1, through the process of exploration, in operation, observation, analysis and other activities, comprehensively use relevant knowledge to solve the problem of the number of exposed surfaces, and then find the area of exposed surfaces.

2, can orderly, multi-angle observation, and find the law in the experience.

3. In operation and communication, experience the thinking method of induction and replacement, and further develop the concept of space.

Teaching preparation:

Multimedia courseware, 8 identical cubes in each group, record cards, cardboard, etc.

Teaching process:

First, the introduction of conversation, the use of methods

1, Teacher: Please look at the big screen. This is a set of three-dimensional figures. Let's see who can see it first: How many small cubes does it consist of? (There are 8 small cubes)

Teacher: Can you tell me what you think?

2. Teacher: It seems that observation alone is not enough. It is necessary to add reasonable inference on the basis of observation and think about what you can't see in your mind before you can draw a correct conclusion. In this lesson, we will continue to discuss "appearance" (blackboard writing topic) by observing and inferring these two methods.

Second, operating experience and exploring new knowledge

1, teacher (please look at the big screen): A small cube is placed in the corner. How many faces are exposed? Which ones?

2. Teacher: Keep looking at the big screen. How many small cubes are there?

Students may answer: There are four small cubes. )

Teacher: How many faces are exposed? what do you think?

Students may answer: nine faces are exposed. The small cube above has three faces exposed, the small cube in front also has three faces exposed, and so does the small cube on the right, 3+3+3=9, so a * * * has nine faces.

The teacher asked, aren't there four small cubes? Why did you only count three?

Students may answer: there is a small cube whose face is completely covered. If none of it is exposed, you don't have to look at it. )

Teachers and students count the exposed faces together in the order of up, left and right.

Teacher: That's how he counts. Who thinks differently from him?

(Students may answer: Let me look at the front, a * * *, with three small squares; Look at the top, there are also three small squares; Look at the right, there are also three small squares. 3+3+3=9, so a * * * has nine faces exposed)

Teacher: Who listened clearly? How did he count it?

(repeated birth method)

Teachers and students use this method.

But I have a question: why don't you look left, or at the bottom or back?

Students may answer: because those three sides are blocked. )

Teacher: Now let's compare these two methods. What is the difference?

(The first method is to count small cubes one by one; The second way is to look from different directions, first at the top, then at the front and right)

Teacher (summarizing while demonstrating): The first one is to observe each small cube one by one, count the number of exposed faces respectively, and then add them up; The second is to look at the three exposed directions, front, top and side, and count the number of exposed surfaces from different directions, and then add them up. No matter which method is used, as long as it is observed in a certain order, it will not be repeated or omitted.

3, student operation

Teacher: These four cubes are put together in the corner. Besides the arrangement we have seen, how can we arrange it? Think about it and communicate with your peers.

Teacher (combined with blackboard writing) concluded: they are all set with four small cubes, but the number of exposed faces is different because of the different setting methods; Even if the number of exposed surfaces is the same, the arrangement is still different.

Third, cooperate to explore and discover laws.

Teacher: Just now, we put four small cubes together at random, and the number of exposed faces is different. Now we use a few small cubes and put them regularly in a certain way. How will the number of exposed surfaces change?

1, displaying cooperation tips.

(1) Group students discuss and choose a way, and then put it regularly according to this way (such as horizontal pendulum, vertical pendulum ...).

(2) First set up a small cube and write down the number of exposed surfaces; Then add the small cubes one by one, and record the number of exposed faces of the small cubes in turn.

Observe while recording the data and write down your findings.

Teacher: Do you understand the hint? There are several requirements.

What is a regular pendulum?

2. The team will cooperate in exploration and fill in the record sheet.

Number of small cubes 123456 ...

Number of exposed surfaces

The pattern I found

3, the whole class communication

Teacher: Which group would like to come to the front to demonstrate how your group did it and talk about your findings? (Set several possible situations for students in advance and deal with them according to the actual situation in teaching. )

Default value:

(Show student record sheet)

Number of small cubes 123456 ...

The number of exposed surfaces is 3579 1 1 13. ...

The rule I found: every time I add a small cube, I add two faces.

Teacher: Do you add these two sides every time? You point to it.

The teacher pointed to the top surface and asked, isn't this surface changing, too? Why not add noodles?

Students may answer: although it has changed, it has not increased. The original upper surface was covered and the other upper surface was exposed, so the upper surface did not change. )

Teacher: It turns out that the surface above has always played a substitution role, and its number has never changed, so we don't need to consider this substitution surface when counting the number of added surfaces.

Teacher (to the class): Now, let's look at this table together. How many cubes will be exposed if you keep putting them like this? 10 What about the cube? What about 20 What did you find? Students can also be prompted to observe the relationship between the number of small cubes and the number of exposed surfaces. )

Fourth, practice consolidation.

1, basis

2. Different

3. Development

Verb (abbreviation of verb) abstract

What did you get today?

The second teaching content:

Textbook 20-2 1 Page "Exposed Face"

Teaching objectives:

1. Through operation, observation, analysis and other activities, comprehensively apply relevant knowledge to solve problems related to the surface area of objects and develop students' spatial concepts (key points and difficulties);

2. Experience the process of inquiry and stimulate the desire of active inquiry;

3. Cultivate students' ability to cooperate and communicate with others.

Teaching emphases and difficulties:

It can accurately calculate the exposed surface area when multiple cuboids and cubes are stacked.

Teaching process:

First, create situations, stimulate interest and expose topics.

1. Introduce the dialogue, show the drawings of the packaging cartons in the corner, and let the students observe how many faces are exposed.

2. Introduce a new lesson: exposed face;

Second, the combination of support and release to explore new knowledge

1. Put a cube in the corner and guide the students to observe how many faces are exposed.

2. Stack four cubes in the corner and guide the students to observe: How many faces are exposed?

3. Guide students to observe the change of exposed surface by changing the method of stacking cubes;

4. Arrange the cube 1, 2, 3 … into a layer, and guide the students to observe the exposed surface rule: 3n+2.

5. Guide students to explore the law of vertical arrangement: 4n+ 1.

6. Guide students to explore the multi-line and multi-layer law: 5N+4

Thirdly, feedback correction and implementation of double bases.

1. Show your textbook, exercise 2, question 4.

2. Use the cube model to pose different situations and guide students to find out what the law of exposed surface is.

Fourth, summarize and evaluate the layout preview

1. Guide students to summarize in class.

2. Extracurricular preview arrangement: 24 pages of the textbook "Arrival Number"

Blackboard design:

free end/face

1. Cubes are stacked in the corner, and the method of observing the exposed surfaces: (1) See how many exposed surfaces there are; (2) Seen from the front, side and top, there are several exposed faces in each direction;

2. The rule of tiling in rows: exposed surface = number of cubes × 3+2, that is, exposed surface = 3n+2;

3. Vertical arrangement rule: exposed surface = number of cubes × 4+ 1, that is, exposed surface = 4n+1;

4. Multi-row and multi-layer arrangement rule: exposed surface = number of vertical rows of cubes × 5+4, that is, exposed surface = 5n+4.

Teaching reflection:

1. Pay attention to let students experience the process of exploring laws, adopt interactive inquiry teaching, base on "guiding learning" and accumulate experience in exploring graphic surface area;

2. Pay attention to cultivate students' orderly observation and develop their spatial concept.

3. Paying attention to the creation of rich life situations is conducive to stimulating students' interest in inquiry;

Article 3 Teaching objectives:

1, can know cuboids and cubes, and has a preliminary imagination of three-dimensional space.

2. Combined with the specific stacking scene of multiple cuboids and cubes, the exposed surface areas of multiple cuboids and cubes can be accurately calculated through the process of exploring their exposed surface areas.

3. Let students feel the close relationship between the surface areas of cuboids and cubes and their lives, and cultivate their good interest in learning mathematics.

Key points and difficulties:

It can accurately calculate the exposed surface area when multiple cuboids and cubes are stacked.

Teaching methods:

Teachers and students are the same in induction and reasoning.

Teaching preparation:

Multiple cubic boxes

Teaching process:

First, check the import.

The teacher asked the students to review the surface areas of cuboids and cubes they studied last class and ask questions.

The student answers: the surface area of a cuboid = (length× width+length× height+height× width) × 2; Surface area of cube = side length × side length ×6)

Second, teach new lessons.

The teacher showed the textbook illustrations 1. Ask the students to observe how many faces are exposed when a box with a length of 50 cm is placed in the corner. How many square centimeters is the exposed area?

Look at the picture and calculate the exposed area in square centimeters.

The teacher asked the students to answer this question. (There are three exposed faces; The exposed area is 50×50×3=750 (square centimeter).

The teacher shows illustration 2. Ask the students to observe four 50 cm cube cartons stacked in the corner. How many faces are exposed? What is the exposure area?

How many faces are exposed from the front, sides and top? And calculate the exposed area.

The teacher asked the students to answer this question. (9 faces are exposed, with an exposed area of 50×50×9. )

The teacher asked the students to try different stacking methods with their four cube learning tools and discuss and communicate with each other at the same table.

Third, the class summary

Students, what knowledge have you learned in this class? (Ask students to answer)

Blackboard design:

free end/face

How many faces are exposed from the front, side and top?