Tisch
First, the teaching purpose 1. In the practice of assembling and observing three-dimensional graphics, students' abilities of observation, operation and spatial imagination are cultivated.
2. In the practice of assembling three-dimensional graphics, experience and initially learn to describe the relative position of cubes with words such as up, down, left, right, front and back.
Second, teaching focus: learn to describe the relative position of the square with up, down, left, right, front and back.
Third, teaching difficulties: can correctly set up three-dimensional graphics according to certain instructions.
Fourth, teaching AIDS: cubes
5. Learning tools: cubes and crayons.
Sixth, the teaching process:
(1) Review and introduce:
1. The teacher drew a figure with three squares. The teacher asked: How many directions can you observe? How many squares do you see?
(2) Autonomous learning and cooperative exploration.
1. Scene 1.
(1) Quote: Shall we play games today?
I put a figure with four squares, but you can't see the figure I put. Please follow my instructions and create the same number as me.
Teachers guide and promote activities.
(2) Play the game in pairs.
Rules of the game: A. Two people are not allowed to look at each other's photos.
B. the instructions should be as few as possible.
(3) student activities.
(4) student reports.
2. Scene 2.
(1) We are here to play the second game.
Teacher: I put a graph, please ask me questions, and then build the same graph as me according to my answer.
(2) Play the game in pairs.
Rules of the game: A. Two people are not allowed to look at each other's photos.
B. the instructions should be as few as possible.
(3) student activities.
(4) student reports.
(3) summary.
What did you get?
Blackboard design:
take?it?for?a?spin
First field
Second field
Exercise 3
First, the teaching purpose
1. In the process of assembling three-dimensional graphics, the shapes seen from different positions may be different.
2. Can correctly identify the shape of three-dimensional graphics observed from the front, side and above.
Second, the focus and difficulty of teaching
Key point: experience observing three-dimensional graphics from different positions, and the shapes you see may be different.
Difficulties: the shape of three-dimensional graphics observed from the front, side and above can be correctly recognized.
Third, teaching AIDS: situation map.
Learning tools: sticks, cards
Fourth, the teaching process:
(1) Review and introduce:
Give the password according to the name. Students put a three-dimensional picture according to the password.
(2) Basic exercises:
1.p 16 question 1 and 2.
(1) Do it independently.
(2) modification.
2.P 17 Question 3.
(1) Do it independently.
(2) Build independently.
3.P 17 Question 4.
(1) Independent painting.
(2) modification.
(3) Expanding exercises:
1, synchronous exercise P 16
2. Autonomous world P 10
(4) summary.
What did you get?
extreme
Teaching objectives: (1) knowledge and skills: let students understand the meaning of the circle by themselves; Through group cooperation and exploration, the perimeter of plane figure is obtained by various appropriate methods; Cultivate students' ability of observation, comparison and operation.
(2) Process and method: Put large graphics in class to attract students' interest, let students actively participate in personal experience, and let students perceive the meaning of perimeter by walking, watching, drawing and measuring.
(3) Emotion, attitude and values: speak with your own personal experience, actively participate in the exploration of knowledge and put forward your own opinions.
Emphasis and difficulty in teaching: understanding the meaning of perimeter.
Teaching aid preparation: all kinds of graphic cardboard and exercise paper.
Teaching process:
Before class, a figure was put in the middle of the classroom. )
First, create situations and introduce new lessons:
T: Are the children particularly surprised today? The teacher surrounded a big shot in the middle of our classroom. Please observe this number carefully and tell us what you find.
Students are in appearance, straight line curve and symmetry. )
T: Observe very carefully. Children should observe everything carefully as they do today. Well, then we observed that the teacher wanted to invite a child for a walk. Teacher's demonstration: let a child follow the teacher and walk around the edge of the figure from a point to let other children pay attention. (Students leave)
T: Did you walk well? (Great! ) Your observation is better. The teacher rewarded everyone with a question: What did the child walk along this figure just now? In mathematics, we call the edge or outline of this figure "perimeter" (blackboard writing: the perimeter of the figure)
Second, cooperation and communication, * * * and exploration:
Teaching perimeter
So, can you tell what the circumference is in your own words? (student exchange. )
Teacher's demonstration: let's start from any point, walk around its sideline for a week, and then return to this point, then the length of this week is its circumference.
(1) The teacher showed some plane figures () and posted them on the blackboard. Ask the students to choose a figure they like to draw its perimeter.
(2) Look at things around you. Can you point out their boundaries? We also found the circumference of the surface of the object.
T: We find that not only the figure has a perimeter, but also the surface of the object has a perimeter.
(3) Print one, draw one: Use the object on your desk, select one of its faces, and draw the perimeter of the figure on this face by printing one.
(1) It is found that the graphics in the middle of printing are not closed; The teacher also prepared two figures. Please draw their perimeters: why not? Let's start from a point and walk around the edge of the graph. We can't go back to this. This graph is called an unclosed graph. What kind of figure do you think has a perimeter? So in mathematics, we can summarize it in a more concise sentence: the length of a closed figure is its circumference.
Please decide which of the following figures can calculate the perimeter (yes, please sit down, no, please raise your hand. )
(B) the method to explore the perimeter
Teacher: Now that we know the circumference, please try to find out.
Leave this task to your team of four.
Group activity: The teacher put the basic plane graphics displayed on the blackboard into the envelopes of each group, and asked four people in each group to explore the method of finding the circumference.
Communication: Tell me, what did your group ask for? (Measurement, rope circumference, symmetry ...)
Summary: We just found that a figure can be measured with a ruler when it is flat and with a rope when it is bent. We also found that a symmetrical figure only needs half. ...
Third, application migration, consolidation and improvement:
(1) I want to know the perimeter of this leaf. What should I do?
(2) I use two equal-length ropes to form a triangle and a quadrilateral. Whose week grew up?
(3)T: So, can you find the perimeter of the surface pattern of the object just printed by these methods?
The great people who are led to the ground in the classroom can be found in different ways according to the characteristics they find in the classroom. )
(4) The desktop of Xiao Ming's book is a rectangle with a length of 120cm and a width of 50cm. If a square with a side length of 5 cm is cut off from its two corners, what will happen to the pattern? ※? (pictured)
Fourth, summarize and reflect, expand and sublimate:
T: What have you gained from studying together in the same class?
Tisso
The textbook of Grade Two (Volume One) once arranged an "observation of objects", in which objects (toys, teapots, cars, etc. ) is observed from the front, back, left and right, and appropriate figures are selected to represent the shape of the object. This unit continues to teach "observing objects", observing from the front, side and top of objects, and using views to represent the shapes you see. The whole unit textbook is written in two sections. The first section observes cuboids, cubes or articles for daily use of these shapes, as well as objects composed of two cubes with the same size. In the second paragraph, observe an object composed of three cubes of the same size. 1. On the basis of knowing the front, back, left and right of an object, we can know the front, side and top of the object, and realize that when we look at it in different positions, the number of faces we see is often different.
The example on page 86 observes the rectangular bookcase, and first teaches the front, side and top of the bookcase. Because the students have been able to distinguish the front, back and left of the bookcase, the front of the bookcase can be said to be its front, and the left and right of the bookcase are its sides, so the top of the bookcase is easier to understand. Therefore, the textbook directly asks students "Can you point out the front, side and top of the bookcase" from the big cartoon at the bottom of the situation diagram, so that students can realize the transformation of understanding in activities such as pointing, recognizing and speaking. Then teach to observe this bookcase in different positions, sometimes you can see its three faces at the same time, sometimes you can see its two faces at the same time, and sometimes you can only see one face. The textbook draws two such bookcases under the situation map, one of which draws the front, side and top surfaces, and the other only draws the front and side surfaces. Ask the students to judge who saw these two pictures and which faces they saw. Students feel the observation of teachers and girls in situational pictures, which can be understood as that teachers see three sides of the bookcase at the same time, while girls can't see the top of the bookcase, but can only see two sides at the same time. Although there is no case of seeing only one side of the bookcase in the example, students can realize from seeing three sides and two sides that sometimes they can only see one side.
The exercises in Want to Do are roughly divided into three parts. 1 the topic is to consolidate the understanding of the front, side and top of the object. Ask the students to point out which is the front, side and top of the washing machine and which is the front, side and top of the refrigerator. Most students are familiar with these two kinds of electrical appliances, and it is not difficult to point out all aspects of them. They identify the graphics on each side of the washing machine and refrigerator by the appearance of the washing machine and refrigerator in their minds; According to the figures on the front, side and top of the washing machine and refrigerator, imagine what these two objects look like. Textbooks cultivate students' concept of space through the transformation between objects and graphics. If some students are unfamiliar with these two kinds of household appliances and point out that they have difficulties in all aspects, the teacher can provide the following physical drawings to help.
Question 2: Standing in different positions to observe the rectangular pencil case on the table, the number of faces you see is often different, and at most you can only see three faces of the pencil case at the same time. The textbook does not teach this content as knowledge, but requires students to have a preliminary understanding of this content through their own observation. Because the pencil case is relatively small, it is not difficult to see its front, side and top at the same time, and to see its top or front and side at the same time. However, it is not easy to see only its front and side, only its front or side. Only when you put your eyes at the same height as the front and side of the pencil case can you see it. The textbook hopes that students can learn to look at the right height and prepare for the following three views of objects. Questions 3 ~ 5 are about observing geometry. First, identify the front, side and top of cuboids and cubes. Then observe the cube from the front, side and top, and say what you see; Then observe the cuboid composed of two cubes with the same size and point out the figure you see. When observing from the front, side and top of a cube or cuboid, we should guide the observation method. If you look at it from the front, you should stand in front of the object and look perpendicular to the middle of the front of the object. For example, from above, you should stand in front of the object and be close to it, and look down, with your eyes perpendicular to the middle of the object. In addition, when observing cubes and cuboids, we must look at the physical objects, not the physical drawings of cubes and cuboids drawn in textbooks.
2? Transformation between simple geometry and its three views.
Mathematics curriculum standard (experimental draft) regards "geometry and its transformation between three views" as a manifestation of space concept. Generally speaking, a three-view view of an object refers to a plane figure depicting the shapes of its front, side and top. In questions 4 and 5 of "Think and Do" on page 87, students are exposed to three views of cubes and cuboids, and experience the essentials of observing objects from the front, side and top, and initially use the method of choosing views by talking or talking. Pages 88-89 teach three views of simple geometry. For example, let students put three cubes with the same size as the illustrations in the textbook, and then take a look at the front, side and top of the placed objects respectively, and then connect the observation positions with the corresponding views with lines. Placement, viewing and connection are three learning activities arranged in the textbook. Why "swing" first? There are two reasons here: the first reason is that the shape and structure of the object can be understood through the pendulum, and the front, side and top of the object can be distinguished for easy observation; The second reason is to let every student have an observable object to prevent some students from looking at illustrations in textbooks because of the lack of geometry. "Look" is the focus of example teaching. Look at the front, side and top of the object respectively. Here we need to pay attention to three points: first, the front, side and top of the object must be consistent among all students; Second, the observation method should be correct, and the line of sight must be perpendicular to the middle of the surface of the object; The third is to think about the shape you see. The object in the example is composed of three squares from the front, the two squares below are connected side by side, and there is a square above the square on the right. The figure viewed from the side is two squares connected up and down. As can be seen from the above, this is a difficult point in teaching. Although the two squares on the object are a little taller and shorter, they should be two squares connected side by side on the same plane. Students must be allowed to watch and experience. "Lian" is a way to express observation results. Three views of the object are drawn in the textbook, so that students can point out which figure they see from the front, side and top, which appropriately reduces the difficulty of students' expression.
"Try it" puts forward two requirements for students: first, put out the corresponding object according to the designated front view, and then draw the side view and top view of this object, so that students can fully experience the transformation activity of "view-object-view". Placing an object according to the view generally goes through the process of "studying the view-placing the object-verifying the placement method". The Research View should analyze the structure of the view. There are two squares connected side by side, and there is a square of the same size on the left square. Analysis view can enlighten the placement method of objects. "Setting objects" is carried out on the basis of analyzing views and conceiving arrangements, sometimes at the same time as analyzing views. If you see two squares connected side by side under the front view, take out two cubes and arrange them together; I saw another square on the left square, so I put another cube on the left square. Does the posing object meet the requirements? Need verification. The way to verify is to look at the front of the object. If the shape you see is consistent with the specified view, the modeled object meets the requirements. If the shapes you see are not consistent with the specified view, you should rearrange them. After this problem is set, it is necessary to draw the side view and top view of the object. The requirements for drawing views are higher than those for selecting views and connecting lines. Students can draw sketches.
"Think and act" is designed around the mutual transformation of geometry and its three views. Questions 1 and 2 require students to make a pendulum with three cubes first. Among them, the 1 question is arranged according to the geometry drawn in the textbook, and the second question is arranged according to the requirement of "horizontally arranged into a cuboid", which can not be ignored in teaching. Questions 3 and 4 are "Assemble according to the requirements of the view", in which there is only one arrangement for each sub-item in question 3. After arrangement, you should observe and draw the view from the front and side. The fourth problem is open, and there is no unique arrangement that meets the requirements of the front view. After two cubes are vertically (or horizontally) stacked, the third cube can be placed in front of or behind the two cubes. Although the shapes of objects are different, the front view is the same; Although the front view of these two objects is the same, the side view is different. When students experience these differences, their concept of space has been developed. The three objects in the fifth question are all composed of four cubes with the same size. The objects on the left and in the middle can clearly see their four cubes, and the objects on the right can only see three cubes directly, so that students can understand that there are 1 cubes that cannot be seen directly.