1. Excellent courseware for junior high school mathematics
I. teaching material analysis
The content of this section is "Mathematics (May 4th School System), an experimental textbook for compulsory education courses" published by People's Education Publishing House (Tianjin Edition). Chapter 10 Algebraic Addition and Subtraction in Section 1 Algebraic Addition and Subtraction in Section 2.
Second, the design ideas
The content of this section is that students have mastered the extended learning of related concepts of algebraic expressions, which lays a foundation for the subsequent study of algebraic expression operation, factorization, quadratic equation of one variable and function knowledge. It is a formal transition from "number" to "formula" and has a very important position.
Grade eight students have strong numerical operation skills and a sense of "combination" (used to solve a linear equation), as well as preliminary observation, induction and exploration skills. Therefore, based on the teaching materials, with the aim of making every student develop, I use cooperative inquiry learning to carry out teaching activities, guide students by designing targeted and multi-style questions, and provide students with a full and harmonious inquiry space for students to learn. Learning activities not only cultivate students' awareness of simplification and improve their mathematical operation skills, but also make students deeply realize that mathematics is an important tool to solve practical problems and enhance their awareness of applying mathematics.
Third, the teaching objectives:
(1) Knowledge and skill objectives:
1, understand the meaning of similar items and distinguish them.
2. Master the method of merging similar items and be proficient in merging similar items.
3. Master the addition and subtraction of algebraic expressions and operate skillfully.
(2) Process and method objectives:
1. Cultivate students' ability of observation, induction and inquiry by exploring the definition and combination of similar items.
2. Through the combination of addition and subtraction exercises of similar terms and algebraic expressions, students' operation skills and accuracy are improved, students' awareness of simplification is cultivated, and their ability of abstract generalization is developed.
3. Develop students' thinking in images and cultivate students' sense of symbols by studying examples and exploring examples 1.
(3) Emotional value goal:
1. Cultivate students' awareness of cooperation and communication and the spirit of daring to explore unknown issues through communication, consultation and group inquiry.
2. Cultivate students' scientific and rigorous learning attitude through learning activities.
Four, the teaching emphasis and difficulty:
Combine similar terms
Five, the key to teaching:
The concept of similar goods
Six, teaching preparation:
Teacher:
1, select math problems and carefully set the problem situation.
2. Make two physical models of rectangular cartons with different sizes and unfold them.
3. Design multimedia teaching courseware. (It is necessary to highlight ① the characteristics of coefficient, letter and index in a single item ② the perspective view and development diagram of the rectangular box. )
Student:
1, review the concept of monomial, the four operations of rational numbers and the rule of removing brackets)
2. Make two cuboid carton models with different sizes in each group.
2. Excellent courseware of junior high school mathematics
I. teaching material analysis
(A) the status of teaching materials
This lesson is the first lesson of Exploring Pythagorean Theorem, a junior high school textbook for nine-year compulsory education. Pythagorean theorem is one of several important theorems in geometry, which reveals the quantitative relationship between three sides in a right triangle. It has played an important role in the development of mathematics and has a wide range of functions in the world at present. Through the study of Pythagorean theorem, students can have a further understanding and understanding of right triangle on the original basis.
(B) Teaching objectives
Knowledge and ability: master Pythagorean theorem and use Pythagorean theorem to solve some simple practical problems.
Process and method: experience the process of exploring and verifying Pythagorean theorem, understand the method of verifying Pythagorean theorem with puzzles, cultivate students' reasonable reasoning consciousness, the habit of active exploration, and feel the combination of numbers and shapes and the thought from special to general.
Emotional attitude and values: inspire students' patriotic enthusiasm, let students experience their sense of accomplishment in trying to draw conclusions, experience mathematics full of exploration and creation, and experience the beauty of mathematics, so as to understand and like mathematics.
(3) Teaching emphasis: Experience the process of exploring and verifying Pythagorean theorem, and use it to solve some simple practical problems.
Teaching difficulty: using area method (puzzle method) to discover Pythagorean theorem.
The way to highlight key points and break through difficulties: give full play to students' main role, and let students explore in the experiment, understand in the exploration and comprehend in the comprehension through students' hands-on experiments.
Second, the analysis of teaching methods and learning methods:
Analysis of academic situation: Grade 7 students have acquired certain abilities of observation, induction, conjecture and reasoning. They have learned some calculation methods of geometric figure area (including cutting and mending) in primary school, but their awareness and ability to solve problems by using area method and cutting and mending ideas are not enough. In addition, students generally study and participate in classroom activities more actively, but their cooperation and communication skills need to be strengthened.
Analysis of teaching methods: Combining the characteristics of seventh-grade students and the teaching materials in this section, the mode of "problem situation-establishing model-explaining application-expanding and consolidating" is adopted for teaching, and the guided inquiry method is selected. Turn the teaching process into a process of students' personal observation, bold guess, independent exploration, cooperation and exchange, and induction.
Analysis of learning methods: under the guidance of teachers' organization, students adopt the discussion learning mode of independent inquiry and cooperative communication, so that students can truly become the masters of learning.
Third, the teaching process design
1. Create situations and ask questions.
2. Experimental operation and model construction
3. Return to life and apply new knowledge.
4. Expansion, consolidation and deepening of knowledge.
5。 Feel the harvest and assign homework
(A) the creation of questioning situations
(1) Picture Appreciation Pythagorean Theorem Digital Diagram 1955 Greece issued a beautiful Pythagorean tree, a commemorative stamp of 20xx international mathematics. The design intention is to appreciate the beauty of mathematics and feel the cultural value of Pythagorean theorem through graphics.
(2) A fire broke out on the third floor of a building. Firefighters came to put out the fire and learned that each floor was 3 meters high, so they got 6. For a 5-meter-long ladder, if the distance from the bottom of the ladder to the wall base is 2 or 5 meters, can firefighters enter the third floor to put out the fire?
Design intention: Introducing new courses from practical problems reflects that mathematics comes from real life and people's needs, and also reflects the process of knowledge. The process of solving problems is also a "mathematical" process, which leads to the following links.
(2) Construction of experimental operation model
1, isosceles right triangle (several squares)
2, general right triangle (section)
Question 1: What is the relationship between the areas of squares I, II and III for isosceles right triangle?
Design intention: This will help students to participate in exploration, cultivate their language expression ability and experience the idea of combining numbers with shapes.
Question 2: Do the areas of squares I, II and III have the same relationship for a general right triangle? (Digging and filling method is the difficulty of this section, organize students to cooperate and exchange. )
Design intention: It is not only conducive to breaking through difficulties, but also lays a foundation for inductive conclusion, so that students' ability to analyze and solve problems can be improved invisibly.
Through the above experiments, the Pythagorean theorem is summarized.
Design intention: Through cooperation and communication, students summed up the rudiment of Pythagorean theorem, cultivated students' abstract generalization ability, and at the same time played the main role, experiencing the cognitive law from special to general.
(3) Return to life and apply new knowledge.
Let students solve problems in the opening scene, call for help before responding, enhance students' awareness of learning and using mathematics, and increase the fun and confidence of applying what they have learned.
Fourth, the expansion, consolidation and deepening of knowledge
Basic questions, situational questions and inquiry questions.
Design intention: give a group of questions, divide them into three gradients, practice from shallow to deep, take care of students' individual differences and pay attention to students' personality development. The application of knowledge has been sublimated.
Basic question: The right side of a right triangle is 3, the hypotenuse is 5, and the other right side is X. How many mathematical questions can you ask according to the conditions? Can you solve the problem raised?
Design intent: This problem is based on double cardinality. By creating their own situations, students have exercised divergent thinking.
Situation: Xiaoming's mother bought a 29-inch (74 cm) TV set. Xiao Ming measured the TV screen and found that the screen was only 58 cm long and 46 cm wide. He thinks that the salesman must have made a mistake. Do you agree with his idea?
Design intention: to increase students' common sense of life, and also to show that mathematics comes from life and is used in life.
Question: Can a wooden box with a length of 50 cm, a width of 40 cm and a height of 30 cm be put in? Why? Try to explain what you learned today.
Design intention: It is relatively difficult to explore the problem, but teachers use the teaching mode to cooperate and communicate with students, expand students' thinking and develop their spatial imagination.
Five, feel the harvest operation:
What have you gained from this course?
Homework:
1, textbook exercises
2. Collect information about the proof of Pythagorean theorem.
3. Excellent courseware of junior high school mathematics
I. teaching material analysis
This lesson is the sum of the inner angles of the polygon in the third section of Chapter 7 in the second volume of the seventh grade of the compulsory education curriculum standard experimental textbook (63 academic system) published by People's Education Press.
Second, the teaching objectives
1, knowledge goal: to understand the internal angles and formulas of polygons.
2. Mathematical thinking: By transforming polygons into triangles, the application of transformation thinking in geometry can be realized, and at the same time, students can experience the method of understanding problems from special to general.
3. Problem solving: By exploring the internal angles and formulas of polygons, trying to find solutions to problems from different angles can effectively solve problems.
4. Emotional attitude goal: through guessing and reasoning activities, I feel that mathematics activities are full of exploration and certainty of mathematical conclusions, and improve students' learning enthusiasm.
Third, the importance and difficulty of teaching
Focus: Explore the sum of the inner angles of polygons.
Difficulties: How to convert polygons into triangles when exploring the sum of internal angles of polygons?
Fourth, teaching methods: guided discovery method and discussion method.
Verb (abbreviation for verb) teaching AIDS and learning tools
Teaching aid: multimedia courseware
Learning tools: triangle, protractor
Sixth, teaching media: large screen, physical projection.
Seven, the teaching process:
(1) Create situations, set doubts and stimulate thinking.
As we all know, the sum of the internal angles of a triangle is 180. Do you know the sum of the internal angles of a quadrilateral?
Activity 1: Explore the sum of internal angles of quadrilateral.
On the basis of independent exploration, students discuss in groups and summarize the methods to solve problems.
Method 1: Measure the degrees of four angles with a protractor, and then add up the four angles, and find that the sum of the internal angles is 360.
Method 2: Put two triangular cardboard together to form a quadrilateral, and find the sum of the internal angles of the two triangles as 360.
Next, on the basis of the second method, the teacher guides the students to connect the diagonals of the quadrilateral with the method of auxiliary lines to transform a quadrilateral into two triangles.
Teacher: Do you know the sum of the internal angles of a Pentagon? How about a hexagon? How about a decagon? How did you get it?
Activity 2: Explore the sum of internal angles of pentagon, hexagon and decagon.
Students think about each question independently before group discussion.
Concern:
(1) Can students draw a correct conclusion by quadrilateral analogy?
(2) Whether students can adopt different methods.
Students discuss and communicate in groups (sum of internal angles of pentagon)
Methods 1: Divide the Pentagon into three triangles, and the sum of the three 180 is 540.
Method 2: Starting from a point inside the Pentagon, divide the Pentagon into five triangles, and then subtract a fillet 360 from the sum of five 180. The result is 540.
Method 3: Divide the Pentagon into four triangles from any point on one side of the Pentagon, and then subtract a right angle 180 from the sum of the four 180, and the result is 540.
Method 4: Divide the Pentagon into triangles and quadrilaterals, and then add 180 to 360 to get 540.
Teacher: How clever you are! I have applied what I have learned.
After the communication, students use the geometric sketchpad to demonstrate and verify the method.
After getting the sum of the internal angles of the pentagon, the students seriously discussed the sum of the internal angles of the hexagon and the decagon. By analogy with the discussion method of quadrilateral and pentagon, it is finally concluded that the sum of internal angles of hexagon is 720 and that of decagon is 1440.
(B) to expand thinking and cultivate innovative ability
Teacher: From the previous discussion, can you know the sum of the inner angles of polygons?
Activity 3: Explore the internal angles and formulas of arbitrary polygons.
Thinking:
What is the relationship between the sum of internal angles of (1) polygons and the sum of internal angles of triangles?
(2) What is the relationship between the number of sides of a polygon and the sum of internal angles?
(3) What is the relationship between the number of diagonal triangles drawn from a vertex of a polygon and the number of sides of the polygon?
Students discuss with thinking questions and exchange the results after discussion.
It is found that the sum of 1: quadrilateral internal angles is the sum of two 180, pentagonal internal angles is the sum of three 180, hexagonal internal angles is the sum of four 180, and decagon internal angles is the sum of eight 180. Discovery 2: The number of sides of a polygon increases by 1, and the sum of internal angles increases by 180.
It is found that there is a (n- 2) relationship between the number of diagonal triangles drawn from the vertices of N-polygons and the number of sides N. ..
The formula for the sum of polygons' internal angles is (n-2) 180.
(C) practical application, complementary advantages
1, oral answers: (1) and ()
(2) nonagon's internal angle and ()
(3) The sum of the internal angles of the decagon ()
2. Answer first: (1) The sum of the inner angles of the polygon is equal to 1260. How many polygons are there?
(2) If the sum of the internal angles of a polygon is 1440 and the internal angles are equal, then the degree of each internal angle is ().
3. Discuss the answer: The sum of the internal angles of a polygon is 540 more than the sum of the internal angles of a quadrilateral, and all the internal angles of this polygon are equal. How many degrees is each inner angle of this polygon equal to?
(4) Summary storage
Students' self-summary:
1, polygon interior angle and formula
2. Use transformation ideas to solve mathematical problems
3. Solve problems by combining numbers with shapes.
(5) Homework: Page 93, 1, 2, 3.
4. Excellent courseware of junior high school mathematics
Teaching objectives:
1, the initial experience that the same object may see different graphics from different directions;
2. Be able to understand the three views of simple objects and the rationality of the three views of objects;
3. Can draw three views of the cube and its simple combination;
Process and method:
1, in the process of "observation" activities, accumulate experience in mathematical activities and develop the concept of space;
2. Be able to express your thinking process reasonably and clearly in the process of communicating with others;
3. Infiltrate the thinking method of multi-directional observation and analysis;
Emotions and attitudes:
Through a series of activities that students are interested in, they form a positive feeling about learning mathematics, stimulate their curiosity about learning space and graphics, and gradually form a sense of cooperation and communication with others.
Teaching emphases and difficulties:
Key point: realize that different results may be obtained by looking at the same object from different directions.
Difficulties: Can draw three views and simple combinations of cubes.
Teaching rules:
① Discovery teaching method
② The method of combining hands-on practice with thinking.
Teaching process design:
First, create situations and introduce new lessons.
1, watch the video;
2. Observe Lushan Mountain from the ancient poems familiar to students;
3. The floor plan of the house.
Second, observation experience and exploration conclusion
Activity 1: Observe a group of pictures and find out the conclusion.
Activity 2: Observe the pictures and pay attention to the shooting angles of these pictures. Can you pick out a set of three views?
Activity 3: Guess: Take pictures from different angles and guess what the real thing is.
Activity 4: Observe the picture below.
If you look at these three geometries from the front, left and above, what plane figure will you get?
Third, learn to draw three views of simple geometry
Give a combined figure composed of four small cubes, and observe and draw the corresponding plane figure from the front, left and top.
Do: take a group as a unit, build different geometric bodies with six small cubes, and then draw plane figures observed from the front, left and top according to the built geometric bodies, and exchange verification within the group to see who draws the most standard picture. Then the whole class combines three-dimensional graphics according to a set of three views.
Fourth, summary and reflection:
1. What is the main content of this lesson?
2. What effect does the mathematics knowledge of this course have on the usual study and life?
Five, exercises and homework:
Ability homework: Draw three views of our teaching building (from the front facing south), or draw the plan (or design) of your house.
5. Excellent courseware of junior high school mathematics.
First, the teaching purpose:
1. Understand and master the definition of diamond and two judgment methods; Will use these judgment methods to carry out relevant argumentation and calculation;
2. Cultivate students' observation ability, practical ability and logical thinking ability in the exploration and comprehensive application of diamond judgment method.
Second, the key points and difficulties
1. Two methods for judging diamonds.
2. Teaching difficulties: the proof method and application of judgment method.
Third, the intention analysis of examples
There are two examples in this lesson, of which example 1 is example 3 of the textbook P 109, and example 2 is a supplementary topic. These two topics are the direct application of diamond judgment method, the main purpose of which is to enable students to master diamond judgment method and use these judgment methods to carry out relevant argumentation and calculation. The reasoning of these topics is relatively simple, so students will have no difficulty in mastering them and can do it by themselves.
Fourth, classroom introduction
1. Review
Definition of (1) rhombus: a group of parallelograms with equal adjacent sides;
(2) The quality of the diamond is 1. All four sides of the diamond are equal; Property 2 The diagonals of the rhombus are equally divided, and each diagonal is equally divided into a set of diagonals;
(3) How many conditions do diamonds need to meet with the definition of diamonds? (Decision: 2 conditions)
Step 2: Questions
Is there any other way to judge whether a quadrilateral is a diamond according to the definition?
explore
(Exploration in textbook P 109) Use two pieces of wood, one is long and the other is short, fix a small nail at their midpoint, make a rotatable cross, and then enclose it with a rubber band to make a quadrilateral. Turn up the pieces of wood. When will this quadrangle become a diamond?
Through the demonstration, it is easy to get:
Parallelograms with diagonal lines perpendicular to each other are diamonds.
Note that this method includes two conditions:
(1) is a parallelogram.
(2) The two diagonals are perpendicular to each other.
What's the telephone number of China Ministry of Education Office?
Mailing address of Ministry of Education: No.37 Dada Hutong,