Tisch
Teaching content:
Beijing Normal University Edition teaches the sixth grade "the volume of a cylinder"
Teaching objectives:
1, combined with specific conditions and practical activities, to understand the meaning of cylinder volume.
2. After exploring the calculation method of cylinder volume, mastering the calculation method of cylinder volume can correctly calculate the volume of cylinder and solve some simple practical problems.
3. Cultivate students' preliminary spatial concept and thinking ability;
Teaching focus:
Understand and master the formula for calculating the volume of a cylinder, and you will find out the volume of the cylinder.
Teaching difficulties:
Understand the derivation process of cylindrical volume calculation formula.
Teaching aid preparation:
Demonstration teaching aid for cylindrical volume.
Teaching process:
First of all, old knowledge paved the way.
1, talk introduction
Recently, we learned about cylinders and cones and learned to calculate the surface area of cylinders. Now look at the teacher's cylindrical cup. Who is bigger than this cylinder? What does size actually mean here? (Student answers)
2. Question: What is volume? We know the number of those numbers? How to calculate? (The answer is written on the blackboard by the teacher)
In this lesson, we will learn the volume of a cylinder.
Second, explore independently and solve problems.
(1) Understand the meaning of cylindrical volume.
What exactly does the volume of a cylinder mean? Who can give an example?
(2) Derivation of cylinder volume calculation formula.
1, we have learned the calculation of cuboids and cubes. What is the volume of a cylinder related to? What kind of guess would you have? (group discussion)
2. Recall the derivation process of circular area.
3. Teaching aid demonstration.
(1) Take the cylinder model.
(2) Cut the cylinder in half.
(3) Divide the two halves into several small pieces.
(4) begin to assemble an approximate cuboid.
(3) Inductive formula.
(blackboard writing: cylinder volume = bottom area × height)
Expressed in letters: (blackboard writing: V=Sh)
Third, consolidate new knowledge.
1. The bottom radius of this cup is 6 cm, and the height is 16 cm. What is its volume?
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.
Now this cup is filled with 2/3 water. How much water is there?
Step 2 Complete "Give it a try"
3. "Jump": unify the calculation method of straight cylinder volume.
Fourth, class summary, expansion and extension.
What did you learn in this class? How to calculate the volume of a cylinder and how to get this formula? What numbers does this formula apply to? What do they have in common?
Verb (abbreviation for verb) assigns homework.
Exercise 1-5.
extreme
Teaching content: Page 5-6 of Mathematics Grade 6 published by Beijing Normal University.
Teaching objectives:
1. Make students understand the meaning of cylinder lateral area and cylinder surface area, and master the calculation method of cylinder lateral area and surface area.
2. According to the relationship between cylinder surface area and lateral area, students can learn to use what they have learned to solve simple practical problems.
Teaching emphasis: objective 1.
Teaching difficulty: Goal 2.
Teaching process:
Activity 1: Review the old knowledge and consolidate the learned formula.
1, a circle with a diameter of 100 mm, find the circumference.
2. Find the perimeter and area of a circle with a radius of 3 cm.
What is the area of a rectangle with a length of 3 meters and a width of 2 meters?
Show me the model of the cylinder and tell me its characteristics.
Activity 2; Explore new knowledge.
1. How much cardboard does it take to make a cylindrical carton? (excluding interface)
What is it to solve this problem?
2. What is the surface area of a cylinder?
3. What is the key to calculate the surface area of a cylinder?
4. Explore the calculation method of cylindrical side area.
1) What is the shape of the unfolded side of the cylinder? A rectangular piece of paper can be rolled into a cylinder.
2) What is the relationship between the length and width of the cylinder side development diagram and this cylinder? How to find the lateral area of a cylinder?
3) division; The lateral area of a cylinder is to find the area of a rectangle. Multiply the length by the width.
4) The length is the circumference of the bottom circle of the cylinder, and the width is the height of the cylinder.
5) Please summarize the calculation method of cylindrical lateral area.
6) The lateral area of the cylinder is 2∏rh, and the surface area of the cylinder is calculated by lateral area plus two bottom areas.
Activity 3: Application of new knowledge.
1. Find the surface area of a cylinder with a base radius of10cm and a height of 30cm.
2. The teacher writes on the blackboard:
Transverse area: 2 ╳ 3.14 ╳10 ╳ 30 =1884 (square centimeter)
Bottom area: 3.14 ╳10 ╳10 = 314 (square centimeter)
Surface area:1884+314 ╳ 2 = 2512 (square centimeter)
Ask to write step by step.
2. Give it a try.
Make a cylindrical iron drum without a cover. The diameter of the bottom is decimeter and the height is 5 decimeter. What kind of iron do you need at least?
To know how much iron sheet is needed, at least know the surface area of the bucket.
What should we pay attention to in this question? There is no cover, it is just a bottom surface. If this kind of problem is an integer, one method is generally used.
3. practice. Page 6, question 1.
Three small problems: Find the surface area of a cylinder by knowing the diameter or the perimeter and height of the bottom. Focus on discussion: knowing the perimeter of the bottom surface and finding the surface area.
Tisso
Teaching objectives:
1, understand the meaning of cylinder volume (including volume), and further understand the meaning of volume and volume.
2. After exploring the calculation method of cylinder volume, mastering the calculation method of cylinder volume can correctly calculate the volume of cylinder and solve some simple practical problems.
3. Cultivate the initial concept of space and thinking ability; Further understand the thinking method of "transformation"
Teaching focus:
Understanding and mastering the calculation formula of cylinder volume is helpful for us to find the volume of cylinder.
Teaching difficulties:
Understand the derivation process of cylindrical volume calculation formula.
Teaching tools:
Demonstration teaching aid for cylindrical volume.
Teaching process:
First of all, retell the review content and introduce the new lesson.
Review the following in pairs: (Ask the team members of the question 1 to tell the team leader, and the team leader will supplement it. Ask each other at the same table. Sit down after you say that. )
1, say: (1) What is volume? What are the commonly used unit of volume?
(2) How to calculate the volumes of cuboids and cubes? How to express it in letters?
The volume of cuboids and cubes = () × is represented by the letter ().
2. Find the area of the following circle (only explain the idea of the question, not counting. )
( 1)r = 1cm； (2)d=4 decimeters; (3)C=6.28 meters.
(2) Reveal the topic
Want to know the "column volume" on the top left of page 8 of the textbook? Do you want to know "how much water can a cylindrical cup hold"? Today we are going to learn about the volume of a cylinder. (blackboard writing topic)
Second, ask questions and guide reading.
Please read pages 8-9 of the textbook carefully and complete the following questions.
(1) packet completion problem 1 and 2.
1, guess that the volume of the cylinder may be equal to () × ()
2. When we study the formula for calculating the area of a circle, we point out that the circle can be divided into several equal parts to form an approximate rectangle. The area of this rectangle is the area of this circle. The bottom of the cylinder can also be transformed into an approximate rectangle as mentioned above, and the cylinder can also be transformed into an approximate cuboid by cutting and splicing (as shown in the lower right picture on page 8 of the textbook). Observe the relationship between the spliced cuboid and the original cylinder.
(1) The bottom area of the cylinder becomes a cuboid ().
(2) The height of the cylinder becomes the height of the cuboid ().
(3) After a cylinder is transformed into a cuboid, its volume remains unchanged. Because the volume of a cuboid = () ×), the volume of a cylinder = ()×). If the letter V represents the volume of a cylinder, S represents the bottom area and H represents the height, then the volume formula of a cylinder can be expressed as ().
[Reporting communication, the teacher demonstrates and explains 2 questions with teaching AIDS]
(2) Complete questions 3 and 4 independently.
3. If it is known that the bottom radius of the column in the upper left corner of page 8 of the textbook is 0.4m and the height is 5m, how to calculate the volume of the column?
Find the bottom area first, and calculate it continuously ()
Find the volume again and calculate it continuously ()
Comprehensive formula ()
4. Know "How much water can a cylindrical cup hold?" You can use the "() × ()" of the cup (ignoring the thickness of the cup).
Requirements: After completion, check each other in groups and discuss disputes in groups of four.
Teachers choose some groups to report and communicate according to students' problems, and evaluate the learning situation of the groups.
Third, self-test
1, 9 pages in the textbook, try it.
2. Exercise textbook page 9 1 title (only in column form, not counting)
Requirements: after completion, the group will check each other and the teacher will evaluate it.
Fourth, consolidate practice.
Exercise 2, 3 and 4 in the textbook.
Requirements: The team leader first explains the thinking of the problem to the team members, and then completes it together in the group.
The teacher analyzed the wrong questions.
Verb (abbreviation of verb) expansion exercise
1, exercise 5 questions in the textbook
2. There is a grain mat, which is 6.28 meters long and 2.5 meters wide. How can we enclose a cylindrical grain depot? How many cubic meters of grain can you hold at most?
Requirements: discuss and determine the idea of solving the problem in the group first, and then complete it.
Six, class summary, homework assignment
1, summary: In this section, we transform a cylinder into a cuboid by transformation method and derive its volume formula. Remember to calculate the volume of a cylinder with "bottom area × height".
2. Homework: Practice six questions in the textbook.