Lecture notes on "discovering the law"

Lecture notes on "discovering laws" in primary school mathematics

As a tireless people's teacher, we often have to write an excellent lecture draft, through which the shortcomings of lectures can be well corrected. So what is an excellent lecture? The following is my lecture notes on "discovering the law" in primary school mathematics. Welcome everyone to learn from it, I hope it will help you.

Lecture Draft of Searching for Laws 1 I. Talking about Teaching Materials

"Discovering the law" is the teaching content of Unit 5 of the fourth grade primary school mathematics (Volume I) in the curriculum standard textbook of Jiangsu Education Edition. The content of this unit is to let students explore the simple rules in the arrangement of two objects at intervals and apply them simply. Interval problem is an implicit law in common life phenomena. Students are familiar with the prototype in real life, and it is easy to find the corresponding laws, which is also beneficial for students to accumulate experience in learning mathematics and gain a sense of pleasure and success in learning. I feel that mathematics is around us.

To this end, I have designed the following teaching objectives:

1. By exploring the quantitative relationship between two kinds of objects arranged at intervals and the simple mathematical laws in similar phenomena, students initially know and understand the laws of the quantitative relationship between objects arranged at intervals, and initially learn to solve some simple practical problems by combining the discovered laws.

2. Be able to use this law to explain the phenomena in life and solve the problems in life.

3. Make students feel the connection between mathematics and life in the process of learning, and cultivate their initial consciousness and ability to analyze life phenomena from the perspective of mathematics; Curiosity about mathematics gradually forms a sense of cooperation with others and self-confidence in learning.

Teaching emphases and difficulties

Teaching emphasis: the exploration process of simple laws in the phenomenon of experience interval.

Teaching difficulty: describe this rule in an appropriate way.

Second, the teaching methods of speaking

"Mathematics teaching activities must be based on students' cognitive development level and existing knowledge and experience. Teaching should stimulate students' enthusiasm for learning, provide students with opportunities to fully engage in mathematical activities, and help them truly understand and master basic mathematical knowledge and skills, mathematical ideas and methods in the process of independent exploration and cooperative communication, so as to gain extensive experience in mathematical activities. Students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning. " This is one of the basic ideas of mathematics teaching activities put forward by the Mathematics Curriculum Standard for Full-time Compulsory Education (Experimental Draft). Based on the above ideas, I have constructed such a teaching mode.

1, observe and discover, and deduce rules.

2. Create situations and explore laws.

3. Use the law to solve problems

4, in-depth experience, feel the law.

5. Summarize the evaluation and extend the law.

Let me talk about my thoughts in each link:

First of all, the observation leads to the law.

At the beginning of the class, I first show the three numbers 1, 2, 3, and ask students to guess the following numbers, and then show a set of numbers for students to guess the following numbers. Students communicate first, and then the teacher points out that the arrangement of these numbers and figures has certain rules. As long as we observe them carefully, we can find the law by comparing them before and after.

Here, I introduce numbers and shapes to students, let them guess, and feel the existence of laws in mathematics from simple numbers games, so as to stimulate students' curiosity about new knowledge and lay a psychological foundation for discovering laws. ]

Second, create a situation and explore the law

This link is the focus of this course. (First, multimedia presentation: the scene of rabbits singing and dancing happily in music) I designed the following teaching links:

1. Ask the students: What did you see in the home of the little white rabbit? Can you tell everyone?

2. Exchange the information you obtained.

3. Q: Can you find the relationship between these information?

4, layered observation, experience the law.

Previous observations may be problematic. On this basis, I will guide the students to observe in order: How many groups of objects are drawn on the screen? What are the two in each group? How do rabbits line up? What else is in the rabbit? (There is a mushroom between every two rabbits) Can you count rabbits and mushrooms?

Then observe the pictures of other clips and handkerchiefs, stakes and fences, trees and ropes, and write them on the blackboard according to the students' answers. Read these data carefully again, look at the pictures and think about the arrangement of two objects in each group-rabbits and mushrooms, clips and handkerchiefs, stumps and fences, trees and ropes. What's the relationship between their number? And talk about your ideas with the students in the group. Then through classroom communication, students can intuitively see that there is a mushroom between every two rabbits, and the number of rabbits is more than that of mushrooms 1. There are/kloc-0 handkerchiefs between every two clips, and the number of clips is more than that of handkerchiefs 1 handkerchief. ...

5. induction

When two objects are arranged every other time, there are more objects arranged outside than inside by 1, and fewer objects arranged inside by 1.

[The above links, make full use of modern educational technology, create realistic problem situations for students, highlight students' theme inquiry activities, and guide students to observe, discover and communicate in an orderly manner on the basis of students' casual observation of preliminary perceived information, so that each student has experienced different inquiry processes, had different experiences and discoveries, expressed the law of discovery in his own way, and enhanced his interest and ability to explore and study problems. ]

Third, use the law to solve problems.

First of all, the teacher pointed out that there are many such phenomena in life. Now let's take a look on the road (the computer shows the picture of the first question "Think and Do") and say what you see. This question can be directly observed and answered according to the law of discovery.

Then encourage students to think and solve the second problem "think and do" and "saw wood".

Fourth, experience deeply and feel the law.

In this section, I launched a queuing game activity.

1. Please invite four male students and three female students first. Requirements: One female classmate stands between every two male students.

2. Please ask another female classmate to come up in line, and the requirements are the same as last time.

The purpose of this activity is to enable students to analyze and solve practical problems by using the laws they have learned, to make students realize the connection and difference between interval phenomena in a straight line and interval phenomena in a closed figure, to understand the development and changes of the laws, to inspire students to solve problems correctly according to the actual situation, to improve their ability to solve problems and to make students realize that mathematics comes from life!

Fifth, summarize the evaluation and extend the law.

First of all, ask the students to talk about what rules are found in this class. How did you find this pattern? Sum up together: Through observation, discussion and comparison, we found two kinds of objects arranged at intervals. If they are arranged in a row, there will be one more object at both ends than in the middle; If arranged in a circle, the number of two objects is the same.

Finally, a practical assignment is arranged: make a small design by using the rules found in class and combining with the actual life. For example, decorate the classroom with colored lights, decorate your bedroom with beautiful patterns, design beautiful and generous squares, and design creative games. ).)

By arranging open homework, we can further link what we have learned with real life, cultivate students' innovative ability and make them experience the value of mathematics.

Lecture Notes of "Seeking the Law" 2 I. Talking about the Teaching Content

1, lecture content:

Examples and related exercises on page 48 of the first volume of fourth grade primary school mathematics in Jiangsu Education Press.

2. teaching material analysis:

"Exploring the law" is a part of the field of "number and number" in the mathematics curriculum standard. Students have been exposed to the intuitive and simple content of "discovering laws" in the first issue, but it is the first time that it appears as an independent unit in textbooks. Its content is to let students explore the simple rules in the arrangement of two kinds of objects at intervals and apply them simply. The textbook takes interesting fairy tale scenes as materials to guide students to explore some simple mathematical laws in life. Learning such content can enable students to use the existing mathematics learning methods and experience, discover the laws of mathematics, feel the exploration and value of mathematics, and establish self-confidence in learning mathematics well.

3. Design concept:

"Mathematics Curriculum Standards" clearly points out: "Effective mathematics learning activities cannot rely solely on imitation and memory. Hands-on practice, independent exploration and cooperation are important ways to learn mathematics. " Therefore, teachers must change their roles, design exploratory and open questions according to students' characteristics, give students opportunities for independent thinking, independent inquiry and cooperative communication, and let students learn and understand mathematics in the process of observation, conjecture, experiment, induction, analysis and arrangement. In order to do this, students can learn about "law" through practical activities such as taking a look and posing, and initially establish the concept of "law".

4. Teaching objectives

(1) Make students know and understand the laws between the number of objects arranged at intervals, and learn to solve some simple practical problems by combining the discovered laws.

(2) To enable students to initially develop their thinking abilities such as analysis, comparison, synthesis and induction in exploration activities.

(3) Make students feel the connection between mathematics and life in the learning process, cultivate their initial awareness and ability to analyze life phenomena from the perspective of mathematics, generate their curiosity about mathematics, and gradually form their awareness of cooperation with others and self-confidence in learning.

5. Teaching emphases and difficulties

Teaching emphasis: let students "discover" the law between the number of objects arranged at intervals, and cultivate students' exploration consciousness and ability to learn mathematics through "discovery".

Teaching difficulties: cultivating students' logical reasoning ability and innovative consciousness.

6. Preparation of teaching AIDS

Teaching AIDS: thematic wall charts, teaching courseware.

Learning tools: Each student prepares sticks and stones.

Second, the teaching methods of speaking

1. In teaching thought, students are the main body, and teachers are only the organizers, guides and collaborators of learning, so that students can always participate in teaching activities.

2. In terms of teaching methods, we use intuitive method, game method, hands-on operation, inquiry and other methods, from support to release, so that students can understand and create laws in the process of observation, comparison, attempt, exploration, practice and re-practice.

Third, learning theory.

Students are the main body of learning, and teachers are the organizers, guides and collaborators of learning mathematics activities. Therefore, in teaching, I attach great importance to guiding students, providing them with opportunities such as "independent exploration, cooperation and exchange, and practical innovation", so that students can find out the rules in the process of cooperation and exchange and operation.

Fourth, talk about teaching procedures.

Stimulate interest in introducing and revealing topics

Teacher: Students, shall we play a game? The name of this game is "Guess". Please see:

1, showing:

Guess what color the next balloon is?

2. Display:

Please guess which fruits should be placed in the middle to make them orderly and more beautiful.

Teacher: You are great! Can guess the answer to the question accurately. Who can say that in the process of guessing just now, you guessed according to what you were looking for?

Health: find a pattern.

Teacher: Yes! You found out about their arrangement.

Writing on the blackboard: discovering the law

Teacher: There are many regular arrangements like this around us. As long as we find the rules, we can solve many problems. Today, we will learn the arrangement rules of some common objects in life.

(2) Create scenarios and understand the rules.

Show the teaching theme map: rabbit paradise

Teacher: The teacher shows the students around: Rabbit Paradise!

1, ask questions and discuss in groups

Teacher: Please tell your classmates what you saw and thought in Rabbit Paradise.

Step 2 observe the numbers

Teacher: Please observe carefully. How many objects are there in each row? What are the characteristics of their arrangement?

The teacher put forward three questions in the textbook in turn, and guided the students to count in three parts to get the number of two kinds of objects. Then, according to the order of the questions and the result of the number of students, they write three lines on the blackboard to show how many there are.

3. Comparison results

(1) Teacher: What rules can you find by comparing two objects in each row? Talk to your deskmate first.

(2) Organize the whole class to communicate and let the students talk about the rules found in their own words. Teachers can help students make their words fluent and clear.

4. induction

(1) Teacher: What laws have we found in the scene of "Rabbit Paradise" through observation, comparison and communication?

② Students' inductive rules.

③ Understand the law.

Put a pendulum for comparison. Who can find the pattern?

(1) Teacher: Please take out your study tools, line up a few sticks on the table, and then put a stone in the middle of each stick. Count the number of sticks and stones and see what you will find. Tell your deskmate what you have found, and compare it with the pattern found before. Is it the same?

② Organize the whole class to communicate.

Design concept: this link is the reappearance of new knowledge, which plays the role of checking, consolidating and improving new knowledge, and has a deeper understanding of the law, which is conducive to the completion of teaching objectives.

(4) Take practical examples to understand the laws of beauty.

1, life is regular everywhere.

Teacher: Can you find such a regular example in your life? Think carefully, talk to your classmates first, and then tell the whole class.

2. Appreciate the beauty of regularity in life.

Show the beauty of regularity in life

Design concept: linking mathematics with life, so that students can truly appreciate the application value of mathematics, and at the same time, it also opens students' thinking and broadens their knowledge. )

Use the law to solve problems

In order to consolidate new knowledge and develop students' thinking, I have designed the following questions:

1, Xiaoming goes home from school and crosses a road. He found that there were 10 poles on one side of the road, and there was a billboard between every two poles. Can you help him count how many billboards there are?

2. There are 75 willows planted on one side of the dam, and a peach tree is planted between every two willows. How many peach trees have been planted?

There are 25 willows planted around the circular pond, and a peach tree is planted between every two willows. How many peach trees can you plant?

Design concept: The first two questions are about foundation reinforcement, and the last one is about expansion and extension. This design has both levels and slopes, which plays a role in checking and consolidating the knowledge learned and also discovers the students' thinking ability. )

(6) make laws

What a nice student! I can find a pattern and use it to solve practical problems. Now the teacher tests you: Who can arrange some male students and some female students in our class and let them arrange them regularly?

(Design concept: Cultivating students' innovative consciousness by using existing learning resources)

(7) Summary

Teacher: Can you tell the students what you have learned in this class? (Students raise their hands to speak) In life, in the kingdom of mathematics, there are more wonderful laws waiting for you to explore. As long as students carefully observe and seriously think, they will certainly discover the mystery!

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