1. In operation, people realize that the volume of a cuboid is related to its length, width and height.

2. The volume formula of length and cube can be used to calculate the volume of length and cube. And can use the knowledge to solve some practical problems.

3. With the help of students' own hands-on operation, oral expression and dynamic demonstration of courseware, cultivate students' spatial concept.

Teaching focus:

Application of volume formula and its derivation process.

Teaching difficulties:

The derivation process of empirical formula.

Teaching process:

First, compare the size, review and introduce.

1, one to one. Show your schoolbag and pencil box. Q: Who is older? Who is younger?

In fact, what did we compare with them just now? What does volume mean?

2. What is the volume of the picture below? what do you think? (All cubes with side length 1 decimeter)

Summary: To know the volume of an object, we only need to know how many such unit of volume it contains.

3. Show me the eraser. Q: What shape? Does it have volume? What is the volume? Please estimate and guess how big it is.

4. reveal the topic.

Second, hands-on operation, perception and understanding.

1. Take out 1 cubic decimeter 12 cubes, and group them into a cuboid. What are its length, width and height? What is the volume?

2. report and exchange. Q: What are the length, width and height of the cuboid you set? Can you tell me how your group is set up? What is the volume?

Are there any different arrangements? The students are talking when the teacher demonstrates four different arrangements. )

3. Observation and discovery: What did you find by observing these data through the pendulum just now?

4. Collaborate again, and the primary school mathematics teaching plan is "the volume of a cuboid". What is the length, width and height of the cuboid you set? How is it placed?

Third, inspire exploration and build independently.

1. Show me a cuboid with a length of 5 decimeters, a width of 3 decimeters and a height of 2 decimeters.

Q: How many cubes with a side length of 1 decimeter are needed to form such a cuboid? What is the volume of cubic decimeter? Can you swing it with your school tools? (I started activities and found that it was not enough)

Q: What should I do if it is not enough? Can you imagine it in your mind and make it complete? (Start the activity again)

2. report and exchange. And demonstrate the process of pendulum.

Show me a cuboid with a length of 8 cm, a width of 4 cm and a height of 3 cm. Can you play this?

4. Listen to the requirements.

(1) Set yourself a cuboid with a length of 6 cm, a width of 3 cm and a height of 2 cm, and talk about its volume.

(2) Imagine a cuboid 9 meters, 7 meters wide and 4 meters high, and talk about its volume.

5. Think and summarize. What is the relationship between volume and length, width and height? And quickly verify the data on the blackboard.

Fourth, solve the problem and use it to expand.

1, solve the volume of rubber. What do you need to know to ask its volume? The teacher provides measurement data for students to find the volume.

2. Find your own math book.

3. Introduction: Yaguang Carton Factory produces a cubic carton with a side length of 8 decimeters. What is the volume of cubic decimeter?

4. Summarize the volume formula of the cube.

Verb (abbreviation of verb) class summary

The second part of the cuboid volume teaching design [teaching objectives]

1. Explore and master the cuboid volume formula independently in specific situations, and correctly calculate cuboid volume by applying the formula to solve some simple practical problems.

2. Through mathematical activities such as operation, observation, guess and induction, I have experienced the exploration process of volume formula, accumulated the learning experience of three-dimensional graphics, strengthened the concept of space and developed mathematical thinking.

3. Further understand the relationship between mathematics and real life, gain successful learning experience and stimulate the interest in mathematics learning.

[Teaching preparation]

Teachers prepare multimedia courseware made of cuboid model, cuboid packaging box and 1cm3 cube; Each group prepares a cube of 1cm3 and an experimental record sheet.

[Teaching process]

First, create situations and introduce new lessons.

Dialogue: Last class, we already knew the volume and unit of volume. Today, the teacher brought a cuboid made of a small cube of 1cm3 (showing a cuboid model with a length of 4cm, a width of 3cm and a height of 2cm). Do you have any idea how many cubic centimeters this cuboid is?

Clear: To know the volume of an object depends on how many unit of volume it contains.

Demonstration: Calculate cuboid volume according to the length, width and number of small cubes in high school of cuboid model)

Disclaimer: Just now, the teacher's cuboid model was made of a small cube of 1 cubic centimeter, but there are many cuboid or cube objects in life that are inseparable. For example, how can we know the volume of this rectangular box? In this lesson, we will learn the calculation methods of cuboids and cubes. (blackboard writing topic)

Design intention: By calculating the number of cubes contained in a cuboid, let students further understand that finding the volume of an object is finding the number of unit volumes contained in this object. At the same time, some preparations are made for counting the number of small cubes in order. ]

Second, explore the operation and discover the law

Revelation: In the third grade, we learned the rectangular area. Remember how the rectangular area formula was derived?

After the students recall, the computer demonstrates the process of deducing the formula of rectangular area.

Show an orthographic drawing of a cuboid. Discuss: What do you think the cuboid's volume might be related to? How can we study the volume of a cuboid?

Students may think that the volume of a cuboid is related to its length, width and height; A cuboid can be divided into cubes with sides of 1cm, 1cm or 1m, and the unit of volume number contained in the cuboid is its volume.

Dialogue: Does the student's idea make sense? Look at the big screen again. Let's imagine: If the length of a cuboid increases or decreases, what will its volume be like? What will happen to its volume if you change its width or height?

Dialogue: It seems that the students' guesses are really reasonable. In order to study the relationship between cuboid volume and its length, width and height, we need some cuboids as the research objects. Next, let's put some cuboids together.

Clear activity requirements:

(1) Work together at the same table, and use several cubes of 1cm3 to arbitrarily put out four different cuboids and number them.

(2) Observe the length, width and height of the cuboid, the number and volume of small cubes used, and complete the record table.

(3) After filling in the form, check the deskmate data and share your findings.

Students communicate as required, and teachers patrol.

Organizational feedback. The collected data will be reported by name, and taking one of the cuboids as an example, how to check its length, width and height in centimeters is described. How to count the number of cubes, what is the volume of cuboids, and what do you find according to the data in the table? )

Blackboard writing: cuboid volume = length × width × height.

Inspiration: Students arrange cuboids with a small cube of 1cm3, and find that the cuboid volume is equal to the product of its length, width and height. Are all cuboids the product of length, width and height? This needs further verification.

[Design Intention: Guide students to migrate the method of exploring the area of plane graphics to three-dimensional graphics through analogy from the experience of exploring rectangular areas, which is not only conducive to cultivating students' preliminary reasoning ability, but also the guidance of specific learning methods; The operation of placing a cuboid with a small cube of 1cm3 aims to guide students to discover the relationship between cuboid volume and its length, width and height through operation and communication, and to cultivate hands-on operation ability, develop mathematical thinking and understand inductive thinking methods in the process. ]

Third, explore and verify the law again.

Show a cuboid of 4× 1× 1 Say: This is a cuboid with a length of 4cm, a width of 1cm and a height of 1cm. Do you know its volume?

Students may think that this cuboid can be obtained by arranging four small cubes of 1cm3 in a row, and its volume is 4cm3. You can also use "4× 1× 1" to calculate its volume.

Draw the corresponding dividing line on the cuboid according to the students' answers, and confirm that the cuboid's volume is 4cm3. (see figure 1)

Show a cuboid of 4×3× 1 Talk: What are the length, width and height of this cuboid? If you don't use the small cube of 1cm3, can you imagine how many small cubes of 1cm3 are contained in this cuboid? Draw a picture on the cuboid first, and then communicate with your classmates.

Question: What is the volume of this cuboid? what do you think? (Show Figure 2 according to the students' answers)

Clear: In this cuboid, four small cubes of 1cm3 can be placed in one row and three rows along the width direction, then the volume of this cuboid can be calculated by "4×3× 1".

Show a 4×3×2 cuboid. Talk: Let's look at this cuboid again. What are its length, width and height? Can you imagine how many cubes 1cm3 are in this cuboid? Try it yourself first.

Feedback: What is the volume of this cuboid? what do you think? (After the students answer, Figure 3 is displayed.)

Question: If a small cube is used to place the third cuboid, how many cuboids can be placed along a long row? How many lines can you put along the width? How many floors can I put along the height? How to calculate its volume?

Ask again: If there is a cuboid with a length of 5cm, a width of 4cm and a height of 3cm, how many cubes 1cm3 are used to form this cuboid? How many cubic centimeters is its volume?

Guide students to show their thinking process with schematic diagrams.

Design intention: Through the exploration of three cuboids, students are guided to experience the process of "imagination-drawing-reasoning", so that students can clearly understand the relationship between the cuboid volume and the increase of the number of rows and layers of its length, width and height. The fourth cuboid only gives the data of length, width and height, which is intended to encourage students to internalize the pendulum process into an orderly calculation process on the basis of existing intuitive experience. Today, the calculation method of cuboid volume has come to the fore. ]

Fourth, guide the generalization and get the formula.

Question: What do you think is the relationship between the volume of a cuboid and its length, width and height? Is the conjecture we put forward before correct?

The cuboid volume formula is revealed, and it is pointed out that the cuboid volume can be calculated directly with this formula in the future.

Explanation: If V represents the volume of a cuboid, and A, B and H represent the length, width and height of the cuboid respectively, can letters represent the cuboid volume formula?

Blackboard: V=abh.

Talk to your deskmate about what else you know.

Ask students to calculate the number of questions orally and communicate the thinking process when calculating.

Verb (the abbreviation of verb) consolidates practice and expands application.

1, complete "give it a try".

Show me this rectangular box. Speaking: At the beginning of the class, we still didn't know the size of this box. Can it be solved now? What conditions do you need to know to find the volume of this rectangular box? Is there any way to know these data?

Guide measurement, record data and answer independently.

Show me the cube box. This is a cubic box with a length of 12cm. How many cubic centimeters is its volume?

Students organize feedback after completing independently.

2. Complete the question 1 on page 26.

First, let the students tell the length, width, height (or edge length) of each cuboid or cube by looking at the picture, and then calculate their volumes with their mouths, and count how many small cubes of 1cm3 each solid figure consists of.

3. Complete Question 2 of Exercise 6.

Show the questions and let the students read freely.

Question: To calculate the volume of refrigerated trucks, why should we measure them from the inside?

Students complete the calculation independently and organize feedback.

Sixth, the whole class summarizes and combs the learning methods.

Question: What did we learn together today? What did you get from this lesson? Looking back at the learning process of this lesson, how do we explore the volume formula of cuboids?

Seven. classwork

Exercise 6, Question 1.

Teaching Design of Cuboid Volume Part III Teaching Objectives

(1) Understand the meaning of volume.

(2) Know the commonly used unit of volume: cubic meter, cubic decimeter and cubic centimeter.

(3) Can correctly distinguish the difference between length units, area units and unit of volume.

Process and method

(1) Understand the meaning of volume through observation experiments.

(2) Perceive the size of unit volume in combination with things in life.

Emotional attitudes and values

(1) Develop students' spatial concept and cultivate their thinking ability.

(2) dialectical materialism permeated with the universal connection of things.

Teaching focus

Let the students feel the volume of the object, and initially establish the concepts of 1 cubic meter, 1 cubic decimeter and 1 cubic centimeter.

Teaching difficulties

Help students to establish the representation of the volume of 1 m3, 1 decimeter cubic and 1 cm cubic, and we can correctly estimate the volume of common objects with unit of volume.

training/teaching aid

Teacher's preparation: Fill it in red.

A big glass of water, a big stone, a pile of sand tied with a rope; A projector and a wooden shelf of 1 m3; A cube with a volume of 1 cubic decimeter and a cube with a volume of 1 cubic centimeter. Students prepare: 12 cubic learning tools 1 cubic centimeter.

teaching process

First, reveal the topic.

We studied cuboids and cubes and mastered the calculation method of their surface areas. In this lesson, we will continue to learn and study some knowledge about cuboids and cubes.

Second, exploration and research.

1. Experimental observation

Observation (1): What happens to the water level when a stone is put into a glass filled with red water? Why is this?

Observation (2): This cup is full of fine sand. Now pour out the fine sand and put it aside. Take a piece of wood and put it back in the cup. What did you find? Why?

Observation (3): In (1), stones are replaced by smaller stones. What did you observe? Why?

Photo observation: projection shows the matchbox, toolbox and cement board in the textbook. Which object takes up more space?

Conclusion: The size of the space occupied by an object is called the volume of the object. (Title of blackboard writing: Volume)

Deepen understanding:

(1) Do you know what a cuboid and a cube are?

(2) Can you tell which objects around you are bigger? Which objects are smaller?

(3) Do it on page 30.

2. The teaching unit of volume.

(1) was introduced to unit of volume.

Commonly used unit of volume are: cubic meter, cubic decimeter and cubic centimeter.

(2) What are the volumes of 1 m3, 1 m3 and1cm3 respectively?

1 cm3:

Ask the students to take out a small cube of 1 cubic centimeter and measure its side length.

Look around us. The volume is about 1 cm3.

1 decimeter: Show me a cube with the length of 1 decimeter. Do you know its volume? What objects in our life have a volume of about 1 cubic decimeter?

1 m3: Show the wooden frame of 1 m3, and let the students come up and see the size of 1 m3. In our life, which objects have a volume of about 1 m3?

(3) Establish the representation and perceive the size

Show the second question on page 36 by projection and ask the students to answer it orally.

3. The connection and difference between length unit, area unit and unit of volume.

The projection shows the first question "Do it" on page 365438 +0. Let the students say it.

Third, classroom practice.

1, do the 1 problem in Exercise 7, and ask the students to take out the prepared 12 cubes, and put them away first.

2. Do the third question in Exercise 7, and the students will correct it collectively after doing it independently.

Fourth, class summary.

Students summarize what they have learned today.

Teaching Design of Cuboid Volume Part IV Teaching Content:

Page 29-30 of Volume 10 of Mathematics published by People's Education Press and corresponding exercises.

Teaching purpose:

1. Explore the formula of cuboid volume through experiments, and apply the formula to solve the corresponding practical problems.

2. Let students experience the derivation process of cuboid volume formula and understand the volume calculation formula.

3. Cultivate students' spelling ability, observation and inductive reasoning ability.

Teaching focus:

Derivation process and application of volume formula.

Teaching difficulties:

The derivation process of volume formula (the relationship between the number of rows, the number of rows and the number of layers and the length, width and height of a rectangle).

Teaching preparation:

Students are divided into two groups, and each group prepares some small cubes and exercise sheets.

Teaching process:

First, direct import

Teacher: Earlier, we studied the commonly used unit of volume. Today we will discuss the solution of cuboid volume.

Blackboard: the volume of a cuboid.

Second, guess and tell the direction of students' exploration

1, courseware demonstration: a cuboid. Teacher: Is there any way to know the volume of this cuboid?

2. Courseware demonstration: cut the cuboid into small cubes and count the number of rows, columns and layers; And the number of rows × the number of rows × the number of layers = the total number (that is, the number of volumes).

3. Department:

(1) Can the method of counting small cubes solve all cuboid volume problems? It seems necessary to get a formula for calculating the volume of a cuboid.

(2) Guess what the cuboid volume may be related to?

4, courseware demonstration, let students understand that the volume of a cuboid is related to its length, width and height.

Thirdly, explore the derivation process of volume formula.

1, Teacher: Next, we will explore the relationship between the cuboid volume and its length, width and height by spelling a small cube.

2, deskmate cooperation: courseware demonstration: cooperation requirements:

(1) simultaneous reading requirements.

(2) first place, then observe, and finally fill in the form.

3. Students begin to operate, and teachers patrol for guidance.

4, the whole class communication:

(1) The team reports the results.

(2) Observe the table and think: What did you find? Talk to your deskmate first.

(3) The whole class found that.

(4) The teacher added the question: What is the relationship between the number of rows, rows and layers and the cuboid? What is the relationship between them?

According to the students' answers, observe a group of cuboids and understand the corresponding relationship between the number of rows, columns and layers and their length, width and height. Draw a few more students to talk about their relationship.

5. Teacher: Can you deduce the formula for calculating the volume of a cuboid? The students answered, and the teacher wrote on the blackboard at the right time: cuboid volume = length × width × height; V=abh .

6. Review the deduction process just now and communicate with each other at the same table.

7. Practice in time: Show a rectangular pencil case.

Teacher: What are the requirements for the size of this rectangular pencil case? The teacher gives the length, width and height, and the students calculate and emphasize the writing format.

Fourth, classroom exercises.

1, fill in the form orally (see list).

2. Judges:

(1) Two cuboids with the same volume must have the same length, width and height. ()

(2) When the length, width and height of a cuboid are doubled, its volume is also doubled. ()

3, the construction site to dig a 50 meters long, 30 meters wide, 50 cm deep cuboid pit, a * * * to dig out how many square meters of soil? (This project 1m3 soil, sand, stone, etc. Abbreviated as "1m3").

Test you: How many cubic centimeters is the cuboid below? (The side length of the small cube is 1cm) (see the questionnaire).

Fifth, summarize the class.

What did you gain from your study? (in terms of methods and knowledge) blackboard writing: the volume of a cuboid The number of units contained in a cuboid = number of rows × number of rows × number of layers; Cuboid volume = length× width× height; V=abh .

Reflection after class:

1, the key point of the derivation process is not prominent enough, that is, the relationship between the number of rows, the number of rows, the number of layers and the length, width and height of a cuboid is not understood enough, so students should talk more and demonstrate it through courseware.

2. The teacher's language is not accurate and refined, and the mathematical questions raised can be more accurate and directional, which is not reasonable enough to guide key places.

3. It should be written on the blackboard: 1 m3 = 1 m3. Strengthen students' understanding of the relationship between the two units.

4. The schedule of this class is similar, much more reasonable than the last class, basically completed according to the scheduled time, which is what I am most satisfied with this class.