one by one

5. Expansion exercises

Students cooperate and complete the discussion and exchange (show the question in courseware 11)

Note: This question is related to what you just learned The connection and difference between the questions (are both ends consistent?)

Student report, teacher summary

6. Summary of the whole lesson (shown in Courseware 12)

Teacher : What have you learned through studying this lesson? How to write a teaching design on tree planting issues

1. Teaching objectives:

1. Knowledge and skill objectives: through hands-on practice and cooperation Inquiry allows students to experience from real-life problems to mathematical modeling in the process of doing mathematics, and understand and master the relationship between the number of trees planted and the number of intervals.

2. Process and method goals: Through students’ independent experimentation, exploration, communication, and discovery of rules, we will cultivate students’ abilities in hands-on operation, cooperation and communication, and their ability to flexibly solve problems according to the characteristics of different problems.

3. Emotional and attitude goals: Let students experience the joy of successful learning and understand the importance of inductive rules for subsequent learning in the process of exploring, modeling, and using models, and cultivate students' ability to explore inductive rules. Awareness and understanding of the ideological methods to solve the problem of tree planting.

2. Teaching focus: Understand the relationship between tree planting and interval number.

Teaching difficulties: Be able to apply the model of tree planting problems to flexibly solve some related practical problems.

3. Preparation of teaching aids: multimedia courseware and unfinished forms.

IV. Teaching process:

Preparation before class: (Multimedia screening of the story of Newton and Apple)

Teacher: What inspirations do the stories of scientists give you? ( Diligent in observation, good at thinking, and bold in guessing?)

Introduction to the conversation: It is better to do what you say, let us start from now on and see who observes the most carefully, who thinks the most actively, and who You can also discover patterns from ordinary things in class, are you ready?

(1) Ask questions, trigger thinking, and explore patterns.

1. Thinking caused by hands.

Teacher: Stretch out your left hand, spread your fingers, and take a look at it with a mathematical eye. What do you find?

Teacher: Everyone has a pair of sharp mathematical eyes. Discover that there is also math between fingers and intervals. In fact, as long as you observe and think carefully about common phenomena in life, you can discover their mathematical mysteries. In this lesson, we'll delve into math problems like fingers and intervals.

2. Overall perception and determination of research direction.

Courseware presentation: Plant trees on the side of a 15-meter-long path, planting one every 5 meters. How many possible situations are there?

Show the students’ guesses: (plant at both ends, ***4 trees) (plant only at one end, 3 trees) (not plant at both ends, only 2 trees)

Understanding: ?interval?, ?number of intervals?, ?number of trees?.

(2) Cooperate in groups and explore the rules

1. Ask questions.

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Students’ guesses may have different results: 1000; 1001; 1002)

2. Independent exploration.

What is the relationship between the number of trees and the number of intervals? Let students make bold guesses and verify them using the diagram.

The courseware shows: Plant one tree every 10 meters, then plant another tree every 10 meters?, and keep painting until 1000 meters! Students will feel: This method of painting one tree at a time is okay, but it is too It's troublesome and a waste of time.

Guide students: To study the relationship between the number of trees and the number of intervals, is there an easier way?

Let students think and communicate, try to start simple, use? Study the method of converting large numbers into decimals, and penetrate the mathematical idea of ??turning complex into simple.

3. Discover patterns.

The students began to draw pictures, fill out tables, perform comparative analysis, and then present their research results. They found that when both ends of the small data were planted, the number of trees was 1% more than the number of intervals. law.

Teacher: The rule that the number of trees is 1 more than the number of intervals was studied by students using smaller data. If the data increases, will this rule still hold?

Dynamic demonstration of the courseware: one interval corresponds to one tree, and if the correspondence continues, there will be 1,000 trees in 1,000 intervals. Have you finished planting?

Teacher: If this road becomes very long, infinitely long, Is there such a rule for planting at both ends? Let students realize that no matter how big the number is, use the "one-to-one correspondence" method, and finally add one tree to achieve the result of planting at both ends. This link subtly penetrates the idea of ??"limit".

4. Summary.

Summarize the problem-solving strategies to simplify the complex. Let students realize that research problems can start from simple ones, turn difficult ones into easy ones, and turn complex ones into simple ones. In this way, problems can be solved effectively. Integrate abstract mathematical thinking into teaching, allowing students to experience the value of mathematical thinking methods in a "moisturizing and silent" way, and improve the quality of thinking.

5. Summarize the rules.

Teacher: Can you use a formula to express the pattern?

Number of intervals written on the blackboard 1 = number of trees - 1 = number of intervals

6 , contact life

There are many phenomena similar to tree planting issues in our lives, have you discovered it?

Let students understand the widespread application of tree planting issues in life through examples . At the same time, students can clearly realize that life phenomena such as street lamp arrangement and queuing have the same mathematical structure as the tree planting problem, and this mathematical idea can also be fully modeled.

(3) Click Life

① (Find the number of intervals) Judgment: During the Lantern Festival, 200 red lanterns are hung from beginning to end on one side of China Street. If To hang a Chinese knot between every two lanterns, 201 Chinese knots are needed ( )

② (Find the interval length) The total length of the bus route is 9 kilometers, from the starting station to the terminal station** *There are 10 stations. How many kilometers is the distance between two adjacent stations?

③(Find the number of trees) The teacher climbed the ancient pagoda. Each floor has 11 steps, starting from the first floor** *Walked 55 steps, which floor did Teacher Long reach?

④ (See full length) The bell on the tower was struck. Starting from the first strike, it was struck every 4 seconds. By the fifth strike, How many seconds is the interval between one and the other?

(4) Expansion and extension.

(The courseware shows world-famous mathematical problems)

Teacher: There is a tree planting problem of "20 trees" in the history of mathematics, which has aroused the research interest of scientists for centuries. This is: ? 20 trees, if there are four trees in each row, how to plant so that there are more rows?

As early as the 16th century, ancient Greece and other countries completed the arrangement of sixteen rows. (Show Figure 1)

In the 18th century, the American mathematics master Sam completed an eighteen-line diagram. (Show Figure 2)

Entering the 20th century, mathematics enthusiasts drew a twenty-line diagram, setting a new record that remains today. (Show Figure 3)

(Conclusion) Today has entered the 21st century, with 20 trees, 4 trees in each row, can there be any new progress? The mathematics community is waiting eagerly! We look forward to students boldly exploring , think positively, I believe you will definitely gain more!

Reflecting on the entire teaching process, I think the following points were done better in this class:

1. Creation Easy-to-understand life prototypes bring mathematics closer to life.

Creating learning situations that are closely related to students’ living environment and knowledge background and are of interest to students will help students actively participate in mathematics activities. During pre-class activities, I chose students’ small hands as the material to introduce the study of tree planting issues. During the activities of bringing their fingers together and spreading them out, students can clearly see that there is a difference of 1 between the number of fingers and the number of spaces. Then we played a quick question and answer game to enable students to intuitively understand and summarize the relationship between intervals and points, which paved the way for the following learning and also aroused students' interest in learning.

2. Pay attention to students’ independent exploration and experience the joy of inquiry.

Experience is the process of students transferring from old knowledge to implicit new knowledge. During teaching, I created situations, provided students with multiple opportunities to experience, created a democratic, relaxed, and harmonious learning atmosphere for students, and gave students 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 using graphics to help students understand is a crutch for students to construct knowledge. With this crutch, students can walk more steadily and better. Therefore, in the teaching process, I paid attention to the penetration of the awareness of the combination of numbers and shapes.

After the life scene diagram is introduced, example illustrations are presented, and students are guided to fill in the form after observing and counting the images, and discover the relationship between the trees and the number of intervals when planting trees at both ends! When students have a clear understanding of the physical diagram, The teacher abstracts the visual graphics into line segment diagrams, so that students can still discover the relationship between trees and interval numbers after breaking away from the physical diagrams. During the computer demonstration, the students intuitively understood the relevant quantities in the tree planting problem. After observing and thinking, the students further verified the relationship between the tree and the number of intervals. In this way, the entire process of analysis, thinking, and problem solving is displayed, allowing students to experience this process and learn some problem-solving methods and strategies.

3. Utilize student resources to strengthen student-student cooperation

There are differences between students’ cognitive starting points and the logical starting points of knowledge structures. The differences between students are resources for learning. This resource should be fully displayed and reasonably utilized on the platform of group communication.

IV. Focus on the expansion and application of the tree-planting problem model

The tree-planting problem model is an amplification of a similar type of event in the real world. It originates from reality and is higher than life. Therefore, it has wide application value in reality. In order to allow students to understand the significance of this modeling and strengthen the practice of model application functions, the exercises in this lesson have the following two levels:

(1) Directly apply the model to solve simple practical problems. In class, students are arranged to independently complete the exercises of finding the number of trees with a known total length and spacing, and finding the total length with a known number of trees and spacing. Students are allowed to start from both positive and negative aspects and directly apply the model to solve simple practical problems. Train students' ability to think in both directions and reversibly.

(2) Extend it to some issues similar to tree planting issues, allowing students to further understand many different events in real life, such as the placement of flower pots on campus and incidents at bus stops. , all contain the same quantitative relationship as the tree planting problem. They can all use the model of the tree planting problem to solve it, and realize the importance of mathematical modeling. How to write the teaching design of tree planting problem

Teaching objectives:

1. Experience the process of abstracting the actual problem into the tree planting problem model, and master the relationship between planting trees and the number of intervals.

2. Be able to apply the tree planting problem model to solve some related practical problems, and cultivate students' application awareness and ability to solve practical problems.

3. Understand that constructing mathematical models is one of the important methods to solve practical problems.

Teaching focus:

Understand the relationship between tree planting and the number of intervals, and be able to apply the tree planting problem model to solve some related practical problems.

Teaching difficulties:

Use the model of tree planting problems to flexibly solve some related practical problems.

Teaching preparation:

CAI courseware, some paper trees

Teaching process:

1. Creating prototypes

1. Teacher: Students, there is mathematics everywhere around us. Please stretch out your hand and spread your fingers. Do you see mathematics? What do you see?

(Evaluate at any time based on the students' answers. If the student only says "hand" or "finger", point out that "this is not mathematics" and say "I hope I can see the problem from a mathematical perspective"; if the student says? Five fingers?, the teacher is sure that he has a mathematical vision)

Teacher: What else did he see?

Teacher: The teacher also saw a number, do you want to know? Then. That’s 4?. Who knows, what does this "4" refer to? (4 "spaces". In mathematical language, the space here is the space between the fingers. That is to say, there are 4 "spaces" between the 5 fingers.) Writing on the blackboard: Intervals

Teacher: What is the relationship between the number of fingers and the number of intervals? Can anyone tell me.

(The number of fingers is 1 more than the number of intervals, or the number of intervals is 1 less than the number of fingers)

Teacher: Can you express the quantitative relationship between the number of fingers and the number of intervals? (We can use the quantitative relationship to express: Number of fingers = number of intervals 1)

Writing on the blackboard: number of fingers = number of intervals 1

2. Teacher: We know the number of fingers = number of intervals 1. In fact, we know that number of fingers = number of intervals 1. In fact, Problems like this can be seen everywhere in our lives. In mathematics, it also has a name, which is the tree planting problem. (Blackboard writing topic: tree planting issue). In today's class, we will study and learn about tree planting together. Are you interested?

2. Build the model

1. Hands-on operation and exploration question 1:

(1) Teacher: Speaking of tree planting, Teacher Liu I really want to ask you all for 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 road into the school gate. Which tree is more beautiful? Should it be planted randomly or at equal distances? (Equal distance) What is needed? How many saplings should be prepared? What do you need to know to figure out this problem? (How long is the road and how often should one be planted?) Children are very good at thinking. The school has collected this information clearly. Let’s take a look at it together. look.

Present question 1: Chuanyi Primary School wants to plant trees on one side of the road outside the school gate. The road is 150 meters long, and trees should be planted every 5 meters (planting at both ends). How many saplings are needed for one ***?

(2) Question review: Who will read the question. What information did you learn from the question? Both ends must be planted? What does it mean?

(Write on the blackboard: Both ends must be planted)

(3) Do the math, one*** How many saplings are needed?

(4) Feedback the answer.

Method one: 150?5=30 (tree)

Method two: 150?5=30 (tree) 30 2=32 (tree)

Method 3: 150?5=30(tree) 30 1=31(tree)

Teacher: There are three answers now, and each answer has many supporters. Which answer is it? Is it correct? This needs to be verified. We can draw a picture to simulate the actual planting. We use this line to represent the path, because we need to plant at both ends. Plant one tree on the left side first, then draw one tree, plant one tree every 5 meters, plant another tree every 5 meters, and plant another tree every 5 meters. tree. Plant another tree 5 meters apart.

Teacher: How many meters have we planted? (30 meters) It took so long to plant 30 meters, and we have to plant 150 meters in one day. How would you feel if you had to plant them one by one? (It’s too troublesome)

Teacher: Yes, the teacher’s hands are sore from painting. In fact, there is a better way to study complex problems like this in mathematics? Simplify complex problems. Use simple examples to study their rules, and then use the found rules to solve the original problem. Do you want to try this method?

(5) Draw and write to discover patterns.

Teacher: Let’s change 150 meters to 20 meters. Read the question together:

Students plant trees on the side of a 20-meter-long path. Plant one tree every 5 meters (planting at both ends). How many trees are needed

A sapling?

Processing: ① Please use the drawing method to simulate planting a tree and do the calculations. During the inspection, the teacher reminded: Count the children who have drawn, are you drawing 20 meters?

Think about it, how many 5 meters are there in 20 meters?

② Please tell each other in a group of four: How many trees did one *** plant? How did you calculate it?

Requirements: The group leader organizes carefully and takes turns speaking one by one. Other students pay attention. Listen, comment and add in a low voice so that the four people in the group can hear it.

③Who can tell me how to calculate it? 20? 5 1 = 5 (trees), how did you draw the picture? (Extraction board performance)

④20? What does 5 mean? (There are 4 5 meters in 20). What number does this 4 correspond to in "Finger Problem"? (Number of intervals)

　⑤Why do we need to add 1?

⑥ The teacher explained (pointing to the picture) and modified it with red chalk: plant one tree every 5 meters, and there are four 5-meter trees in 20 meters. Plant 4 trees (one tree at a time to demonstrate) because they need to be planted at both ends. The last tree has been planted, and there is one more tree to be planted on the far left, so adding one tree means adding the one on the far left.