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

Master the calculation method of surface area of cuboid and cube.

teaching tool

Cuboid, cube paper box, scissors, projector

teaching process

View 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.

New course teaching

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

(1) Please take out the prepared rectangular frames and mark them respectively? Going? 、? Next? 、? Before? 、? After that? 、? Left? 、? Right? Six faces.

Teachers and students review the characteristics of rectangles. Please cut along the cross edge of the front and top of the rectangular frame to get the picture unfolded on the right.

(2) Please take out the prepared cubic cartons and mark them separately? Up, down, front, back, left, right? Six faces, and then teachers and students review the characteristics of the cube. 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+0.5? 0.4+0.7? 0.5+0.7? 0.5 = 0.28+0.28+0.2+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 (m2)

Method 3: (upper area+front area+left area)? 2

(0.7? 0.4+0.5? 0.4+0.7? 0.5)? 2=0.83? 2= 1.66 (m2)

(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.

Summary after class

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?

homework

1, fill in the blanks.

The side length of the (1) cube is 5cm, the side length is (), the surface area is () and the volume is ().

(2) The length, width and height of the rectangular wooden box are all 6 decimeters, the side length is (), the floor area is (), the surface area is () and the volume is ().

(3) Rectangular square steel with a cross-sectional area of 12 cm2, a length of 2 decimeters and a volume of () cubic centimeters.

(4) Rectangular water tank, measured from the inside, with a bottom area of 25m2 and a water depth of 1.6m, can hold () liters of water.

(5) The side length of the cubic ingot is 10 decimeter. If 1 decimeter steel weighs 7.8kg, the ingot weighs () kg.

(6) The side length, side length, surface area and volume of the cube are enlarged by 3 times, () times and () times respectively.

(7) Use a small cube with a length of 5 cm to make a big cube, at least such a small cube is needed ().

(8) The length, width and height of a cuboid are a meter, b meter and h meter respectively. If the height increases by 2 meters, the volume will increase by () cubic meters.

2. Judges. (correct input in brackets? , the typo in brackets? )

A (1) cube is a graph composed of six identical squares. ( )

(2) A cube with a side length of 6 cm has the same surface area and volume. ( )

(3) a? Represents a? 3 。 ( )

(4) A cuboid (excluding a cube) has at most two faces with the same area. ( )

(5) A cuboid (excluding a cube) has at least two faces with equal areas.

Write on the blackboard.

Surface area of cuboid and cube (1)

Surface area of cuboid = (length? Width+length? Height+width? High)? 2

Surface area of cube = side length? Side length? six

Teaching plan of cuboid and cube surface area (2) Teaching objectives

1. 1 knowledge and skills:

(1) Understand the meaning of the surface areas of cuboids and cubes, and master the calculation methods of the surface areas of cuboids and cubes.

(2) In the process of understanding and deducing the calculation methods of the surface area of cuboids and cubes, we should cultivate the ability of abstract generalization, reasoning and flexibility of thinking, and at the same time develop the concept of space.

1.2 process and method:

Learn to solve the problem of calculating the surface area of cuboids and cubes in real life.

1.3 Emotional attitudes and values:

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

Emphasis and difficulty in teaching

2. 1 teaching focus:

Establish the concept of surface area, understand and master the calculation method of surface area of cuboid.

2.2 Teaching difficulties:

Imagine the length and width of each face according to the length, width and height of a given cuboid.

teaching tool

Courseware and title cards

teaching process

First, review the introduction.

(1) Fill in the blanks.

1, a cuboid is generally a three-dimensional figure surrounded by six rectangles (in special cases, two opposite faces are squares).

2. In a cuboid, the opposite faces are exactly the same, and the opposite sides are equal in length.

A cube is a three-dimensional figure surrounded by six identical squares.

(2)

(1) Calculate the area of the front of each cuboid. 4? 2=8 (square centimeter)

(2) Calculate the area of the right side in each cuboid. 3? 2=6 (square centimeter)

(3) Calculate the area of the upper surface in each cuboid. 4? 3= 12 (square centimeter)

Second, explore new knowledge.

1. A preliminary understanding of the surface area of a cuboid.

Teacher: Let's discuss the surface areas of cuboids and cubes first. (Teacher shows cuboid toothpaste box with courseware) Please observe carefully: cut along the edge (cut off the excess part of the carton) and then unfold it. What did you find?

Health 1: It was found that the original three-dimensional map was transformed into a plan.

Health 2: I found that the cuboid is composed of six rectangles when it is unfolded.

2. Know the surface area of the cube.

Teacher: The students observe carefully! (Showing the cube medicine box courseware again) Cut and expand in the same way. What did you find?

Health 1: It is found that the cube has also become a plane figure after expansion.

Health 2: I found that the appearance of the cube after expansion is composed of six squares.

3. Understand the meaning of cuboid and cube surface area.

Teacher: That's right! Please take out the cuboid or cube paper box, cut it in the same way, and then expand it to see the shape after expansion. Then, in the expanded diagram, use? Going? 、? Next? 、? Before? 、? After that? 、? Left? 、? Right? Mark six faces. Teacher: Choose a cuboid and a cube from the students and stick them on the blackboard. Q: By observing the courseware and operating the physical model, who knows the surface area of a cuboid or cube?

Health 1: the surface area of a cuboid or cube refers to the surface area of a cuboid or cube, that is, the sum of the areas of six surfaces, namely, up and down, front and back, left and right.

Health 2: Simply put, it is the total area of six faces of a cuboid or cube, which is called its surface area.

We know the surface areas of cuboids and cubes. How to calculate the surface areas?

4. Exploration activities:

? What is the surface area of the cuboid of demonstration courseware?

The upper and lower sides are _ 0.7m _ _ long, _ 0.5m _ _ wide and _ 0.35m2 _ _ in area.

The front and rear surfaces are _ _ 0.7m in length, _ _ 0.4m in width and _ _ 0.28m _ _ area.

The left and right sides are _ _ 0.5m long, _ _ 0.4m wide and _ _ 0.2m _ in area.

Teacher's warm reminder:

The size of the upper and lower surfaces-

The front and back are equal in size, and it consists of cuboids-and-with the same length and width;

The left and right sides are equal in size, which is the length and width of a cuboid.

How to calculate the surface area of a cuboid?

Teacher's warm reminder:

Find the opposite areas separately and add them up.

Group communication: collective discussion:

Students sum up, the teacher wrote on the blackboard:

Cuboid surface area: length? Wide? 2+ long? Tall? 2+ high? Wide? 2

Or: (long? Width+length? High+high? Guang)? 2

5. Example 1

How many square meters of cardboard do you need to make a microwave oven packaging box with a length of 0.7 meters, a width of 0.5 meters and a height of 0.4 meters?

Students calculate independently, teachers patrol, choose two algorithms, assign two students to write and dictate the basis of column calculation on the blackboard.

Health 1: Calculate the sum of the areas of three different faces and multiply by 2.

(0.7? 0.5+0.7? 0.4+0.5? 0.4)? 2

Health 2: First, calculate the area sum of two opposite faces respectively, and then add them.

0.7? 0.5? 2+0.7? 0.4? 2+0.5? 0.4? 2

So the surface area of a cuboid = (length? Width+length? Height+width? High)? 2, with the letter S=2 (A? b+a？ h+b？ h)

6. A cubic ink cartridge with a length of 6.5 cm. How many square centimeters of cardboard does it take to make this ink box?

Think about it: what is the requirement of using at least square centimeters of cardboard? Try it yourself!

(6.5? 6.5+6.5? 6.5+6.5? 6.5)? 2

=(42.25+42.25+42.25)? 2

=42.25? 3? 2

=253.5 square centimeters

Because of the characteristics of the cube:

6.5? 6.5? six

=42.25? six

=253.5 square centimeters

A: It takes at least 253.5 square centimeters of cardboard to make this ink cartridge.

Cubic surface area = side length? Side length? 6, expressed in letters: S=6a2.

Third, consolidate and upgrade.

1, calculate the surface area of the figure below. (Unit: cm)

( 15? 12+ 15? 8+ 12? 8)? 2=792 (square centimeter)

( 18? 9)? 4+(9? 9)? 2=8 10 (square centimeter)

25? 25? 6=3750 (square centimeter)

10? 10? 6=600 (square centimeter)

2. A cubic gift box with a length of1.2dm. If the actual paper used is 1.5 times the surface area, how many square decimeters of wrapping paper should be used to package this gift box?

1.2? 1.2? 6=8.64 (square decimeter) 8.64? 1.5= 12.96 (square decimeter)

A: The gift box should be packed with at least 12.96 square decimeter wrapping paper.

The glass fish tank is a cube with a length of 3 meters. How many square decimetres of glass does it take to make this fish tank? There is no lid on the fish tank. )

3? 3? 5=45 (square decimeter)

It takes at least 45 square decimeters of glass to make this fish tank.

4. Liangliang should give a simple wardrobe, which is 0.75m long, 0.5m wide and 1.6m high (as shown below, it has no bottom). How many square meters of cloth do you need at least?

0.75? 0.5+0.5? 1.6? 2+0.75? 1.6? 2

=0.375+ 1.6+2.4

=4.375 square meters

A: At least 4.375 square meters of cloth is needed.

Summary after class

What did you learn in this class?

The total area of six faces of a cuboid or cube is called its surface area.

Surface area of cuboid = (length? Width+length? Height+width? High)? 2, represented by the letter S=2 (a? b+a？ h+b？ h)

Cubic surface area = side length? Side length? 6, expressed in letters: S=6a2.

Write on the blackboard.

Surface areas of cuboids and cubes

The total area of six faces of a cuboid or cube is called its surface area.

Example 1: How many square meters of cardboard does it take to make a microwave oven?

(0.7? 0.5+0.7? 0.4+0.5? 0.4)? 2

=0.35? 2+0.28? 2+0.2? 2

=0.7+0.56+0.4

= 1.66 (m2)

Answer: At least 1.66m cardboard should be used. Example 2: A cubic ink cartridge with a length of 6.5 cm. How many square centimeters of cardboard does it take to make this ink box?

6.5? 6.5? six

=42.25? six

=253.5 square centimeters

A: It takes at least 253.5 square centimeters of cardboard to make this ink cartridge.

Surface area of cuboid = (length? Width+length? Height+width? High)? 2, represented by the letter S=2 (a? b+a？ h+b？ h)

Cubic surface area = side length? Side length? 6, expressed in letters: S=6a2.