1. Through operation, observation, comparison and other activities, we independently explore the calculation formula of trapezoidal area and the mathematical thinking method of infiltration transformation.

2. The formula can be correctly applied to calculate the area of trapezoid, and some simple practical problems in life can be solved.

Emphasis and difficulty in teaching

Teaching emphasis: explore and master the calculation formula of trapezoidal area.

Teaching difficulties: understand the derivation process of trapezoidal area calculation formula and experience the idea of transformation.

teaching process

First, review the introduction and pave the way for knowledge

Calculate the area of the following figure:

Check the answers in class.

Teacher: What are the formulas for calculating the area of parallelogram and triangle respectively?

Teacher: What's the connection between them?

Because two completely coincident triangles can be combined into a parallelogram, half of the parallelogram area calculation formula is the triangle area calculation formula.

The design intention is to prepare for learning new knowledge by reviewing the area calculation methods of parallelogram and triangle and their relationship.

Second, explore the calculation formula of trapezoidal area.

1. Ask questions (the courseware shows the theme map on page 95 of the textbook).

Teacher: What do the students find in the picture?

Teacher: The window glass is trapezoidal. How to find its area?

Teacher: Can you use the method you have learned to derive the formula for calculating the trapezoidal area?

2. Hands-on operation.

(1) Select the appropriate material and operate it. (deskmate cooperation)

(2) Feedback communication.

Let each group fully demonstrate the operation process. The key is to understand the students' thoughts. Are there any questions for the rest of the students? In operation, students will find that only two completely coincident trapezoids can be combined into a parallelogram.

Default value:

(1) Calculate the square;

(2) simple pendulum, converted into parallelogram;

(3) cutting and converting into two triangles;

(4) cutting and transforming into parallelogram and triangle;

(5) cutting, converting into a rectangle and two triangles;

⑥ Digging and filling method, converted into parallelogram.

The link of design intention allows students to operate boldly, constantly discover and solve problems in experiments, and expand their thinking and horizons in peer communication.

3. Formula derivation.

(1) Teacher:

The calculation method in method 1 runs through the idea of excavation and filling method.

Methods (2) to (6) are all about transforming a trapezoid into a graph, and we have learned the area calculation method.

Take method ② as an example to observe the original trapezoid and the transformed parallelogram. What equivalent relationship do you find between them?

Student: The sum of the upper bottom and the lower bottom of the trapezoid is equal to the bottom of the parallelogram, and the height of the trapezoid is higher than that of the parallelogram. The area of a trapezoid is half that of a parallelogram.

Students talk and teachers demonstrate courseware.

Complete the blackboard writing step by step:

Teacher: If it is expressed by the area of the trapezoid, the upper bottom of the trapezoid, the lower bottom of the trapezoid and the height of the trapezoid, the formula of the area of the trapezoid can also be written as: (blackboard writing).

(2) Teacher: observation method ③. If the trapezoid is cut into two triangles, how to derive the formula for calculating the trapezoid area? What is the equivalent relationship between these two triangles and the original trapezoid?

Student: The bottom of triangle 1 is the upper bottom of trapezoid, and the bottom of triangle 2 is the lower bottom of trapezoid. The height of the two triangles is equal to the height of the trapezoid. The sum of the areas of two triangles is the area of a trapezoid.

The students speak and the teacher demonstrates on the blackboard.

Teacher: For convenience, we directly use to indicate the upper bottom of the trapezoid, and use to indicate the lower bottom of the trapezoid, indicating the height of the trapezoid.

Teacher: This is the same as the formula for calculating the trapezoidal area deduced earlier.

(3) Teacher: Observation method 4 If the trapezoid is divided into parallelogram and triangle, how to deduce the formula? What is the equivalent relationship between parallelogram, triangle and original trapezoid?

Student: The base of parallelogram is the upper base of trapezoid, the base of triangle is equal to the lower base of trapezoid minus the upper base, and the heights of parallelogram, triangle and trapezoid are equal. The area of parallelogram plus the area of triangle equals the area of trapezoid.

The students speak and the teacher demonstrates on the blackboard.

The calculation process is a bit complicated and can be completed with the teacher's explanation.

Teacher: This is the same as the previous conclusion.

(4) Teacher: Look at the method ⑤. Divide the trapezoid into a rectangle and two triangles. How can we deduce the formula? Let's talk about the equivalence between them first.

Student: The length of rectangle is the upper bottom of trapezoid, and the height of rectangle, triangle and trapezoid is equal. The area of a rectangle plus two triangles is the area of a trapezoid.

Students find that the bottoms of two triangles are indescribable and uncertain. At this time, put two triangles together and it becomes a triangle. The bottom of the new triangle is the lower bottom of the trapezoid minus the upper bottom.

Teacher's blackboard demonstration.

Teacher: The following derivation process is the same as method 4.

(5) Teacher: Method ⑥, the trapezoid is transformed into a parallelogram by digging and filling method. What is the equivalent relationship between them?

Student: The base of parallelogram is the sum of the upper and lower base of trapezoid, and the height of parallelogram is higher than half the height of trapezoid. The area of parallelogram is equal to the area of trapezoid.

The teacher's courseware demonstration.

Teacher: Through the above transformation method, we know the calculation formula of trapezoidal area. Now do you know what data is needed to calculate the area of trapezoid? (Upper bottom, lower bottom and height)

The design intention is not satisfied with the formula derivation of one method, but to show various methods, develop students' thinking, communicate the connections and differences between various derivation methods, and highlight the role of transforming ideas.

Third, apply what you have learned.

1. Show example 3 on page 96 of the textbook.

Example: The dam section of the Three Gorges Hydropower Station in China is trapezoidal. What is its area?

Teacher: What is a cross section?

Ask students to solve independently and check their answers in class.

Teacher: Because I just started to learn the area formula of trapezoid, I am not familiar with the formula, so I can write the formula first and then list the calculation formula. Skilled, the formula can be omitted.

2. Practice and show the textbook page 96? Do it. .

Teacher: This question needs to be seen clearly. What is this? What is their field? So the question is? What is the area of the left trapezoid? And then what? What is the area of a right-angled trapezoid? Not letting go? Separate? As? ***? Find the area of the whole large trapezoid.

3. To find the area, only the formula does not count?

4. Find the cross section of this canal?

5. There is a trapezoidal orchard with a bottom of 45 meters, a bottom of 60 meters and a height of 30 meters. If each fruit tree covers an area of 15 square meters, how many fruit trees can be planted in this orchard?

6. Judges:

1. Two trapezoids with equal areas can be combined into a parallel quadrilateral.

Edge shape ().

2. The area of trapezoid is twice that of triangle ().

3. The trapezoid has countless heights ().

4. If the area of the trapezoid is12cm2, they are exactly the same.

The area of a parallelogram composed of trapezoids is 6 square centimeters. ( )

The sum of the upper and lower bottoms of the trapezoid is 20m, and the height is 8m. This ladder

The area of this shape is 80 square meters. ( )。

Design intention because of the first contact of students? Cross section? , so emphasize the right? Cross section? Understand. Apply the formula from the shallow to the deep, and strengthen the understanding of the formula in application.

Fourth, review and reflection.

Teacher: Looking back on what you have learned in this class, what is your biggest gain?

The design intention is to help students further understand and improve their knowledge in summary and review.

Verb (abbreviation for verb) assigns homework.

Complete questions 1 to 5 on page 97 of the textbook.

Trapezoidal regional teaching plan (2) teaching objectives

Teaching objectives:

1. Based on the derivation of parallelogram and triangle area, guide students to adopt the form of cooperative inquiry and summarize the calculation formula of trapezoidal area.

2. Be able to correctly and skillfully use the formula to calculate the trapezoidal area, solve some practical problems in life, and improve students' ability to find, analyze and solve problems; .

3. In operation, observation and comparison, through independent inquiry and group cooperation, students' imagination and thinking ability are cultivated, and students' spatial concept is developed.

4. Infiltrate the idea of mathematical migration and transformation, let students feel the close connection between mathematics and life, and improve their interest in learning mathematics.

Emphasis and difficulty in teaching

Teaching emphasis: Understand and master the trapezoid area formula and calculate the trapezoid area.

Teaching difficulty: independently explore the trapezoidal area formula.

teaching process

Preparation before class: Who will introduce your name, age, school, hobbies and so on, so that everyone can know about you.

Let's introduce this first I believe that the students' performance in class will definitely make all teachers remember you.

First, create a situation to stimulate interest.

(Show the situation map).

Students, today, Miss Li will visit Uncle Wang's fish pond with you. Please observe carefully. What mathematical information can you find?

Health: No.65438 +0 nail fish pond is trapezoidal, with 200 nail fry per square meter.

Teacher: According to the survey results, what math questions can you ask?

Students observe the situation map and ask questions.

Health: 1 what is the area of a fish pond?

Teacher: Your question is very good. Do you want to know? Who else can ask questions?

Health: 1 How many fry can be kept in the nail pond?

Second, explore the area calculation method of trapezoid independently.

1. Teacher: The questions raised by students just now are very valuable. (Courseware) Let's look at these two questions. Need the area of 1 fish pond, that is, what figure is needed?

Health: trapezoidal.

Teacher: Can you work out the area of this trapezoid? So, how to calculate the area of trapezoid? In this lesson, we will explore the area of trapezoid together. Blackboard: the area of trapezoid.

Teacher: If I use this trapezoidal paper to represent the area of a fish pond, think about it. How can you find out the area of this trapezoidal paper? Please think independently first, and then share your methods in the group.

2. Group discussion and exchange, teachers patrol to understand.

3. Presentation, reporting and communication.

Teacher: Which group will talk about your method first? Take your trapezoid to the front and tell your classmates.

1: (Method 1) Divide the trapezoid into parallelogram and triangle, calculate their areas respectively, and then calculate the sum of their areas.

Teacher: Do you think this method will work? You see, the way to find this group is to divide the trapezoid into parallelogram and triangle. Who thinks so?

Teacher: Whose method is different?

Student 2: (Method 2) Divide the trapezoid into two triangles, calculate the area of each triangle, and then calculate the sum of their areas.

Teacher: Your method is also quite good. In this group, the trapezoid is divided into two triangles to find the trapezoid area. Really a good boy who loves to think. If you have the same method as him, please raise your hand. Whose method is different from theirs?

Health 3: (Method 3) Put two identical trapezoids together to form a parallelogram, which is half the area of the parallelogram. The area of parallelogram is equal to the base times the height and then divided by 2, which is the area of trapezoid.

Teacher: This classmate speaks very well. Do you think this method is good?

This classmate's method is to put two identical trapezoids together to form a parallelogram. The area of a parallelogram is equal to the base times the height. Whose base is this? Gaoni

Health: the base of parallelogram, the height of parallelogram.

Teacher: The area of parallelogram is equal to the base multiplied by the height and then divided by 2, which is the area of trapezoid.

Teacher: Look, this student made a parallelogram with two identical trapeziums. Can any two identical trapezoids be combined into a parallelogram?

Teacher: Let's fight with the trapezoid in our hands. Tell the students who come up to fight again.

Teacher: It seems that any two identical trapezoids can form a parallelogram. The area of each trapezoid is half that of the parallelogram. Do you understand this method? Do you have a different one?

Health 4 (Method 4): I made a rectangle with two identical right-angled trapezoid, and the area of one trapezoid is half of this rectangle.

Teacher: Does this method apply to all two identical trapezoids?

Health: It's two right-angled trapezoids.

The teacher concluded: Yes, just now the students came up with these methods to find the trapezoidal area. You are really something. Let's look at these methods. (Courseware demonstration)

The first is to divide the trapezoid into triangles and parallelograms;

The second is to divide the trapezoid into two triangles;

The third type combines two identical trapezoids into a parallelogram.

Zan: These three methods are all solved by transforming the trapezoid into the learned figure. Students can use the transformation method. You are really great. This method is very important, and we will often use it in our future study.

The rectangle, square, parallelogram and triangle we have learned before all have their own area calculation formulas, so the trapezoid also has its own area calculation formula.

Teacher: Let's guess first. Do you think the area of trapezoid may be related to the conditions of trapezoid?

Health: Upper and lower soles, high.

Health: It's related to the waist.

Teacher: What does the area of trapezoid have to do with them? Do you want to study it?

Third, explore the operation and derive the trapezoidal area formula:

(A) show the problem, clear objectives

Let's look at these three methods first. According to our present level, because the first two methods are really difficult for us to study, we will use the third method to study the area of trapezoid in depth.

Let's look at this method together. Students make a parallelogram with two identical trapeziums, and the area of the trapezium is equal to half the area of the parallelogram.

Teacher's blackboard writing: Two identical trapezoids are put together to form a parallelogram.

Area of trapezoid = area of parallelogram? 2

= bottom? Tall? 2。

What is the relationship between the base of parallelogram and the upper and lower bases of trapezoid? What is the relationship between the height of parallelogram and the height of trapezoid? According to these relations, can the calculation method of trapezoidal area be deduced?

Teacher: Let the students spell out the trapezoid in their hands and think about how to deduce the formula for calculating the trapezoid area. Please study in groups.

(B) independent inquiry and cooperative learning

Discuss and communicate in groups.

Students work in groups and teachers patrol for guidance.

Teachers participate in each group for discussion and guidance in order to find and collect information.

(three) exchange results, ask questions and solve problems.

1. The whole class pays off:

Teacher: Which group of students talk about how your group studies? Take the paper in your hand and talk to the classmates in front.

Health: Two identical trapeziums form a parallelogram, and the area of the trapezium is half that of the parallelogram. The base of parallelogram is trapezoid (upper base+lower base), and the height of parallelogram is the height of trapezoid. The area formula of trapezoid is derived, that is, trapezoid (upper bottom+lower bottom) multiplied by height divided by 2.

Teacher's praise: Our group studied very well and deduced the calculation method of trapezoidal area. You got it?

Teacher: Do you think so? Which group will talk about your practice again?

3. Teacher: Just now, after studying, the students deduced the calculation method of trapezoidal area. Let's review the derivation process of trapezoidal area together. (Courseware demonstrates the transformation process)

Trapezoidal area = parallelogram area? 2

Trapezoidal area = bottom? Tall? 2

Teacher: The base of the parallelogram is the sum of the upper and lower bases of the trapezoid, and the height of the parallelogram is equal to the height of the trapezoid, that is, (upper base+lower base)? Tall? 2

Teacher: Then we get the formula of trapezoidal area: trapezoidal area = (upper bottom+lower bottom)? Tall? 2

2. Teacher: Through research, we found that the base of parallelogram is equal to the sum of the upper and lower bases of trapezoid, and the height of parallelogram is higher than that of trapezoid. Who will talk about the calculation method of trapezoidal area? The teacher writes on the blackboard.

Blackboard area formula: trapezoidal area = (upper bottom+lower bottom)? Tall? 2。

Question: (upper sole+lower sole)? What is high computing? Why divide by 2? .

4. Learn to express letters:

Dialogue: Who can express it in letters? Tell me what each letter stands for.

Teacher: S=( a+ b)? h？ 2 (blackboard writing)

Fourth, use knowledge to solve situational problems.

Teacher: In this class, the students learned how to find the area of a trapezoid. The calculation formula of trapezoidal area is derived, and now we use the knowledge we have learned to solve the two problems mentioned above: what is the area of 1 fish pond? How many fry can be stocked? (Courseware presentation topic)

Ask the students to do it in their exercise books. Two students perform on the blackboard, and the rest practice independently. The whole class communicates.

Fourth, the in-class test consolidates the goal.

Teacher: It seems that students will use trapezoidal area calculation method to solve practical problems. Next, we have to challenge ourselves to have confidence.

Challenge yourself:

First of all, judge

1, two trapezoids can be combined into a parallelogram. ( )

2. The area of trapezoid must be smaller than that of parallelogram. ( )

3. In the picture below, the area of parallelogram is twice that of trapezoid. ( )

Teacher: The students have good judgment and a thorough understanding of the problem. I hope the students will challenge to higher goals. Let's look at the trapezoid in real life. Can you calculate their area?

Second, (challenge yourself)

Solve the problem:

1. A trapezoidal platform should be built on the school playground. The plane is trapezoidal, with an upper bottom of 5 meters, a lower bottom of 8 meters and a height of 6 meters. How many square meters is the plane of this trapezoidal podium?

2. Trapezoidal wall with upper bottom15m, lower bottom 5m more than upper bottom and 6m higher. What is the area of this wall?

3. A trapezoid, the sum of the upper and lower bottoms is 36cm, and the height is 12cm. What is its area?

Teacher: It's time to show our wisdom. Please show your talent.

4. Uncle Wang surrounded the sheepfold with a 50-meter-long fence against the wall (pictured). Find the area of this trapezoidal sheepfold.

Students practice independently and communicate with the whole class.

Summary after class

Course summary:

Students, what have you gained from this class? What else don't you understand?

homework

Task:

There is a trapezoidal ditch in front of the school. The mouth of the ditch is 0.9 meters wide, the bottom of the ditch is 0.7 meters wide and the depth of the ditch is 0.5 meters. What is its cross-sectional area?