People's education printing plate fifth grade mathematics volume II cuboid and cube volume teaching plan.

Teaching objectives of cuboid and cube volumes (1)

1. 1 knowledge and skills:

Make students learn to calculate the volumes of cuboids and cubes, and use formulas to calculate them correctly.

1.2 process and method:

In the process of formula derivation, cultivate students' observation ability, spatial imagination ability, consciousness of asking questions and ability to solve practical problems.

1.3 Emotional attitudes and values:

Make students realize that mathematics comes from life, serves life, and produces thoughts and feelings that love mathematics.

Emphasis and difficulty in teaching

2. 1 teaching focus:

2. Master the calculation method of length and cubic volume and solve practical problems.

2.2 Teaching difficulties:

Derivation process of long cube volume formula

teaching tool

Teaching courseware, a cuboid mosaic model (length 4cm, width 3cm, height 2cm), with 24 small wooden blocks in each group, side length 1 cm3.

teaching process

First, review the introduction.

1. What are the lengths, widths and heights of the following cuboids?

Length: 8cm length: 6cm length: 8cm length: 12m

Width: 4cm width: 2.5cm width: 4cm width: 10m

Height: 5cm, height:10mm, height: 4cm, height:1.5m.

2. The figure below is composed of a cube of 1 cm3. How many cubic centimeters are they?

How do you know the volume of this cuboid?

Today, we will learn the volumes of cuboids and cubes together. (blackboard writing: cuboid and cube)

Second, explore new knowledge.

1, cuboid volume.

(1) activity 1:

Teacher: Teacher Zheng puts 12 cubes 1 cm2 and a study sheet in groups of four people. Below we will discuss them in groups of four. First of all, please look at the activity requirements (courseware demonstration):

A, four people cooperate with 12 cubes to place cuboids with different shapes;

B, each please make a record on the study list, and then put down one;

C, think about what you found after you released it, and communicate in groups of four;

D, each group chooses a representative to report.

Students cooperate with each other.

Feedback, student report

Every time a student reports a situation, the teacher writes down on the blackboard on the table:

Teacher: Look at the form. What did you find?

Guide the students to draw a conclusion: just multiply the number of rows by the number of rows to get the unit of the volume contained in a layer, and then multiply it by the number of layers to get the unit of the volume contained in this cuboid.

Blackboard: volume = rows? How many rows? number of plies

Teacher: Just now, the cuboids put out by students with 12 cubes are all 12 square centimeters. Teacher Zheng has just produced two cubes, but the volume is much larger than yours. However, to understand Mr. Zheng's cuboid, you must use your spatial imagination. (Courseware demonstration)

Do you know the volume of these two cuboids? how do you know (Students say that the teacher fills in the form)

(2) Activity 2:

Teacher: In groups of four, can you make a bigger cuboid?

Default: 5 cm long, 5 cm wide and 4 cm high.

Teacher: What did you find? What are the number of rows, columns and layers in each row equivalent to a cuboid?

Health: length, width and height, because the side length of each small cube is 1 cm, so there are several small cubes in each row, the length is just a few centimeters; Put a few rows, just a few centimeters wide; Put a few layers, the height is only a few centimeters.

2. How many unit of volume does the cuboid below have? And point out its length, width and height.

(2) Observing the relationship between the above parts, we can draw the following conclusions:

The first one: 5=5? 1? 1

Second: 15=5? 3? 1

Third: 12=3? 2? 2

Through the above relationship, we can draw the following conclusions: cuboid volume = length? Wide? high

If the letter V is used to represent the volume of a cuboid, and A, B and C are used to represent the length, width and height of the cuboid respectively, then the formula for calculating the volume of the cuboid can be written as: V=a? b？ C.

According to the relationship between cuboid and cube, can you figure out how to calculate the volume of cube?

3. The volume of the cube.

Because of the nature of the cube, all sides are equal, so the volume of the cube = side length? Side length? edge

If the letter V represents the volume of the cube and A represents the side length of the cube, then the formula for calculating the volume of the cube can be written as: V=a? Answer? Answer.

Answer? Answer? Can a write an a? , read as? The cube of a? A that represents the product of three a's.

The formula for calculating the volume of a cube is generally written as V=a3.

Third, consolidate and upgrade.

1. Calculate the volume below.

V=abh=7？ 3? 3=63(cm？ )

V=a3=4？ 4? 4=64 cm

2. Find the volume of the cuboid below.

8? 4? 5= 160(cm3) 6？ 2.5? 10= 15(dm3) 8？ 4? 4= 128 (cm3) 1.5？ 10? 12= 180 (m3)

The magnificent monument to the people's heroes stands in Tiananmen Square. The monument is 14.7m high, 2.9m wide and 1m thick. What is the volume of this huge granite stone tablet?

Solution: V=abh

=2.9? 1? 14.7

=42.63(m？ )

The volume of this stone tablet is 42.63 cubic meters.

4. Judge right or wrong and explain the reasons.

( 1)0.23=0.2? 0.2? 0.2。 ( ? )

(2)5X3= 10X .( ? )

(3) The side length of the cube is 4 decimeters and the volume is 43= 12 (cubic decimeter). ( ? )

(4) The rectangular body is 5 decimeters long, 4 decimeters wide, 3 centimeters high and 60 decimeters in volume. ( ? )

The cuboid has a volume of 48 cubic decimeters, a length of 8 decimeters and a width of 4 decimeters. What is its height?

48? 8? 4= 1.5 (decimeter)

A: Its height is 1.5 decimeter.

6. The sum of the sides of a cuboid is 96 cm. It is10cm long and 8cm wide. How many cubic centimeters is its volume?

96? 4 = 24cm24-10-8 = 6cm

10? 8? 6=480 (cubic centimeter)

Its volume is 480 cubic centimeters.

7. A rectangular fish tank without a cover is 8 cm long, 6 cm wide and 7 cm high. How many square decimetres of glass does it take to make this fish tank? What is the volume of this fish tank?

(8? 6)+(8? 7+6? 7)? 2=244 (square decimeter)

8? 6? 7=336 (cubic decimeter)

It takes 244 square decimeters of glass to make this fish tank. The volume of this fish tank is 336 cubic decimeters.

Summary after class

What did we learn in this class?

We learned the formulas for calculating the volume of cuboids and cubes.

Volume of cuboid = length? Wide? High, V=a? b？ h

Volume of cube = side length? Side length? Side length, V=a? Answer? a=a3

Write on the blackboard.

Cuboid and cube volume

Volume of cuboid = length? Wide? high

V=a？ b？ h

Volume of cube = side length? Side length? edge

V=a？ Answer? a=a3

Cuboid and Cube Teaching Plans (2) Teaching Objectives

1. Through teaching, guide students to find out the law and summarize the volume formula.

2. Instruct students to correctly calculate the volumes of cuboids and cubes with formulas.

3. Cultivate students' thinking quality of actively thinking and exploring new knowledge.

Emphasis and difficulty in teaching

1. Through teaching, guide students to find out the law and summarize the volume formula.

2. Instruct students to correctly calculate the volumes of cuboids and cubes with formulas.

3. Cultivate students' thinking quality of actively thinking and exploring new knowledge.

teaching tool

courseware

teaching process

View import

1. What is volume? What are the commonly used units for measuring the volume of an object?

2. How to calculate the volume of an object?

New course teaching

1. Calculation of cuboid volume.

The teacher's courseware shows a cuboid building block and a big brick board for building a house.

(1) Question: What are their volumes? what do you think?

Ask the students to answer: a cuboid building block can hold a cube of 1 cubic centimeter. 1 cubic centimeter How many cubes are there? How many cubic centimeters is its volume? However, it is more troublesome to measure with 1cm3 or 1dm3, compared with large brick slabs.

Teacher: Please think about it. If we want to know the volume of a larger object, can we use the mathematical knowledge we have learned to calculate it?

(2) Observe the operation and explore the cuboid volume formula.

Work in groups. Use 24 prepared cubes of 1cm3 to make different cuboids at will, and then fill in the data in the table below.

Students piece together, then fill in the form and report collectively. The teacher tabulated algebraic numbers.

It shows that students have many styles of spelling cuboids. Here are just a few. Observation: What do you find from this table?

Students think independently, then discuss and communicate in groups and come to a conclusion.

Summary: The volume of a cuboid is equal to the number of unit volumes contained in a cuboid, and the number of unit volumes contained in a cuboid is exactly equal to the product of the length, width and height of a rectangle.

Blackboard writing: cuboid volume = length? Wide? high

Narrator: If the volume formula of a cuboid is represented by the letter V, it can be written as: V=abh.

(3) Question: What conditions do you need to know to find the volume formula of a cuboid?

2. Explore the volume formula of the cube.

(1) inspiration. According to the relationship between cube and cuboid, and connecting with cuboid product formula, this paper thinks about how to calculate the volume of cube.

(2) Guide students to be clear. Volume of cube = side length? Side length? The side length (blackboard writing) is represented by letters: V=aoaoa=a3(a stands for side length) (a3 is read as the cube of A, which means three times a).

3. Solve problems with cuboid volume formula.

(1) Show the example on page 30 of the textbook 1.

(2) Look at the picture and understand the meaning of the question.

(3) Say the information given in the question and the question you want.

(4) Name the cuboid volume formula.

(5) Name the students who perform on stage, and other students will judge.

(6) The teacher corrects the composition. V=abh=7？ 4? 3=84 (cubic centimeter)

(7) look at the picture. Students finish independently in exercise books.

(8) The board of directors shall call the roll and make collective corrections.

Homework done in the classroom

Finish page 3 1 of the textbook? Do it. Questions 1 and 2.

Course summary