Optimal teaching design of cuboid and cube surface area

Excellent teaching design of cuboid and cube surface area 1 teaching content

Examples 1 and 2 on page 24, and questions 1, 2, 3, 4, 6, 7 in exercise 6 on page 25-26.

Teaching objectives

1. Students master the concepts of surface areas of cuboids and cubes through operation, and initially master the calculation methods of surface areas of cuboids and cubes.

2. I can solve simple problems in life by finding the surface areas of cuboids and cubes.

3. Cultivate students' analytical ability and develop the concept of space.

Emphasis and difficulty in teaching

Key points: master the meaning of surface area of cuboid and cube.

Difficulties: Learn how to calculate the surface areas of cuboids and cubes.

teaching process

First, check the import.

1. What are the length, width and height of a cuboid? What is the side length of a cube?

2. Point out the length, width and height of the rectangular frame, and tell the characteristics of the rectangular frame. Point out the side length of a cube and tell its characteristics.

Second, the new teaching

1. Teach the concepts of cuboid and cube surface area.

(1) Please take out the prepared rectangular paper box and mark it with six faces: top, bottom, front, back, left and right.

Teachers and students review the characteristics of rectangles. Please cut the rectangular carton along the cross edge between the front and the top to obtain the unfolded drawing.

(2) Please take out the prepared cubic carton and mark it with six faces, namely "up, down, front, back, left and right". Then the teacher and the students review the characteristics of the cube together. Ask the students to cut along the edges of the cube respectively. Get the correct cubic expansion diagram.

(3) Observe the expanded drawings of cuboids and cubes to see which faces have equal areas, and what is the relationship between the length and width of each face in cuboids and the length, width and height of cuboids?

After the observation, the group held a discussion. Guide students to summarize the concept of surface area of cuboid. The total area of six faces of a cuboid or cube is called its surface area.

2. Learn how to calculate the surface areas of cuboids and cubes.

(1) Which cuboids or cubes often need to be calculated in daily life and production?

(2) Show the example on page 24 of the textbook 1.

Understand the analysis, how many square meters of cardboard does it take to make a packing box, and what is it actually? (Surface area of this cuboid rice packing box)

First, determine the length and width of each face, then calculate the area of each face separately, and finally add up the area of each face to be the surface area of this cuboid.

(3) Try to answer independently.

(4) Collective communication and feedback.

The teacher writes on the blackboard according to the students' thinking of solving problems.

Method 1: The surface area of a cuboid = the sum of the areas of six faces.

0.7 × 0.4+0.7 × 0.4+0.5 × 0.4+0.7 × 0.5+0.7 × 0.5 = 0.28+0.28+0.2+0.35+0.35 =1.66 (m2

Method 2: The surface area of a cuboid = the areas of the upper and lower sides+the areas of the front and rear sides+the areas of the left and right sides.

0.7× 0.4× 2+0.5× 0.4× 2+0.7× 0.5× 2 = 0.7+0.56+0.4 =1.66 (square meter)

Method 3: (upper zone+anterior zone+left zone) ×2

(0.7× 0.4+0.5× 0.4+0.7× 0.5 )× 2 = 0.83× 2 =1.66 (square meter)

(5) Comparing the three methods, what do you think is the key to find the surface area of a cuboid? Which of these three methods do you prefer?

(6) Let the students try to solve the example 2 on page 24 of the textbook, collective communication algorithm, and let the students talk about how you solve the calculation of cube surface area.

Third, class assignments.

1. Complete "Do" on page 23 of the textbook.

2. Complete the "doing" on page 24 of the textbook.

3. Complete Exercise 6, Question 1, 2, 3, 4, 6, 7 on pages 25 to 26 of the textbook.

Fourth, class summary.

Today, we learned the surface areas of cuboids and cubes, and mastered the calculation methods of the surface areas of cuboids and cubes. Through studying, can you tell us what you have gained?

blackboard-writing design

Surface area of cuboid and cube (1)

The surface area of a cuboid = (length× width+length× height+width× height) ×2.

Surface area of cube = side length × side length ×6

Teaching reflection

This lesson mainly teaches the concept and calculation method of surface area of cuboid and cube. Textbooks first help students understand the concept of surface area by unfolding the six faces of a rectangular box or a cubic box. In this way, the concept of surface area can be well connected with the characteristics of cuboids and cubes just established, which will prepare for the later study and calculation of surface area. Then through the example 1, the calculation method of cuboid surface area is taught. Then arrange a "try" to learn the calculation method of cube surface area. There is no formula for calculating the surface area of a cuboid in the textbook, but it inspires students to calculate it in different ways. This arrangement is helpful for them to better grasp the concept of surface area and related calculations, and to better develop students' spatial concept.

Excellent Teaching Design of Cuboid and Cube Surface Area II [Teaching Content]

Example 5 on page 16 of the textbook and the corresponding "try" and "practice", exercise 4, question 6 ~ 10 and thinking questions.

[teaching material analysis]

[Teaching objectives]

1. Let students understand and master the calculation of the surface area of cuboids and cubes through exploration.

2. Let students master and apply what they have learned to solve practical problems.

3. Let students feel the surface areas of cuboids and cubes in the process of observation, analysis, abstraction, generalization and communication, and develop their preliminary abstract ability; In the process of learning and exploring, cultivate the ability of independent thinking and cooperation with others.

[Teaching Focus]

Judging which faces of a cuboid or cube should be summed according to the actual situation.

First, review the basics and introduce new courses:

1, Dialogue: Last class, we learned about surface area. Who remembers?

2. Calculate the surface area of the following objects.

(1) The rectangle is 5cm long, 6cm wide and12cm high.

(2) The side length of a cube is 5 decimeters.

Name the board and perform in groups.

Second, explore and comprehend, and summarize the methods:

Talk: In actual production, sometimes we have to calculate the area sum of some faces in a cuboid or cube according to actual needs.

Example 5: A cuboid fish tank, 5 centimetres long, 3 centimetres wide and 3.5 centimetres high. How many square decimetres of glass does it take to make this fish tank?

1, talk about: Please talk about the fish tank.

Q: Ask how much glass you need.

Let the students understand how much glass is needed for the surface area of this fish tank.

Inspire students to think:

According to the actual situation, it is necessary to calculate the sum of the areas of several surfaces. Which two faces are equal in area?

The students answered by roll call as they spoke.

Clear: Find the front, back, left, right and bottom areas respectively, and then add them. You can also calculate the total area of six faces first, and then subtract the area above.

2, column solution:

Students are required to complete it independently.

Dialogue: Can you tell me the basis of your formula? Let students know the meaning of the formula.

The camera shows:

5×3.5+5×3+3×3.5+3×3.5+5×3

(5×3+5×3.5+3×3.5)×2-5×3

3. Dialogue: Is there any other way? Choose a method to calculate the result, and then communicate with each other.

Step 4 practice:

Question 1, let the students know that the area of this trademark paper is the sum of the areas of the front, back, left and right sides of this cuboid, which is the side area of this cuboid.

Question 2: Let the students know the sum of the areas of several surfaces to be calculated, and then finish it independently and name the board.

After completion, collectively modify and name it according to the presentation.

Third, consolidate the exercises:

Exercise 4, question 6, the question to think about is to calculate the sum of the areas of which faces? According to the given conditions, what are the length and width of these surfaces? Then let the students answer independently.

Fourth, class assignments:

1. Exercise 4, question 7, learn to make it clear that the board is up and down, left and right, and the sand net is front and back.

2. Exercise 4 Question 8 makes it clear that the floor of the classroom (that is, below the corresponding cuboid) does not need to be painted; After calculating the total area of the top surface and four walls, the areas of doors, windows and blackboards should be deducted.

3. Exercise 4 Question 9 helps students understand that the floor area of steps should be the sum of the upper areas of steps at all levels, that is, 0.3×6×5=9 (square meter). The floor tile area is the sum of the areas above and in front of all steps, that is, 9+0.2×6×5= 15 (square meter).

4. Exercise 4 Question 10 reminds students to measure relevant data in centimeters. The measurement result can be retained to one decimal place.

Five, thinking about the problem:

Remind students that each group of opposite faces in the object has the same area. So the calculation method of surface area is: (7+7+6)×2=40 (square centimeter). The minimum required cube side length is 3 cm.