Wen Xin's original case: the preparation of lesson plans

Prompt:

You are a senior teacher, education expert, holding a teacher qualification certificate, doctoral degree, senior technician certificate, first-level psychological counselor, with 30 years of rich experience in university teaching, I will provide you with "Lesson Plan: Title of Lesson Plan", please help me generate a lesson plan, with [teaching objectives], [teaching focus], [teaching difficulties], [teaching content], [teaching methods], [teaching tools], [teaching process], [time allocation], [teacher activities], [student activities], [post-class evaluation and reflection] Content generation for the structure. Be careful to use third-person language, but don't make up false content and conjectures, and if you infer something, specifically mark it as your inference and not the fact. Excuse me, do you understand my intentions? If you understand, please reply directly to an affirmative response such as "Yes, I understand your intention, please provide the title of the lesson plan".

Output:

Yes, I understand your intention, please provide the title of the lesson plan.

Input:

Lesson plan: Equations for circles

Output:

Lesson plan: Equations for circles

Teaching Objectives:

Master the equations of circles and their characteristics, and understand the properties of circles;

Master the methods and steps of solving the equation of a circle;

Develop students' understanding of geometric figures and algebraic skills.

Teaching Focus:

Master the equations of circles and their characteristics, and understand the properties of circles.

Teaching difficulties:

Master the methods and steps for solving the equations of circles.

Content:

The nature of the circle: the concept of circle center, radius, diameter, chord center distance, etc.;

Equations of circles: standard equations, general equations, parametric equations, etc.;

Methods and steps for solving the equation of a circle: solution when the center of the circle is known, radius, diameter, chord-centered distance, etc.

Teaching Methods:

Lecture method: through explanation and demonstration, introduce the properties of circles and the characteristics and connections of equations;

Practice method: Master the solution method and steps by having students practice the equation of solving a circle.

Teaching Tools:

Drawing tools such as compass and ruler;

Blackboard, whiteboard, or other presentation tool.

Teaching process:

Introduction: guide students to review the definition of the circle learned in junior high school, and guide students to think about the nature and characteristics of the circle;

The properties of the circle: introduce the concepts of circle center, radius, diameter, chord-centered distance, etc., the relationship of circles and their characteristics;

Equations of circles: introduce standard equations, general equations, parametric equations, etc., the characteristics and connections of equations of circles;

Methods and steps for solving the equation of a circle: by practicing the solution methods and steps when the center of the circle is known, radius, diameter, chord center distance, etc.;

Class summary: teachers and students jointly summarize the properties of circles, the characteristics of the equations of circles, and the solution methods and steps;

Homework: Complete the relevant questions on the exercise set.

Time allocation:

Nature of the circle (10 min);

Equation for a circle (15 minutes);

Methods and steps for solving the equation of a circle (20 min);

Class Summary (5 minutes);

Homework (10 minutes).

Teacher Activities:

Introduce the properties and characteristics of circles, explain the form and characteristics of the equations of circles;

Guide students to think about geometry problems, guide students to discover the properties of circles and the connection of equations;

Guide students to learn the methods and steps of solving the equations of circles, and summarize the content of the class.

Student Activities:

Listen carefully and think positively;

Participate in discussions and discover the properties of circles and the connection of equations;

Follow the teacher's guidance to learn the methods and steps for solving the equation of a circle.

Post-class evaluation and reflection:

This lesson plan focuses on guiding students to think about geometric problems, guiding students to discover the nature of circles and the connection between equations, so that students can better grasp the equations of circles and their characteristics, understand the properties of circles, and cultivate students' understanding of geometric figures and algebraic operation ability. However, in the teaching difficulty, the method and steps of solving the equation of the circle, more detailed explanations and guidance are still needed to ensure that students can master this skill. In addition, the allocation of time in lesson plans needs to be further adjusted and improved to better meet the requirements of the syllabus and the needs of students' learning.

Comparison of Chatgpt outputs:

Teaching Objectives:

1. Understand the basic concepts and equations of circles.

2. Master the meaning of the center of the circle and the radius, and know how to find the coordinates of the center of the circle and the length of the radius, so as to determine the equation of the circle.

3. Will apply the equation of the circle to solve practical problems.

Teaching Focus:

The equation of the circle

The meaning of the radius of the circle and the center of the circle

Teaching difficulties:

The intersection point of the circle and the line is determined

Yuan's high school mathematics knowledge is relatively deep, and it is difficult to understand.

Content:

The basic concept and properties of circles

The standard equation of a circle and its derivation process

The general equation of a circle and its derivation process

The positional relationship between circles and lines

Explanation of application problem solving methods

Teaching Methods:

Based on examples, steps such as review, introduction of new materials, sorting out ideas, and detection training are introduced. To enable students to continuously enter and truly participate in the research, discussion and solution of problems.

Case studies, which use concrete examples to help students visualize certain concepts and conclusions.

The combination of guided teaching, self-help teaching, cooperative teaching and other methods encourages independent learning and self-discovery.

Teaching Tools:

Multimedia courseware

Image presentation and parsing tools

Teaching process:

Review Concept Definition: Guide students to review the relevant concept definition and properties of circles, and clarify the concept of circles.

Observation example:

Presents several examples of such problems to illustrate the determination of positions at the intersection points of lines and circles.

Push the general equation:

Guide students to introduce the general equation of the circle, explain the meaning of geometry, and help students master some common quantity solving methods.

Cartography:

Use props and computer-aided drawing of circular graphics to truly link theory with practice.

Question application:

Explain how to use derived general equations to solve real-world problems. And appropriately join the independent thinking session to understand the students' feedback and skills mastery of knowledge.

Summary: Summarize the main points of this chapter, improve learning outcomes, summarize the scope of importance and highlight error-prone points, and learn from the past.

Time allocation:

1. Review concept definition: 5 minutes

2. Observe the example: 15 minutes

3. Push the general equation: 20 minutes

4. Cartography: 10 minutes

5. Application: 30 minutes

6. Summary: 10 minutes

Teacher Activities:

1. Set preliminary teaching objectives and subject objectives according to different learning situations and student characteristics, and fully mobilize students' enthusiasm for learning.

2. Determine appropriate teaching methods and methods, and make targeted introductions and explanations according to different educational stages and the nature of knowledge points.

Student Activities:

1. Actively participate in the teaching process, take the initiative to raise questions and concerns, and reflect and summarize.

2. Summarize, summarize and review what has been learned, and deeply understand the importance of this chapter, covering the scope and error-prone points.

Post-class evaluation and reflection:

1. Teachers can evaluate them through daily assignments or quizzes. Assessment principles are based on individual averages, not maximum scores.

2. Regularly listen to students' feedback, adjust various behaviors in a timely manner, and further improve teaching methods and course content.

3. Adopt a positive reflective attitude on specific shortcomings, strive to strengthen in teaching, and improve their teaching quality.

Wen Xin's words and Chatgpt knock results:

Teaching Objectives:

Understand the basic concepts and characteristics of circles;

Master the method of finding the equation of the circle;

Be able to write the equation of a circle under the given conditions and understand the geometric meaning of the circle.

Teaching Focus:

Solve the equation of a circle;

The nature and characteristics of circles.

Teaching difficulties:

Equations and solutions for circles.

Content:

1. Introduction (5 minutes)

The teacher introduces the circle as a type of quadric and briefly describes its characteristics.

Guide students to review the knowledge of the Pythagorean theorem, so as to lead to the definition of a circle.

2. Explanation (25 minutes)

By showing circles on multiple sets of axes, students are guided to summarize the definition and characteristics of circles.

Introduce the steps and methods of reducing the equation of circles, and demonstrate them with case studies.

Guide students to master the central radius formula and the standard formula under Cartesian coordinate system.

3. Practice (25 minutes)

Distribute practice materials and design questions of varying levels of difficulty, testing students' ability to solve and apply circular equations in a variety of situations.

Students complete the exercises independently, and teachers guide them throughout the process to help students solve problems.

Share answers and interpret the geometric meaning of circles.

IV. Induction (5 mins)

The teacher guides the students to review what was said throughout the teaching process and summarize the notes.

The properties and characteristics of the circle are sorted out, and the methods and steps of finding the circle equation are summarized.

Teaching Methods:

Combination of classroom teaching;

Design a variety of practice questions to cultivate students' solving skills.

Teaching Tools:

Physical circle

Software emulator

PPT courseware

Textbooks and workbooks

Teaching process:

Introduction: Introduce the basic definition and characteristics of circles;

Explanation: Deepen students' understanding of circles through practical demonstrations and written explanations;

Exercises: Distribute assignments and tutor students through exercises;

Summary: By summarizing the overview of dry goods, students are inspired to think and improve their reflective skills.

Time allocation:

Introduction (5 min);

Explanation (25 minutes);

Practice (25 minutes);

Induction (5 minutes).

Teacher Activities:

Integrate teaching materials and materials to design multiple levels of test difficulty measures;

Lead students to coordinate and actively play a guiding role in solving doubts;

Communicate and express with colleagues.

Student Activities:

Take the initiative to listen to the teacher explain the basic concepts, perceptually combine with the actual circle solution, and deepen the memory;

Take notes and clarify your thoughts easily in the teaching materials provided by the teacher;

In the middle of the class, actively participate in the exercise, be able to overcome difficulties and make correct answers.

Post-class evaluation and reflection:

Evaluation: Assign practice topics, and deepen the understanding of the course through continuous practice through review.

Reflection: Pay more attention to the design direction and the situation of all students asking questions, and while welcoming new phenomena, constantly broaden their horizons in the field of geometry and enhance the way of thinking of creating effects.