Lecture Draft of Interest Measurement 1 1. Talking about Teaching Materials:
"Interesting Measurement" is the content of Unit 4, Book 10 of Primary Mathematics, Beijing Normal University Press. This paper mainly studies the calculation method of irregular object volume, which is extended by students on the basis of mastering the calculation of cuboid and cube volume. Mainly to let students solve practical problems through practical operation and comprehensive application of the knowledge and methods they have learned. The main method to measure the volume of an irregular object is to put the object into water and calculate the volume of rising water, so as to get the volume of the object. From the explicit aspect, this is "equal product deformation", so from the implicit aspect, it is to transform the unknown into the known. Students can not only solve one or two practical problems, but also solve a large number of such problems by analogy. Therefore, in teaching, we should not only stay in the explicit connection of knowledge, but also infiltrate this implicit mathematical thought, so that students can truly grasp the connection between mathematical knowledge.
Second, tell the teaching objectives:
Combined with the requirements of the new curriculum, the characteristics of this class and the students' reality, I have specially set the following goals:
Knowledge and skill goal: experience the experimental process of measuring the volume of stones and explore the method of measuring the volume of irregular objects in combination with specific activity situations.
Process and Methods Objective: To experience the process of exploring the method of measuring the volume of irregular objects and the mathematical method of transformation. By comprehensively applying the learned knowledge, we can obtain the activity experience and specific methods of measuring the volume of irregular objects, and cultivate the team spirit and problem-solving ability.
Emotion, attitude and values: Feel the interrelation between mathematics knowledge, experience the close connection between mathematics and life, and establish confidence in using mathematics to solve practical problems.
Third, talk about the difficulties in teaching:
The content of this class is actually a math practice activity class. According to the students' cognitive level, thinking ability and practical conditions, I will focus on this lesson: to enable students to explore and master the measurement and calculation methods of irregular object volume. The determination difficulty is as follows: Design the measurement scheme.
Teaching preparation: stone, rectangular water tank, water, scale, measuring cup.
Fourth, preach the law:
According to the requirements of curriculum standards, teaching objectives, teaching difficulties, students' cognitive ability and existing knowledge and experience, this course adopts the following teaching strategies: intuitive demonstration, question induction, operation discovery, etc., to guide students to master knowledge, enrich appearances, enhance experience and form thinking in a large number of practical activities on the basis of full perception.
Effective mathematics learning activities are not simply dependent on imitation and memory, but a purposeful and positive process of knowledge construction. To this end, I attach great importance to the guidance of students' learning methods. In this class, the methods I guide students to learn are: observation and discovery, hands-on operation, independent inquiry and cooperative communication, so that they can explore the volume measurement and calculation methods of irregular objects in a series of practical activities.
Five, the teaching process theory:
This lesson is carried out according to the following four main links: review and consolidation, revealing topics-inspiring induction, exploring methods-consolidating application, deepening understanding-summarizing review, evaluating reflection. This fully embodies the teaching design concept of "problem" and "problem solving" in mathematical practice activities. In the process of activities, teachers give targeted guidance on the basis of students' independent thinking and cooperative communication, so that students have more room for independent development, stimulate students' interest in learning, cultivate students' ability to find, ask and solve problems independently, and feel the close relationship between mathematics and life.
(A), review and consolidate, revealing the topic
First, review the volume calculation of regular objects. Through the introduction of cuboid water tank and Rubik's cube, let the students talk about their own volume calculation methods, so as to review the cuboid volume calculation formula and make full preparations for this lesson. Then he took out the stone and asked, "Can its volume be directly calculated by measuring the relevant conditions?" Guide students to observe and compare it with Rubik's cube and sink, lead out "irregular objects" and reveal the theme of this lesson. Stone is a familiar living material for students. It feels very intimate and there are questions: How to calculate its volume? Students' strong thirst for knowledge and interest in learning are stimulated.
(B), inspire induction, explore methods
This course is divided into three levels.
1。 Autonomous learning, guessing method.
Independent thinking: how can we measure the volume of a stone? Please state your thoughts in simple language.
Let the students know fairly well before cooperation and exchange, and have their own preliminary ideas first.
2。 Paired learning, carding method.
On the basis of autonomous learning, combined with the experimental equipment given by the teacher, the students choose the equipment at the same table and say the operation steps. Focus on the experience that the volume of stone can change the volume of rising, falling or overflowing water, clarify the steps of experimental operation and experience the idea of "transformation". This experimental method is sorted out to pave the way for the following measurement and calculation.
3. Cooperative learning, measurement and calculation.
Now there are only equipment: stones, rectangular water tanks, water and scales. How to calculate the volume of stone?
I arranged a group of four to communicate:
Answer: What data should be measured in the experiment and how?
B, how to calculate the volume of the stone according to the measured data?
During the reporting process, four people work together to report, including the operator, recorder and lecturer. They cooperate to present the report, and finally the team leader is responsible for explaining the calculation method. This link is the focus of this class and the most wonderful place. Let the students sum up the main points of this lesson through their own measurement and calculation, and find the general law of measuring irregular objects. You may remember it after listening, but after the operation, students will understand and understand the knowledge, and students will be impressed.
When summing up the idea of converting the volume of irregular objects into the volume of regular cuboids or cubes, I suddenly have a question: how to measure the volume of objects floating on the water, such as oranges and apples? Once again arouse students' thinking and discussion, so as to make it clear that a key point of measurement is to "completely immerse" in water. At this time, the teacher added another measurement method "sand measurement" for students to understand, which may inspire students to think a lot.
(C), the extension of classroom practice
Practice is an effective means to consolidate new knowledge, form skills, develop thinking and improve students' ability to analyze and solve problems in mathematics teaching. In order to strengthen students' understanding and enable them to use the formula correctly, I designed multi-level exercises:
1, fill in the blanks.
(1) There is a measuring cup with 300ml of water in it. When an iron block is placed (completely submerged), the scale of the water surface is 380ml, and the volume of the iron block is ().
(2) Add two identical glass balls (completely submerged) into a measuring cup filled with water, and the water level will rise 12ml. The volume of the glass ball is ().
(3) An egg is completely immersed in a glass filled with water, and there is 40 ml at this time. After taking out the egg, there is only 22 ml of water left, and the volume of the egg is ().
These three fill-in-the-blank questions aim to further consolidate the actual calculation of several water measurement methods provided by students, deepen students' understanding of these methods and learn to apply them.
2. I am best at solving problems.
(1) A cuboid container with a bottom of 2dm and a width of 1. 5dm, after a potato was put in, the water level rose by 0. 2dm, what is the volume of this potato?
(2) A cube fish tank with a side length of 12cm, which contains some water. Now put in 10 small fish, and the water level will rise 1cm. What is the average volume of each small fish?
This problem is to consolidate and improve students' ability to apply knowledge to solve practical problems. The exercise of the second question laid a foundation for mastering the volume measurement of smaller objects.
3. Design the experiment.
How to measure the volume of a soybean?
This is a design experiment based on the second question, which returns to "interesting measurement" again, so that students can not only calculate, but also find ways to measure the volume of many irregular objects in life, which is also the purpose of our class.
After the practice, the teacher will take the students into the mathematics kaleidoscope in time, feel the elegance of Archimedes more than two thousand years ago, stimulate students' interest in mathematics, and enhance their awareness of actively exploring scientific knowledge.
(4) Summary, review, evaluation and reflection
In this link, let students talk about their own gains and feelings, let students evaluate themselves, let students experience the pleasure of successfully exploring and solving problems, establish confidence in learning mathematics well, and provide a broader space for students to explore independently.
Sixth, talk about blackboard design.
In this class, I use an outline book with key contents, which is simple and clear, and the key points are prominent. Use the difference of different colors to attract students' attention and highlight the important idea of "transformation"
Lecture Notes on "Interest Measurement" 2 I. Lecture Contents
The outline clearly points out the basis of choice: "Let children feel the quantitative relationship of things from life and games, and experience the importance and fun of mathematics". The measurement activity of large class children is natural measurement, which refers to the use of natural objects (such as chopsticks, footsteps, sticks, ropes, etc. ) as a measuring tool, and is limited to the measurement of simple tools rather than standard tools.
The content of the activity comes from the real life of children. In the usual corner activities, we often put many different materials, such as sticks, ropes, rulers, straws, pencils and so on. , in the math corner. We often see children testing the east and the west, and seem to be very interested in these measurement activities. In addition, it will be very interesting for children to measure with all parts of their bodies, so that children can feel the pleasure of measurement through constant physical exercise and games throughout the activity. Children explore and try by themselves, so that children can learn many good learning methods, which is also conducive to their lifelong development. As a result, today's activities came into being.
Second, talk about the determination of activity objectives
1, try to measure with various parts of the body, and make a simple record to experience the fun of measuring activities.
2, know the relationship between the measurement results and measuring tools.
3. Learn to negotiate with peers, respect other people's opinions, solve problems together, and experience the happiness of cooperation with peers.
Activity focus: explore and learn various measurement methods.
Activity difficulty: record the measurement results.
Third, talk about the preparation of activities.
Knowledge preparation
1, corner activity: Teachers and children have found many tools that can be used for measurement.
2, observation activities: children will use some common record forms in life.
(2) Preparation of materials
1. Prepare the venue in advance.
2, pen, paper, record sheet, etc.
Fourth, talk about teaching methods and learning methods.
Psychologist Piaget pointed out that children's knowledge construction must be completed by children through their own operational activities. According to this concept, I start with the operation activities that children are most interested in. Through experiments, games and records, children can actively gain direct experience of measurement. Through recording, sharing and communication, children can continuously accumulate learning experience and discover and construct mathematical knowledge through interaction with environmental materials.
Children's independent exploration activities must be experienced by children themselves, which is irreplaceable by others. Therefore, children should be given more space and time for independent activities in the activities, and the steps should not be too detailed and too dead, so that they can fully experience, which can help children get direct experience, attract children and let them explore more freely. In the process of sharing, they can communicate and express independently, so that their sporadic experience can be popularized and developed, thus forming the basic knowledge of measurement and understanding measurement.
The whole activity mainly adopts exploratory operation method. According to the characteristics of children's love of moving, asking and learning, let them explore for themselves. Inquiry operation is not only a means to review and consolidate knowledge, but also an effective way for children to explore knowledge and seek the internal relationship between knowledge. This learning method conforms to the law of children's thinking development, because it is impossible to explore the unknown only by understanding and memory. It is necessary to actively analyze, synthesize, compare and summarize, and get the measurement methods and results that are beneficial to the development of children's cognitive ability.
Five, said the activity process
(1) Ask questions, set suspense and arouse children's interest. Teacher: Today, the teacher will take the children to the forest cabin to play, but before we go, we have to help the teacher solve a problem first. We have to measure how far it is from here to the cabin. Do you have any good ideas?
The children discussed freely and came up with various measurement methods. At this time the teacher will ask questions again.
Teacher: But today, the teacher didn't bring any measuring tools. We can only measure it with our own bodies. How should it be measured?
(design intent: children are born with a strong thirst for knowledge. Teachers create situations for children to find problems, stimulate children to actively participate in the activity process, and explore the interest in finding problems. )
(2) Discussion and inquiry: Find the measurement methods and say them respectively.
1. Children are free to explore measurement methods. When children explore, teachers patrol and observe and guide them to find their own bodies and find different measurement methods in time.
2. Let the children demonstrate.
(c) Children looking for cooperative measurement methods.
Children can find their own measurement methods and then cooperate with others to come up with more and better methods, which will help children actively cooperate with others in their future studies.
(Children's cognitive structure mainly emphasizes intuitive thinking. In teaching, instead of teaching children how to do it, it is better to let them try and think while doing it. Children's understanding of the objective world is mediated by inquiry activities. Children explore independently, which seems to be a "waste" of time, but actually wins time. This kind of inquiry has the most practical significance. The educational purpose of exploring games requires teachers to pay more attention to the process of children's learning rather than the results. )
(four) to guide children to record the results of measurement or cooperative measurement on the record form.
Recording the process and results of activities is a good habit for children, but it is also what children lack most. How children record their own measurement process and the results after measurement is the difficulty of our class.
(5) Record, share and communicate the process and results of measurement Teacher: I found that many children have come up with many methods of measurement. Please take your record sheet to the children, and let's have a look at the children's measurement results. (Ask the children to introduce the measurement method and results) Is there anything different from the children? Please introduce and discuss (children find different results); Why are children's measurement results different? Measure again and guide children to find and explore the reasons for the difference.
(Integrate children's communication experiences into their own experiences and verify them again, so that children's abilities and knowledge can be subtly consolidated and absorbed. ) Summary: We used different measurement methods in the measurement, so the measured results are different.
Children's cognitive ability is limited by their age characteristics, and there are often many mistakes in exploration. As teachers, children should be allowed to make mistakes. By creating a relaxed and free environment for children, encouraging them to express their opinions boldly, correcting their mistakes and further improving their experience by actively participating in discussions, exchanges and sharing the process and results of exploration. )
(6) Collective cooperation to measure children's use of collective strength to find different measurement methods. The children measured again in the form of games. The whole activity was carried out in the game, and the children were full of fun.
(7) Talking about the angular activity of the activity extension area: Try to use various objects as measuring tools before measuring.
Sixth, say characteristics:
1, with strong operability. In teaching, children are very interested in operation, using their own body parts as measuring tools to explore and experience the process and happiness of exploration through operation-game. During the activity, the children improved their observation and hands-on ability while exploring, and also improved their attention and listening.
2. Gamification of activity design. Children especially like games, because they can play in middle schools and schools without any pressure. For individual children with weak ability, teachers take the form of collective and individual counseling to provide them with opportunities in activities so that children with weak ability will not be afraid; I always encourage and respect children's new ideas and discoveries and share them with them.
3. The whole activity design comes from a point of interest in children's daily life. In the process of activities, children are always in an independent and positive state. The activity level is clear and the transition is natural. Through individual quantity, group cooperation quantity and collective quantity, children can gain relevant experience in the interaction with activity materials, teachers and peers, which truly embodies the interaction between teachers and children, students and things.
Our activity mainly embodies the following spirit of the Outline:
1, follow the laws of children's physical and mental development and learning characteristics, and pay attention to the wit and fun of education.
2. Infiltrate the contents of various fields and promote the development of children's emotions and abilities from different angles.
3. Make full use of the important educational resources of teachers and peers to make the knowledge and experience acquired by children more specific and comprehensive.
"Interesting Measurement" Lecture Notes 3 I. teaching material analysis:
This section belongs to Unit 4, Book 5 of Primary School Mathematics of Beijing Normal University Press "Cuboid (2)". After learning the calculation of cuboids and cubes, we can further understand and deepen. It is its comprehensive application and close to life, which is of great help and role in solving some practical problems in life.
Second, the target analysis
According to the content of this lesson and the requirements of the new curriculum standard, I have determined the following teaching objectives:
1. Knowledge and skills: Through observation, experiment, guessing, proof and other mathematical activities, students can experience the mathematical method of "equivalent substitution" and develop their awareness of mathematical application.
2. Process and method: Feel the close connection between mathematics and human life, and cultivate students' practical ability and innovative spirit.
3. Emotion and value: actively participate in mathematics activities, have curiosity and thirst for knowledge about mathematics, cultivate a sense of cooperation, feel the value of mathematics, and experience the joy of learning.
Third, the teaching focus:
Measurement method and calculation of irregular object volume
Teaching difficulty: designing investigation scheme
Preparation of teaching AIDS: transparent containers, irregular plasticine, stones, soybeans, cubes and cuboids.
Fourth, the analysis of learning situation:
In terms of composition, some students in Class 5 (1) belong to the original central primary school. They study seriously, practically and consciously, with a solid foundation, eager to learn and make progress, while most of the students come from rural areas and teaching classes, with poor foundation, poor foundation, mixed students and passive learning. I am not interested in mathematics, and some students are young and obviously have children's nature in them, such as hyperactivity, curiosity, easy distraction and poor self-control. Therefore, in view of the students' personality characteristics and the actual situation of this class, I adopt the following teaching methods.
Analysis of teaching methods of verbs (abbreviation of verb);
I first draw students' attention to the classroom by telling stories, and then guide students to find and explore ways to solve problems through hands-on operations, demonstrations and other activities, encourage students to find different methods and means independently, make boring mathematics both informative and interesting, and stimulate students' interest in learning and cultivate students' various abilities. "Interesting" and "measurement" are two key points in my design of this course. It is challenging for students to transition from measuring the volume of regular objects to measuring irregular figures. How to make students acquire new knowledge easily and happily, I adopt a three-step strategy: ① First, choose plasticine to test, because students have played it, so it is easy to understand; Secondly, take out potatoes that students are very familiar with to measure, because potatoes can be pinched and deformed like plasticine after being cooked, and the results can be found soon. (3) The stone reappears for students to explore and find the best simple scheme. (4) Finally, on the basis of practice and consolidation, end this lesson through practical application and divergent thinking.
Teaching process design of intransitive verbs: (7 links)
1, review the old knowledge, first review the calculation method of cuboid (positive) volume, and tell the calculation formula used by * * *.
2, talk to reveal the topic:
Who knows the story of the crow drinking water? Why can crows drink water? Are we not smarter than animals? Attract students' attention, stimulate their interest in learning, and dare to compare with crows in learning enthusiasm. The atmosphere in the classroom suddenly enlivened. At this time, plasticine, potatoes, stones and other objects are presented, and the concepts of regular body and irregular body are obtained from the appearance. Who can tell their shapes? These objects and shapes are not as regular as the shape of a cuboid (positive) and have no fixed shape. They are called irregular objects. Today we are going to learn about the measurement of the volume of irregular objects (blackboard writing: the measurement of the volume of irregular objects). Prompt the topic.
3. Q: How to calculate their volumes and see who can figure out a way? It is also the difficulty of this class to let students actively think about the scheme, fiddle with possible situations in time and let students explore boldly.
① estimation; 2 Knead like mud into a cuboid (front); ③ Boiled potatoes are pressed into cuboids (positive); ④ Grind the stone (iron) into a cuboid (positive).
What if rocks, iron, eggs, etc? Not easy to change shape or not allowed to change shape. Can tips be inspired by the story of crows drinking water? Introduce the fifth scheme.
Teacher's demonstration: sink the stone into the water. (Students observe carefully): ① What has changed? ② Discussion: Why does the water surface rise? (Volume increases) ③ Where is the increased part? What does it have to do with the volume of the stone? (4) What happened to the stone after it was thrown into the water? What hasn't changed? The length and width are constant, but the height of the water surface changes. ⑤ How to calculate the volume of stone? What conditions do I have to know? Length, width and water height of the container: the original water height.
The height of the water after putting the stone in.
The height of rising water
To answer the above questions, the volume of the stone = the length of the container × the width × the height of the rising water. Students can easily find a way to measure the volume of irregular objects.
Explain why crows can drink water.
The above is the focus of this section, from easy to difficult, from shallow to deep, thus highlighting the breakthrough of difficult points.
4. Guide students to think from different angles: Who can think of other ways?
① Inverse method; ② Fill with water. Encourage students again.
5. Consolidation exercise: from mathematics in life to practical application.
Example: Show a small blackboard.
Iron volume = bottom area × height, from which two other formulas can be obtained:
Bottom area = volume/height = volume/bottom area
Let students learn to use it flexibly, so as to achieve the effect of changing a subject, drawing inferences from others and achieving mastery. Finally, the water regulation should be unified with the iron unit of volume. (L=dm3)
6. Summary: This section is a comprehensive application of the knowledge learned, which fully embodies that mathematics comes from life and serves life. Only by understanding can we turn book knowledge into our own knowledge, and then solve practical problems in life. In the whole class, students' thinking is always in a state of excitement. By answering teachers' questions, they can find different ways to solve problems, which is also in line with the requirements of the new curriculum standard "teachers are the organizers and guides of the class, and students are the masters of learning".
7, homework layout:
P55 questions 1, 2, 2 as after-class thinking questions: it is also the extension and expansion of this section of knowledge, cultivating students' divergent thinking. 1, how to measure the volume of a soybean? 2. In the experiment just now, can we only grow water?