1. 1 knowledge and skills:

1. According to the specific situation, we can flexibly use circular area and rectangular area to understand the surface area of a cylinder.

2. Through imagination, hands-on operation and other activities, we can understand that the side of the cylinder is rectangular, deepen our understanding of the characteristics of the cylinder and develop the concept of space.

3. Explore the calculation method of cylinder side area, master the calculation method of cylinder side area and surface area, and correctly calculate the side area and surface area of a cylinder.

1.2 process and method:

In the process of explaining the surface area of cylinder, cultivate students' preliminary observation ability, imagination and generalization ability.

1.3 Emotional attitudes and values:

Guide students to further experience the planarization of three-dimensional graphics, feel the fun of mathematical exploration activities themselves, and enhance their confidence in learning mathematics well.

Emphasis and difficulty in teaching

2. 1 teaching focus:

Let students understand the calculation method of cylinder surface area.

2.2 Teaching difficulties:

Can distinguish the difference between lateral area and surface area, and reasonably apply it to daily life.

teaching tool

Courseware, multimedia equipment, etc.

teaching process

First, situational introduction

Teacher: Students, in our daily life, we often meet some cylinders, such as the water cup in my hand. Do you know what it is made of?

Student: Students raise their hands to answer.

Teacher: What kind of noodles is this cup made of?

Health: upper bottom surface, lower bottom surface and side surface.

Teacher: Multimedia animation

Teacher: We can see that it consists of three parts.

Teacher: Now think about what these three parts are.

Health: upper and lower bottom (round), side (rectangular)

Teacher: Add up these three areas, which is the surface area of the cylinder we are going to learn today.

Student: Please raise your hand and dictate the answers.

Teacher: The courseware shows the answers.

Side area of cylinder = perimeter of bottom surface? high

Teacher: Now, let's look at some quantitative relations:

① The areas of the upper and lower bottom surfaces of the cylinder are equal;

(2) cylinder side length = bottom circumference

③ Width of cylinder side = height of cylinder.

Second, explore new knowledge.

(1) lateral area

Teacher: Now let's see how the lateral area of a cylinder is calculated.

Student: Please raise your hand to speak.

In the process of answering questions, teachers should use encouraging language to stimulate students' ability to explore knowledge.

Teacher: Multimedia presentation of answers

Side area of cylinder = length? Width = bottom perimeter x height

Teacher: Now let's see how it is calculated in practical application. (Multimedia presentation questions)

1. It is known that the radius of the bottom circle of the cylinder is 50px and the height is 125px. How long are the sides of this cylinder?

Student: Raise your hand and answer.

Teacher: Multimedia presentation of answers

Solution: perimeter =2? r=2？ 2? =4?

Lateral area = circumference? Height =45=20? cm？

Teacher: Students should carefully observe the writing steps.

(2) Surface area

Teacher: Now let's see how the surface area of a cylinder is calculated.

Student: Raise your hand and answer the question.

Teacher: Multimedia presentation of answers

Cylindrical surface area = side surface area+bottom surface area = side surface area+upper bottom surface area+lower bottom surface area.

Teacher: Let's do another exercise!

2. How many pieces of iron do you need to make a cylindrical iron drum with a bottom radius of 2dm and a height of 10dm?

Teacher: Students can calculate the side area and bottom area first, and then calculate the surface area.

Students: By competing with each other, students' interest in learning mathematics is improved.

Analysis:

Solution: perimeter =2? r =2？ 2? =4?

Lateral area = circumference? Height =4 10=40?

Area of base circle =? r？ =4?

Cylinder surface area = side surface area +2 bottom surface area =40? +2x4？ =40? +8? =48?

A: 48? dm？ iron sheet

Third, consolidate the practice.

Teacher: Now look at this question on the screen. Can you solve the problem in groups? (Courseware presentation topic)

1, the weather is cold, and rural students have to make a fire. The chimney is made of iron. A section of chimney is 2000px long and the chimney radius is 100px. How much iron does it take to make such a chimney?

Teacher: Find out the key to the problem, clear your mind and solve the problem seriously.

Students: Students discuss and communicate with each other, complete the whole topic, and cultivate students' independent thinking ability.

Analysis:

Solution: perimeter =2? r=2？ 4? =8?

Surface area = side area =8 10=80?

A: It takes 80 yuan to make such a chimney. cm？ iron sheet

Teacher: Next, let's look at another topic, this time in groups, to see which group can do it quickly and well. (Courseware presentation topic)

2. Now we need to build a cylindrical water cellar. It is estimated that the depth of the water cellar is 3m, and the bottom diameter of the water cellar is1.5m. How many square meters of concrete should be plastered on the whole water cellar now?

Student: Every group enjoys the fun of gaining knowledge in the competition.

Analysis: perimeter =? d= 1.5？

Surface area = lateral area+bottom area = 1.53+2.25? =6.75?

Does the whole cellar need to be leveled before 6.75? Square meters of concrete

Teacher: Now, let's finish the following questions independently.

3. It is known that the surface area of a cylinder is 15700px? , where the radius of the bottom surface of the cylinder is 50px, find the height of the cylinder.

Solution: let the height of the cylinder be H.

According to: surface area = lateral area +2 bottom area.

628=2? 2? h+22？

628=4? h+8？

628=4? 3. 14h+8？ 3. 14

20=4h+8

h=4

Answer: The height of the cylinder is 4 meters.

7 homework

Teacher: Complete the following two questions in the exercise book.

1, a cylinder, if the bottom radius is 5 and the cylinder height is 10, then find the lateral area and surface area of the cylinder?

Solution: perimeter =2? r=2？ 5? = 10?

Lateral area = circumference? Height = 10 10= 100?

Bottom area =? r？ =25?

Surface area = lateral area +2 bottom area = 100? +2? 25? = 150?

Now we need to color the cylindrical paper products. Now we know that the radius of the bottom circle of the artwork is 50px and the height of the cylinder is 125px. Please find the surface area of the cylinder.

Solution: perimeter =2? r=2？ 2? =4?

Lateral area = circumference? Height =45=20?

Bottom area =? r？ =4?

Surface area = lateral area +2 Bottom area =20? +4? =24?

Summary after class

In this class, by studying the surface area of a cylinder, students can use what they have learned to solve some practical graphic area problems. Mainly for students to build rich imagination and the ability to transform three-dimensional graphics into plane graphics, the teaching mode of student interaction and group learning is integrated into the teaching, which truly reflects the students' dominant position. Let students move in class, discover and experience knowledge, and improve their imagination and abstract thinking ability through practice.

Write on the blackboard.

Section 2 Cylinders (Surface Area of Cylinders)

Teaching plan of cylinder surface area (II) Teaching objectives

1. Make students understand and master the calculation method of lateral area and surface area of cylinder, and correctly use the formula to calculate lateral area and surface area of cylinder.

2. Cultivate students' ability to observe, operate and summarize, as well as the ability to analyze and solve practical problems reasonably and flexibly by using what they have learned.

3. Cultivate students' sense of cooperation and their learning quality and practical ability to actively explore knowledge.

Emphasis and difficulty in teaching

Teaching emphasis: calculation of cylindrical surface area.

Teaching difficulty: derivation of calculation method of cylinder side area.

teaching tool

Ppt courseware

teaching process

First, check and review, introduce a new lesson (review the characteristics of cylinders)

1, review the formula of circumference and area of a circle and the formula of area of a rectangle.

2. Teacher: Last class, we got to know a new geometric cylinder. Know that it is a three-dimensional figure surrounded by planes and surfaces.

Q: What are the two circular planes above and below a cylinder? What is their relationship? What is the distance between the two bottom surfaces? What's the name of this noodle?

Lead-in: Together, the two bottom surfaces and side surfaces are the surface of a cylinder. In this lesson, we will learn the surface area of a cylinder together.

Second, guide inquiry and learn new knowledge.

(A) the significance of teaching cylindrical surface area.

Doubt: The total area of six faces of a cuboid is called its surface area. Which surfaces have the total area of a cylinder?

Blackboard: bottom area? 2+ side area = surface area

To ask for the surface area of a cylinder, we must first calculate its bottom area and lateral area.

(2) According to the conditions, calculate the bottom area of the cylinder.

The bottom of the cylinder is round. Will the students find its area?

(Multimedia shows cylinders and conditions one by one, calculates their bottom area, and records the results. )

Condition: (cm) r=3 d=4 c=3 1.4

Bottom area (square centimeter) 28.26 12.56 78.5

(3) Teaching the calculation of the side area of the cylinder.

1, a guide to the calculation method of lateral area of cylinders.

(1) Problem: The side of a cylinder is a curved surface. How to calculate its area? Think about it, can this surface be transformed into the plane figure we have learned, and how to calculate the lateral area when we find it?

(2) Group cooperation and exploration. (Cutting cylindrical paper tube)

(3) Report and exchange research results, and show them with multimedia courseware.

(4) Summary: Students can use their brains to think and skillfully use the method of transforming curved surfaces into planes. It is found that the side area of a cylinder is exactly equal to the product of its bottom circumference and height.

2. Calculate the transverse area of the cylinder.

The multimedia returns to the first three cylinders, gives the heights of the three cylinders one by one, and finds their lateral area. And record the results.

Condition (cm) h=5 h=8 h= 10

Transverse area (square centimeter) 94.2 100.48 62.8

(4) The teaching of finding the surface area of cylinder.

1, doubt: how to calculate the surface area of a cylinder after learning to calculate the bottom area and lateral area?

2. Students calculate according to the data?

3. Report the calculation method and results, and the media will show the results for verification.

Surface area (square centimeter) 150.72 125.6 69.08

(5) Summary: Significance and calculation method of cylindrical surface area.

Third, practice consolidation and flexible use.

1. Find the side area of the cylinder below.

(1) The perimeter of the bottom surface is 1.6m and the height is 0.7m ..

(2) The radius of the bottom surface is 3.2dm and the height is 5dm.

2. Trademark paper is attached to the side of the cylindrical tea bucket, and the radius of the bottom surface of the cylinder is 5cm and the height is 20cm. What is the area of this trademark paper?

Fourth, sum up reflection and talk about gains.

What did you gain from this class?

Write on the blackboard.

Surface area of cylinder

Surface area of cylinder = two bottom areas+side area.

Side area of cylinder = perimeter of bottom surface? high

Area of rectangle = length? extensive