Is it easy to test the Pythagorean theorem in junior middle school mathematics in the teacher recruitment exam?

You may take the exam, you can design it like this:

1. Analysis of teaching materials

(1) The status of teaching materials

This lesson It is Chapter 19, Section 2, Chapter 19, Section 2, of the standard experimental textbook for the nine-year compulsory education course of East China Normal University. Exploring the Pythagorean Theorem. The Pythagorean Theorem is one of several important theorems in geometry. It reveals the relationship between the three sides of a right triangle. Quantitative relationship. It has played an important role in the development of mathematics and has a wide range of roles in the current world. By studying the Pythagorean Theorem, students can have a further understanding of right triangles based on the original knowledge.

(2) According to the curriculum standards, the teaching objectives of this lesson are:

1. Be able to tell the content of the Pythagorean Theorem.

2. Be able to initially use the Pythagorean theorem to perform simple calculations and practical applications.

3. In the process of exploring the Pythagorean Theorem, let students experience the mathematical ideas of "observation-conjecture-induction-verification", and experience the combination of numbers and shapes and the special to general thinking methods.

4. By introducing the study of the Pythagorean Theorem in ancient China, it inspires students to love the motherland and the long culture of the motherland, and encourages students to study hard.

(3) The teaching focus of this lesson: Exploring the Pythagorean Theorem

The teaching difficulty of this lesson: Calculation of the area of ??a square with a right triangle as its side.

2. Analysis of Teaching and Learning Methods

Teaching Method Analysis: Based on the knowledge structure and psychological characteristics of the second-grade students, this lesson can choose the guided exploration method, from the shallower to the deeper. , asking questions from the specific to the general. Guide students to explore independently, cooperate and communicate. This teaching concept reflects the spirit of the times, is conducive to improving students' thinking ability, and can effectively stimulate students' thinking enthusiasm. The basic teaching process is: raising questions-experimental operations-inductive verification-problem solving —Class summary—Assign six parts of homework.

3. Teaching process design

(1) Introduction to the history of mathematics

Introducing a new lesson based on Pythagoras’ discovery of the Pythagorean theorem is not only natural, but also It reflects the basic view that mathematics comes from real life and mathematics arises from human needs. It also reflects the generation process of knowledge, and the process of solving problems is also a "mathematical" process.

(2) Experimental operation

1. Project the textbook picture on the right triangle problem and ask students to calculate the areas of squares A, B, and C. Students may have different methods, regardless of Whether to find it by directly counting the number of small squares, or by dividing C into 4 congruent isosceles right triangles, etc., various methods should be affirmed, and students should be encouraged to express them in language to guide students to discover The quantitative relationship between the areas of squares A, B, and C. Through the relationship between the areas of the squares, students can easily find that for an isosceles right triangle, the sum of the squares of the two right-angled sides is equal to the square of the hypotenuse. This will help students participate in exploration and feel the process of mathematics learning. It will also help students develop their language expression ability and experience the idea of ??combining numbers and shapes.

2. Then let students think: If it were other general right triangles, would it also have this conclusion? Therefore, projecting Figures 1-3 and 1-4 also allows students to calculate the area of ??a square. However, the area of ??square C is not easy to find. Students can draw figures on the graph paper prepared in advance, cut them, and put them together. After a puzzle, it is not difficult for students to find that for ordinary right triangles with integers as side lengths, the sum of the squares of the two right-angled sides is equal to the square of the hypotenuse. This design not only helps break through difficulties, but also lays the foundation for inductive conclusions, allowing students to experience the ideas of observation, conjecture, and induction, and also allows students to invisibly improve their ability to analyze and solve problems, which will be helpful for the following Learning and helpful.

3. Given a right triangle with side length units of 5, 12, and 13, including decimals, let students calculate whether this conclusion is also satisfied. The purpose of the design is to make students realize that the conclusion is more meaningful. general.

(3) Inductive verification

1. Induction of the three-side relationship of an isosceles right triangle with an integer side length to a general right triangle and then to a right triangle with a decimal side length Research, let students use mathematical language to summarize general conclusions. Although what students say may not be completely correct, it is beneficial to cultivate students' ability to use mathematical language to abstract and generalize. It also plays the main role of students and facilitates memory. and understanding, which is much better than teachers directly teaching students a conclusion.

2. Verification In order to make students convinced of the correctness of the conclusion, guide students to make a right triangle on the paper and verify the correctness and extensiveness of the conclusion through hands-on operation of the puzzle. This process is conducive to cultivating students' rigorous and scientific learning attitude. Then guide students to express in symbolic language, because converting literal language into mathematical language is a basic ability for learning mathematics. Then the teacher introduced the meaning of "hook, strand, string" and the Pythagorean theorem to the students, asked some questions, and pointed out that the Pythagorean theorem only applies to right triangles. Finally, the students were introduced to the research on the Pythagorean Theorem at home and abroad in ancient and modern times, and the students were educated in patriotism and mathematical culture.

(4) Problem Solving

Let students solve practical problems in life, from which students can experience the joy of success. Complete the textbook "Think About It" to further understand the application of the Pythagorean Theorem in real life. Mathematics is closely connected with real life.

(5) Class Summary

Mainly through students' recall of what they learned in this lesson, a summary will be made first from the aspects of content, application, mathematical thinking methods, and ways to obtain new knowledge, and then Teacher summary.

(6) Assigning homework

Exercise 19.2 (1-5)