People's education printing plate, the sixth grade of primary school, the second volume of mathematical cylinders, the teaching plan.
Teaching objectives:
1. Knowledge and skills: With the help of the migration law and the derivation method of the circular area calculation formula, students are guided to derive the volume calculation formula of the cylinder, and the volume of the cylindrical object can be calculated by using the volume formula of the cylinder.
2. Method and process: through the process of guessing, verification and cooperation. Experience and understand the derivation process of cylinder volume formula.
Emotion, attitude and values: create situations to stimulate students' enthusiasm for learning. On the basis of active learning, students can gradually learn transformed mathematical ideas and methods, and cultivate their ability to solve practical problems and abstract and general thinking.
Teaching emphases and difficulties:
The derivation process of cylindrical volume formula; Correctly understand the derivation process of cylindrical volume formula.
Teaching tools:
Demonstration teaching aid of cylindrical volume formula, demonstration courseware of cylindrical volume formula
Teaching process:
First, the teaching review
1, explaining the task: We know the cylinder and learn its surface area. In this lesson, we will learn the volume of a cylinder.
2. Memory import
(1), please think about it. When we study the area of a circle, how can we turn the circle into a learned figure and then calculate the area?
(2) We have all learned the volume formulas of those three-dimensional figures.
Second, the learning objectives:
1, understand the meaning of cylindrical volume.
2. Through operating activities, explore the calculation method of cylindrical volume and feel the mathematical thought of transformation.
3, can correctly use the volume formula of cylinder to calculate.
Third, actively participate in exploring feelings.
1, using the deduction of circular area, guess that the volume of cylinder is related to those conditions. Teach yourself the textbook 19 and think about the following three questions.
1. What 3D figure do you want to convert the cylinder into?
2. How did you transform it into this three-dimensional figure?
3. What is the relationship between the transformed 3D figure and the cylinder?
2. Explore and deduce the volume calculation formula of cylinder. (Computer demonstration)
Group discussion:
(1) What three-dimensional figure have we learned to cut the cylinder into?
(2) What happened to the two objects before and after splicing? What hasn't changed?
(3) What is the connection between the two objects before and after splicing?
The courseware demonstrates the process of spelling and grouping, and at the same time demonstrates a set of animations (dividing the bottom of a cylinder into 32 parts and 64 parts), so that the more sectors students clearly divide, the closer the three-dimensional figure is to a cuboid.
(1) After the cylinder is spliced into a cuboid, the shape changes and the volume remains unchanged. (blackboard writing: cuboid volume = cylinder volume)
(2) The bottom area of the spliced cuboid is equal to the bottom area of the cylinder, and the height is the height of the cylinder. Cooperate with the answers, demonstrate the courseware, flash the corresponding parts and write the corresponding contents on the blackboard. )
(3) The volume of the cylinder = the bottom area? The high letter formula is V=Sh (blackboard formula).
2. Exercise: A cylindrical piece of wood with a bottom area of 75 square centimeters and a length of 90 centimeters. What is its volume?
3. What conditions must be known to calculate the volume of a cylinder with this formula?
4. Summary: The volume of cuboids, cubes and cylinders can be calculated by multiplying the bottom area by the height.
5. Try it: fill in the form.
6. Discussion: (1) Given the radius and height of the bottom of the cylinder, how to find the volume of the cylinder?
V= á r2？ h
(2) Given the diameter and height of the bottom surface of the cylinder, how to find the volume of the cylinder?
V= Wu (d? 2)2? h
(3) Given the circumference and height of the bottom surface of the cylinder, how to find the volume of the cylinder?
V= Wu (c? Hey? 2) ? h
Third, consolidate the practice.
1, fill in the blanks
(1), the cylinder is transformed into an approximate () body by splicing. The bottom area of this cuboid is equal to the bottom area of the cylinder (), and the height of this cuboid is higher than the height of the cylinder (). Because the volume of a cuboid is equal to () and the volume of a cylinder is equal to ().
(2) judgment.
(3) Given the radius and height of the bottom surface of the cylinder, how to find the volume of the cylinder?
Given the diameter and height of the bottom surface of a cylinder, how to find the volume of the cylinder?
(3) Given the circumference and height of the bottom surface of the cylinder, how to find the volume of the cylinder?
Four. Summary or query
Five, five, homework
Six, blackboard design:
Cylinder volume
Volume of cuboid = bottom area x height
Volume of cylinder = bottom area x height
V=Sh
The sixth grade of primary school, the second volume of mathematical cylinder, exercises.
First of all, judge right or wrong:
1. The larger the bottom area of a cylinder, the larger its volume. ( )
2. If the volumes of two cylinders are equal, their heights must be equal. ( )
3. When the height of the cylinder is constant, the diameter of the bottom surface expands to twice and the volume expands to eight times. ( )
4. Two cylinders with equal bottom areas have equal volumes. ( )
5. The area at the bottom of the cylinder is doubled, the height is reduced to 12, and the volume remains unchanged. ( )
6. If the volumes of two cylinders are equal, their heights are not necessarily equal. ( )
7. For two cylinders with the same height, the cylinder with a large bottom area must be large. ( )
Second, the basic training:
1. The formula for calculating the volume of a cylinder is ()
2. A cylindrical barrel with a bottom area of 6 square meters and a height of 0.5 meters. What is its volume?
3. What is the volume of a cylinder with a bottom radius of 4 cm and a height of 5 cm?
4. A cylinder with a base diameter of 10 cm and a height of 6 cm, how many cubic centimeters is its volume?
5. The circumference of the cylinder bottom is 50.24 decimeters, and the height is 15 decimeters. How many cubic decimeters is its volume?
6. Expand one side of the cylinder to get a square. The radius of the bottom of the cylinder is 5 cm. What is the height of this cylinder? How many cubic centimeters is the volume?
Three. Expansion and upgrade:
1. The diameter of the bottom surface of the cylinder is 12 cm, and the height is 25 of the diameter of the bottom surface. This cylinder
How many cubic centimeters is the volume of?
2. Cylindrical pile, cut along the diameter, with a square cross section and a circumference of the bottom of the cylinder of
6.28 decimeters, find the volume of the cylinder.
3. Cylindrical reservoir, measured from the inside, with a circumference of 25. 12m and a depth of 2.4m.
The water surface in the pool is 0.8m away from the bottom of the pool. How many tons of water are there in the reservoir? (1 m3 water weight 1 ton)
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