Lecture notes on cuboid and cube volumes in elementary mathematics

As an excellent teacher, it is inevitable to write speeches and carefully draft them. So how should I write it? The following is a lecture on "cuboid and cube volume" in primary school mathematics, which I carefully arranged, hoping to help you.

Lecture Notes on "Cuboid and Cube Volumes" in Primary Mathematics 1 1. Textbooks

1, lecture content:

Nine-year compulsory education, six-year primary school mathematics textbook, volume 10, page 3 1~33, complete the questions in "doing one" and questions 4~7 in exercise 7.

2, the status and role of teaching content:

Cuboid and cube are the most basic three-dimensional figures. It is a leap for students to learn three-dimensional graphics on the basis of knowing some plane graphics. Although cuboids and cubes have been touched in the cognitive graphics in the second volume, they are only intuitive and difficult to rise to rational understanding.

This unit basically understands the characteristics and properties of cuboids and cubes, learns the calculation of surface area, and grasps the concept and common units of volume. In this lesson, we will learn the volume calculation of cuboids and cubes, know the source of the volume formula, and master the meaning and usage of the formula.

Learning the volume calculation of cuboids and cubes is the basis of learning the volume rate unit, and it is also the basis of learning the volume in the future. Therefore, the volume calculation of cuboids and cubes must be mastered skillfully.

Learning the volume calculation of cuboids and cubes has certain practical value. Learning some measurement and calculation knowledge through students' practical operation activities can help them learn to actually measure and calculate the volume of some objects and solve some practical problems in their future production and life. Through the calculation of learning volume, students can further understand that knowledge comes from practice and is used in practice, and learn some methods to study problems. It is of great significance to the formation of the concept of learning space.

3, the determination of teaching objectives:

To sum up, the volume calculation of cuboids and cubes is the basis for continuing to learn geometry knowledge in the future. Therefore, this class should let students know the source of cuboid and cube volume formulas, understand their meanings, and skillfully use the formulas to solve some practical problems.

In the process of learning knowledge, students should receive some ideological education, establish the view of "practice first", learn some methods to study problems, develop their thinking ability through learning knowledge, and gradually form their spatial concept.

4. Textbook arrangement features:

The arrangement of the textbook in this section can be divided into two parts, the volume calculation of cuboid and the volume calculation of cube.

The teaching of cuboid volume calculation adopts intuitive teaching method. Ask students to form a cuboid with unit of volume number (65,438+0 cubic centimeter). Through this cognitive process from whole to part and from part to whole, students can realize that a cuboid can be regarded as several unit of volume. Then inspire students to observe and think about the relationship between cuboid volume and its length, width and height, and get a written formula for calculating cuboid volume: cuboid volume = length × width × height and letter formula: V=abh. Finally, the formula is used to guide the application and solve the example 1.

Using the transition of cuboid volume calculation, the volume calculation of cube is obtained. By asking students to review the knowledge that the length, width and height of a cube are equal, which is called the side length, the volume formula of the cube is directly obtained, and the meaning of a3 is also explained. Finally, guide the application and solve Example 2. The knowledge structure of this course is arranged scientifically, which conforms to the students' cognitive law.

5. Teaching emphases and difficulties:

The two parts of this lesson should focus on the first part. In the calculation of cuboid volume, the key point is to understand the meaning of volume formula and use it to solve practical problems. The difficulty lies in understanding the meaning of the formula. To highlight the key points and break through the difficulties, the key is to understand the source of the formula through repeated operations, and to move from perceptual knowledge to rational knowledge through thinking activities.

Second, the choice of teaching methods and learning methods.

Teaching methods and learning methods are a unified whole. Teachers' "teaching" should adapt to students' "learning", and students' learning cannot be separated from teachers' guidance. Teaching methods should permeate the teaching process, knowledge should be scientific, and it should be suitable for students' cognitive laws, so that students can understand and master knowledge.

1. There is enough intuitive operation.

The characteristics of students' thinking generally start with perceptual knowledge, then form appearances, and rise to rational knowledge through a series of thinking activities. The teaching of this course adopts intuitive operation method, which is an important link.

2. Inspire students to think independently.

Students are the main body of learning. Only by guiding students to find problems independently, think about problems independently and solve problems independently can we get twice the result with half the effort. For example, on the basis of operation, let students observe and discuss in groups: what are the numbers in each row, row and floor? What is the relationship between the length, width, height and volume of a cuboid is an important way to summarize and understand the formula.

3. Combination of teaching and practice.

The teaching content of this lesson is divided into two parts. After learning the cuboid volume and completing the example 1, you can give a set of exercises to let students master the cuboid volume formula skillfully. Then teach the volume of the cube, and then show a set of exercises after example 2, so that students can master the volume calculation of the cube skillfully. Finally, make a simple summary of the knowledge of this lesson, and then let the students do comprehensive exercises.

4. Make full use of the law of knowledge transfer to guide students to master new knowledge.

When learning the volume calculation of cubes, you can directly call the volume calculation method of cuboids, so that students can obtain the volume formula of cubes independently.

Third, the teaching program design

(A) innovation, create a situation

Any new knowledge is based on the original knowledge group, so the exercises I designed in the review are just to pave the way for this class.

1. What is volume and what is the common unit of volume? What are 1 cubic centimeter, 1 cubic decimeter and 1 cubic meter (the teacher shows the model of the unit of volume)?

Complete this question and let the students further establish the concept of space to pave the way for this class.

With unit of volume, we can measure the volume (projection) of an object.

Q: ① Can you calculate the volume of this cuboid?

(2) Cut it into cubes with a side length of 1 cm, and count how many cubes with a side length of 1 cm this cuboid consists of and how many cubic centimeters its volume is. (presented by projection)

Summary: Cut a cuboid into a small cuboid with a side length of 1 cm, and its volume can be calculated.

(2) Passion attracts interest and reveals the theme.

The teaching effect of a class is related to students' psychological state. According to the psychological characteristics of students, I often encounter the problem of calculating the volume of cuboids and cubes in real life. If I want to produce packaging boxes for TV sets and refrigerators, I must know the sizes of TV sets and refrigerators. I want to measure the volume of a pool of water. Can I still cut it? The "tangent number" method is not feasible in real life. So what should we do? This is the volume calculation of cuboids and cubes that we are going to learn today. Reveal topics, encourage students to make progress, give full play to students' subjective initiative, and let them actively and vividly explore new knowledge.

(3) Use your imagination to derive the formula.

1. The thinking characteristics of primary school students are mainly thinking in images, and gradually transition to abstract thinking. According to this feature, students are guided to use intuitive learning tools for intuitive operation and thinking, and the specific operation, thinking and language expression are closely combined, and then gradually separated from intuitive operation and gradually abstracted by representation. The specific process is:

The teacher showed the cuboid by projection.

(1) Please take out a small cube with a side length of 1 cm and pose the cuboid. Think about it when you pose. (1) put a few per line? ② How many rows are there on each floor? ③ How many floors are there? (4) How much is a * * *? What is the volume of this cuboid?

(2) Students' operational thinking and teachers' presentation are as follows.

Total number of rows of cuboids Number of rows per layer

①

②

③

(3) Students answer the results orally, and the teacher writes them on the blackboard in turn in the form.

(4) As mentioned above, volume is the unit number of volume, so "volume" can be used instead of "total number" (the teacher writes "volume" under "total number" on the blackboard).

(5) Think about it, how can we know the total quickly?

2. The teacher shows the cuboid.

Please put this cuboid with that small cube just now, and think about it when you put it. How many do you discharge? How many rows are there on each floor? How many floors are there? How much is a * *? What is the volume of this cuboid? How did you work out the total quickly?

3. Through the above two operations, think: ① What is the relationship between the number of rows and layers and the total number, and guide students to sum up: total number = number of rows × number of layers × number of layers; ② If there are 6 rows in each row and 4 rows and 5 layers in each layer, the volume of a cuboid is how many small cubes it contains. Let the students answer orally, and through the students' hands-on operation, first attract the students, stimulate the senses, enlighten the thinking and improve the interest, which is also the process of guiding the students from image thinking to abstract thinking.

(4), according to the law, inductive formula.

In order to let students actively participate in learning, I guide students to observe the cuboid and discuss the following questions in groups:

① Number of rows

, the number of rows per layer, the number of layers is a cuboid? (Length, Width and Height) ② Through the above experiments, have you found the relationship between the number of units of the volume contained in a cuboid and its length, width and height?

Students express their opinions, give full play to students' subjectivity, and guide students to sum up according to their own answers: total number = length × width × height, cuboid volume = length × width × height.

If "V" is used to represent the volume of a cuboid, "A, B and H" are used to represent the length, width and height of the cuboid respectively. The formula for calculating the volume of a cuboid is expressed in letters and can be written as V=abh. Further, let the students memorize the formula and say the conditions that must be known to find the volume of a cuboid. By guiding students to get the volume formula of cuboid. Ask students to calculate the example 1. Students do it independently and teachers patrol. Through calculation, students can master the cuboid volume formula correctly and skillfully. Finally, complete the example 1.

(5), using the relationship, analogy formula.

Judging whether the teaching is successful or not according to the feedback information. Through timely feedback, correction and effective regulation, students' learning can be improved and the teaching process can be optimized. I designed the following table, asking students to calculate cuboids with their mouths.

Rectangular length (cm), width (cm), height (cm) and volume (cm 3)

①42 1

②432

③444

After the students answer, ask: What are the characteristics of the length, width and height of Cuboid 3? What's the name of this cuboid? How to calculate its volume? Why do you count like this? Students discuss and communicate, and the teacher answers the volume formula of the cube according to the students on the blackboard.

Cubic volume = side length × side length × side length

If V is used to represent the volume of a cube and the letter "A" is used to represent the side length, what should be the formula for finding the volume of the cube? V = a.a.a It can also be written as a3, which is read as the cube of A, that is, three A's are multiplied. Don't mistake а for multiplying by 3. When writing "а3", 3 is written in the upper right corner of A. It should be written smaller, so the cube volume formula is generally written as:

V=а3

This kind of teaching is to strengthen the connection between old and new knowledge, make students feel that new knowledge is not new, new knowledge is not difficult, realize a smooth transition, let students establish confidence in learning new knowledge and solving new problems, let students independently complete Example 2, teachers patrol, pay attention to whether students write "53" correctly, and correct it collectively after answering.

(6) Consolidate exercises and use formulas.

Exercise 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 formulas correctly, I designed multi-level exercises:

1 Ask the students to do the first question on page 33 of the textbook to help them understand the relationship between the volume of a cuboid and its length, width and height, and remember the formula for calculating the volume of a cuboid.

2. Do the second question on page 33, and the students will finish it independently first. This question is to consolidate the knowledge of "cube" just learned, so that students can understand when it can be written into the cube of numbers and how to calculate the cube of numbers. When doing problems, if students are found to have confused the addition and multiplication of three identical numbers, teachers should correct them in time.

3. Complete Exercise 7, Question 1, and let the students use the formula to calculate.

When you finish the seventh question in Exercise 7, pay attention to the operation order of this formula.

5. The teacher shows the matchbox and calculates its volume.

Q: What if there is no quantity in this matchbox? After students measure its length, width and height clearly, let them measure and calculate. This design not only makes students master the calculation method of calculating cuboid, but also helps to cultivate students' practical operation ability.

(7) class summary.

(1) Let the students talk about what they have learned in this lesson.

(2) Teacher's summary.

The purpose of this design is to comprehensively review, sort out and internalize new knowledge, and at the same time cultivate students' ability of induction and summary.

Seven assignments. Exercise 7, question 5.

Attached book design:

Volume calculation of cuboids and cubes

Total number of cuboids = number of rows × number of rows per layer × number of layers

Volume length, width and height

143 1 12

243224

3645 120

Volume of cuboid = length× width× volume of high cube = side length× side length× side length.

V=abhV=a a a

V=a3

Lecture Notes 2 (6) of "Cuboid and Cuboid Volume" in primary school mathematics: usage relation and analogy formula.

Through the previous study, students already know that the cube is a special cuboid, and in the experiment just now, some students put the cube out, so students can easily deduce the cuboid volume formula from the cuboid volume formula. It should be noted that when the formula is expressed in letters, students can make it clear that the product of three A's can also be written as a3, and 3 can be written in the upper right corner of A. ..

(3) Consolidate practice and expand application.

1 Let the students finish the first question "Do" on page 33 of the textbook, and let them do it first. This will help students understand the relationship between the cuboid volume and its length, width and height, and master the calculation formula of cuboid volume.

2. Do the second question "Do" on page 33, consolidate the knowledge of "cube" just learned, and let students know when it can be written into the cube of numbers and how to calculate the cube of numbers. When doing problems, if students are found to have confused the addition and multiplication of three identical numbers, teachers should correct them in time.

3. Complete Exercise 7, Question 1, and let the students use the formula to calculate.

When you finish the seventh question in Exercise 7, pay attention to the operation order of this formula.

5. Take out the cuboid objects prepared before class and calculate the volume at the same table.

Before calculating the volume, students should measure its length, width and height. This design not only enables students to master the calculation method of calculating cuboid, but also helps to cultivate students' practical ability and ability to solve practical problems.

(4) The whole class summarizes, questions and dispels doubts.

(1) Let the students talk about what they have learned in this lesson. Is there a problem?

The purpose of this design is to comprehensively review, sort out and internalize new knowledge, and at the same time cultivate students' ability to summarize and review and reflect.

Primary school mathematics "cuboid and cube volume" lecture 3 teacher:

Hello!

Today, the content of my speech is Volume 10 "Volume Calculation of Cubes and Cubes" in Mathematics for Six-year Primary Schools with Nine-year Compulsory Education. Below I will talk about my ideas from the aspects of teaching materials, learning situation, teaching methods, learning methods, teaching process, blackboard design and so on.

First of all, talk about textbooks.

(A) Teaching content

People's Education Press Nine-year Compulsory Education Six-year Primary School Mathematics Volume 10 Unit 2 Section 3 Volume Calculation of Cuboid and Cube. That is, example 1 on P33 and example 2 on P34 and related exercises.

(B) teaching material analysis and target setting

Cuboid and cube are the most basic three-dimensional figures. It is a leap for students to learn three-dimensional graphics on the basis of knowing some plane graphics. This unit basically understands the characteristics and properties of cuboids and cubes, learns the calculation of surface area, and grasps the concept and common units of volume. In this lesson, we should learn the volume calculation of cuboids and cubes, know the source of the volume formula, and master the meaning and usage of the formula. Volume calculation of cuboids and cubes is the basis of continuing to learn geometry knowledge in the future. According to the analysis of the structure and content of the above textbooks, and taking into account the psychological characteristics of students' existing cognitive structure, I have formulated the following teaching objectives:

① Knowledge objective: To enable students to master the formulas for calculating the volume of cuboids and cubes and learn to calculate the volume of cuboids and cubes.

② Ability goal: to cultivate students' practical operation ability, reasoning ability and ability to solve practical problems with knowledge.

③ Emotional goal: guide students to experiment and deduce the volume calculation formulas of cuboids and cubes. Let students experience the process of exploring knowledge, stimulate students' enthusiasm for exploration, and cultivate students' exploration and challenge. At the same time, the infiltration theory comes from the concept of practice.

(3) Teaching emphases and difficulties.

According to the relationship between cuboid and cube, the key and difficult points should be located in the following aspects:

(1) teaching emphasis: guide students to explore the formation process of cuboids and cubes.

(2) Teaching difficulty: understanding the meaning of the formula.

Second, talk about learning.

Volume is a new concept for students. Before class, students have a preliminary understanding of volume and its units, and have a vague understanding of the volume of objects. In teaching, teachers should pay attention to the cultivation of students' spatial concept, proceed from students' reality, make full use of and create conditions to make students study in a relaxed and happy atmosphere; The interactive multimedia course is used to guide students to enrich their perception of the body by observing, measuring, combining, drawing and making objects and models, so as to cultivate their preliminary spatial concept and abstract generalization ability.

Third, oral teaching methods

Dostoevsky said: A bad teacher gives up the truth, while a good teacher teaches people to discover the truth. According to the requirements of the new curriculum standard, I think I will change my mind, not just impart knowledge, but become a guide, supporter and collaborator of children's life, and strive to create suitable activity environment and learning conditions for them, so that they can actively explore, find problems and sum up the rules themselves. Based on children's cognitive characteristics, the teaching of this course emphasizes entertaining and intuitive images, and adopts heuristic and inquiry teaching methods to let students participate in it and draw their own conclusions.

Fourth, the methods of speaking and learning

1. Inspire students to think independently.

Students are the main body of learning. Only by guiding students to find problems independently, think about problems independently and solve problems independently can we get twice the result with half the effort. For example, on the basis of operation, let students observe and discuss in groups: what are the numbers in each row, row and floor? What is the relationship between the length, width and height of a cuboid and its volume? This is an important way to summarize and understand the formula.

2. Let students learn by solving problems.

Problem is the core of mathematics teaching, and it is also the best motivation to stimulate students' desire to explore. In teaching design, I try to take the mathematical knowledge of "cuboid and cube volume" as the carrier, and make students' mathematical cognitive structure based on their own practical experience and active construction through the inquiry process of students' active participation, finding conclusions and guessing, thus changing students' learning methods and embodying the spirit of curriculum reform.

Fifth, talk about the teaching process.

Teaching preparation

1. Several groups of small cube building blocks operated by students.

2. Self-made courseware.

(B) Teaching process

(1), create scenarios and introduce new lessons.

1. The courseware is shown below. Ask the students to tell what their volume is.

2. Is it ok to measure a larger object as 1 cubic centimeter? Can you use the mathematical knowledge you have learned to calculate?

(2) Interaction between teachers and students to explore new knowledge.

1 experimental exploration

The thinking characteristics of primary school students are mainly image thinking and gradually transition to abstract thinking. According to this feature, students are guided to use intuitive learning tools for intuitive operation and thinking, and the specific operation, thinking and language expression are closely combined. The specific process is:

1) Do the experiment in groups of five and record:

Take 24 small cube building blocks with a ratio of 1 cubic decimeter, and arbitrarily put them together into a cuboid, and then record the numbers in the table.

2) Verify the operation through courseware demonstration and according to the student's record form. Group discussion: What did you find when filling in the form?

2 inductive generalization

1) Study the relationship between numbers.

Discuss in groups: What do you find from these figures?

① Relationship between volume and number of rows, columns and layers.

Cuboid volume = number of rows × number of rows × number of layers

② The relationship between the unit of volume number contained in a cuboid and its length, width and height.

(The cuboid volume is equal to the unit of volume number contained in the cuboid, and the unit of volume number contained in the cuboid is exactly equal to the product of the length, width and height of the rectangle).

2) Summarize the volume formula.

① Guide students to watch the courseware and summarize the cuboid volume formula by themselves.

Cuboid volume = length × width × height V=a×b×h V=abh

[Example 1 explanation. ] Further, let the students memorize the formula and say the conditions that must be known to find the volume of a cuboid. Ask students to calculate the example 1.

② According to the relationship between cuboid and cube, can the formula for calculating cube volume be derived?

Cube volume = side length × side length × side length v = a.a.av = a3 [v = a.a.a], which can also be written as a3, which means three A's are multiplied. Don't mistake а for multiplying by 3. When writing "а3", 3 is written in the upper right corner of A.]

[Example 2. In order to make students have confidence in learning new knowledge and solving new problems, students are asked to complete Example 2, Teachers' Patrol independently.

(3) Feedback practice and practical application.

(1), pile up the wood and calculate the volume.

(2) Let the students finish the first question "Do something" on page 34 of the textbook, and let them act first, which will help to understand the relationship between the cuboid volume and its length, width and height, and remember the calculation formula of cuboid volume.

(3) Do the second question on page 34, and the students will finish it independently first. This question is to consolidate the knowledge of "cube" just learned, so that students can understand when it can be written into the cube of numbers and how to calculate the cube of numbers. When doing problems, if students are found to have confused the addition and multiplication of three identical numbers, teachers should correct them in time.

(3) class summary.

(1) Let the students talk about what they have learned in this lesson.

(2) Teacher's summary.

The purpose of this design is to comprehensively review, sort out and internalize new knowledge, and at the same time cultivate students' ability of induction and summary.

Six, using the blackboard design:

Volume calculation of cuboids and cubes

Cuboid volume = number of rows × number of rows × number of layers

Cuboid volume = length × width × height

V=a×b×h

V=abh

Cubic volume = side length × side length × side length

V=a a a

V=a3

;

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