Mathematics knowledge points of sixth grade in primary school: cylinder and cone
1. Know cylinders and cones and master their basic characteristics. Know the bottom, sides and height of a cylinder. Know the bottom and height of the cone.
2. Explore and master the calculation method of lateral area and surface area of cylinder, as well as the calculation formula of cylinder and cone volume, and use the formula to calculate the volume to solve simple practical problems.
3. By observing, designing and making cylinder and cone models, we can understand the relationship between plane graphics and three-dimensional graphics and develop students' spatial concept.
4. The two circular surfaces of a cylinder are called the bottom surface, the surrounding surfaces are called the side surfaces, the bottom surface is a plane, and the side surfaces are curved surfaces.
5. The side of the cylinder is rectangular after being unfolded along the height, the length of the rectangle is equal to the circumference of the bottom of the cylinder, and the width of the rectangle is equal to the height of the cylinder. When the perimeter and height of the bottom are equal, the edge height is square after expansion.
6. The surface area of a cylinder = lateral area of the cylinder+bottom area ×2, that is, S table =S side +S bottom ×2 or 2πr×h+2×π.
7. lateral area of cylinder = perimeter of bottom × height, that is, S-side =Ch or 2πr×.
8. The volume of the cylinder = the bottom area of the cylinder × the height, that is, V=sh or πr2×.
Step-by-step method: More materials are actually used than the calculated results. Therefore, when you want to keep numbers, the omitted digits are 4 or less, and you must go forward 1. This approximate method is called step-by-step method.
9. A cone has only one bottom surface, and the bottom surface is a circle. The side of a cone is a curved surface.
10. The distance from the apex of the cone to the center of the bottom is the height of the cone. The cone has only one height. (Measuring the height of the cone: firstly, lay the bottom of the cone flat, place a flat plate horizontally above the apex of the cone, and measure the distance between the flat plate and the bottom vertically. )
1 1. Expand the side of the cone to get a sector.
12. The volume of a cone is equal to one third of the volume of a cylinder with the same height as its bottom surface, that is, V-cone = 1/3Sh or πR2×h \
13. Common cylindrical cone solving problems:
(1) Road surface area (transverse area) of the roller;
(2) The length of the road surface pressed by the roller (find the perimeter of the bottom surface);
(3) Tin bucket (side area and bottom area);
(4) Chef's hat (side area and bottom area); Ventilation pipe (side area).
Important and difficult knowledge points of mathematics in the sixth grade graduation examination of primary school
Engineering problems
Basic formula:
① Total amount of work = working efficiency × working hours
(2) Work efficiency = total workload ÷ working hours.
(3) Working hours = total workload ÷ working efficiency
Basic idea:
① Assume that the total workload is "1" (independent of the total workload);
(2) Assuming that a convenient number is the total workload (generally the least common multiple of the time they need to complete the total workload), then the work efficiency and working time can be simply expressed by the above three basic relationships.
Key questions:
Determine the correspondence between workload, working hours and work efficiency.
Math learning methods in the sixth grade of primary school
Students need to take notes in class and record the main points of the teacher's lecture, supplementary questions, experiences and lessons, etc., so as to facilitate review and memory in the future. However, many children can't accurately grasp the records of primary school math notes, and they need to work hard to find suitable methods.
First, why do you want to take notes?
Notes can facilitate focused and undistorted review in the future.
The course of Olympic Mathematics usually contains a lot of information, including definitions, formulas, problem-solving skills and so on. It is difficult for most students to fully grasp all the contents of a class. In particular, our classroom often contains some classic questions and supplementary questions, and one-time memory alone can not provide enough ruminant material.
Second, take notes to avoid misunderstanding.
However, many students take notes for the sake of taking notes, because they are not confident or perfunctory to their parents-the notes are "fixed" after they are written and put on the shelf. As we all know, the knowledge recorded in your mind is your own knowledge, and it is a mistake to take notes without reviewing them.
Third, the form of taking notes.
Is there much content in your notebook? The schoolbag is full, can you find the notebook conveniently? Does a person feel rich when reading notes? If you answered "No" to all three questions, please consider moving all your notes to the handout.
Notes must be convenient for future reference. In the process of writing, the handwriting is not required to be beautiful, but at least intuitive.
The extension of a topic is recorded next to the topic. The combing of a lecture can be placed before the chapter, the supplementary topic can be placed after the chapter, and the personal experience can be placed in the header and footer. If you have any supplementary materials, you can paste them or insert them into the handout.
In short, the formal requirements of notes are: to record the most content in the smallest space, and to separate clear levels at the same time.
Articles on knowledge points in the second volume of sixth grade mathematics published by Jiangsu Education Publishing House;
★ Mathematics review outline of the sixth grade of Jiangsu Education Edition.
★ Jiangsu Education Press, review materials of the sixth grade mathematics volume.
★ Jiangsu Education Publishing House, total review materials for the sixth grade mathematics volume.
★ Review materials for the second volume of the sixth grade science Su Education Edition.
★ The sixth grade Su Jiaoban primary school mathematics Volume II always reviews questions and answers.
★ Su Jiaoban Sixth Grade Volume II Mathematics General Review Teaching Plan (2)
★ Mathematics exercises in the second volume of the sixth grade of Jiangsu Education Edition.
★ The plan of the second volume of the sixth grade mathematics of Jiangsu Education Edition
★ Su Jiaoban Sixth Grade Mathematics General Review Teaching Plan
★ The sixth grade mathematics teaching plan Volume II Su Jiaoban (2)