Interview for teachers in Yanling to talk about mathematics.

The sum of the inner angles of polygons is the content of the fourth quarter of Chapter 6 of 8th grade, the second volume of Beijing Normal University. The formula of polygon interior angle reflects the quantitative relationship between polygon elements and is the basic property of polygon. The formula of polygon interior angle sum is the application, popularization and deepening of triangle interior angle sum theorem, which originates from and includes triangle interior angle sum theorem. The formula of polygon inner angle sum provides a knowledge base for learning the formula of polygon outer angle sum and the related angles of quadrilateral and regular polygon.

Second, talk about learning.

Next, I will talk about my classmates. They have a good understanding and application of knowledge, like cooperative inquiry learning and have a strong interest in mathematics learning. In the past study, students' practical ability has been cultivated to a certain extent, and this class will further cultivate students' ability in these aspects.

Third, the teaching objectives

Teaching goal is the direction of teaching activities, the expected result, and the starting point and destination of all teaching activities. I have carefully designed the following teaching objectives:

Knowledge and skills

Master the formula of polygon interior angle sum, and use the formula to find the polygon interior angle sum correctly.

Process and method

Through the exploration of "polygon interior angle sum formula", the ability of analyzing and solving problems is improved, and the idea of mathematical transformation is fully understood.

Emotional attitudes and values

Through a series of processes of guessing, inducing and reasoning formulas, experiencing mathematics activities is full of exploration and creativity, which improves the interest and innovative spirit of learning mathematics.

Fourthly, the difficulties in teaching.

Based on the new curriculum standards, through in-depth reading of textbooks and understanding of students' characteristics, I found the following difficulties:

focus

Explore the formula of the sum of angles in polygons.

difficulty

The derivation process of the formula of polygon internal angle sum.

Verb (abbreviation of verb) teaching method

According to the teaching objectives, teaching materials and students' cognitive characteristics, I adopt heuristic and exploratory teaching methods, aiming at helping students acquire knowledge from practice through observation and hands-on. The whole process of inquiry learning is full of communication and interaction between teachers and students, which shows that teachers are the organizers and guides of teaching activities, while students are the main body of learning.

Sixth, the teaching process.

The teaching process is a process of active participation, interaction and development between teachers and students. The specific teaching process is as follows:

(A) the introduction of new courses

In this section, I will show through PPT that the center of the square I found when I visited the square on weekends is a Pentagon, the internal angle of the Pentagon and how many degrees it is, thus leading to today's topic. Then show triangles, quadrilaterals, pentagons and mixed figures. Let students recall that the sum of the internal angles of a triangle is 180 through the question "What is the sum of the internal angles of a triangle". . So what is the sum of the internal angles of the quadrilateral? Pentagon, hexagon ... what about n polygons? Will there be a relationship between the inner angles of polygons and triangles? " This leads to students' thinking, and then leads to the topic: the sum of the inner angles of polygons.

(Design intent: In this session, PPT is used to present graphics, which will guide students to review that the sum of the interior angles of a triangle is 180, and help students to establish the relationship between the sum of the interior angles of a polygon and the sum of the interior angles of a triangle. )

(2) Explore new knowledge

1. Find the sum of internal angles of quadrilateral, pentagon and hexagon.

In this session, I will ask students to draw a rectangle or a square in the exercise book first, and then draw a quadrilateral at will. And consider this question: the sum of the internal angles of a square and a rectangle is equal to 360, so is the sum of the internal angles of any quadrilateral equal to 360? Can you prove your conclusion? Let the students think for themselves first, and then discuss the process of solving the sum of the internal angles of any quadrilateral with their deskmates as a group. During this period, I will also guide students to analyze the problem-solving ideas in time-how to sum the internal angles of triangles and quadrilaterals. It is further found that only one diagonal line needs to be connected, that is, a quadrilateral is divided into two triangles. The internal angle sum problem of quadrilateral is transformed into all internal angle sum problems of two triangles. After that, I will ask students to explore the process of the sum of internal angles of any quadrilateral by analogy, and explore the sum of internal angles of pentagons and hexagons. Students think independently first, then discuss in groups of four people in the front and back tables, and then ask representatives of one or two groups to report their thoughts and results. By analogy with the research process of the sum of internal angles of quadrangles, students will draw the following conclusions: starting from a vertex of a pentagon, two diagonals can be made, and starting from a vertex of a hexagon, three diagonals can be made. Three triangles and four triangles are obtained respectively, so the sum of the internal angles of pentagon and hexagon is sum respectively. At this time, I will also explain why pentagons and hexagons are missing two triangles from the perspective of vertices and sides. Because the selected vertex and two adjacent vertices cannot be diagonal, the selected vertex and its two sides cannot form a triangle.

(Design intention: This session guides students to operate, think and discuss in groups, from quadrangles to pentagons to hexagons, and further understands the reduction process of dividing polygons into several triangles through knowledge transfer. The influence of the number of sides, diagonals and triangles on the sum of internal angles of polygons is further clarified, which lays a foundation for the study of the sum of internal angles from concrete polygon abstraction to general N-polygon. )

2. Explore and prove the internal angles and formulas of N-polygon.

(Design intention: This link allows students to experience the method of studying problems from concrete to abstract, and realize the function of returning to thinking. Filling in the form can help students review the exploration ideas of the sum of internal angles of N polygons. )

(3) Deepening new knowledge

In this section, I will show an example with multimedia courseware: If the diagonal of a quadrilateral is complementary, what does the other diagonal matter?

Ask the students to draw a picture and translate the written language into symbolic language according to the picture. It is clear that ∠ A+∠ C = 180 is known, and what is sought is ∠ B+∠ D. After the students finish the problem solving process independently, I will lead them to a conclusion: if one set of corners of the quadrilateral is complementary, then the other set of corners is also complementary.

(4) Consolidate and improve

In this session, I will say two questions orally: 1. What is the sum of the internal angles of an octagon? 2. Given that all internal angles of a polygon are 120, how many polygons is this polygon? Ask students to complete and answer independently.

(Design intention: The topic of oral description aims to enable students to use the formula of polygon internal angle sum from both positive and negative aspects to solve simple calculation problems related to polygon internal angle sum. )

(5) Summarize the homework

In the conclusion session, I will ask students to answer the following three questions: (1) What did you learn in this class? (2) How do we get the formula of polygon interior angle? (3) What is the function of connecting diagonals in the process of exploring the formula of polygon internal angles?

(Design intention: By summing up, guide students to sum up their own gains from two aspects: knowledge content and learning process. By establishing the relationship between knowledge, we highlight the idea of transforming complex graphics into simple graphics, and emphasize the method of studying problems from special to general. )

In the homework section, I will ask students to do a good job in the preview of polygon outer angles and knowledge on the basis of reviewing polygon inner angles and knowledge.

(Design intention: Students can have a preliminary understanding of new knowledge through pre-class preparation and promote the smooth progress of new knowledge learning. )

Seven, blackboard design

In order to reflect the knowledge points in the textbook and make students understand and master it, I used a graphic blackboard writing, which is my blackboard writing design.