Excellent teaching plan model of the first volume of seventh grade mathematics "Geometry"
1, content structure analysis
Nine-year compulsory education curriculum standard experimental textbook &:middot seventh grade mathematics volume I Chapter IV "Preliminary Geometry". This chapter is the beginning of the field of "space and graphics" in the third stage of compulsory education. On the basis of the contents of "space and graphics" learned in the previous two sections, this chapter allows students to further appreciate the colorful graphic world, watch more three-dimensional graphics and plane graphics, get a preliminary understanding of the relationship between three-dimensional graphics and plane graphics, and get to know some simple things through line segments and angles.
2. Teaching emphases and difficulties:
Teaching focus:
(1) Mathematics is closely related to our growth;
(2) Mathematics is accompanied by the progress and development of human beings, and human beings cannot do without mathematics;
(3) Everyone can learn mathematics and stimulate students' interest in learning mathematics;
(4) Transforming practical problems into mathematical problems;
5. Actively participate in mathematics learning activities, experience mathematics activities full of exploration and creation, and feel the rigor of mathematics and the accuracy of mathematical laws.
Teaching difficulties:
(1) Understanding mathematics is closely related to our growth;
(2) Students use gymnastics to cut out pictures and puzzles;
⑶ Try to find, put forward and solve mathematical problems, and realize the importance of cooperation and communication with others.
3. Teaching objectives:
(1) Knowledge and skills:
Intuitively understand three-dimensional graphics and master the basic knowledge of plane graphics; Draw three views and plane expansion drawings of simple three-dimensional graphics, and draw some simple physical drawings according to the three views; Carry out simple calculation of line segments, correctly distinguish line segments, rays and straight lines, master the basic concept of angle and carry out related operations; Consolidating the knowledge of diagonal measurement and operation can solve some practical problems.
(2) Process and method:
Through the study of this chapter, learn to abstract and summarize the mathematical principles in two specific situations; Learn to imagine rationally and think simply and methodically in the process of solving problems; Solve mathematical problems through group cooperation, hands-on operation and experimental verification.
(3) Emotion, attitude and values:
In the process of exploring the relationship and application of knowledge, we can experience the significance of reasoning and gain learning experience.
4. Class allocation
4. 1 geometry 4 class hours
4.2 Line, ray and line segment 3 class hours
4.3 Angle 2 class hours
4.4 Project learning 2 class hours
Summarize 3 class hours
3 class unit test and evaluation
Excellent teaching plan model of the first volume of seventh grade mathematics "Geometry"
Teaching objectives:
Knowledge and skills:
Know common geometric figures and describe their characteristics in your own language.
Process and method:
1. Through the process of abstracting geometric figures from the real world, the objects of geometric research are summarized by comparison.
2. Establish the correspondence between physical objects and geometric figures, establish the concept of geometric figures and develop the concept of space on the basis of reviewing the plane figures learned in primary schools.
Emotions, attitudes and values:
Experience the fun of mathematics learning and improve the consciousness of mathematics application.
Teaching focus:
Students can recognize geometry through observation, discussion, thinking and practice.
Teaching difficulties:
Abstract the concept of geometry from concrete objects
Teaching methods:
Query type
Teaching tools:
Geometric model, physical object, multimedia
Teaching process design:
I. Observing and thinking
Teacher: 1. Show some things in life: cups, books, pencils, pen containers, table tennis, apples, checkers and ice cream cones. 2. The teacher prepares some pictures before class or demonstrates them in class.
Question: Which of these objects are similar in shape but different in size?
Students think positively and speak enthusiastically.
Guide the students to briefly explain the reasons in their own language and describe the characteristics of these geometric figures.
Teacher: Have you considered their color, material and quality when classifying them?
Health: No.
Teacher: There are many objects with similar shapes in our life. If we only pay attention to their shapes, sizes and positions without considering their colors, materials and quality, we will get the geometric figures we will learn in the future.
Find out what geometry you know.
Health: conical, cylindrical and spherical
Teacher: Let's get to know them together. (The computer displays the geometric figures abstracted from the above objects) Write down the names of each geometric figure (in Chinese and English). Please observe, what geometry does the object just look like on the screen?
Cylindrical, conical, square, cuboid, prismatic, spherical
Circle, cylinder, circle, cone, cube, cuboid, prism, sphere.
Health: Think and answer.
Teacher: Let's recall what objects we have seen in our daily life are similar in shape to the above geometry (establish the corresponding relationship between objects and geometric models).
Second, do it.
Teacher: Print P3 pictures in the book on the screen, and let the students do it together to consolidate the concept.
Third, explore together.
1. The computer demonstrates seven kinds of geometry, and the students name them.
2. Think about it, which geometric figures are the plane figures we have learned?
After a period of thinking, students communicate at the same table and split some geometric figures to let students know the difference between geometric figures and plane figures.
Further make students think:
(1) What's the difference between three-dimensional graphics and plane graphics?
(2) How many parts are there in the geometry?
Four. abstract
Students, what is the harvest of this class?
Harvest: (1) got a preliminary understanding of geometric figures, including three-dimensional figures and plane figures.
(2) Classification of 3D graphics
Have you read carefully the teaching schedule of mathematics, geometry and graphics in the first volume of the seventh grade I provided you? Finally, I wish the students academic progress.
Model Wensan, an excellent teaching plan of Geometry, the first volume of seventh grade mathematics.
first kind
Understanding of plane graphics
Teaching goal: Through review, students can further understand the concepts of angle, verticality and parallelism, triangle and quadrilateral, and master their characteristics and properties, thus connecting with various figures. & amplsquo
Teaching process:
Straight line, ray, line segment.
Question: 1) What are straight lines, rays and line segments?
What's the difference between line, ray and line segment?
Complete "Done" on page 123. (Students write with pens)
corner
Question: 1) What is a corner?
2) What does the angle have to do with?
Finishing: Complete the blanks in the form.
Complete the questions on page 123 1 and 2.
acute angle
right angle
blunt angle
flat angle
perigon
Greater than 0&; deg
Less than 90&; deg
Vertical and parallel
Ask questions:
1) What is the mutual position of two straight lines in the same plane?
2) Which two straight lines are perpendicular to each other?
What two straight lines are parallel to each other?
Answer: Which two straight lines are perpendicular to each other in the following groups of straight lines? Which group of two straight lines are flat with each other?
Complete "Doing" on page 124 of the textbook.
Triangle.
Ask questions:
1) What is a triangle?
2) In the triangle below, which side does the opposite side of vertex A refer to?
Write first: draw the height of the triangle with the opposite side of vertex A as the base, and mark the base and height. (Picture on the previous page)
Fill in the names and characteristics of triangles in the table below.
name
chart
trait
Answer: The connection and difference between acute triangle, right triangle and obtuse triangle.
quadrilateral
Question: What is a quadrilateral?
Answer: Look at the picture and tell the characteristics of the picture below, then tell what the letters in the picture mean.
Think about it: Why are rectangles and squares special parallelograms? Why is a square a special rectangle?
Complete the questions in "Doing" on page 125 1 and 2.
Excellent teaching plan model of the first volume of seventh grade mathematics "Geometry"
Understand the three-dimensional graphics and plane graphics in 1
Teaching objectives
1. Geometric figures can be abstracted from the shapes of simple objects, and the difference between three-dimensional figures and plane figures can be understood;
2. Can judge whether the geometric figure is a three-dimensional figure or a plane figure, and can accurately identify prisms and pyramids.
teaching process
First, situational introduction
Observe objects and enjoy pictures:
We live in a graphic world, which is rich and colorful and contains a lot of geometric figures. In this section, we will study graphics.
Second, cooperative exploration.
Exploration point 1: 3D graphics
Type 1: Understand how to abstract 3D graphics from physical drawings.
Example 1 Observe the following physical model. The one with a cylinder shape is ().
Analysis: the top and bottom surfaces of a cylinder are all circles, so the correct one is D.
Methods Summary: Combined with physical objects, we can know common three-dimensional figures, such as cuboid, cube, cylinder, cone, sphere, prism and pyramid.
Name and classification of type 2 three-dimensional graphics
Example 2 shows eight three-dimensional graphs.
Among them, the serial number of the cylinder is _ _ _ _ _ _ _ _, the serial number of the cone is _ _ _ _ _ _ _ _, and the serial number of the sphere is _ _ _ _ _ _ _ _.
Analysis: According to the definitions of cylinder, cone and sphere, it can be concluded that cylinder is 1257⑧, cone is 467 and sphere is ③, so fill in1257 ⑧; ④⑥; ③.
Methods Summary: Correctly understanding the definition of three-dimensional graphics is the key to solve the problem.
Exploration point 2: understanding of plane graphics
Recognition of plane graphics
Example 3 has the following figures: ① triangle, ② rectangle, ③ parallelogram, ④ cube, ⑤ cone, ⑦ cylinder, ⑦ circle and ⑧ sphere, in which the number of plane figures is ().
A.5 B.4
C.3 D.2
Analysis: According to the definition of plane figure: all parts of a figure are in the same plane, it can be judged that 1236 is a plane figure, so B.
Method summary: to distinguish plane graphics, we should remember the characteristics of plane graphics, that is, all parts of a graphic are in the same plane.
Type 2 is a graph composed of planar graphs.
Example 4 As shown in the figure, what simple plane graphics are the graphics of each sign mainly composed of?
Solution: (1) consists of 5 graphs;
(2) It consists of two squares and 1 rectangle;
(3) It consists of three quadrangles.
Methods Summary: The key to solve this kind of problem is to correctly distinguish the shape and name of graphics.
Third, blackboard design.
1. Stereoscopic
Features: The parts of the geometric figure are not in the same plane.
2. Plane graphics
Features: all parts of the geometric figure are in the same plane.
Teaching reflection
In this section, the courseware connects with real life by showing pictures, arouses students' interest in learning, arouses their enthusiasm, and allows students to devote themselves to learning in the best state. Through hands-on operation, students' hands-on operation ability is cultivated, and their understanding of three-dimensional graphics and plane graphics is deepened, so that students can summarize the characteristics of three-dimensional graphics and plane graphics on the basis of discussion and communication.
In the second class, look at the three-dimensional diagram and its expanded diagram from different directions.
Teaching objectives
1. After observing the activity process of an object from different directions, I have a preliminary understanding: observing the same object from different directions may get different results;
2. Be able to draw some simple geometric bodies in different directions and their simple combinations to get plane graphics, understand the unfolded drawings of straight prisms, cylinders and cones, or judge the three-dimensional graphics according to the unfolded drawings. (Key points and difficulties)
teaching process
First, situational introduction
Cylinder wall
Su Dongpo
Seen from the side of the mountain, the peaks are different in height.
I don't know the true face of Lushan Mountain, but I am only on this mountain.
This poem depicts two different pictures the poet saw when facing Lushan Mountain. Can you outline them with simple figures?
Second, cooperative exploration.
Inquiry point 1: Observe the 3D graphics from different directions.
Type one judges the graphics seen from different directions.
Example 1 The object after cutting off a part along the diameter of the upper bottom surface of the cylinder is as shown in the figure, and the figure it sees from above is ().
Analysis: From the above, you can still get the combination diagram of two semicircles. So choose D.
Methods Summary: This question examines the observation of objects from different directions. When solving problems, we should pay attention to drawing invisible lines as dotted lines and visible lines as solid lines.
The second type draws graphs seen from different directions.
Example 2 is a three-dimensional figure composed of five small cubes as shown in the figure. Please draw a plan from the front, left and top respectively.
Analysis: From the front, there are three columns from left to right, including 1, 1 and two small squares; Seen from the left, there are two columns from left to right, with 2 1 small squares respectively; Seen from above, there are three columns from left to right, which are 2 1 and 1 cubes.
Solution: As shown in the figure:
Method summary: Draw the shape of the object from different directions: first observe the object, draw the outline of the view, and then complete the view, in which the outline of the visible part is usually drawn as a solid line and the outline of the invisible part is usually drawn as a dotted line. When drawing three kinds of views, the graphics seen on the front and top should be long and aligned, the graphics seen on the front and left should be high and uniform, and the widths of the graphics seen on the front and left should be equal.
Excellent teaching plan model of the first volume of seventh grade mathematics "Geometry"
Teaching objectives
1. Knowledge and skills
(1) can abstract geometric figures from objects and correctly distinguish three-dimensional figures from plane figures;
(2) Some problems of three-dimensional graphics can be transformed into plane graphics for research and treatment. Bull; Explore the relationship between plane graphics and three-dimensional graphics.
2. Process and method
(1) Experience and explore the relationship between plane graphics and three-dimensional graphics, develop the concept of space,&; Bull; Cultivate the ability of observation, analysis, abstraction and generalization, and cultivate the ability of hands-on operation.
(2) Go through the process of solving problems and improve the ability to solve problems.
3. Emotional attitudes and values
(1) Actively participate in the process of teaching activities and form a conscious and serious learning attitude. Bull; Cultivate the spirit of facing learning difficulties and feel the beauty of geometric figures;
(2) On the basis of independent thinking, advocate the spirit of self-study and group cooperation; Bull; Can benefit from group communication, correctly evaluate the learning process and realize the importance of cooperative learning.
Key points, difficulties and key points
1. key point: abstract geometric figures from physical objects. Bull; It is the key to transform three-dimensional graphics into plane graphics.
2. Difficulty: It is difficult to convert three-dimensional graphics into plane graphics.
3. Focus: Proceed from the actual situation and conduct the experiment by hands-on operation. Bull; Combining group communication and learning is the key.
training/teaching aid
Geometric models such as cuboid, cube, sphere, cylinder and cone, teaching wall chart of ink bottle packaging box (one for each student).
teaching process
First, the introduction of new courses.
1. Open the textbook and look at the modern urban architecture on page 1 17. Students watch carefully.
2. Question: What are the familiar geometric figures?
Second, new funding.
1. Students fully express their opinions after reviewing the pictures they have just seen, and accumulate experience in group activities by exchanging supplementary opinions in groups.
2. Assign a student to answer the questions and name these geometric figures correctly. Students answer: there are cylinders, cuboids, cubes and so on.
Teacher's activity: correct the mistakes in the names of geometric figures mentioned by students, and show the corresponding geometric models for students to observe their characteristics.
3. The concept of three-dimensional graphics.
(1) Cubes, cubes, spheres, cylinders and cones are all three-dimensional figures.
(2) Student activities: After reading the textbook Figure 4. 1-3, students think: What kind of three-dimensional graphic image do these objects give us? (Prisms and Pyramids)
(3) Use the teaching wall chart to show Figure 4. 1-4.
(4) Question: What simple plane graphics does the wall chart contain?
(5) Explore ways to solve problems.
Students communicate in groups, and the teacher guides each group. Get the answer to the question through communication.
② Students answer: Plane figures include rectangle, circle, square, polygon and triangle.
4. The concept of plane graphics.
Rectangle, square, triangle, circle, etc. Are all plane figures that we are very familiar with. Note: the concepts of three-dimensional graphics and plane graphics do not require a complete definition, but only require students to distinguish them correctly.
5. Conversion between three-dimensional graphics and plane graphics.
(1) From different directions: Show the workpiece model shown in the textbook Figure 4. 1-7( 1). Bull; Let the students look at it from different directions.
(2) ask questions.
What kind of plane figure do you get from the front, the left and the top? Can you draw the plane figure you see?
(3) Explore ways to solve problems.
① Student activities: Let students look at the workpiece model from different directions and draw various plane figures independently.
② Communicate in groups, evaluate their own conclusions and draw correct conclusions; Assign three students to draw on the blackboard.
6. Think about it and do it.