Judging from the teaching situation of grade six, most students in the class can keep up with the existing progress. Through this lesson, we can flexibly use the calculation method of cylindrical volume to solve some simple problems in life, understand the derivation process of cylindrical volume formula, and master the calculation formula through imagination and operation. The formula will be used to calculate the volume of the cylinder.
Teaching objectives:
1. By cutting the cylinder and assembling it into an approximate cuboid, the volume formula of the cylinder is derived, which permeates and transforms ideas to students.
2. Develop students' analytical reasoning ability by deducing the formula of cylinder volume.
3. Understand the derivation process of cylinder volume formula and master the calculation formula; The formula will be used to calculate the volume of the cylinder.
Teaching focus:
Calculation of cylinder volume
Teaching difficulties:
Derivation of cylinder volume formula
Teaching tools:
Cylindrical learning tool,
Teaching process:
First, review and introduce new ideas.
1. Find the area of each circle below (answer).
( 1)r = 1cm； (2)d=4 decimeters; (3)C=6.28 meters.
Find a solution to the problem.
2. Question: What is volume? What are the commonly used unit of volume?
3. Given the bottom area S and height H of a cuboid, how to calculate its volume? (blackboard writing: cuboid volume = bottom area × height)
Second, explore new knowledge.
1, according to the learned concept of volume, talk about what is the volume of a cylinder. (blackboard writing topic)
2. Formula derivation. (Conditional can be grouped)
(1) Please indicate the bottom area and height of the cylinder.
(2) Review the derivation of the formula of circular area. (cut and transform)
3. Review the derivation of the area formula of a circle, what is the inspiration?
Answer: Convert a cylinder into a cuboid to calculate the volume.
4. Hands-on operation.
Ask two students to bring teaching AIDS to the stage to demonstrate and explain at the same time.
Divide the bottom of the cylinder into 16 parts, cut it and put it into an approximate cuboid.
Ask several groups of students to come to the stage to explain and improve the language.
Q: Why use the word "approximate"?
5. Teacher's demonstration.
Combine cylinders into an approximate cuboid.
6. If the bottom of a cylinder is divided into 32 parts and 64 parts ... what will happen to the object after cutting?
Answer: The spliced object is getting closer and closer to the cuboid.
Q: Why?
Answer: The more average copies, the smaller each copy, the shorter the arc, and the more approximate the length of the assembled cuboid to a line segment, so that the whole shape is more similar to a cuboid.
Just now we cut the cylinder into an approximate cuboid by hands-on operation.
Teacher: What is the connection between the assembled cuboid and the original cylinder? Please communicate with your classmates?
Show me the discussion questions.
(1) What is the relationship between the bottom area of the spliced cuboid and the bottom area of the original cylinder? Why are they equal?
(2) What is the relationship between the height of the spliced cuboid and the height of the original cylinder? Why are they equal?
(3) What is the relationship between the volume of the spliced cuboid and the volume of the original cylinder? Why?
Blackboard writing:
A cuboid has a high volume and a high bottom area.
The bottom area of the cylindrical volume is higher.
8. According to the above experiments and discussions, think about how to find the volume of a cylinder.
Answer: cut the cylinder into an approximate cuboid. The bottom area of a cuboid is equal to that of a cylinder, and the height of the cuboid is higher than that of the cylinder. Because the volume of a cuboid = bottom area × height, and the volume of a cylinder = bottom area × height.
9. How to express it in letters?
V=sh
10, summary.
How is the volume of a cylinder derived? What conditions must be known to calculate the volume of a cylinder?
1 1, teach a math course.
Examine the questions. Question: Can you finish this problem by yourself? Assign one student to perform on the blackboard, and the rest of the students to perform in the exercise books. Collective modification: what is the basis of presentation? What problems should we pay attention to? The end result is unit of volume)
12, teach "give it a try"
Summary: To require the volume of a cylinder, you must know the bottom area and height. If you don't know the bottom area and only know the radius r, how can you find the volume of a cylinder? What if we know d? Do you know C. If we know R, D and C, we must first find the bottom area and then the volume.
Third, consolidate the practice.
The exercises in the "exercises" after class.
Fourth, class summary.
What did you learn in this class? How to calculate the volume of a cylinder and how to get this formula? It is pointed out that in this lesson, we cut the cylinder into a cuboid by transformation, and (write on the blackboard under the topic: Cylinder becomes a cuboid) we get the formula for calculating the volume of the cylinder V=Sh.
Teaching design and thinking of cylinder volume (2) learning objectives
1, explore and master the volume calculation formula of cylinder.
2, can use the formula to calculate the volume of the cylinder, and solve practical problems.
learning process
First, the blackboard writing topic
Teacher: Students, today we are going to learn the volume of a cylinder.
Second, indicate the goal.
The goal of our class is: (show)
1, explore and master the volume calculation formula of cylinder.
2, can use the formula to calculate the volume of the cylinder, and solve practical problems.
Please read this book carefully in order to achieve your goal.
Third, show self-study guidance.
Read carefully the contents of Example 5 and Example 6 from page 19 to page 20 of the textbook, focusing on the derivation process of cylindrical volume formula and the problem-solving process of Example 6, and think:
How is the volume formula of 1 and cylinder derived?
2. What is the formula for calculating the volume of a cylinder? How to express it in letters?
After 5 minutes, let's see who can do the right test!
Teacher: read carefully and teach yourself. Compared with the person who studies most seriously, self-study has the best effect. Let's start the self-study contest.
Fourth, learn first.
(1) Reading
Students read carefully, teachers patrol and urge everyone to read carefully.
(2) Test (find two students to perform on the blackboard and write the rest in the exercise book)
20 pages of "doing" and 2 1 page of question 5.
Requirements: 1. Observe carefully, write correctly, and write out every step.
2. Students who have finished writing carefully check.
Post-education of verb (abbreviation of verb)
(1) correction
Teacher: If you have finished, please raise your hand. Next, please look at these questions on the blackboard together. Please raise your hand if you find any problems. (From poor to medium to good)
(2) Discussion
1. Look at the question 1: Please raise your hand if you think the formula is correct.
Volume of cylinder = bottom area × height
2. Look at question 2: Please raise your hand if you think the formula is right? what do you think?
3. Look at the calculation process and results, raise your hand if you feel right?
4. Evaluate the correct rate and write it on the blackboard, and ask the students at the same table to correct it.
You did well today, and the teacher is very happy for you. Teacher, here are some exercises. Do you dare to try? (display)
Sixth, supplementary exercises:
1, a cylindrical steel, the bottom area is 30 cubic centimeters, the height is 60 centimeters, and the volume is how many cubic centimeters?
2. Cylinders and rectangles are equal in volume and height, so their bottom areas ().
3. Expand one side of the cylinder to get a square. The radius of the bottom of the cylinder is 5cm, the height of the cylinder is () cm, and the volume is () cubic cm. .
Below, let's do our homework with what we have learned today, and compare who can do the classroom homework quickly and correctly with the correct font.
Seven, in-class training (textbook exercise 3, 2 1 page)
Homework: Write the 3rd, 4th, 7th and 8th questions in the homework book.
Exercise: Write in the notebook 1 and in the exercise books 2, 6, 9 and 10.
Eight, blackboard design
Topic 3: The volume of a cylinder
Volume of cylinder = bottom area × height
Reflection after class:
The teaching content of this lesson is the volume of cylinder, the second volume of the sixth grade of nine-year compulsory education. When I teach this content, I don't follow the traditional teaching methods, but adopt new teaching concepts, so that students can practice by themselves, explore independently, cooperate with each other, and experience in practice, thus gaining knowledge. In this regard, I put forward the following thoughts:
First, students have learned valuable knowledge.
The knowledge acquired by students through practice, exploration and discovery is alive, which will play a positive role in promoting the development of students' own intelligence and creativity. All the answers are not from the teacher, but from the students' hard work, which has personal significance and deeper understanding.
Second, cultivate students' scientific spirit and methods.
The new curriculum reform clearly puts forward that it is necessary to "emphasize students' awareness of inquiry and innovation through practice, learn scientific research methods, and cultivate scientific attitude and spirit". The process of students' hands-on practice and observation to draw conclusions is the process of scientific research.
Third, promote the development of students' thinking.
Traditional teaching only pays attention to how much knowledge is taught to students and regards students as "containers" of knowledge. Students' learning is only passive acceptance, memory and imitation. Often students only know what it is but don't know why, and their thinking can't be developed at all. Here, rich teaching scenes have been created. Students have experienced the process of independent inquiry, independent thinking, analysis and arrangement, cooperation and communication, found the existence of teaching problems, experienced the process of knowledge generation, understood and mastered the basic knowledge of mathematics, thus promoting the development of students' thinking.
This class has adopted new teaching methods and achieved good teaching results. The disadvantage is that students spend more time discussing, practicing and thinking freely, and less time practicing.
Teaching Design and Thinking of Cylindrical Paper Part III: Analysis of Teaching Materials;
This section includes the derivation of the formula for calculating the volume of a cylinder, which is directly calculated by the formula and solved by the formula: Volume 11 of the open class of the volume of a cylindrical object and the volume of a cylinder. The textbook makes full use of what students have learned to pave the way, and guides students to turn the cylinder into the three-dimensional figure they have learned by transfer method. Then, by observing and comparing the relationship between the two graphs, the calculation formula of cylinder volume can be deduced.
Teaching purpose:
1. Using the law of migration, students are guided to derive a formula for calculating the volume of a cylinder with the help of the deduction method of the formula for calculating the factor area, and understand this process.
2. Can use the volume of cylinder to calculate the volume and volume of cylindrical objects, and use formulas to solve some simple problems.
3. Guide students to learn the transformed mathematical ideas and methods step by step, and cultivate students' ability to solve practical problems.
4. With the help of physical demonstration, cultivate students' abstract and general thinking ability.
Teaching AIDS: cylindrical volume formula demonstration teaching AIDS, multimedia courseware.
Teaching process:
First, the scene is introduced.
1, show me the cylindrical water cup.
The teacher filled the cup with water. Think about it. What shape is the water in the glass?
(2) Can you calculate the volume of water by the method you have learned before?
(3) Report after discussion: Pour water into a cuboid container, and then calculate after measuring the data.
(4) Talk about the calculation formula of cuboid volume.
2. Create a problem scenario. (Courseware presentation)
If you need the volume of the front wheel of the roller cylinder, or calculate the volume of the cylinder, can you still use the previous method? The method just now is not a panacea, so when calculating the volume of a cylinder, is there a formula similar to a cuboid or a cube?
Today, let's learn the calculation method of cylinder volume. Topic: Volume of a Cylinder Design Intention: The problem is thinking and motivation. By creating problem scenarios, students are guided to use their existing life experience and old knowledge to actively think, explore and solve practical problems, create cognitive conflicts, and form a "task-driven" inquiry atmosphere. )
Second, the new teaching:
Question: By changing a circle into a straight circle and a Fiona Fang, we can derive the formula for calculating the area of a circle. Now, can we use a similar method to cut the cylinder into a learned three-dimensional figure and find its volume? Today we will discuss this problem together. Words on the blackboard: the volume of a cylinder.
1. Explore and deduce the volume calculation formula of cylinder.
The courseware demonstrates the process of spelling and grouping, and at the same time demonstrates a group of animations (dividing the bottom of the cylinder into 32 and 64 copies, etc. ), let the students clearly divide the more sectors, the closer the three-dimensional figure is to the cuboid. C, solve the above three problems in turn. (1) After the cylinder is spliced into a cuboid, the shape changes and the volume remains unchanged. (blackboard writing: cuboid volume = cylinder volume) ② The bottom area of the spliced cuboid is equal to the bottom area of the cylinder, and the height is the height of the cylinder. Cooperate with the answers, demonstrate the courseware, flash the corresponding parts and write the corresponding contents on the blackboard. (3) Cylinder volume = bottom area × high letter formula is V=Sh (blackboard formula)
Discuss and draw a conclusion. Can you get a formula for calculating the volume of a cylinder according to this experiment? Why? Let the students discuss it again: the cylinder is transformed into an approximate body by cutting and splicing. The bottom area of this cuboid is the same as that of the cylinder, and the height of this cuboid is the same as that of the cylinder. Because the volume of a cuboid is equal to the bottom area multiplied by the height, the formula for calculating the volume of a cylinder is: (blackboard: cylinder volume = bottom area × height) expressed in letters:. (blackboard writing: V=Sh) (design intent: in the new class teaching, let students review old knowledge, understand through observation and summarize through comparison. Through these measures, students can actually experience the cylindrical volume formula, which fully embodies the leading role of teachers and the main role of students. Primary school mathematics teaching plan "Volume 11: Open Class of Cylindrical Volume". This kind of teaching not only helps students to understand arithmetic and master algorithms, but also helps students to understand learning methods and cultivate their learning ability, abstract generalization ability and logical thinking ability in the process of formula derivation.
What conditions must be known to calculate the volume of a cylinder with this formula?
Fill in the form: Please look at the screen and answer the following questions.
Bottom area (㎡) Height (m) Cylindrical volume (m3)
63
0.58
Fifty two
(Design intention: Design exercises can help students draw inferences, thus training students' skills. This is the first basic exercise. Through this question, students can better grasp the key points of this lesson and lay a solid foundation.
Example: The inner diameter of the bottom of the cylindrical oil drum is 6 decimeters and the height is 7 decimeters. How many cubic decimeters is its volume? (Keep whole cubic decimeter)
Solution: d=6dm, h=7dm.r=3dm.
S base = π R2 = 3.14× 32 = 3.14× 9 = 28.26 (dm2)
V=S bottom H = 28.26× 7 =197.5438+098 dm3 A: The volume of oil drum is about 198 cubic minutes.
(Design intention: let students pay attention to the problem-solving format and the cubic unit of volume)
Three. Integrated feedback
1. Find the volume of the cylinder below. (Unit: cm)
The students perform on the blackboard, and the rest do it in the exercise books. On the blackboard, the students explain their own problem-solving methods, and the teacher summarizes the problem-solving methods used by the students, emphasizing the format in the problem-solving process. (design intent: this is a second-level variant exercise. It is a training problem for students to understand the formula on the basis of mastering it and learn to use it flexibly. Through the extended understanding of the formula, students can further understand and master the cylindrical volume formula, and also cultivate their own logical thinking ability. )
Exercise: (Back to thinking) The diameter of the bottom surface of a cylindrical cup is 10cm and the height is 15cm. It is known that the volume of water in a cup is 2/3 of the whole cup. How to calculate the volume of water in the cup?
(Design intention: This is a three-level developmental exercise, which is closely related to real life, so that students can solve two problems with formulas in the introduction process, and the actual experience mathematics exists around them. )
Step 4: Expand your practice.
1. A rectangular piece of paper is 6 decimeters long and 4 decimeters wide. Use it to surround two cylinders respectively. A is 6 meters high at the bottom, and B is 6 meters high at the bottom. Are they the same size? Please calculate and explain the reason. (The result remains π)
2. In a cylindrical container with a bottom diameter of 20cm, the water level in the container rises by 4cm after irregular iron castings are placed. What is the volume of this cast iron part? 、
(Design intention: The exercises closely related to real life are arranged, so that students can solve two problems with formulas in the introduction, so that students can realize the value of mathematics and realize that mathematics is very useful for understanding the world around them and solving practical problems; It can make students' thinking in a positive state and achieve the purpose of cultivating students' thinking flexibility and creative problem-solving ability. )
Verb (abbreviation of verb) course summary:
1. Talk about what you have gained from this class.
2. What aspects should we pay attention to when solving problems?
(Design intent: The harvest includes all-round experience of knowledge, ability, method and emotion. Here, the question-based summary is used to let students talk about the gains and find out the shortcomings, which can not only train students' language expression ability, but also cultivate students' induction and generalization ability; At the same time, through the summary and review of the knowledge learned in this section, the knowledge learned by students can be systematized and integrated. )
Distribution of intransitive verbs
1. Exercise 2.7
2. Expand Exercise 2 Questions
Teaching reflection:
The teaching of this lesson is embodied in: 1. Introduce new courses by using the law of migration to create a good learning environment for students; Second, follow students' cognitive rules, guide students to observe, think and reason, and mobilize multiple senses to participate in learning; Third, correctly handle the relationship between "two masters", give full play to students' main role, and pay attention to students' participation process and knowledge acquisition process, so that students can have high enthusiasm and good learning effect. To achieve the expected results, the disadvantage is that students have too little control over the discussion time, and individual students will not use formulas flexibly after class.