Finding the Volume of Irregular Objects Lesson Notes

As an unknown and selfless educator, I often have to write lecture notes according to teaching needs. With the help of lecture notes, teaching efficiency can be effectively improved. So have you ever read the lecture notes? The following is a textbook on finding the volume of irregular objects that I carefully compiled (selected 5 articles). It is for reference only. Let’s take a look. Lecture Notes on Finding the Volume of Irregular Objects 1

1. Teaching Materials

Textbook Analysis:

Cuboids and cubes are the most basic three-dimensional figures. After understanding Learning three-dimensional graphics on the basis of some flat graphics is a leap in students' understanding. Although students have been exposed to cuboids and cubes before, they only have an intuitive understanding of them, and it is still difficult to rise to a rational understanding. In the first few lessons of this unit, we have learned about the characteristics of cuboids and cubes, and learned the calculation of surface area. In this lesson, we need to master the concept of volume and commonly used volume units, learn the volume calculation of cuboids and cubes, and master the meaning and usage of formulas. This is the basis for learning the unit rate of volume in the next step, and it is also the basis for learning volume in the future. Therefore, you must be proficient in calculating the volume of cuboids and cubes.

Teaching objectives:

1. Combined with specific operations, guide students to explore and master the calculation formulas for the volume of cuboids and cubes, and be able to skillfully use the formulas to solve some practical problems.

2. Through exploration activities, cultivate students’ analysis and generalization abilities and develop students’ spatial concepts.

3. Cultivate students’ application awareness of mathematics.

Key points: Master the calculation methods of the volume of cuboids and cubes, and use formulas to solve practical problems.

Difficulty: Understand the meaning of the volume formula.

2. Preaching method

Learning situation analysis

Students are the main body of learning. Deep in the hearts of children, there is a deep-rooted need, which is They hope to be a discoverer, researcher, and explorer, and their curiosity prompts them to try everything by themselves. Their thinking characteristics generally start with perceptual knowledge, then form representations, and then rise to rational knowledge through a series of thinking activities. Therefore, it is necessary to guide students to discover, think about and solve problems independently through their own exploration and practice, so that they can truly understand the content they have learned and then internalize it as their own, so that teaching can achieve twice the result with half the effort.

Teaching method: students make it manually, and cooperate with multimedia courseware demonstration.

3. Talking about the program

This part of the content is taught in 3 lessons. The first lesson teaches the concept of volume and commonly used volume units; the second lesson teaches the calculation methods of the volume of cuboids and cubes. In the third lesson, comprehensive application is carried out to improve students' ability to use the knowledge they have learned to solve practical problems.

(1) Passionately attracts interest and reveals the subject.

Any new knowledge is based on the original knowledge system, so during the review I designed the following content to pave the way for the new lesson.

1. What is volume? What are the commonly used units of volume? Use hand gestures or other methods to describe how big 1 cubic centimeter, 1 cubic decimeter, and 1 cubic meter are.

2. The multimedia courseware shows a cuboid and a cube, and uses animation to cut them into small cubes with an edge length of 1 cm. Ask students to tell them what their volumes are? How to know. From this, students can realize that a cuboid and a cube are composed of how many small cubes with an edge length of 1 cm, and its volume is how many cubic centimeters.

At this time, students will have questions: Most of the problems encountered in life in calculating the volume of a rectangular cube cannot be counted by cutting it. This method does not work in real life, so what should we do? This creates an undecided state in the students' minds. On the one hand, it naturally leads to the "volume calculation of cuboids and cubes" to be learned in this lesson. On the other hand, it also arouses students' strong desire to explore new knowledge.

(2) Use imagination and explore formulas.

The thinking characteristics of primary school students are mainly image thinking and gradually transition to abstract thinking.

According to this characteristic, intuitive learning tools are first used to guide students to conduct experimental operations. First, they attract students, stimulate their senses, enlighten their thinking, increase their interest, establish clear images in their minds, enrich their perceptual knowledge, and also guide students' thinking step by step. From image to abstraction.

The specific process is:

(1) Let students work in groups to place a cuboid with a small cube with an edge length of 1 cm, and record the length and width in the table while arranging it. , height and volume

(2) Reporting and communication, students demonstrate and explain on the projection of things, and the teacher writes on the blackboard in turn.

(3) Ask students to observe the relationship between the length, width, and height of the rectangular parallelepiped and its volume?

Here we need to give full play to the subjectivity of the students, give them sufficient discussion time, and give them the opportunity to express their opinions. Then based on the students’ answers, we can finally conclude: Volume of the cuboid = length ×width×height.

(4) Use letters to express formulas, and pay attention to the guidance of writing forms.

(5) Complete Example 1, apply what you have learned, and deepen your understanding.

(6) Use relationships and analogy formulas

Through the previous studies, students have already known that the cube is a special rectangular parallelepiped, and in the experimental operation just now, some students also laid out the cube , so students can easily derive the volume formula of the cube from the volume formula of the cuboid. It should be noted that when using letters to express formulas, students should be clear that the multiplication of three a can also be written as a3, and 3 is written in the upper right corner of a.

(3) Consolidate practice and expand application

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 To help students understand and use formulas correctly, I designed multi-level exercises:

1. By asking students to complete the first question of "Do it" on page 33 of the textbook, let the students take action first. Operation, this will help students understand the relationship between the volume of a cuboid and its length, width, and height, and master the formula for calculating the volume of a cuboid.

2. Do the second question of "Do it" on page 33 to consolidate the knowledge of "cubic" you just learned and make students understand under what circumstances they can write the cube of a number. How to calculate a number cubed. When doing a problem, if it is found that a student confuses the continuous addition and continuous multiplication of three identical numbers, the teacher should correct them promptly.

3. Complete Question 1 of Exercise 7 and ask students to use formulas to calculate.

4. Complete Question 7 of Exercise 7, and pay attention to the order of operations of the formula in this question.

5. Take out the rectangular objects prepared before class, and work together with your deskmates to calculate their volumes.

Students clearly need to measure the length, width and height before calculating the volume. This design can not only enable students to deepen their mastery of calculation methods for calculating cuboids, but also help cultivate students' hands-on operations and ability to solve practical problems.

(4) Summarize the whole lesson and answer any questions.

Ask students to talk about what they learned in this class? Any questions. This design aims to conduct a comprehensive review, sorting out and internalization process of new knowledge, and at the same time cultivate students' ability to summarize and the habit of review and reflection. Lesson Notes on Finding the Volume of Irregular Objects 2

1. Teaching Materials

1. Brief Analysis of Teaching Materials

First, let’s talk about the content of this lesson. Cone is the content of the last unit of elementary school geometry. It is a new three-dimensional figure that students learn on the basis of plane figures and three three-dimensional figures: cuboid, cube and cylinder. (Play courseware) The volume of a cone is also an extension of the volume of cuboids, cubes and cylinders learned, and also lays the foundation for students to systematically learn solid geometry in the future. (Play the volume formula courseware)

2. Analysis of academic situation

Through the study of the previous few lessons, students have a clear understanding of the basic characteristics of cylinders and cones and the names of each part. Understand, know the calculation method of cylinder volume, and be able to use the calculation formula of cylinder volume to solve specific problems, and have experienced the derivation process of cylinder volume calculation method, and have a preliminary sense of analogy thinking.

The vast majority of students have relatively strong hands-on practical abilities, but their spatial imagination needs further training due to their age characteristics.

3. Teaching objectives

Based on the above, I have formulated the teaching objectives of this lesson:

Knowledge and skill objectives: Understand and master the conical volume formula The derivation process, learn to use the cone volume calculation formula to find the volume of the cone;

Process and method goals: be able to solve some practical problems related to cones, and enhance students' practical ability through derivation experiments of the cone volume formula and observation and comparison ability;

Emotional and value goals: Through experiments, guide students to explore the inner connection of knowledge, penetrate and transform ideas, and cultivate team spirit of communication and cooperation.

4. Key and difficult points in teaching

Based on students’ academic situation and teaching objectives, I have established the following key and difficult points in teaching.

Teaching focus: be able to correctly use the volume calculation formula of a cone to find the volume of a cone.

Teaching difficulty: Understand the derivation process of the cone volume formula.

5. Preparation of teaching aids and learning aids

Multimedia teaching software, hollow cylinders, conical containers, and buckets filled with water.

2. Preaching Method

The "Mathematics Curriculum Standards" clearly point out that teachers should stimulate students' enthusiasm for learning, provide students with opportunities to fully engage in mathematical activities, and help them explore independently In the process of cooperation and communication, we can truly understand and master basic mathematical knowledge and skills, ideas and methods, and gain extensive experience in mathematical activities. In this class, I mainly use the guided discovery method and experimental operation method, and also use multimedia and other teaching methods to increase the teaching capacity and improve the teaching quality.

Polya said: "The best way to learn any knowledge is to discover it yourself, because this kind of discovery has the deepest understanding and is the easiest to grasp the inner laws, properties and connections." Therefore. , the experiment I designed in the classroom allows students to operate and derive the volume formula of a cone, which helps develop students' spatial concepts and cultivate observation, thinking and hands-on abilities.

3. Learning method

There is a very good saying: "Everyone learns valuable mathematics, and everyone can obtain the necessary mathematics. Different people gain in mathematics." "Different development" is the basic concept of mathematics curriculum in the new century. The new curriculum standards also emphasize guiding students to actively participate, practice in person, think independently, and explore cooperatively. Therefore, while I pay attention to teaching methods, I pay more attention to the guidance of students' learning methods.

1. Experimental transformation method

Some knowledge cannot be truly understood by students through explanation alone. Only through experiments and repeated operations can the inner mysteries be deeply understood. When guiding students to perform experimental operations, I focus on three aspects: first, let students prepare for the operation; second, tell them the methods and steps of the operation and what to pay attention to; third, guide students to compare and discover during the operation. ,Summarize. In this way, the volume formula of a cone is deduced through experimental operations, which cultivates students' abilities of observation and comparison, communication and cooperation, and generalization.

2. Try the practice method

Suhomlinsky believes: "The joy of success is a huge emotional power, which can promote children's desire to learn well." This book When teaching examples in each class, let students try to answer their own independent questions, tap students' potential, let them experience the joy of successful learning, mobilize students' enthusiasm and initiative in learning, give full play to students' main role, and develop good study habits.

4. Teaching procedures

I have designed the following six teaching procedures for this lesson:

1. Review old knowledge and prepare the ground.

Use to review the understanding of cylinders and cones and the derivation and application of the volume formula of a cylinder to pave the way for the transfer of new knowledge. By introducing the new from the old, students can not only feel the connection between cones and cylinders, but also experience the intimacy of new knowledge, thus creating a desire to learn new knowledge.

2. The conversation is exciting and introduces new lessons.

Many students like to eat ice cream. Look, what is the shape of an ice cream cone? Have you ever wondered how much ice cream can fit in a cone? (Blackboard writing topic) How to find its volume? Can we convert it into the volume of the shapes we have already learned? What graphics is most suitable to convert it into? Guess what? Let's discuss this issue below. (Chat through a series of questions to stimulate interest and activate the atmosphere to introduce topics)

3. Experimental operations to explore new knowledge.

This link is divided into three steps.

Step One: Experimental Operation

Through the conversation just now, students are eager to confirm their conjectures through experiments, so they are full of interest in learning, highly focused, and actively engaged in experiments middle.

1. I am going to create a cylinder and a conical container. First let the students observe the relationship between the two objects and guide them to tell the equal bases and equal heights. (In this process, I will take two containers to the students so that they can not only see but also touch them, so that they can more intuitively feel the equal bases and equal heights.)

　2. Interest in questioning< /p>

I will ask a question: Students, if you fill the cone with water and then put it into the cylinder, how many times can the cylinder be filled with water? (Let students make bold guesses based on their own cognition)

3. Hands-on operations, experiments to gain true knowledge

Do experiments with questions and guesses. Invite two groups of students to operate, and other students to help them record. The result of the experiment is that it can be filled three times. (Play the courseware to demonstrate the experimental process)

4. Question repeatedly and solve it experimentally

Do all cones fill the cylinder exactly three times? (Strengthen the understanding of equal bases and equal heights, and discuss in groups to express their opinions) Now take a smaller conical container and continue the experiment. Experiments have shown that only cones with equal bases and equal heights need to be filled with water and poured into the cylinder three times.

Step 2: Derivation of the formula

1. Discussion: What is the relationship between the volume of the cone and the volume of the cylinder? Let students fully communicate. Finally, we reached the realization that the volume of a cylinder is three times the volume of a cone with equal base and equal height, that is, the volume of a cone is the volume of a cylinder with equal base and equal height. At this time, I used multimedia to demonstrate the decomposition of the volume of water in a cylindrical container, once again confirming the accuracy of the students' own opinions.

2. How to calculate the volume of a cone? What is the calculation formula? According to the students’ answers, write on the blackboard: (show courseware) V cone = 1/3 SH This step rises from perceptual knowledge to rational knowledge, further understands and consolidates new knowledge, cultivates students’ rigorous logical thinking ability, and the orderliness and accuracy of language expression. Highlight the key points of teaching.

4. Try to practice and consolidate and improve.

For the above two questions, nominate students to write down the problem-solving process on the blackboard and revise collectively. The new knowledge discovered is applied in practice in a timely manner, and teachers receive teaching information feedback to adjust teaching content. Students experience the joy of "recreation" and "success", further stimulating their learning autonomy.

5. Expand, deepen, and comprehensively apply

There is a sand pile that is similar to a cone on the construction site. Can you figure out its volume? Discuss methods of measurement and calculation.

The exercise design starts from basic questions, transitions to variant questions, develops to comprehensive questions, and extends to thinking questions, which is in line with the teaching principle of starting from the shallower to the deeper and step by step. During the practice process, students' problem-solving abilities and skills are trained, and their ability to use the knowledge they have learned to solve practical problems is trained.

6. Evaluation, reflection, and self-improvement

At the end of the class, I guided the students through chatting to sort out the knowledge points of the lesson through reflection and evaluation, forming a systematic knowledge structure, and further consolidating the lesson. Lesson teaching content. Here's what I talked about.

①What did you learn in this class? Questions are used here to guide students to review and summarize the knowledge content and learning methods they have learned, which can strengthen the understanding and memory of knowledge and promote students to master the learning methods.

②What do you have to say to yourself and others? Allowing students to evaluate their own and others' learning processes and learning effects can strengthen their self-confidence, self-reliance, and self-improvement, and stimulate the inner motivation for independent development.

③Assign homework: related exercises for exercise four.

Appropriate amount of homework can provide timely feedback on students' learning status and cultivate students' good study habits and qualities.

5. Design of blackboard writing

Based on the key and difficult points of this course and the cognitive characteristics of students, I designed a simple, clear and intuitive blackboard writing. This kind of blackboard design reflects the formation process of new knowledge, and also shows specific problem-solving methods, highlighting the teaching focus and being intuitive.

6. Reflection on teaching

1. Learn mathematics in connection with life. During teaching, I deeply realize that in order for students to learn mathematics well, they must understand that mathematics comes from life and is ultimately applied to life. If we want students to love mathematics, we must first let them love life. This requires us to prepare lessons It is not limited to teaching materials, but should be combined with real life to prepare lessons. 2. Teachers must dare to give students a lot of time and space, so that students can go through the whole process of "discovering problems - making bold guesses - experimental verification - solving problems", so that students can Their talents and wisdom are put to full use, and the concept of students as the main body is throughout, giving full play to students' autonomy to generate and construct their own knowledge system.

3. The problem reported by students after class is that the calculation problem is huge. The formulas can be used but there are problems with calculation. In the future, students’ calculation skills should be trained more.

(For the first two points, I briefly summarized my theoretical support and design ideas for this lesson. The third point is the problems reported by students after class.) My design for this lesson reflects the core of mathematics. Literacy includes number sense, spatial concept, geometric intuition, data analysis, computing ability and reasoning ability. In preliminary research, the effect remains to be seen. Finding the Volume of Irregular Objects Lesson 3

Teaching objectives:

1. Be able to identify the remaining seven directions, and use these words to describe the location of the object, and experience mathematics and reality. close connection with life.

2. Understand angles intuitively, be able to identify right angles, acute angles and obtuse angles and be able to correctly count the number of angles.

Teaching focus:

Understand angles intuitively, be able to identify right angles, acute angles and obtuse angles and correctly count the number of angles

Teaching difficulties: < /p>

Cultivate students’ observation ability and practical ability, develop students’ spatial imagination ability, and infiltrate ideological education in a timely manner.

Teaching process:

1. What did you learn?

The purpose of this column is to allow students to review and organize the knowledge they have learned. This activity helps cultivate students' active learning spirit and better master relevant knowledge. These two pictures are a reminder of the knowledge students have learned. The picture on the left is about knowledge about understanding graphics, and the picture on the right can use the data presented to practice addition and subtraction. Teachers can use this picture to guide students to talk about what they think of, and encourage students to ask questions and solve them.

2. My Growth Footprints

The purpose of this column is to allow students to review their experiences and progress in the learning process. It reflects the method of student growth recording advocated in the mathematics curriculum standards for full-time compulsory education and is a reflection of students’ self-development. A way of assessment. The textbook raises three aspects of questions, which is a step higher than the sorting and review (1). Students can show their most satisfactory work, organize students to display and communicate in different ways, and provide appropriate guidance

Review points: plane graphics

1. Fill in the number table Supplementary comments:

Acute angle () Right angle () Obtuse angle ()

Independent completion

Method of communicating numbers

2. Folding Fold and cut to answer the question

After cutting off one corner of a square piece of paper along a straight line, what is the remaining part of the polygon? How many corners does it have? What are the corners?

Let students practice it. Because there are different cutting methods, there are different answers:

(1) Three sides, three angles, one right angle and two acute angles; < /p>

(2) Four sides, four angles, two right angles, one acute angle, and one obtuse angle;

(3) Five sides, five angles, three right angles, and two obtuse angles .

Lesson Notes on Finding the Volume of Irregular Objects 4

Activity objectives:

1. Through operations, perceive the relationship between cubes and plane figures, and understand the characteristics of cubes.

2. Be able to use your brain to design and produce teaching aids.

Activity preparation:

1. A number of square building blocks and a number of white and colored square papers of the same size.

2. Make several plane graphics and cube inserts for the gift box.

3. Glue and colored pens.

Activity process:

1. Group operations to perceive the characteristics of the cube

Group 1: Make gift boxes. Use graphic paper with 6 squares of the same size drawn on it and use your hands and brain to make a gift box.

The second group: Make math corner teaching aids. "Count how many square faces this building block has of the same size. Take such a square piece of paper and write a number or symbol (+, one, ×) on each square piece of paper. Write the sticker. On every facet of the building blocks for mathematical teaching games.”

Group 3: Make the building blocks beautiful. "These building blocks are old. Can you count how many faces they have and what shape and size they have?" "Please use colored paper of the same size and shape to stick the building blocks together."

Four groups: insert building blocks. Use the insert to insert a cube. 2. The teacher guides the children to introduce their own small productions

(1) "What is the shape of the gift box? Count how many sides it has, what is its size? What shape is it? "

(2) "What is the shape of the teaching aids you made for the math corner? How many shapes and sizes does it have? "How many numbers are there on each side?" Can you put the toys together to give the children an arithmetic problem?"

(3) "These colorful building blocks are so beautiful! Count how many shapes and sizes are used for one building block? What kind of paper is it made of? Stack the blocks together."

(4) "With so many blocks, what shape are they in? How many inserts are needed to insert one block? ? Are the inserts the same size? How many building blocks are there? Can you use these building blocks to build a large cube? "Design instructions for finding the volume of irregular objects.

Cultivating students’ spatial concepts is somewhat difficult for first-year students. This is a step-by-step process. Based on this, the design of this lesson mainly focuses on the following two aspects:

1. Hands-on operation to stimulate students' strong interest in learning.

In the review, sufficient learning tools are prepared for students, and group learning is used to allow students to operate, discuss and communicate. Through independent inquiry, cooperation and communication in group learning, we can truly achieve the purpose of fully mobilizing each student's learning enthusiasm and learning autonomy.

2. Cultivate students’ preliminary spatial concepts.

The formation of students' preliminary spatial concepts must not only be achieved through regular teaching, but also allow students to have more opportunities for hands-on operations. Therefore, in teaching, we focus on allowing students to draw and spell by themselves, and organically combine students' vision, hearing, touch, and thinking. This can better implement the teaching objectives.

Preparation before class

Teacher preparation

PPT courseware, various graphic models

Student preparation

Various graphic models and jigsaw puzzle learning tools

Teaching process

⊙Situation introduction, highlighting topics

1. Situation creation: The courseware presents the jigsaw puzzle pieces Beautiful pattern.

Teacher: Students, are these patterns beautiful? What plane graphics have we learned here?

(1) Student report and exchange.

(2) Teacher’s supplement: In addition to these graphics, what other graphics have we learned?

2. Identify the topic.

Teacher: Today, we will continue to review the related knowledge of graphics and geometry.

(Blackboard writing: graphics and geometry)

Design intention: through intuitive presentation, stimulate students' interest in learning, allow students to review the knowledge they have learned, and quickly enter the learning state.

⊙Teachers and students cooperate to review and organize

1. Characteristics of plane graphics.

(1) The courseware presents multiple chaotically arranged plane graphics, allowing students to classify these graphics based on their existing knowledge.

(2) Communication within the group: How do you distinguish rectangles? What have we learned about rectangles?

(3) Answer by name: What are the characteristics of a square?

(4) Discussion: What is the difference between a parallelogram, a rectangle and a square?

(5) Let’s talk about how many sides a triangle has.

(6) Let’s talk about the difference between the circle and the above plane figures.

2. The combination of graphics.

(1) Fight hard.

① What shape can be formed by using two identical triangles? After the students have finished spelling, ask them to talk about what shapes they spelled out and how they were spelled out.

②What shape can be made with 4 identical squares? After the students have finished spelling, ask them to talk about what shapes they spelled out and how they were spelled out.

(2) Design pattern.

① Please use the tangram puzzle to design a pattern.

②Report and presentation: Let students present on stage and talk about their design ideas.

3. One point. (The courseware presents 20 graphics from question 3 on page 94 of the textbook)

(1) Let students answer what graphics they are.

(2) After the students answer, the teacher asks the students to talk: What do you think? Especially after students say that the 11th, 15th, and 17th figures are parallelograms, teachers should emphasize asking students to say: What do you think?

(3) Teacher’s question: We have just figured out what each figure is, so how many figures are there in each type?

Design intention: Through review activities, students can consolidate their understanding of plane graphics, further feel the characteristics of plane graphics and their relationships, accumulate experience in mathematics teaching activities, enhance their interest in learning, and develop students' creativity. Strength, and at the same time pay attention to cultivating students' listening and communication abilities in mutual discussions.