Teaching content: Hebei Education Edition, fourth grade mathematics, Volume II, pages 78 and 79.
Teaching objectives:
1. In the independent mathematical activities such as drawing triangles, measuring, inducing and communicating, I experienced the process of exploring that the sum of the internal angles of triangles is 180.
2. Knowing that the sum of the angles in the triangle is 180, we can calculate the degree of the other angle according to the degrees of the two known angles.
3. Actively participate in exploration, communication and other activities, feel the certainty of mathematical conclusions, and develop a preliminary concept of space.
Preparation before class: ruler, protractor, teachers and students prepare an acute triangle, a right triangle and an obtuse triangle.
Teaching process:
First, create situations and introduce new lessons.
(Play the recording): Students, the Triangle Kingdom is going to elect a new king. What should the new king have? Lao Wang thinks that since we are triangles, let's compare the angles! Whoever has a big inner corner is king. The obtuse triangle spoke first: "I have an obtuse angle, and the sum of my internal angles must be the largest." Of course, the acute triangle is not convinced: "How can I see it? I don't know! " So everyone argued endlessly. Just when the old king was in a dilemma, the right triangle, which had been silent, said, "Your Majesty, I think it is better to ask the fourth-grade students to help me calculate this problem and see who has the bigger inner angle. Do you think so? " Hearing this, the king nodded.
Teacher: Are the students willing to help?
Health: Yes (Qi A)
Teacher: OK! Now please take out the triangle prepared before class. Who can tell me what triangle you have prepared and what are its characteristics?
(simple answer)
(Comments: Make full use of children's curious psychological characteristics, introduce topics through interesting fairy tales, and then let students guess, which can not only arouse students' interest in learning, but also point out what they have learned in this lesson and attract them ideologically.
Students actively participate in learning activities. )
Second, explore new knowledge.
Teacher: It seems that the students have a good grasp of the classification and characteristics of triangles. Look, the teacher has also prepared a triangle here. (The teacher pasted the acute triangle he drew and marked 1, 2, 3 on the three corners. )
Teacher: Look at the pictures posted by the teacher. What did you find?
Health 1: This is an acute triangle.
Health 2: The teacher wrote 1, 2, 3 in three corners respectively.
Teacher: The teacher told you that all three corners of the triangle we know have a name, which is called the inner corner of the triangle.
Teacher: So, which triangle has the largest internal angle, and who should be king? Students guess first.
Health 1: The sum of the inner angles of an obtuse triangle is large.
Health 2: The sum of the internal angles of an acute triangle is large.
Health 3: Same size.
……
Teacher: Now there are several different opinions. Whose idea is right? Students, start measuring quickly! Mark the three inner corners like a teacher. Pay attention to make measurement records.
(Health measurement, teacher tour, individual guidance)
Teacher: Please sit down. Now, please ask a group of students at the front and back tables to fill in the table on page 78 of the textbook and calculate the sum of the three internal angles. (Students calculate in groups and fill in the form)
Teacher: Now which group would like to share your measurement and calculation results with you?
(roll call report, several groups write on the blackboard)
Teacher: Through the reports of several students just now, students will definitely find that because everyone draws different triangles, the degree of measurement is different. So what do you find from the results of our calculation of the sum of internal angles?
1: I found that the sum of the internal angles of the triangle is close to 180.
Health 2: I found that the sum of the internal angles of a triangle is 180.
……
Teacher: Yes, the teacher told you that the sum of the inner angles of any triangle is 180. This is another important feature of the triangle. (blackboard writing: the sum of the inner angles of the triangle is 180. )
Teacher: Who can explain why some students' calculation results are not exactly 180?
Health 1: Because the measurement is not accurate.
Health 2: Because there is an error in the measurement.
(Comment: Suhomlinski said: In people's heart, there is a deep-rooted need to be a discoverer, researcher and explorer, and this need is particularly strong in children's spiritual world. Teachers adapt to students' needs, push students to the stage of autonomous learning, and let students communicate, experience and have the opportunity to share themselves in activities.
And other people's ideas and achievements, so that you can truly become the master of learning.
Third, the operation verification
Teacher: The students' analysis is very good. We know that the sum of the internal angles of a triangle is 180 through measurement and calculation. Then, if you don't measure and calculate, can you verify that the sum of the internal angles of the triangle is 180? Ok, please try to cut it yourself with the graphics in your hand. (Students start to cut and spell, teachers patrol and guide, and pay attention to students with learning difficulties)
Teacher: Who can tell you your method?
1: tear off two of the angles, and then put the three angles together to form a right angle, so the sum of the inner angles of the triangle is 180.
Health 2: There is another kind here, that is, draw a height first, and then fold three angles inward, so the sum of the inner angles of the triangle is 180.
……
Teacher: It seems that no matter what method students use, the conclusion is the same, that is, the sum of the inner angles of the triangle is 180. Since the sum of the internal angles of the triangle is 180, it is impossible to choose a new king that is larger than the sum of the internal angles. The old king had no choice, and the election of the triangle kingdom came to an end temporarily.
(Comments: After the students came to the conclusion that the sum of the internal angles of the triangle is 180 through independent inquiry, the teacher designed some applied exercises to consolidate the exercises in time, which is beneficial for students to internalize what they have learned. )
Fourth, consolidate new knowledge and expand practice.
(1) Teacher: Triangles are also widely used in life. Let's walk into life together and triangle together. (Computer display)
1. Show your bike and find the triangle. It is known that ∠ A = 80 and ∠ B = 30. How many degrees is ∠C?
2. Show the bridge and find the triangle (right triangle). Given ∠ A = 40, what is ∠B?
3. Show the palace and find the triangle. ∠ A = 25 is known. What are the degrees of ∠B and ∠C respectively?
(2) 1. Teacher: Students, you can't choose a new king by comparing the sum of internal angles, so Lao Wang decided to compare the sum of two acute angles in the triangle, and the obtuse triangle, right triangle and acute triangle argued again. Who can win? Please think about it, discuss it and explain your reasons. (Students think independently and communicate in groups)
Teacher: Who will report the result of your discussion?
Health: The sum of any two acute angles of an acute triangle is greater than 90.
The sum of two acute angles of a right triangle is equal to 90 degrees.
The sum of two acute angles of an obtuse triangle is less than 90 degrees.
Teacher: It seems that the acute triangle finally won, and the fierce election finally came to an end.
There will be a grand dance in the palace to celebrate the success of this election. Many triangles come to participate. Please guess what triangles they are according to the hint. (Computer display)
(1), I have two acute angles, both 15.
(2) One of my angles is 30 and the other is 60.
(3) One of my angles is 50 and the other is 48.
I have two horns, both 45.
I have three angles, all 60.
There is a portrait of the old queen in the palace, which has faded after years of erosion. The painters want to restore this painting, but they only know that one of the angles is 65, and they don't know the degrees of the other two angles. According to records, the old queen is an isosceles triangle. Are students interested in solving this problem?