The degree reasoning of "the sum of angles in a triangle" is an important link in a triangle, and it is also one of the important contents in the field of "space and graphics", which lays a foundation for students to further understand the relationship between three angles and three sides of a triangle. This lesson first lets students review the characteristics of triangles, then creates interesting dynamic situations in textbooks, introduces new lessons, stimulates students' interest, clarifies the meaning of "sum of interior angles", and then leads students to explore how many degrees the sum of interior angles of triangles equals, which can be verified in different ways. Three activities are arranged in the teaching, through which we can experience the nature and exploration process of "the sum of internal angles of a triangle".

Second, the analysis of learning situation

Some students may know from various channels that the sum of the internal angles of a triangle is 180, so the focus of this lesson is to understand why the sum of the internal angles of a triangle is 180 through mathematical activities, so that students can master this knowledge more deeply. After continuous experiments in curriculum reform, children have acquired certain abilities of independent inquiry and cooperative communication. They like to feel and express their views in practice and have a strong interest in mathematics.

1. Knowledge: Students have mastered the concept and classification of triangles and are familiar with the knowledge of obtuse angle, right angle, acute angle and right angle.

2. Ability: I have preliminary practical ability and inquiry ability, and can perform simple computer operations.

Third, teaching methods.

Infiltration conjecture-verification-conclusion-application-expansion

Teaching objectives:

1. Through intuitive operation, it is found that the sum of the three internal angles of a triangle is equal to 180 degrees. Experience the process and method of exploration in practical activities.

2. Some simple problems can be solved by applying the properties of triangle interior angle sum.

Teaching focus:

Through the whole process of the formation, development and application of the knowledge that the sum of the internal angles of a triangle is 180, I can apply the internal angles of a triangle to solve practical problems.

Teaching difficulties:

This is a process of exploring and verifying attributes.

Fourth, teaching AIDS and learning tools.

Triangle, protractor, scissors, white paper

Teaching process of verbs (abbreviation of verb)

(A), a wonderful introduction, revealing the theme

1, Teacher: Guess who, class?

The shape is like a mountain, solid and firm, and the three poles are connected end to end. The knowledge is not simple (make a geometric figure). Triangle (blackboard writing) We already know what a triangle is. Who can tell us what its characteristics are? The students answered. (Complement each other) (Courseware demonstrates the process of three line segments forming a triangle)

After the three line segments form a triangle, three angles are formed in the triangle (the courseware flashes three angles and their arcs respectively), and we call these three angles in the triangle the inner angles of the triangle respectively.

2. Now, let's play a game related to the corners of the triangle. As long as you tell the degrees of any two angles of a triangle, the teacher can guess the third angle. Can you believe it?

Four people in each group are required to take out their schoolbags prepared in advance. There are four different triangles, including at least one right triangle, an acute triangle and an obtuse triangle, with different sizes. )

3, activity-measure a quantity: each person arbitrarily takes out a triangle with his own belt, measures the degrees of three angles in the triangle with a protractor, and writes it in the triangle. (done independently, without grouping. )

Then several students were asked to quote the degrees of two angles of different triangles, and the teacher immediately said the degrees of the third angle. (Explain to the students in advance that the error is only about 3 or 4 degrees. )

Do you know how the teacher guessed?

What's the secret between them? We will uncover the secret in today's class.

(2), hands-on operation, explore new knowledge

1. Find the sum of internal angles of special triangles.

Take out two triangles and ask: What triangles are they? (right triangle)

Please take out your own two triangular rulers, talk about the degrees of the three angles on each triangular ruler in the group, and find the sum of the inner angles of these two right triangles. What did you find from the calculation of the sum of the internal angles of the two triangles just now?

The sum of the internal angles of these two triangles is 180. These two triangles are both right triangles, and they are special triangles.

Design intention triangle is a very familiar learning tool for students, and the degree is also very clear. This conclusion is verified by calculating the sum of the internal angles of the triangle that students are familiar with, which is easy for students to accept.

2. Find the sum of the internal angles of a general triangle.

(1) guess.

What is the sum of the internal angles of other triangles? (It may be 180)

(2) The sum of the internal angles of a general triangle is verified by operation as 180.

Is the sum of the internal angles of all triangles 180? How can you prove it? (You can measure the degree of each inner angle first, and then add it up. )

Then please count together in the group! Students are divided into acute triangle group, right triangle group, obtuse triangle group and isosceles triangle group by grouping method. Each group randomly draws triangles on white paper, measures the degree of each internal angle, and calculates the sum of the internal angles of the triangle. The team leader statistics recorder records the internal angle and situation of each group.

(3) The group reports the results.

Each group is required to report the survey results. Q: What did you find?

Summary: Through measurement and calculation, we find that the sum of the three internal angles of each triangle is around 180.

The design aims to let students draw triangles at will, including large triangles, small triangles and various types of triangles. No matter what kind of triangle it is, students will work out the sum of internal angles by themselves. This exploration process is simple and easy for students to accept.

3. Operational verification

(1) Hands-on verification guess.

There is no unified result. This method is not convincing. What shall we do? Is there any other way? Please think about it, can you verify it by hands-on operation? (Discuss in groups first, then report the method)

(2) Students' operation and teachers' patrol guidance.

(3) The whole class communicates and reports the verification methods and results.

Students put it on the projector and show it to everyone. (Cut, Tear and Fold)

What conclusion can we draw? (The sum of the internal angles of the triangle is 180)

By cutting, tearing and folding, students are guided to find that all three internal angles of various triangles can form a right angle, which proves that the sum of the internal angles of triangles is indeed 180, and there are errors in measurement and calculation.

The design intention is to let students cut the three internal angles of the triangle into a right angle through hands-on operation, and visually explain the conclusion that the sum of the internal angles of the triangle is 180 degrees.

5. Distinguish concepts and understand them thoroughly.

(Show a big triangle) What is the sum of its internal angles?

(Show a small triangle) What is the sum of its internal angles?

What is the sum of the internal angles of the triangle ruler and 180? What is the sum of the internal angles of a big triangle composed of two identical triangular rulers? (Some students answered 360, and some students answered 180. )

Divide the big triangle into two parts equally. What is the sum of the internal angles of each small triangle? (Some students answered 90, others answered 180) There are two answers to these two questions, which one is right? Why? All the students have questions on their faces. )

You can spell with a triangular ruler in the group, or you can draw a picture to discuss with each other.

Students found that no matter the position, size and shape of a triangle, the sum of its internal angles is always 180.

(3) Summary

Just now, the students proved in many ways that the sum of the internal angles of any triangle is 180. Now, let's read our discovery with pride and affirmation: "The sum of the inner angles of a triangle is 180".

(4) Consolidate practice and expand application.

Next, we will solve some related mathematical problems according to the knowledge of the sum of the angles in the triangle. (courseware)

1, find the degree of an unknown angle in a triangle.

In a triangle, it is known that ∠ 1 = 85, ∠ 2 = 65, and find ∠3.

2. Judges

The degrees of the three internal angles of the (1) triangle are 90 degrees, 75 degrees and 25 degrees respectively. ()

(2) A triangle has at least two acute angles. ()

(3) The sum of the internal angles of the obtuse triangle is greater than the sum of the internal angles of the acute triangle. ()

(4) The sum of the two acute angles of a right triangle is equal to 90. ()

3. Solve practical problems in life.

(1) Dad bought Xiaohong an isosceles triangle kite. One of its base angles is 70 degrees. What is its vertex angle?

(2) The traffic warning sign "Let" is an equilateral triangle. Find the degree of one of the angles.

4. Expand practice.

Let the sum of the internal angles of the triangle be 180. What is the sum of the internal angles of the quadrilateral and hexagon below? (courseware)

Discuss with the students in the group to see who can find the way.

Sixth, the class summary

What did you get from this lesson?

Chapter II Teaching Objectives:

1. Through group cooperation and intuitive operation, it is found that the sum of the internal angles of the triangle is equal to 180. Some simple problems can be solved by using the properties of the sum of angles in a triangle.

2. Experience the process of hands-on practice and exploring the sum of triangles, and experience the mathematical thinking methods of "measuring one", "calculating one", "spelling one" and "folding one" to improve hands-on operation ability and mathematical thinking ability.

3. Make students have a successful experience in mathematical activities and feel the fun of exploring mathematical laws. Cultivate students' innovative consciousness, exploration spirit and practical ability, and feel the beauty of reason in students' hands-on practice and induction.

Teaching focus:

1. It is found that the sum of degrees of the sum of three internal angles of a triangle is equal to 180o.

2. Knowing the degrees of two angles of a triangle, we can find out the degrees of the third angle.

Teaching difficulties:

Knowing the degrees of the two angles of a triangle, we can find out the degrees of the third angle.

Teaching preparation:

On the blackboard, students and teachers prepare several triangles and protractors with different shapes.

Teaching process:

First of all, pre-inspection

Talk about the feeling of operation in preview class, what problems should be paid attention to, and what is the sum of the internal angles of the triangle? Revision of intra-group communication.

Second, the scene is imported to present the target

Introduction to the story. One day, the big triangle said to the small triangle, "My head is big, so the sum of my inner angles must be bigger than yours." Little Triangle said disappointedly, "Really?" Reveal the topic and indicate the goal. Ask questions and introduce new lessons.

Third, explore new knowledge.

Autonomous learning

1, activity 1, comparison.

2. Activity 2. Measuring quantity

(1) What is an internal angle?

(2) How to find the sum of the internal angles of a triangle?

(3) Group activities. Students in each group draw several triangles with different sizes and shapes. Measure the degrees of three internal angles respectively and find their sum.

(4) Fill in the group activity record. It is found that the sum of degrees of each triangle with different sizes and shapes is close to the sum of degrees of three internal angles.

3. Say and do.

(1) Let's tear off the three corners and put them together to see what happens.

(2) Fold the three corners together, and the three corners are on a straight line. Therefore, the sum of the three internal angles of a triangle is equal to () degrees.

Fourth, in-class training (small blackboard display content)

1, the sum of the internal angles of the triangle is (), an isosceles triangle, one of its base angles is 26, and its vertex angle is ().

2. Three sticks with lengths of 5cm, 8cm and () cm cannot form a triangle.

3, the triangle has ().

4. One angle in a triangle is 45, the other angle is twice as large, and the third angle is (), which is a triangle ().

5. According to the angle, triangles can be divided into () triangle, () triangle and () triangle.

6. The third question of the exchange study plan. Do it independently first, and then communicate in groups.

V. Inspiration and sublimation

The sum of the degrees of three angles of an arbitrary triangle is equal to 180 degrees. Independent thinking group exchange summary method teacher's guidance.

Sixth, the class summary

Do you have any new gains or questions through the study of this class? Speak in the group first, and then communicate in class.

Seven, expand and improve

Mother bought an isosceles triangle kite for Scampy. Its vertex angle is 40 degrees. What is its base angle? Do it independently first, and then communicate in groups. Blackboard design:

Sum of internal angles of triangle

Measure the sum of degrees of three angles.

Article 3 Teaching objectives:

1. Grasp that the sum of the interior angles of a triangle is 180, and apply this rule to solve some practical problems.

2. Let students experience the formation process of knowledge such as "conjecture, hands-on operation, intuitive perception, exploration, induction and application", master the mathematical thinking method of "transformation", cultivate students' hands-on practice ability and develop their spatial thinking ability.

3. In the activity, let students experience the fun of actively exploring the laws of mathematics, experience the value of mathematics, stimulate students' enthusiasm for learning mathematics, and at the same time make students develop the good habit of independent thinking.

Teaching focus:

Let students experience the whole process of the formation, development and application of the knowledge that the sum of the internal angles of a triangle is 180 degrees.

Teaching difficulties:

Exploration and verification of triangle interior angle sum.

Teaching preparation:

Various types of triangular (cardboard) triangles.

Teaching process:

First, set questions to stimulate interest and introduce new courses

Teacher: Today, the teacher brought a friend (courseware) to show you the triangle.

Teacher: What do you know and understand about triangles?

Health: There are acute triangle, right triangle and obtuse triangle.

Health: A plane figure surrounded by three line segments is called a triangle.

Teacher: introduce the inner angle, the inner angle and.

The angle formed by every two sides of a triangle is called the inner angle of the triangle.

Teacher: How many internal angles does a triangle have?

Health: three.

Teacher: The sum of these three angles is called the sum of the inner angles of a triangle. Do you know how many degrees the sum of the angles in a triangle is?

Health 1: I know it through a right triangle.

Health 2: All four corners of a rectangle are right angles, which is 360 degrees, and a triangle is half of a rectangle, so it is 180 degrees.

S3: I have previewed that the sum of the internal angles of a triangle is 180 degrees.

Teacher: Is it true that the sum of all the internal angles of a triangle is 180 degrees?

Second, independent exploration and verification.

Teacher: How are you going to verify it?

Health 1 measure the degree of each angle with a protractor, and add it up to see if it is 180 degrees. Health 2: Tear off the triangle.

Teacher: How to tear it? Tear like this? (tearing), can you be more specific? Health 2: (supplement), tear off the three corners and put them together to see if they can be made into right angles.

S3: You can draw these three corners in order.

Health 4: The method of spelling.

Teacher: OK! Students have come up with so many methods, so let's use your favorite method to verify it. Teacher: Cai multimedia courseware display operation requirements:

Cooperative investigation:

1, a group of four people, choose at least two triangles in each group, and verify it with your favorite method.

2. Look at the organization's new and diverse verification methods.

Teacher: I'm on patrol, giving personal instructions.

Third, exchange the methods and achievements of exploration.

There may be three ways for children to explore:

Health 1: First measure each angle with a protractor, and then calculate the sum of the degrees of the three angles in the triangle. The result obtained by this method may be 180 degrees, may be less than 180 degrees, and may be greater than 180 degrees.

Health 2: The second is to cut off the three angles in the triangle and put them together to form a right angle, so the sum of the three angles in the triangle is 180 degrees.

Health 3: The third is to fold three angles together to form a right angle, so that the sum of the three angles in the triangle is 180 degrees.

Fourth, summarize and experience success.

Teacher: Children, what is the sum of the degrees of the three angles in a triangle?

Health: 180 degrees.

Fifth, expand applications.

1, basic exercise

2, equilateral triangle, isosceles triangle, right triangle

Sixth, the class summary

Talk about your own learning gains.