The teaching goal of the volume teaching plan of cuboid and cube in the second volume of fifth grade mathematics (1);
1. Make students experience the derivation process of cuboid and cube volume formulas and understand the calculation formulas of cuboid and cube volume; Initially learn to calculate the volume of cuboids and cubes;
2. Cultivate students' practical operation ability and develop students' spatial concept;
3. Make students feel the close connection between mathematics and real life in the activities, and experience the fun of learning and using mathematics, thus stimulating students' interest in learning.
Teaching emphasis: explore the calculation method of cuboid volume.
Teaching difficulties: understanding the derivation process of cuboid and cube volume formulas.
Teaching aid preparation: courseware, several small squares of 1 cubic centimeter.
Preparation of learning tools: 1 cubic centimeter cube 16.
Teaching process:
First of all, the introduction of passion
1, review and introduction
Teacher: Last class, we learned about volume and unit of volume. Who can say what is the volume of an object? Please fill in the blanks with the appropriate unit of volume.
I have a good grasp of yesterday's knowledge. Today we will use this knowledge to explore the volume of cuboids and cubes (blackboard writing topic). Please read the learning objectives of this lesson together.
3. I believe that students can use their own learning tools, be diligent in hands-on, be good at thinking, cooperate happily and gain new knowledge.
Second, people-oriented learning.
Teacher: Obviously, to measure the volume of an object depends on how many unit of volume it contains. Please look at the big screen. What is the volume of this cuboid?
(Understand lust)
Health 1, can be divided into cubic centimeters of small pieces, see a * * *, how many cubic centimeters.
Health 2, you can test it.
3. All these methods have limitations. We can find out the formula of cuboid volume by deducing the area of parallelogram.
The teacher thinks this proposal is good, don't you?
Teacher: Who can guess how to calculate the volume of a cuboid? Is this conjecture correct? Let's verify it together. Ok, please look at the first study task today.
Task demonstration:
Use some small cubes with the volume of 1 cubic centimeter to form different cuboids, and complete the following table:
Show me the form. Students are in groups of four, and each group has a form.
long
(cm)
extensive
(cm)
high
(cm)
The number of small cubes
Volume of cuboid
Teacher: Please use a cube of 1 cubic centimeter to form four different cuboids, observe the length, width and height of cuboids, and fill in the form completely. Discuss your findings in the group.
Autonomous learning
Student activities, teacher inspection.
Display communication
Teacher: The students took out many different cuboids and filled in the forms. Which group will report?
Show the form in front of the blackboard and make a detailed report.
Guide students to observe the form,
Teacher: What can you find by observing the data in the table?
Teacher: Through observation and comparison, the students have made an important discovery: the volume of a cuboid is equal to the product of its length, width and height. (blackboard writing:) cuboid volume = length × width × height.
Task 2: Continue verification
Show courseware: How many cuboids do you need to spell out the following cuboids with the cube of 1 cubic centimeter? Think about it before you put it on. Please ask a classmate to operate on the stage.
1, length 4 cm, width 1 cm and height 1 cm.
2. It is 4cm long, 3cm wide and 1 cm high.
3, 4 cm long, 3 cm wide and 2 cm high.
Teacher: These are three different cuboids. According to the discovery just now, can you tell their volumes? Answer: 4× 1× 1=4 cubic centimeters 4×3× 1= 12 cubic centimeters 4×3×2=24 cubic centimeters.
Teacher: Is that right? Let's do it again.
Discuss in groups, do it yourself, and call the roll for the rest of your life. Organize patrols.
Teacher: Is it the same as our previous guess?
Teacher: According to the verification just now, the previous conclusion is correct. Cuboid volume = length × width × height. If V is used to represent the volume of a cuboid, and A, B and H are used to represent the length, width and height of the cuboid, can letters be used to represent the volume of the cuboid?
V=abh
Teacher: If you are given a cuboid with a length of 7 cm, a width of 4 cm and a height of 3 cm, how many cubes 1 cm do you need to make a * *? What is its volume? Example 1
Courseware demonstration:
Teacher: 7×4×3=84 cubic centimeters, so its volume is 84 cubic centimeters.
Teacher: What is the figure of a cuboid with equal length, width and height? Can you write the volume formula of the cube directly? Talk about your ideas in the group.
Student report:
Because cubes are special cuboids. In a cube, the length, width and height are all equal, so the length, width and height in the formula are all called side length, and the volume of the cube = side length × side length× side length. Although the modified cuboid and cube volume formulas are different, the essence of the calculation method is the same, which is length × width × height.
The courseware shows cubes and formulas.
Teacher: The volume formula of a cube can also be expressed in letters. However, there are some special places when using letters to express the volume formula of cubes, which are explained in detail in the book. Please open your textbook and have a look. Students read textbooks. Courseware demonstration
Volume of cube: V=a?
Teacher: When writing, 3 should be written in the upper right corner of A, and it should be smaller.
Small training: Finish Example 2, finish it in the exercise book, and revise it collectively.
Third, consolidate the application
1, oral answer
2. True or false
Step 3 answer questions
Fourth, expand and extend.
Teacher: cuboids and cubes are used a lot in life. Let's have a look.
Teacher: What does this formula mean?
Show:
Name: Cubic storage stool
Size: 30×30×30
Material: polyester +PP non-woven fabric+fiberboard
Color: black and white
Teacher: Can you understand this instruction?
Teacher: If you want to put a toy box with a length of 40cm, a width of 20cm and a height of 10cm here, can you put it on the storage stool?
Teacher: It seems that we can't just compare the size of the volume, but also contact the reality to see if the length, width and height meet the requirements.
Verb (abbreviation of verb) course summary
Teacher: In this class, we learned the volume calculation of cuboids and cubes together. What have you gained?
Volumes of Cuboids and Cuboids (Volume II of Grade Five Mathematics) Learning Contents:
Volume calculation of cuboids and cubes (contents on pages 29~3 1 in the textbook, examples on page 30 1 in the textbook, and questions 5~6 in exercise 7 on page 32).
Learning 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.
Teaching focus:
Volume calculation of cuboids and cubes.
Teaching difficulties:
Volume calculation of cuboids and cubes
Teaching aid application:
Some cubes.
Teaching process:
First, check the 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?
Second, the new 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 draw 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 × width × height
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. The volume of a cube = side length × side length × side length (blackboard writing) is expressed in letters: V=a? Answer? A=a3(a stands for side length) (a3 is pronounced as the cube of A, which means the product of three A's).
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(cm3)
(7) look at the picture. Students finish independently in exercise books.
(8) The board of directors shall call the roll and make collective corrections.
Third, class assignments.
Complete questions 1 and 2 on page 3 1 of the textbook.
Fourth, class summary.
1. What did you get from this lesson?
2. What problems should be paid attention to when calculating the volume of cuboids and cubes?
Verb (abbreviation for verb) homework after class
Complete the exercises in this lesson in the workbook.
Volumes of Cuboids and Cuboids (Volume II of Grade Five Mathematics) Teaching Objectives:
1, so that students can understand the meaning of volume, know the common units of volume: cubic meter, cubic decimeter and cubic centimeter, and cultivate a preliminary concept of space.
2. Let the students know how big an object is, depending on how many unit of volume it contains.
Teaching focus:
1, establish the concept of mass.
2. Know the unit of volume.
Teaching difficulties:
Establish the concept of volume.
Teaching tool: schoolbag.
Teaching process:
Introduction: You have all heard the story of crows drinking water. How does a clever crow drink water? What is the truth in this?
Second, the new grant:
1, which means volume.
(1), preparation: Let's do an experiment and take two glasses of the same size. Fill the cup with water first; What happens when you put a pebble in another cup and then pour the water from the first cup into the second cup? Why? What does this mean? Pebbles occupy a certain space. )
(2) Every object occupies a certain space. Which of the following TV, DVD player and mobile phone takes up more space?
[3], inspire students to sum up: the size of the space occupied by an object is called the volume of the object. (blackboard writing)
Which of the above three objects has the largest volume? Which is the smallest?
(4) Contrast: Use the stationery in students' hands. Whose volume is big? Whose size is small?
Teacher: The classroom is a big space, and desks, platforms, classmates and teachers occupy a part of the classroom space. The whole school is a big space. Teachers, offices, playgrounds, flower ponds, leading desks and flag desks all occupy a certain space and have their own size. The whole universe is a big space, and the earth is only a part of the space. The mountains, rivers, all buildings and people on the earth account for a part of the earth.
2. unit of volume:
(1), talk: length should be measured in length units, area should be measured in area units, and volume should be measured in unit of volume. (blackboard writing)
Know the unit of volume:
Commonly used unit of volume are: cubic meter, cubic decimeter and cubic centimeter. Can be written separately
(2), know cubic centimeters:
Show me: a cube with a side length of 1 cm. What is its side length?
Description: Its volume is 1 cubic centimeter.
Whose volume is close to 1 cubic centimeter? The volume of a dice or a fingertip is about 1 cubic centimeter.
(3) Understanding cubic decimeter: (The method is the same as cubic centimeter)
The volume of the chalk box is close to 1 cubic decimeter.
(4), know cubic meters:
(1) Show 1 cubic meter of teaching AIDS. Through observation, it is concluded that the volume of a cube with a side length of 1 m is 1 m3.
② Know the space size of 1 m3.
1 m3 of water can fill about 500 thermos bottles. 1 m3 of wood can make about 50 desks.
Summary:
What are the commonly used unit of volume? Which unit is bigger? Which unit is smaller?
What is the purpose of unit of volume?
(5), exercise: choose the right unit:
Use () for eraser, () for train and () for schoolbag.
(6) Comparison:
What units of measurement have we learned so far? (blackboard writing)
Differences in length, area and volume;
(7), practice:
① Say: Measure the size of the basketball court in units of ().
Measure the height of the school flagpole in units of ().
It takes () units to measure the volume of a wooden box.
② The side length of the cube is 1 (), the surface area is () and the volume is (). How do you want to fill it out? )
③ Judgment: The rectangular carton with a surface area of 52 square decimeters and a volume of 24 cubic decimeters has a large surface area. ( )
3. Preliminary understanding of volume:
(1) Determine the size by looking at the number of unit volumes it contains.
A. Demonstration: Make a cuboid with four cubes with side length of 1 cm. What is its volume?
B, said the volume of the following objects (3 unit volume, 4 unit volume,)
C. Swing: Please also pose an object with a volume of 3 cubic centimeters. Take out an object with a volume of 4 cubic centimeters.
D. summary: how do you know the volume of a cuboid?
The same volume can be put in different shapes.
(2) start to put a pendulum:
Please make a cuboid (or cube) with a volume of 8 cubic centimeters from the small cube in your hand. Think about the volume of the object you spell. ) how do you say it?
Third, summary:
In this lesson, we learned the meaning of volume and unit of volume. What did you get?